Finite Group Databasebeta

← #31741597

Subgroups — #31741597

Order 17152.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574525C211yesmaximal, characteristic, complemented
2#22572536C211yesmaximal, characteristic, complemented
3#22572477C211yesmaximal, characteristic, complemented
4#22572395C211yesmaximal, characteristic, complemented
5#22572335C211yesmaximal, characteristic, complemented
6#22572215C211yesmaximal, characteristic, complemented
7#22572200C211yesmaximal, characteristic, complemented
8#22572159C211yesmaximal, characteristic, complemented
9#22572111C211yesmaximal, characteristic, complemented
10#22571965C211yesmaximal, characteristic, complemented
11#22571917C211yesmaximal, characteristic, complemented
12#22571841C211yesmaximal, characteristic, complemented
13#22571829C211yesmaximal, characteristic, complemented
14#22571795C211yesmaximal, characteristic, complemented
15#22571750C211yesmaximal, characteristic, complemented
16#22571750C211yesmaximal, characteristic, complemented
17#22571705C211yesmaximal, characteristic, complemented
18#22571303C211yesmaximal, characteristic, complemented
19#22571259C211yesmaximal, characteristic, complemented
20#22571070C211yesmaximal, characteristic, complemented
21#22571061C211yesmaximal, characteristic, complemented
22#22571046C211yesmaximal, characteristic, complemented
23#22570970C211yesmaximal, characteristic, complemented
24#22570500C211yesmaximal, characteristic, complemented
25#22570438C211yesmaximal, characteristic, complemented
26#22569524C211yesmaximal, characteristic, complemented
27#22569495C211yesmaximal, characteristic, complemented
28#22569461C211yesmaximal, characteristic, complemented
29#22569427C211yesmaximal, characteristic, complemented
30#22569257C211yesmaximal, characteristic, complemented
31C67×#3487C211yesmaximal, characteristic, complemented
32C2×#14524074C2211yescharacteristic, complemented
33C2×#14524068C2211yescharacteristic
34C2×#14524068C2211yescharacteristic
35C2×#14524068C2211yescharacteristic, complemented
36C2×#14524063C2211yescharacteristic, complemented
37C2×#14524063C2211yescharacteristic, complemented
38C2×#14524063C2211yescharacteristic, complemented
39C22×#11761615C2211yescharacteristic, complemented
40#16864142—21no—
41#16864134—21no—
42#16864111C2211yescharacteristic, complemented
43#16864092C2211yescharacteristic, complemented
44#16864086C2211yescharacteristic, complemented
45#16864073—21no—
46#16864067C2211yescharacteristic, complemented
47#16864050C2211yescharacteristic, complemented
48#16864042C2211yescharacteristic, complemented
49#16864042C2211yescharacteristic, complemented
50#16864035—21no—
51D4×D268C2211yescharacteristic, complemented
52#16864017C2211yescharacteristic
53#16864001C2211yescharacteristic
54#16863998—21no—
55#16863982—21no—
56#16863974C2211yescharacteristic
57#16863961—21no—
58#16863960C2211yescharacteristic
59#16863956—21no—
60#16863907C2211yescharacteristic
61C2×#14524017C2211yescharacteristic
62#16863786C2211yescharacteristic, complemented
63#16863783C2211yescharacteristic, complemented
64#16863778C2211yescharacteristic, complemented
65#16863772C2211yescharacteristic, complemented
66#16863760C2211yescharacteristic, complemented
67#16863755C2211yescharacteristic, complemented
68#16863750C2211yescharacteristic, complemented
69#16863742C2211yescharacteristic, complemented
70#16863737C2211yescharacteristic, complemented
71#16863734C2211yescharacteristic, complemented
72#16863729C2211yescharacteristic, complemented
73#16863720C2211yescharacteristic
74#16863720C2211yescharacteristic, complemented
75#16863720C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic, complemented
77#16863717C2211yescharacteristic, complemented
78#16863717C2211yescharacteristic, complemented
79#16863712C2211yescharacteristic, complemented
80#16863712C2211yescharacteristic, complemented
81#16863707C2211yescharacteristic, complemented
82#16863703C2211yescharacteristic, complemented
83#16863703C2211yescharacteristic, complemented
84#16863691C2211yescharacteristic, complemented
85#16863681C2211yescharacteristic, complemented
86#16863652C2211yescharacteristic, complemented
87#16863647C2211yescharacteristic, complemented
88#16863647C2211yescharacteristic, complemented
89#16863647C2211yescharacteristic, complemented
90#16863647C2211yescharacteristic, complemented
91#16863644C2211yescharacteristic, complemented
92#16863640C2211yescharacteristic, complemented
93#16863640C2211yescharacteristic, complemented
94#16863630C2211yescharacteristic, complemented
95#16863630C2211yescharacteristic, complemented
96#16863630C2211yescharacteristic, complemented
97#16863630C2211yescharacteristic, complemented
98#16863630C2211yescharacteristic, complemented
99#16863627C2211yescharacteristic, complemented
100#16863627C2211yescharacteristic, complemented
101#16863623C2211yescharacteristic, complemented
102#16863618C2211yescharacteristic, complemented
103#16863618C2211yescharacteristic, complemented
104#16863615C2211yescharacteristic, complemented
105#16863608C2211yescharacteristic, complemented
106#16863608C2211yescharacteristic, complemented
107#16863608C2211yescharacteristic, complemented
108#16863596C2211yescharacteristic, complemented
109#16863596C2211yescharacteristic, complemented
110#16863593C2211yescharacteristic, complemented
111#16863588C2211yescharacteristic, complemented
112#16863588C2211yescharacteristic, complemented
113#16863588C2211yescharacteristic, complemented
114#16863558C2211yescharacteristic, complemented
115#16863558C2211yescharacteristic, complemented
116#16863558C2211yescharacteristic, complemented
117#16863558C2211yescharacteristic, complemented
118#16863556C2211yescharacteristic, complemented
119#16863552C2211yescharacteristic, complemented
120#16863552C2211yescharacteristic, complemented
121#16863547C2211yescharacteristic, complemented
122#16863546C2211yescharacteristic, complemented
123#16863541C2211yescharacteristic
124#16863541C2211yescharacteristic
125#16863541C2211yescharacteristic
126#16863541C2211yescharacteristic
127#16863541C2211yescharacteristic
128#16863541C2211yescharacteristic, complemented
129#16863541C2211yescharacteristic, complemented
130#16863541C2211yescharacteristic, complemented
131#16863541C2211yescharacteristic, complemented
132#16863541C2211yescharacteristic, complemented
133#16863541C2211yescharacteristic, complemented
134#16863541C2211yescharacteristic, complemented
135#16863539C2211yescharacteristic, complemented
136#16863539C2211yescharacteristic, complemented
137#16863539C2211yescharacteristic, complemented
138#16863535C2211yescharacteristic
139#16863535C2211yescharacteristic, complemented
140#16863535C2211yescharacteristic, complemented
141#16863535C2211yescharacteristic, complemented
142#16863535C2211yescharacteristic, complemented
143#16863535C2211yescharacteristic, complemented
144#16863530C2211yescharacteristic
145#16863530C2211yescharacteristic, complemented
146#16863530C2211yescharacteristic, complemented
147#16863529C2211yescharacteristic, complemented
148#16863529C2211yescharacteristic, complemented
149#16863529C2211yescharacteristic, complemented
150#16863501C2211yescharacteristic, complemented
151#16863494C2211yescharacteristic, complemented
152#16863494C2211yescharacteristic, complemented
153#16863494C2211yescharacteristic, complemented
154C4×#11761618C2211yescharacteristic, complemented
155C4×#11761615C2211yescharacteristic, complemented
156C4×#11761615C2211yescharacteristic, complemented
157C4×#11761615C2211yescharacteristic, complemented
158#16863474C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic, complemented
160#16863468C2211yescharacteristic, complemented
161#16863468C2211yescharacteristic, complemented
162#16863468C2211yescharacteristic, complemented
163#16863468C2211yescharacteristic, complemented
164D4×C67⋊C8C2211yescharacteristic, complemented
165D4×C67⋊C8C2211yescharacteristic, complemented
166#16863457C2211yescharacteristic, complemented
167#16863457C2211yescharacteristic, complemented
168#16863405C2211yescharacteristic, complemented
169#16863397C2211yescharacteristic, complemented
170#16863397C2211yescharacteristic, complemented
171#16863397C2211yescharacteristic, complemented
172#16863392C2211yescharacteristic, complemented
173#16863392C2211yescharacteristic, complemented
174#16863392C2211yescharacteristic, complemented
175C2×#14523967C2211yescharacteristic, complemented
176#16863363C2211yescharacteristic, complemented
177#16863363C2211yescharacteristic, complemented
178#16863360C2211yescharacteristic, complemented
179C2×C22⋊(C67⋊C8)C2211yescharacteristic, complemented
180C2×2−1+4×C67C2211yescharacteristic, complemented
181C22×#41×C67C2211yescharacteristic, complemented
182#550×C67—21no—
183#550×C67—21no—
184#550×C67C2211yescharacteristic
185#550×C67C2211yescharacteristic, complemented
186#550×C67C2211yescharacteristic, complemented
187#550×C67C2211yescharacteristic, complemented
188#548×C67—21no—
189#548×C67—21no—
190#548×C67C2211yescharacteristic
191#548×C67C2211yescharacteristic, complemented
192#548×C67C2211yescharacteristic, complemented
193#548×C67C2211yescharacteristic, complemented
194#535×C67—21no—
195#535×C67—21no—
196#535×C67C2211yescharacteristic, complemented
197#535×C67C2211yescharacteristic, complemented
198#525×C67—21no—
199#525×C67—21no—
200#525×C67C2211yescharacteristic
201#525×C67C2211yescharacteristic, complemented
202#519×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761628C2311yescharacteristic
205C2×#11761627—21no—
206C22×D268C2311yescharacteristic
207C22×D268C2311yescharacteristic
208C22×C22⋊D67—21no—
209C2×D4×D67—21no—
210#14524074—42no—
211#14524068—42no—
212#14524068—42no—
213#14524068—42no—
214#14524063—42no—
215#14524063—42no—
216#14524063—42no—
217C2×#11761618C2311yescharacteristic
218C2×#11761618C2311yescharacteristic
219C2×#11761618C2311yescharacteristic
220C2×#11761616C2311yescharacteristic
221C2×#11761616C2311yescharacteristic
222C2×#11761616C2311yescharacteristic
223C2×#11761615—42no—
224C2×#11761615C2311yescharacteristic
225C2×#11761615C2311yescharacteristic
226C2×#11761615C2311yescharacteristic
227C2×#11761615C2311yescharacteristic
228C2×#11761615C2311yescharacteristic
229C2×#11761615C2311yescharacteristic
230C2×#11761615C2311yescharacteristic
231C2×#11761615C2311yescharacteristic
232C2×#11761615C2311yescharacteristic
233C2×#11761613C2311yescharacteristic
234C2×#11761613C2311yescharacteristic
235C2×#11761613C2311yescharacteristic
236C2×#11761613C2311yescharacteristic
237C2×#11761613C2311yescharacteristic
238C2×#11761613C2311yescharacteristic
239C2×#11761613C2311yescharacteristic
240C2×#11761613C2311yescharacteristic
241C2×#11761613C2311yescharacteristic
242C2×#11761612C2311yescharacteristic
243C2×#11761612C2311yescharacteristic
244C2×#11761612C2311yescharacteristic
245C2×#11761612C2311yescharacteristic
246C22×C67⋊C8C2311yescharacteristic
247C22×C67⋊C8C2311yescharacteristic
248C22×C67⋊C8C2311yescharacteristic
249C22×C67⋊C8C2311yescharacteristic
250#14524043C2311yescharacteristic
251#14524040C2311yescharacteristic
252#14524039—21no—
253#14524039—21no—
254#14524038—21no—
255#14524038—21no—
256#14524036—21no—
257#14524035C2311yescharacteristic
258#14524033—21no—
259#14524032—21no—
260#14524031C2311yescharacteristic
261#14524029—21no—
262#14524029—21no—
263#14524029—21no—
264#14524028—21no—
265#14524028—21no—
266#14524028—21no—
267#14524028—21no—
268#14524027—21no—
269#14524027—21no—
270#14524026—21no—
271#14524025—21no—
272#14524025—21no—
273#14524024—21no—
274#14524023—21no—
275#14524022C2311yescharacteristic
276#14524022C2311yescharacteristic
277#14524022C2311yescharacteristic
278#14524021—21no—
279#14524019—21no—
280#14524018—21no—
281#14524017—21no—
282#14524017—21no—
283#14524017C2311yescharacteristic
284#14524017C2311yescharacteristic
285#14524017C2311yescharacteristic
286#14524017C2311yescharacteristic
287#14524017C2311yescharacteristic
288#14524017C2311yescharacteristic
289#14524017C2311yescharacteristic
290#14524017C2311yescharacteristic
291#14524017C2311yescharacteristic
292#14524016—21no—
293#14524016—21no—
294#14524016—21no—
295#14524016—21no—
296#14524016—21no—
297#14524016—21no—
298#14524015—21no—
299#14524015—21no—
300#14524015—21no—
301#14524014—21no—
302#14524014—21no—
303#14524013—21no—
304#14524013—21no—
305#14524012—21no—
306#14524011—21no—
307#14524011—21no—
308#14524011—21no—
309#14524011—21no—
310C4×Dic134C2311yescharacteristic
311C4×D268C2311yescharacteristic
312C4×D268C2311yescharacteristic
313C4×D268C2311yescharacteristic
314#14524005—21no—
315C4×C22⋊D67—21no—
316C4×C22⋊D67—21no—
317(C22⋊D67)⋊C4—21no—
318#14524002C2311yescharacteristic
319#14524002C2311yescharacteristic
320#14524001—21no—
321#14523999—21no—
322C2×C4⋊Dic67C2311yescharacteristic
323C2×C4⋊Dic67C2311yescharacteristic
324C2×(C2×D67)⋊C4—21no—
325C22⋊C4×D67—21no—
326C22⋊C4×D67—21no—
327#14523976C2311yescharacteristic
328#14523976C2311yescharacteristic
329#14523976C2311yescharacteristic
330#14523976C2311yescharacteristic
331#14523974C2311yescharacteristic
332#14523974C2311yescharacteristic
333#14523974C2311yescharacteristic
334#14523974C2311yescharacteristic
335C4⋊(C67⋊C8)C2311yescharacteristic
336C4⋊(C67⋊C8)C2311yescharacteristic
337C4⋊(C67⋊C8)C2311yescharacteristic
338C4⋊(C67⋊C8)C2311yescharacteristic
339#14523967C2311yescharacteristic
340#14523967C2311yescharacteristic
341#14523967C2311yescharacteristic
342#14523967C2311yescharacteristic
343#14523967C2311yescharacteristic
344#14523967C2311yescharacteristic
345#14523967C2311yescharacteristic
346#14523967C2311yescharacteristic
347#14523967C2311yescharacteristic
348#14523967C2311yescharacteristic
349#14523967C2311yescharacteristic
350#14523967C2311yescharacteristic
351#14523966C2311yescharacteristic
352#14523966C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523964C2311yescharacteristic
355#14523964C2311yescharacteristic
356#14523964C2311yescharacteristic
357#14523964C2311yescharacteristic
358#14523964C2311yescharacteristic
359#14523964C2311yescharacteristic
360#14523964C2311yescharacteristic
361#14523964C2311yescharacteristic
362#14523964C2311yescharacteristic
363#14523964C2311yescharacteristic
364#14523964C2311yescharacteristic
365#14523963C2311yescharacteristic
366#14523963C2311yescharacteristic
367#14523963C2311yescharacteristic
368#14523963C2311yescharacteristic
369#14523963C2311yescharacteristic
370#14523963C2311yescharacteristic
371C22⋊(C67⋊C8)C2311yescharacteristic
372C22⋊(C67⋊C8)C2311yescharacteristic
373C22⋊(C67⋊C8)C2311yescharacteristic
374C22⋊(C67⋊C8)C2311yescharacteristic
375C22⋊(C67⋊C8)C2311yescharacteristic
376C22⋊(C67⋊C8)C2311yescharacteristic
377C22⋊(C67⋊C8)C2311yescharacteristic
378C22⋊(C67⋊C8)C2311yescharacteristic
379C22⋊(C67⋊C8)C2311yescharacteristic
380C22⋊(C67⋊C8)C2311yescharacteristic
381C22⋊(C67⋊C8)C2311yescharacteristic
382C22⋊(C67⋊C8)C2311yescharacteristic
383#14523954C2311yescharacteristic
384#14523954C2311yescharacteristic
385C4×C67⋊C8C2311yescharacteristic
386C4×C67⋊C8C2311yescharacteristic
3872−1+4×C67—42no—
3882−1+4×C67—42no—
389C2×#41×C67—21no—
390C2×#41×C67—21no—
391C2×#41×C67—21no—
392C2×#41×C67—21no—
393C2×#41×C67—21no—
394C2×#41×C67—42no—
395C2×#41×C67—42no—
396C2×#41×C67C2311yescharacteristic
397C2×#41×C67C2311yescharacteristic
398C2×#41×C67C2311yescharacteristic
399C2×#41×C67C2311yescharacteristic
400C2×#41×C67C2311yescharacteristic
401C2×#41×C67C2311yescharacteristic
402C2×#41×C67C2311yescharacteristic
403C2×#41×C67C2311yescharacteristic
404C22×Q8×C67—21no—
405C22×Q8×C67C2311yescharacteristic
406C22×Q8×C67C2311yescharacteristic
407C22×Q8×C67C2311yescharacteristic
408C22×D4×C67—21no—
409C22×D4×C67C2311yescharacteristic
410C23×C4×C67—21no—
411C23×C4×C67C2311yescharacteristic
412#127×C67—21no—
413#127×C67—21no—
414#127×C67—21no—
415#127×C67—21no—
416#127×C67—21no—
417#127×C67C2311yescharacteristic
418#127×C67C2311yescharacteristic
419#124×C67—21no—
420#124×C67—21no—
421#124×C67—21no—
422#124×C67—21no—
423#124×C67—21no—
424#124×C67C2311yescharacteristic
425#124×C67C2311yescharacteristic
426#123×C67—21no—
427#123×C67D411yescharacteristic
428#123×C67D411yescharacteristic
429C22⋊Q8×C67—21no—
430C22⋊Q8×C67—21no—
431C22⋊Q8×C67—21no—
432C22⋊Q8×C67—21no—
433C22⋊Q8×C67D411yescharacteristic
434C22⋊Q8×C67D411yescharacteristic
435C22⋊Q8×C67C2311yescharacteristic
436C22⋊Q8×C67C2311yescharacteristic
437#121×C67—21no—
438#121×C67—21no—
439#121×C67—21no—
440#121×C67—21no—
441#121×C67—21no—
442#121×C67—21no—
443#121×C67—21no—
444#121×C67—21no—
445#121×C67—21no—
446#121×C67—21no—
447#121×C67—21no—
448#121×C67—21no—
449#121×C67—21no—
450#121×C67—21no—
451#121×C67D411yescharacteristic
452#121×C67D411yescharacteristic
453#121×C67C2311yescharacteristic
454#121×C67C2311yescharacteristic
455#121×C67C2311yescharacteristic
456#121×C67C2311yescharacteristic
457#121×C67C2311yescharacteristic
458#121×C67C2311yescharacteristic
459#120×C67—21no—
460#120×C67—21no—
461#120×C67—21no—
462#120×C67—21no—
463#120×C67—21no—
464#120×C67D411yescharacteristic
465#120×C67D411yescharacteristic
466C4×Q8×C67—21no—
467C4×Q8×C67—21no—
468C4×Q8×C67C2311yescharacteristic
469C4×Q8×C67C2311yescharacteristic
470C4×Q8×C67C2311yescharacteristic
471C4×Q8×C67C2311yescharacteristic
472C4×D4×C67—21no—
473C4×D4×C67—21no—
474C4×D4×C67—21no—
475C4×D4×C67—21no—
476C4×D4×C67—21no—
477C4×D4×C67—21no—
478C4×D4×C67—21no—
479C4×D4×C67—21no—
480C4×D4×C67—21no—
481C4×D4×C67—21no—
482C4×D4×C67C2311yescharacteristic
483C4×D4×C67C2311yescharacteristic
484C4×D4×C67C2311yescharacteristic
485C4×D4×C67C2311yescharacteristic
486#117×C67—21no—
487#117×C67—21no—
488#117×C67C2311yescharacteristic
489#117×C67C2311yescharacteristic
490C23×D67—21no—
491C23×D67—21no—
492#11761628—41no—
493#11761628—41no—
494#11761628—41no—
495#11761628—41no—
496#11761627—82no—
497C2×Dic134—21no—
498C2×Dic134C2411yescharacteristic
499C2×D268—21no—
500C2×D268—21no—
501C2×D268—21no—
502C2×D268—21no—
503C2×D268—41no—
504C2×D268—41no—
505C2×D268—41no—
506C2×D268—41no—
507C2×D268C2411yescharacteristic
508C2×D268C2411yescharacteristic
509C2×D268C2411yescharacteristic
510C2×C22⋊D67—21no—
511C2×C22⋊D67—21no—
512C2×C22⋊D67—21no—
513C2×C22⋊D67—21no—
514C2×C22⋊D67—21no—
515C2×C22⋊D67—21no—
516C2×C22⋊D67—21no—
517C2×C22⋊D67—21no—
518C2×C22⋊D67—21no—
519C2×C22⋊D67—21no—
520C2×C22⋊D67—21no—
521C2×C22⋊D67—82no—
522D4×D67—82no—
523C22×Dic67—21no—
524C22×Dic67—21no—
525C2×C4×D67—21no—
526C2×C4×D67—21no—
527C2×C4×D67—21no—
528C2×C4×D67—21no—
529C2×C4×D67—21no—
530#11761618—22no—
531#11761618—22no—
532#11761618—41no—
533#11761616—41no—
534#11761616—41no—
535#11761616—41no—
536#11761615—22no—
537#11761615—22no—
538#11761615—22no—
539#11761615—22no—
540#11761615—22no—
541#11761615—22no—
542#11761615—41no—
543#11761615—41no—
544#11761615—41no—
545#11761613—41no—
546#11761613—41no—
547#11761613—41no—
548#11761613—41no—
549#11761613—41no—
550#11761613—41no—
551#11761613—41no—
552#11761613—41no—
553#11761613—41no—
554#11761612—41no—
555#11761612—41no—
556#11761612—41no—
557#11761612—41no—
558C2×C67⋊C8—41no—
559C2×C67⋊C8—41no—
560C2×C67⋊C8—41no—
561C2×C67⋊C8—41no—
562C2×C67⋊C8C2411yescharacteristic
563C2×C67⋊C8C2411yescharacteristic
564C2×C67⋊C8C2411yescharacteristic
565C2×C67⋊C8C2411yescharacteristic
566C2×C67⋊C8C2411yescharacteristic
567C2×C67⋊C8C2411yescharacteristic
568C2×C67⋊C8C2411yescharacteristic
569C2×C67⋊C8C2411yescharacteristic
570C4⋊Dic67—21no—
571C4⋊Dic67—21no—
572C4⋊Dic67—21no—
573C4⋊Dic67C2411yescharacteristic
574C4⋊Dic67C2411yescharacteristic
575C4⋊Dic67C2411yescharacteristic
576C4⋊Dic67C2411yescharacteristic
577Dic67⋊C4—21no—
578Dic67⋊C4—21no—
579Dic67⋊C4—21no—
580Dic67⋊C4—21no—
581Dic67⋊C4—21no—
582Dic67⋊C4—21no—
583C22⋊Dic67—21no—
584C22⋊Dic67—21no—
585C22⋊Dic67—21no—
586C22⋊Dic67—21no—
587C22⋊Dic67—21no—
588(C2×D67)⋊C4—21no—
589(C2×D67)⋊C4—21no—
590(C2×D67)⋊C4—21no—
591(C2×D67)⋊C4—21no—
592(C2×D67)⋊C4—21no—
593(C2×D67)⋊C4—21no—
594(C2×D67)⋊C4—21no—
595(C2×D67)⋊C4—21no—
596(C2×D67)⋊C4—21no—
597(C2×D67)⋊C4—21no—
598(C2×D67)⋊C4—21no—
599(C2×D67)⋊C4—21no—
600(C2×D67)⋊C4—21no—
601(C2×D67)⋊C4—21no—
602C4×Dic67—21no—
603C4×Dic67—21no—
604C4×Dic67—21no—
605C24×C67—21no—
606C24×C67C2×D411yescharacteristic
607#41×C67—22no—
608#41×C67—22no—
609#41×C67—22no—
610#41×C67—22no—
611#41×C67—22no—
612#41×C67—22no—
613#41×C67—41no—
614#41×C67—41no—
615#41×C67—41no—
616#41×C67—41no—
617#41×C67—41no—
618#41×C67—41no—
619#41×C67—41no—
620#41×C67—41no—
621#41×C67—41no—
622#41×C67—41no—
623#41×C67—44no—
624#41×C67—44no—
625#41×C67—44no—
626#41×C67—44no—
627#41×C67—44no—
628C2×Q8×C67—22no—
629C2×Q8×C67—22no—
630C2×Q8×C67—21no—
631C2×Q8×C67—21no—
632C2×Q8×C67—21no—
633C2×Q8×C67—22no—
634C2×Q8×C67—22no—
635C2×Q8×C67—41no—
636C2×Q8×C67—41no—
637C2×Q8×C67—44no—
638C2×Q8×C67C2×D411yescharacteristic
639C2×Q8×C67C2411yescharacteristic
640C2×Q8×C67C2411yescharacteristic
641C2×Q8×C67C2411yescharacteristic
642C2×D4×C67—21no—
643C2×D4×C67—21no—
644C2×D4×C67—21no—
645C2×D4×C67—21no—
646C2×D4×C67—21no—
647C2×D4×C67—21no—
648C2×D4×C67—21no—
649C2×D4×C67—21no—
650C2×D4×C67—21no—
651C2×D4×C67—21no—
652C2×D4×C67—21no—
653C2×D4×C67—21no—
654C2×D4×C67—21no—
655C2×D4×C67—21no—
656C2×D4×C67—21no—
657C2×D4×C67—21no—
658C2×D4×C67—21no—
659C2×D4×C67—21no—
660C2×D4×C67—41no—
661C2×D4×C67—41no—
662C2×D4×C67—44no—
663C2×D4×C67C2×D411yescharacteristic
664C2×D4×C67C2×D411yescharacteristic
665C2×D4×C67C2×D411yescharacteristic
666C2×D4×C67C2×D411yescharacteristic
667C2×D4×C67C2×D411yescharacteristic
668C2×D4×C67C2×D411yescharacteristic
669C2×D4×C67C2×D411yescharacteristic
670C2×D4×C67C2411yescharacteristic
671C2×D4×C67C2411yescharacteristic
672C2×D4×C67C2411yescharacteristic
673C22×C4×C67—21no—
674C22×C4×C67—21no—
675C22×C4×C67—21no—
676C22×C4×C67—21no—
677C22×C4×C67—21no—
678C22×C4×C67—21no—
679C22×C4×C67—21no—
680C22×C4×C67—21no—
681C22×C4×C67—21no—
682C22×C4×C67—21no—
683C22×C4×C67—41no—
684C22×C4×C67—41no—
685C22×C4×C67—44no—
686C22×C4×C67C2×D411yescharacteristic
687C22×C4×C67C2×D411yescharacteristic
688C22×C4×C67C2×D411yescharacteristic
689C22×C4×C67C2411yescharacteristic
690C22×C4×C67C2411yescharacteristic
691C22×C4×C67C2411yescharacteristic
692C22×C4×C67C2411yescharacteristic
693C22×C4×C67C2411yescharacteristic
694C4⋊C4×C67—21no—
695C4⋊C4×C67—21no—
696C4⋊C4×C67—21no—
697C4⋊C4×C67—21no—
698C4⋊C4×C67—21no—
699C4⋊C4×C67—21no—
700C4⋊C4×C67C2×D411yescharacteristic
701C4⋊C4×C67C2×D411yescharacteristic
702C4⋊C4×C67C2×D411yescharacteristic
703C4⋊C4×C67C2×D411yescharacteristic
704C4⋊C4×C67C2×D411yescharacteristic
705C4⋊C4×C67C2×D411yescharacteristic
706C4⋊C4×C67C2411yescharacteristic
707C4⋊C4×C67C2411yescharacteristic
708C22⋊C4×C67—21no—
709C22⋊C4×C67—21no—
710C22⋊C4×C67—21no—
711C22⋊C4×C67—21no—
712C22⋊C4×C67—21no—
713C22⋊C4×C67—21no—
714C22⋊C4×C67—21no—
715C22⋊C4×C67—21no—
716C22⋊C4×C67—21no—
717C22⋊C4×C67—21no—
718C22⋊C4×C67—21no—
719C22⋊C4×C67—21no—
720C22⋊C4×C67—21no—
721C22⋊C4×C67C2×D411yescharacteristic
722C22⋊C4×C67C2×D411yescharacteristic
723C22⋊C4×C67C2×D411yescharacteristic
724C22⋊C4×C67C2×D411yescharacteristic
725C22⋊C4×C67C2×D411yescharacteristic
726C22⋊C4×C67C2×D411yescharacteristic
727C22⋊C4×C67C2×D411yescharacteristic
728C22⋊C4×C67C2×D411yescharacteristic
729C22⋊C4×C67C2×D411yescharacteristic
730C22⋊C4×C67C2×D411yescharacteristic
731C42×C67—21no—
732C42×C67—21no—
733C42×C67—21no—
734C42×C67—21no—
735C42×C67—21no—
736C42×C67C2411yescharacteristic
737C42×C67C2411yescharacteristic
738C23×C67—21no—
739C23×C67—21no—
740C23×C67—21no—
741C23×C67—41no—
742C23×C67—41no—
743C23×C67—41no—
744C23×C67—42no—
745C23×C67—81no—
746C23×C67—81no—
747C23×C67C22×D411yescharacteristic
748C23×C67C22×D411yescharacteristic
749C23×C67C22×D411yescharacteristic
750C23×C67C22×D411yescharacteristic
751C23×C67C22×D411yescharacteristic
752C22×D67—21no—
753C22×D67—21no—
754C22×D67—21no—
755C22×D67—42no—
756C22×D67—81no—
757C22×D67—81no—
758C22×D67—81no—
759C22×D67—81no—
760C22×D67—81no—
761Q8×C67—24no—
762Q8×C67—21no—
763Q8×C67—21no—
764Q8×C67—21no—
765Q8×C67—21no—
766Q8×C67—41no—
767Q8×C67—42no—
768Q8×C67—42no—
769Q8×C67H(5,𝔽2)12yes—
770Q8×C67H(5,𝔽2)12yes—
771D4×C67—21no—
772D4×C67—21no—
773D4×C67—21no—
774D4×C67—21no—
775D4×C67—21no—
776D4×C67—21no—
777D4×C67—41no—
778D4×C67—41no—
779D4×C67—41no—
780D4×C67—41no—
781D4×C67—41no—
782D4×C67—41no—
783D4×C67—41no—
784D4×C67—42no—
785D4×C67—42no—
786D4×C67—42no—
787D4×C67—42no—
788D4×C67—42no—
789D4×C67—42no—
790D4×C67—42no—
791D4×C67—42no—
792D4×C67—81no—
793D4×C67—81no—
794D4×C67—81no—
795D4×C67—81no—
796D4×C67—81no—
797D4×C67—81no—
798D4×C67—81no—
799D4×C67—81no—
800D4×C67—81no—
801D4×C67—81no—
802C2×C4×C67—24no—
803C2×C4×C67—21no—
804C2×C4×C67—21no—
805C2×C4×C67—21no—
806C2×C4×C67—21no—
807C2×C4×C67—21no—
808C2×C4×C67—21no—
809C2×C4×C67—21no—
810C2×C4×C67—21no—
811C2×C4×C67—21no—
812C2×C4×C67—21no—
813C2×C4×C67—21no—
814C2×C4×C67—21no—
815C2×C4×C67—21no—
816C2×C4×C67—21no—
817C2×C4×C67—21no—
818C2×C4×C67—41no—
819C2×C4×C67—41no—
820C2×C4×C67—41no—
821C2×C4×C67—42no—
822C2×C4×C67—42no—
823C2×C4×C67—42no—
824C2×C4×C67—42no—
825C2×C4×C67—42no—
826C2×C4×C67—42no—
827C2×C4×C67—42no—
828C2×C4×C67—42no—
829C2×C4×C67—42no—
830C2×C4×C67C22×D411yescharacteristic
831C2×C4×C67C22×D411yescharacteristic
832C2×C4×C67C22×D411yescharacteristic
833C2×C4×C67C22×D411yescharacteristic
834C2×C4×C67C22×D411yescharacteristic
835C2×C4×C67C22×D411yescharacteristic
836C2×C4×C67C22×D411yescharacteristic
837C2×C4×C67C22×D411yescharacteristic
838C2×C4×C67C22×D411yescharacteristic
839C2×C4×C67C2511yescharacteristic
840C22⋊D67—42no—
841C22⋊D67—81no—
842C22⋊D67—81no—
843C22⋊D67—81no—
844C22⋊D67—81no—
845C22⋊D67—81no—
846C22⋊D67—81no—
847C22⋊D67—81no—
848C22⋊D67—81no—
849C22⋊D67—81no—
850C22⋊D67—81no—
851C2×Dic67—21no—
852C2×Dic67—21no—
853C2×Dic67—21no—
854C2×Dic67—21no—
855C2×Dic67—21no—
856C2×Dic67—42no—
857C2×Dic67—81no—
858D268—21no—
859D268—21no—
860D268—21no—
861D268—21no—
862D268—21no—
863D268—21no—
864D268—81no—
865D268—81no—
866D268—81no—
867D268—81no—
868C4×D67—81no—
869C4×D67—81no—
870C4×D67—81no—
871C4×D67—81no—
872C4×D67—81no—
873Dic134—21no—
874Dic134—21no—
875Dic134—81no—
876C67⋊C8—21no—
877C67⋊C8—21no—
878C67⋊C8—21no—
879C67⋊C8—21no—
880C67⋊C8—21no—
881C67⋊C8—21no—
882C67⋊C8—21no—
883C67⋊C8—21no—
884C22×C67—21no—
885C22×C67—21no—
886C22×C67—21no—
887C22×C67—21no—
888C22×C67—21no—
889C22×C67—21no—
890C22×C67—21no—
891C22×C67—21no—
892C22×C67—21no—
893C22×C67—21no—
894C22×C67—21no—
895C22×C67—21no—
896C22×C67—21no—
897C22×C67—21no—
898C22×C67—21no—
899C22×C67—41no—
900C22×C67—41no—
901C22×C67—41no—
902C22×C67—41no—
903C22×C67—41no—
904C22×C67—41no—
905C22×C67—41no—
906C22×C67—41no—
907C22×C67—41no—
908C22×C67—82no—
909C22×C67—84no—
910C22×C67C23×D411yescharacteristic
911C2×D67—41no—
912C2×D67—41no—
913C2×D67—41no—
914C2×D67—41no—
915C2×D67—41no—
916C2×D67—41no—
917C2×D67—41no—
918C2×D67—41no—
919C2×D67—41no—
920C2×D67—162no—
921C2×D67—162no—
922C4×C67—21no—
923C4×C67—21no—
924C4×C67—21no—
925C4×C67—21no—
926C4×C67—21no—
927C4×C67—21no—
928C4×C67—21no—
929C4×C67—21no—
930C4×C67—22no—
931C4×C67—22no—
932C4×C67—21no—
933C4×C67—41no—
934C4×C67—41no—
935C4×C67—41no—
936C4×C67C2×H(5,𝔽2)11yescharacteristic
937C4×C67C2×H(5,𝔽2)11yescharacteristic
938Dic67—41no—
939Dic67—41no—
940Dic67—41no—
941Dic67—41no—
942Dic67—41no—
943#61616—671nomaximal, Sylow
944C2×C67—41no—
945C2×C67—41no—
946C2×C67—41no—
947C2×C67—41no—
948C2×C67—41no—
949C2×C67—81no—
950C2×C67—81no—
951C2×C67—81no—
952C2×C67#348411yescharacteristic
953C2×C67#358411yescharacteristic
954C2×C67#358511yescharacteristic
955D67—81no—
956D67—81no—
957D67—81no—
958#3542—671no—
959#3487D6711yescharacteristic, complemented
960#3332—671no—
961#3327—671no—
962#3321—671no—
963#3317—671no—
964#3309—671no—
965#3308—671no—
966#3305—671no—
967#3301—671no—
968#3287—671no—
969#3282—671no—
970#3275—671no—
971#3274—671no—
972#3271—671no—
973#3268—671no—
974#3268—671no—
975#3265—671no—
976#3224—671no—
977#3220—671no—
978#3199—671no—
979#3198—671no—
980#3197—671no—
981#3188—671no—
982#3126—671no—
983#3121—671no—
984#3013—671no—
985#3010—671no—
986#3006—671no—
987#3002—671no—
988#2976—671no—
989C67#6161611yescharacteristic, complemented, Sylow
990C2×2−1+4C2×D6711yescharacteristic, complemented
991C22×#41C2×D6711yescharacteristic, complemented
992C2×#137—671no—
993C2×AGL(1,ℤ/8)—671no—
994C2×AGL(1,ℤ/8)—671no—
995C2×AGL(1,ℤ/8)—671no—
996C2×#135—671no—
997C2×#135—671no—
998C2×#135—671no—
999C22×SD16—671no—
1000#562—1341no—
1001#560—1341no—
1002#555—671no—
1003#553—671no—
1004#552—671no—
1005#551—1341no—
1006#550—21no—
1007#550—21no—
1008#550—671no—
1009#550C2×D6711yescharacteristic
1010#550C2×D6711yescharacteristic, complemented
1011#550C2×D6711yescharacteristic, complemented
1012#550C2×D6711yescharacteristic, complemented
1013#548—21no—
1014#548—21no—
1015#548C2×D6711yescharacteristic
1016#548C2×D6711yescharacteristic, complemented
1017#548C2×D6711yescharacteristic, complemented
1018#548C2×D6711yescharacteristic, complemented
1019#547—671no—
1020#546—671no—
1021#546—671no—
1022#546—1341no—
1023D42—671no—
1024#542—671no—
1025#540—671no—
1026#540—1341no—
1027#538—1341no—
1028#537—671no—
1029#535—21no—
1030#535—21no—
1031#535—671no—
1032#535—1341no—
1033#535C2×D6711yescharacteristic, complemented
1034#535C2×D6711yescharacteristic, complemented
1035#534—1341no—
1036#525—21no—
1037#525—21no—
1038#525—671no—
1039#525C2×D6711yescharacteristic
1040#525C2×D6711yescharacteristic, complemented
1041C2×#121—671no—
1042#519C2×D6711yescharacteristic, complemented
1043#496—671no—
1044#496—671no—
1045#495—671no—
1046#493—671no—
1047#490—671no—
1048#489—671no—
1049#488—671no—
1050#486—671no—
1051#485—671no—
1052#485—671no—
1053#484—671no—
1054#482—671no—
1055#482—671no—
1056#482—671no—
1057#482—671no—
1058#482—671no—
1059#482—671no—
1060#481—671no—
1061#481—671no—
1062#480—671no—
1063#479—671no—
1064#479—671no—
1065#477—671no—
1066#475—671no—
1067#470—671no—
1068#469—671no—
1069#469—671no—
1070#469—671no—
1071#469—671no—
1072#468—671no—
1073#468—671no—
1074#468—671no—
1075#466—671no—
1076#466—671no—
1077#466—671no—
1078#466—671no—
1079#466—671no—
1080#465—671no—
1081#465—671no—
1082#465—671no—
1083#464—671no—
1084#464—671no—
1085#464—671no—
1086#463—671no—
1087#463—671no—
1088#463—671no—
1089#460—671no—
1090#460—671no—
1091#460—671no—
1092#459—671no—
1093#459—671no—
1094#459—671no—
1095#452—671no—
1096#452—671no—
1097#452—671no—
1098#452—671no—
1099#452—671no—
1100#451—671no—
1101#451—671no—
1102#450—671no—
1103#450—671no—
1104#449—671no—
1105#449—671no—
1106#449—671no—
1107#449—671no—
1108#449—671no—
1109#449—671no—
1110#449—671no—
1111#449—671no—
1112#449—671no—
1113#449—671no—
1114#449—671no—
1115#449—671no—
1116#449—671no—
1117#449—671no—
1118#449—671no—
1119#448—671no—
1120#448—671no—
1121#448—671no—
1122#448—671no—
1123#448—671no—
1124#448—671no—
1125#447—671no—
1126#447—671no—
1127#447—671no—
1128#447—671no—
1129#447—671no—
1130#447—671no—
1131#441—671no—
1132#440—671no—
1133#440—671no—
1134#440—671no—
1135C4×Q16—671no—
1136C4×SD16—671no—
1137C4×SD16—671no—
1138C4×SD16—671no—
1139#436—671no—
1140#436—671no—
1141#435—671no—
1142#435—671no—
1143#435—671no—
1144#435—671no—
1145C8×D4—671no—
1146C8×D4—671no—
1147#433—671no—
1148#433—671no—
1149#419—671no—
1150#417—671no—
1151#417—671no—
1152#417—671no—
1153#416—671no—
1154#416—671no—
1155#416—671no—
1156C2×#103—671no—
1157#408—671no—
1158#408—671no—
1159#407—671no—
1160C2×C22⋊C8—671no—
11612−1+4—42no—
11622−1+4—42no—
1163C2×#41—21no—
1164C2×#41—21no—
1165C2×#41—21no—
1166C2×#41—21no—
1167C2×#41—21no—
1168C2×#41—42no—
1169C2×#41—42no—
1170C2×#41—671no—
1171C2×#41—671no—
1172C2×#41—1341no—
1173C2×#41C22×D6711yescharacteristic
1174C2×#41C22×D6711yescharacteristic
1175C2×#41C22×D6711yescharacteristic
1176C2×#41C22×D6711yescharacteristic
1177C2×#41C22×D6711yescharacteristic
1178C2×#41C22×D6711yescharacteristic
1179C2×#41C22×D6711yescharacteristic
1180C2×#41C22×D6711yescharacteristic
1181C22×Q8—21no—
1182C22×Q8C22×D6711yescharacteristic
1183C22×Q8C22×D6711yescharacteristic
1184C22×Q8C22×D6711yescharacteristic
1185C22×D4—21no—
1186C22×D4—671no—
1187C22×D4—671no—
1188C22×D4—1341no—
1189C22×D4—1341no—
1190C22×D4C22×D6711yescharacteristic
1191C23×C4—21no—
1192C23×C4C22×D6711yescharacteristic
1193#137—2682no—
1194AGL(1,ℤ/8)—2682no—
1195AGL(1,ℤ/8)—2682no—
1196AGL(1,ℤ/8)—2682no—
1197#135—2682no—
1198#135—2682no—
1199#135—2682no—
1200C2×Q16—671no—
1201C2×Q16—671no—
1202C2×Q16—671no—
1203C2×SD16—2682no—
1204C2×SD16—671no—
1205C2×SD16—671no—
1206C2×SD16—671no—
1207C2×SD16—671no—
1208C2×SD16—671no—
1209C2×SD16—671no—
1210C2×SD16—671no—
1211C2×SD16—671no—
1212C2×SD16—671no—
1213C2×SD16—671no—
1214C2×SD16—671no—
1215C2×SD16—671no—
1216C2×D8—671no—
1217C2×D8—671no—
1218C2×D8—671no—
1219C2×D8—671no—
1220C2×D8—671no—
1221C2×D8—671no—
1222C2×D8—671no—
1223C2×D8—671no—
1224C2×D8—671no—
1225C2×M16—671no—
1226C2×M16—671no—
1227C2×M16—671no—
1228C2×M16—671no—
1229C22×C8—671no—
1230C22×C8—671no—
1231C22×C8—671no—
1232C22×C8—671no—
1233C4⋊Q8—671no—
1234#127—21no—
1235#127—21no—
1236#127—21no—
1237#127—21no—
1238#127—21no—
1239#127—671no—
1240#127—1341no—
1241#127—1341no—
1242#127C22×D6711yescharacteristic
1243#127C22×D6711yescharacteristic
1244#126—1341no—
1245#126—1341no—
1246#126—1341no—
1247#125—671no—
1248#125—1341no—
1249#124—21no—
1250#124—21no—
1251#124—21no—
1252#124—21no—
1253#124—21no—
1254#124—671no—
1255#124—1341no—
1256#124—1341no—
1257#124—1341no—
1258#124—1341no—
1259#124C22×D6711yescharacteristic
1260#124C22×D6711yescharacteristic
1261#123—21no—
1262#123—1341no—
1263#123—1341no—
1264#123—1341no—
1265#123—1341no—
1266#123—1341no—
1267#123—1341no—
1268#123—1341no—
1269#123—1341no—
1270#123—1341no—
1271#123—1341no—
1272#123C22⋊D6711yescharacteristic
1273#123C22⋊D6711yescharacteristic
1274C22⋊Q8—21no—
1275C22⋊Q8—21no—
1276C22⋊Q8—21no—
1277C22⋊Q8—21no—
1278C22⋊Q8—671no—
1279C22⋊Q8—671no—
1280C22⋊Q8—671no—
1281C22⋊Q8—1341no—
1282C22⋊Q8—1341no—
1283C22⋊Q8—1341no—
1284C22⋊Q8C22⋊D6711yescharacteristic
1285C22⋊Q8C22⋊D6711yescharacteristic
1286C22⋊Q8C22×D6711yescharacteristic
1287C22⋊Q8C22×D6711yescharacteristic
1288#121—21no—
1289#121—21no—
1290#121—21no—
1291#121—21no—
1292#121—21no—
1293#121—21no—
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—21no—
1298#121—21no—
1299#121—21no—
1300#121—21no—
1301#121—21no—
1302#121—671no—
1303#121—671no—
1304#121—671no—
1305#121—671no—
1306#121—671no—
1307#121—671no—
1308#121—671no—
1309#121—671no—
1310#121—671no—
1311#121—1341no—
1312#121—1341no—
1313#121—1341no—
1314#121—1341no—
1315#121—1341no—
1316#121—1341no—
1317#121—1341no—
1318#121—1341no—
1319#121—1341no—
1320#121—1341no—
1321#121—1341no—
1322#121—1341no—
1323#121—1341no—
1324#121—1341no—
1325#121C22⋊D6711yescharacteristic
1326#121C22⋊D6711yescharacteristic
1327#121C22×D6711yescharacteristic
1328#121C22×D6711yescharacteristic
1329#121C22×D6711yescharacteristic
1330#121C22×D6711yescharacteristic
1331#121C22×D6711yescharacteristic
1332#121C22×D6711yescharacteristic
1333#120—21no—
1334#120—21no—
1335#120—21no—
1336#120—21no—
1337#120—21no—
1338#120—1341no—
1339#120—1341no—
1340#120—1341no—
1341#120—1341no—
1342#120—1341no—
1343#120—1341no—
1344#120—1341no—
1345#120C22⋊D6711yescharacteristic
1346#120C22⋊D6711yescharacteristic
1347C4×Q8—21no—
1348C4×Q8—21no—
1349C4×Q8—671no—
1350C4×Q8C22×D6711yescharacteristic
1351C4×Q8C22×D6711yescharacteristic
1352C4×Q8C22×D6711yescharacteristic
1353C4×Q8C22×D6711yescharacteristic
1354C4×D4—21no—
1355C4×D4—21no—
1356C4×D4—21no—
1357C4×D4—21no—
1358C4×D4—21no—
1359C4×D4—21no—
1360C4×D4—21no—
1361C4×D4—21no—
1362C4×D4—21no—
1363C4×D4—21no—
1364C4×D4—671no—
1365C4×D4—671no—
1366C4×D4—671no—
1367C4×D4—1341no—
1368C4×D4—1341no—
1369C4×D4—1341no—
1370C4×D4—1341no—
1371C4×D4C22×D6711yescharacteristic
1372C4×D4C22×D6711yescharacteristic
1373C4×D4C22×D6711yescharacteristic
1374C4×D4C22×D6711yescharacteristic
1375#117—21no—
1376#117—21no—
1377#117—671no—
1378#117—671no—
1379#117—1341no—
1380#117—1341no—
1381#117C22×D6711yescharacteristic
1382#117C22×D6711yescharacteristic
1383C2×C4⋊C4—671no—
1384C2×C4⋊C4—671no—
1385C2×C22⋊C4—1341no—
1386C2×C22⋊C4—1341no—
1387C2×C22⋊C4—1341no—
1388#107—671no—
1389#107—671no—
1390#107—671no—
1391#107—671no—
1392#106—671no—
1393#106—671no—
1394#106—671no—
1395#106—671no—
1396C4⋊C8—671no—
1397C4⋊C8—671no—
1398C4⋊C8—671no—
1399C4⋊C8—671no—
1400#103—671no—
1401#103—671no—
1402#103—671no—
1403#103—671no—
1404#103—671no—
1405#103—671no—
1406#103—671no—
1407#103—671no—
1408#103—671no—
1409#103—671no—
1410#103—671no—
1411#103—671no—
1412#103—671no—
1413#103—671no—
1414#102—671no—
1415#102—671no—
1416#102—671no—
1417#102—671no—
1418#102—671no—
1419#102—671no—
1420#102—671no—
1421#102—671no—
1422#102—671no—
1423#102—671no—
1424#102—671no—
1425#102—671no—
1426#102—671no—
1427#102—671no—
1428#102—671no—
1429#102—671no—
1430#102—671no—
1431#102—671no—
1432C22⋊C8—671no—
1433C22⋊C8—671no—
1434C22⋊C8—671no—
1435C22⋊C8—671no—
1436C22⋊C8—671no—
1437C22⋊C8—671no—
1438C22⋊C8—671no—
1439C22⋊C8—671no—
1440C22⋊C8—671no—
1441C22⋊C8—671no—
1442C22⋊C8—671no—
1443C22⋊C8—671no—
1444#97—671no—
1445#97—671no—
1446C4×C8—671no—
1447C4×C8—671no—
1448C24—21no—
1449C24—1341no—
1450C24—1341no—
1451C24C2×C22⋊D6711yescharacteristic
1452#41—22no—
1453#41—22no—
1454#41—22no—
1455#41—22no—
1456#41—22no—
1457#41—22no—
1458#41—41no—
1459#41—41no—
1460#41—41no—
1461#41—41no—
1462#41—41no—
1463#41—41no—
1464#41—41no—
1465#41—41no—
1466#41—41no—
1467#41—41no—
1468#41—44no—
1469#41—44no—
1470#41—44no—
1471#41—44no—
1472#41—44no—
1473#41—2681no—
1474#41—2681no—
1475#41—2681no—
1476#41—2681no—
1477#41—5362no—
1478C2×Q8—22no—
1479C2×Q8—22no—
1480C2×Q8—21no—
1481C2×Q8—21no—
1482C2×Q8—21no—
1483C2×Q8—22no—
1484C2×Q8—22no—
1485C2×Q8—41no—
1486C2×Q8—41no—
1487C2×Q8—44no—
1488C2×Q8—671no—
1489C2×Q8—1341no—
1490C2×Q8C2×C22⋊D6711yescharacteristic
1491C2×Q8C23×D6711yescharacteristic
1492C2×Q8C23×D6711yescharacteristic
1493C2×Q8C23×D6711yescharacteristic
1494C2×D4—21no—
1495C2×D4—21no—
1496C2×D4—21no—
1497C2×D4—21no—
1498C2×D4—21no—
1499C2×D4—21no—
1500C2×D4—21no—
1501C2×D4—21no—
1502C2×D4—21no—
1503C2×D4—21no—
1504C2×D4—21no—
1505C2×D4—21no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—21no—
1511C2×D4—21no—
1512C2×D4—41no—
1513C2×D4—41no—
1514C2×D4—44no—
1515C2×D4—2681no—
1516C2×D4—2681no—
1517C2×D4—2681no—
1518C2×D4—2681no—
1519C2×D4—5362no—
1520C2×D4—5362no—
1521C2×D4—671no—
1522C2×D4—671no—
1523C2×D4—671no—
1524C2×D4—1341no—
1525C2×D4—1341no—
1526C2×D4—1341no—
1527C2×D4—1341no—
1528C2×D4—1341no—
1529C2×D4—1341no—
1530C2×D4—1341no—
1531C2×D4—1341no—
1532C2×D4—1341no—
1533C2×D4—1341no—
1534C2×D4—1341no—
1535C2×D4—1341no—
1536C2×D4—1341no—
1537C2×D4—1341no—
1538C2×D4—1341no—
1539C2×D4C2×C22⋊D6711yescharacteristic
1540C2×D4C2×C22⋊D6711yescharacteristic
1541C2×D4C2×C22⋊D6711yescharacteristic
1542C2×D4C2×C22⋊D6711yescharacteristic
1543C2×D4C2×C22⋊D6711yescharacteristic
1544C2×D4C2×C22⋊D6711yescharacteristic
1545C2×D4C2×C22⋊D6711yescharacteristic
1546C2×D4C23×D6711yescharacteristic
1547C2×D4C23×D6711yescharacteristic
1548C2×D4C23×D6711yescharacteristic
1549C22×C4—21no—
1550C22×C4—21no—
1551C22×C4—21no—
1552C22×C4—21no—
1553C22×C4—21no—
1554C22×C4—21no—
1555C22×C4—21no—
1556C22×C4—21no—
1557C22×C4—21no—
1558C22×C4—21no—
1559C22×C4—41no—
1560C22×C4—41no—
1561C22×C4—44no—
1562C22×C4—1341no—
1563C22×C4—1341no—
1564C22×C4—1341no—
1565C22×C4—1341no—
1566C22×C4—1341no—
1567C22×C4—1341no—
1568C22×C4—1341no—
1569C22×C4C2×C22⋊D6711yescharacteristic
1570C22×C4C2×C22⋊D6711yescharacteristic
1571C22×C4C2×C22⋊D6711yescharacteristic
1572C22×C4C23×D6711yescharacteristic
1573C22×C4C23×D6711yescharacteristic
1574C22×C4C23×D6711yescharacteristic
1575C22×C4C23×D6711yescharacteristic
1576C22×C4C23×D6711yescharacteristic
1577Q16—2681no—
1578Q16—1342no—
1579Q16—1342no—
1580SD16—2681no—
1581SD16—2681no—
1582SD16—2681no—
1583SD16—2681no—
1584SD16—2681no—
1585SD16—2681no—
1586SD16—1342no—
1587SD16—1342no—
1588SD16—1342no—
1589SD16—1342no—
1590SD16—1342no—
1591SD16—1342no—
1592D8—2681no—
1593D8—2681no—
1594D8—2681no—
1595D8—2681no—
1596D8—2681no—
1597D8—2681no—
1598D8—2681no—
1599D8—2681no—
1600D8—2681no—
1601M16—2681no—
1602M16—2681no—
1603M16—2681no—
1604M16—2681no—
1605C2×C8—2681no—
1606C2×C8—2681no—
1607C2×C8—2681no—
1608C2×C8—2681no—
1609C2×C8—671no—
1610C2×C8—671no—
1611C2×C8—671no—
1612C2×C8—671no—
1613C2×C8—671no—
1614C2×C8—671no—
1615C2×C8—671no—
1616C2×C8—671no—
1617C4⋊C4—21no—
1618C4⋊C4—21no—
1619C4⋊C4—21no—
1620C4⋊C4—21no—
1621C4⋊C4—21no—
1622C4⋊C4—21no—
1623C4⋊C4—671no—
1624C4⋊C4—671no—
1625C4⋊C4—671no—
1626C4⋊C4—671no—
1627C4⋊C4—1341no—
1628C4⋊C4—1341no—
1629C4⋊C4—1341no—
1630C4⋊C4—1341no—
1631C4⋊C4—1341no—
1632C4⋊C4—1341no—
1633C4⋊C4—1341no—
1634C4⋊C4—1341no—
1635C4⋊C4—1341no—
1636C4⋊C4C2×C22⋊D6711yescharacteristic
1637C4⋊C4C2×C22⋊D6711yescharacteristic
1638C4⋊C4C2×C22⋊D6711yescharacteristic
1639C4⋊C4C2×C22⋊D6711yescharacteristic
1640C4⋊C4C2×C22⋊D6711yescharacteristic
1641C4⋊C4C2×C22⋊D6711yescharacteristic
1642C4⋊C4C23×D6711yescharacteristic
1643C4⋊C4C23×D6711yescharacteristic
1644C22⋊C4—21no—
1645C22⋊C4—21no—
1646C22⋊C4—21no—
1647C22⋊C4—21no—
1648C22⋊C4—21no—
1649C22⋊C4—21no—
1650C22⋊C4—21no—
1651C22⋊C4—21no—
1652C22⋊C4—21no—
1653C22⋊C4—21no—
1654C22⋊C4—21no—
1655C22⋊C4—21no—
1656C22⋊C4—21no—
1657C22⋊C4—1341no—
1658C22⋊C4—1341no—
1659C22⋊C4—1341no—
1660C22⋊C4—1341no—
1661C22⋊C4—1341no—
1662C22⋊C4—1341no—
1663C22⋊C4—1341no—
1664C22⋊C4—1341no—
1665C22⋊C4—1341no—
1666C22⋊C4—1341no—
1667C22⋊C4—1341no—
1668C22⋊C4—1341no—
1669C22⋊C4—1341no—
1670C22⋊C4—1341no—
1671C22⋊C4—1341no—
1672C22⋊C4—1341no—
1673C22⋊C4—1341no—
1674C22⋊C4—1341no—
1675C22⋊C4—1341no—
1676C22⋊C4C2×C22⋊D6711yescharacteristic
1677C22⋊C4C2×C22⋊D6711yescharacteristic
1678C22⋊C4C2×C22⋊D6711yescharacteristic
1679C22⋊C4C2×C22⋊D6711yescharacteristic
1680C22⋊C4C2×C22⋊D6711yescharacteristic
1681C22⋊C4C2×C22⋊D6711yescharacteristic
1682C22⋊C4C2×C22⋊D6711yescharacteristic
1683C22⋊C4C2×C22⋊D6711yescharacteristic
1684C22⋊C4C2×C22⋊D6711yescharacteristic
1685C22⋊C4C2×C22⋊D6711yescharacteristic
1686C42—21no—
1687C42—21no—
1688C42—21no—
1689C42—21no—
1690C42—21no—
1691C42—1341no—
1692C42—1341no—
1693C42—1341no—
1694C42C23×D6711yescharacteristic
1695C42C23×D6711yescharacteristic
1696C23—21no—
1697C23—21no—
1698C23—21no—
1699C23—41no—
1700C23—41no—
1701C23—41no—
1702C23—42no—
1703C23—81no—
1704C23—81no—
1705C23—2682no—
1706C23—5361no—
1707C23—5361no—
1708C23—5361no—
1709C23—5361no—
1710C23—5361no—
1711C23—1341no—
1712C23—1341no—
1713C23—1341no—
1714C23C22×C22⋊D6711yescharacteristic
1715C23C22×C22⋊D6711yescharacteristic
1716C23C22×C22⋊D6711yescharacteristic
1717C23C22×C22⋊D6711yescharacteristic
1718C23C22×C22⋊D6711yescharacteristic
1719Q8—24no—
1720Q8—21no—
1721Q8—21no—
1722Q8—21no—
1723Q8—21no—
1724Q8—41no—
1725Q8—42no—
1726Q8—42no—
1727Q8—5361no—
1728Q8—1341no—
1729Q8—1341no—
1730Q8#1452408812yes—
1731Q8#1452408812yes—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—21no—
1738D4—41no—
1739D4—41no—
1740D4—41no—
1741D4—41no—
1742D4—41no—
1743D4—41no—
1744D4—41no—
1745D4—42no—
1746D4—42no—
1747D4—42no—
1748D4—42no—
1749D4—42no—
1750D4—42no—
1751D4—42no—
1752D4—42no—
1753D4—81no—
1754D4—81no—
1755D4—81no—
1756D4—81no—
1757D4—81no—
1758D4—81no—
1759D4—81no—
1760D4—81no—
1761D4—81no—
1762D4—81no—
1763D4—2682no—
1764D4—5361no—
1765D4—5361no—
1766D4—5361no—
1767D4—5361no—
1768D4—5361no—
1769D4—5361no—
1770D4—5361no—
1771D4—5361no—
1772D4—5361no—
1773D4—5361no—
1774D4—5361no—
1775D4—5361no—
1776D4—5361no—
1777D4—5361no—
1778D4—1341no—
1779D4—1341no—
1780D4—1341no—
1781D4—1341no—
1782D4—1341no—
1783D4—1341no—
1784C2×C4—24no—
1785C2×C4—21no—
1786C2×C4—21no—
1787C2×C4—21no—
1788C2×C4—21no—
1789C2×C4—21no—
1790C2×C4—21no—
1791C2×C4—21no—
1792C2×C4—21no—
1793C2×C4—21no—
1794C2×C4—21no—
1795C2×C4—21no—
1796C2×C4—21no—
1797C2×C4—21no—
1798C2×C4—21no—
1799C2×C4—21no—
1800C2×C4—41no—
1801C2×C4—41no—
1802C2×C4—41no—
1803C2×C4—42no—
1804C2×C4—42no—
1805C2×C4—42no—
1806C2×C4—42no—
1807C2×C4—42no—
1808C2×C4—42no—
1809C2×C4—42no—
1810C2×C4—42no—
1811C2×C4—42no—
1812C2×C4—2682no—
1813C2×C4—5361no—
1814C2×C4—5361no—
1815C2×C4—5361no—
1816C2×C4—5361no—
1817C2×C4—5361no—
1818C2×C4—5361no—
1819C2×C4—1341no—
1820C2×C4—1341no—
1821C2×C4—1341no—
1822C2×C4—1341no—
1823C2×C4—1341no—
1824C2×C4C22×C22⋊D6711yescharacteristic
1825C2×C4C22×C22⋊D6711yescharacteristic
1826C2×C4C22×C22⋊D6711yescharacteristic
1827C2×C4C22×C22⋊D6711yescharacteristic
1828C2×C4C22×C22⋊D6711yescharacteristic
1829C2×C4C22×C22⋊D6711yescharacteristic
1830C2×C4C22×C22⋊D6711yescharacteristic
1831C2×C4C22×C22⋊D6711yescharacteristic
1832C2×C4C22×C22⋊D6711yescharacteristic
1833C2×C4C24×D6711yescharacteristic
1834C8—1341no—
1835C8—1341no—
1836C8—1341no—
1837C8—1341no—
1838C8—1341no—
1839C8—1341no—
1840C8—1341no—
1841C8—1341no—
1842C22—21no—
1843C22—21no—
1844C22—21no—
1845C22—21no—
1846C22—21no—
1847C22—21no—
1848C22—21no—
1849C22—21no—
1850C22—21no—
1851C22—21no—
1852C22—21no—
1853C22—21no—
1854C22—21no—
1855C22—21no—
1856C22—21no—
1857C22—41no—
1858C22—41no—
1859C22—41no—
1860C22—41no—
1861C22—41no—
1862C22—41no—
1863C22—41no—
1864C22—41no—
1865C22—41no—
1866C22—82no—
1867C22—84no—
1868C22—2681no—
1869C22—2681no—
1870C22—2681no—
1871C22—2681no—
1872C22—2681no—
1873C22—2681no—
1874C22—2681no—
1875C22—2681no—
1876C22—2681no—
1877C22—10722no—
1878C22—10722no—
1879C22C23×C22⋊D6711yescharacteristic
1880C4—22no—
1881C4—22no—
1882C4—21no—
1883C4—21no—
1884C4—21no—
1885C4—21no—
1886C4—21no—
1887C4—21no—
1888C4—21no—
1889C4—21no—
1890C4—21no—
1891C4—41no—
1892C4—41no—
1893C4—41no—
1894C4—2681no—
1895C4—2681no—
1896C4—2681no—
1897C4—2681no—
1898C4—2681no—
1899C4C2×#1452408811yescharacteristic
1900C4C2×#1452408811yescharacteristic
1901C2—41no—
1902C2—41no—
1903C2—41no—
1904C2—41no—
1905C2—41no—
1906C2—81no—
1907C2—81no—
1908C2—81no—
1909C2—5361no—
1910C2—5361no—
1911C2—5361no—
1912C2#2257384411yescharacteristic
1913C2#2257498011yescharacteristic
1914C2#2257498811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3487C2
socleC22×C67C23×D4
hypercenter#3487D67
hypocenterC67#61616
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #525 ◁ #3487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22574525C2semidirect
2. #22572536C2semidirect
3. #22572477C2semidirect
4. #22572395C2semidirect
5. #22572335C2semidirect
6. #22572215C2semidirect
7. #22572200C2semidirect
8. #22572159C2semidirect
9. #22572111C2semidirect
10. #22571965C2semidirect
11. #22571917C2semidirect
12. #22571841C2semidirect
13. #22571829C2semidirect
14. #22571795C2semidirect
15. #22571750C2semidirect
16. #22571750C2semidirect
17. #22571705C2semidirect
18. #22571303C2semidirect
19. #22571259C2semidirect
20. #22571070C2semidirect
21. #22571061C2semidirect
22. #22571046C2semidirect
23. #22570970C2semidirect
24. #22570500C2semidirect
25. #22570438C2semidirect
26. #22569524C2semidirect
27. #22569495C2semidirect
28. #22569461C2semidirect
29. #22569427C2semidirect
30. #22569257C2semidirect
31. C67×#3487C2semidirect
32. C2×#14524074C22semidirect
35. C2×#14524068C22semidirect
36. C2×#14524063C22semidirect
37. C2×#14524063C22semidirect
38. C2×#14524063C22semidirect
39. C22×#11761615C22semidirect
42. #16864111C22semidirect
43. #16864092C22semidirect
44. #16864086C22semidirect
46. #16864067C22semidirect
47. #16864050C22semidirect
48. #16864042C22semidirect
49. #16864042C22semidirect
51. D4×D268C22semidirect
62. #16863786C22semidirect
63. #16863783C22semidirect
64. #16863778C22semidirect
65. #16863772C22semidirect
66. #16863760C22semidirect
67. #16863755C22semidirect
68. #16863750C22semidirect
69. #16863742C22semidirect
70. #16863737C22semidirect
71. #16863734C22semidirect
72. #16863729C22semidirect
74. #16863720C22semidirect
75. #16863720C22semidirect
76. #16863717C22semidirect
77. #16863717C22semidirect
78. #16863717C22semidirect
79. #16863712C22semidirect
80. #16863712C22semidirect
81. #16863707C22semidirect
82. #16863703C22semidirect
83. #16863703C22semidirect
84. #16863691C22semidirect
85. #16863681C22semidirect
86. #16863652C22semidirect
87. #16863647C22semidirect
88. #16863647C22semidirect
89. #16863647C22semidirect
90. #16863647C22semidirect
91. #16863644C22semidirect
92. #16863640C22semidirect
93. #16863640C22semidirect
94. #16863630C22semidirect
95. #16863630C22semidirect
96. #16863630C22semidirect
97. #16863630C22semidirect
98. #16863630C22semidirect
99. #16863627C22semidirect
100. #16863627C22semidirect
101. #16863623C22semidirect
102. #16863618C22semidirect
103. #16863618C22semidirect
104. #16863615C22semidirect
105. #16863608C22semidirect
106. #16863608C22semidirect
107. #16863608C22semidirect
108. #16863596C22semidirect
109. #16863596C22semidirect
110. #16863593C22semidirect
111. #16863588C22semidirect
112. #16863588C22semidirect
113. #16863588C22semidirect
114. #16863558C22semidirect
115. #16863558C22semidirect
116. #16863558C22semidirect
117. #16863558C22semidirect
118. #16863556C22semidirect
119. #16863552C22semidirect
120. #16863552C22semidirect
121. #16863547C22semidirect
122. #16863546C22semidirect
128. #16863541C22semidirect
129. #16863541C22semidirect
130. #16863541C22semidirect
131. #16863541C22semidirect
132. #16863541C22semidirect
133. #16863541C22semidirect
134. #16863541C22semidirect
135. #16863539C22semidirect
136. #16863539C22semidirect
137. #16863539C22semidirect
139. #16863535C22semidirect
140. #16863535C22semidirect
141. #16863535C22semidirect
142. #16863535C22semidirect
143. #16863535C22semidirect
145. #16863530C22semidirect
146. #16863530C22semidirect
147. #16863529C22semidirect
148. #16863529C22semidirect
149. #16863529C22semidirect
150. #16863501C22semidirect
151. #16863494C22semidirect
152. #16863494C22semidirect
153. #16863494C22semidirect
154. C4×#11761618C22semidirect
155. C4×#11761615C22semidirect
156. C4×#11761615C22semidirect
157. C4×#11761615C22semidirect
158. #16863474C22semidirect
159. #16863474C22semidirect
160. #16863468C22semidirect
161. #16863468C22semidirect
162. #16863468C22semidirect
163. #16863468C22semidirect
164. D4×C67⋊C8C22semidirect
165. D4×C67⋊C8C22semidirect
166. #16863457C22semidirect
167. #16863457C22semidirect
168. #16863405C22semidirect
169. #16863397C22semidirect
170. #16863397C22semidirect
171. #16863397C22semidirect
172. #16863392C22semidirect
173. #16863392C22semidirect
174. #16863392C22semidirect
175. C2×#14523967C22semidirect
176. #16863363C22semidirect
177. #16863363C22semidirect
178. #16863360C22semidirect
179. C2×C22⋊(C67⋊C8)C22semidirect
180. C2×2−1+4×C67C22semidirect
181. C22×#41×C67C22semidirect
185. #550×C67C22semidirect
186. #550×C67C22semidirect
187. #550×C67C22semidirect
191. #548×C67C22semidirect
192. #548×C67C22semidirect
193. #548×C67C22semidirect
196. #535×C67C22semidirect
197. #535×C67C22semidirect
201. #525×C67C22semidirect
202. #519×C67C22semidirect
959. #3487D67semidirect
989. C67#61616semidirect
990. C2×2−1+4C2×D67semidirect
991. C22×#41C2×D67semidirect
1010. #550C2×D67semidirect
1011. #550C2×D67semidirect
1012. #550C2×D67semidirect
1016. #548C2×D67semidirect
1017. #548C2×D67semidirect
1018. #548C2×D67semidirect
1033. #535C2×D67semidirect
1034. #535C2×D67semidirect
1040. #525C2×D67semidirect
1042. #519C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225745252
#225725362
#225724772
#225723952
#225723352
#225722152
#225722002
#225721592
#225721112
#225719652
#225719172
#225718412
#225718292
#225717952
#225717502
#225717052
#225713032
#225712592
#225710702
#225710612
#225710462
#225709702
#225705002
#225704382
#225695242
#225694952
#225694612
#225694272
#225692572
C67×#34872
#6161667