Finite Group Databasebeta

← #31740206

Subgroups — #31740206

Order 17152.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574153C211yesmaximal, characteristic, complemented
2#22573217C211yesmaximal, characteristic, complemented
3#22573080C211yesmaximal, characteristic, complemented
4#22572977C211yesmaximal, characteristic, complemented
5#22572956C211yesmaximal, characteristic, complemented
6#22572809C211yesmaximal, characteristic, complemented
7#22572798C211yesmaximal, characteristic, complemented
8#22572778C211yesmaximal, characteristic, complemented
9#22572359C211yesmaximal, characteristic, complemented
10#22572335C211yesmaximal, characteristic, complemented
11#22572224C211yesmaximal, characteristic, complemented
12#22572200C211yesmaximal, characteristic, complemented
13#22572111C211yesmaximal, characteristic, complemented
14#22572053C211yesmaximal, characteristic, complemented
15#22571841C211yesmaximal, characteristic, complemented
16#22571841C211yesmaximal, characteristic, complemented
17#22571829C211yesmaximal, characteristic, complemented
18#22570932C211yesmaximal, characteristic, complemented
19#22570853C211yesmaximal, characteristic, complemented
20#22570820C211yesmaximal, characteristic, complemented
21#22570500C211yesmaximal, characteristic, complemented
22#22570471C211yesmaximal, characteristic, complemented
23#22570402C211yesmaximal, characteristic, complemented
24#22570387C211yesmaximal, characteristic, complemented
25#22570252C211yesmaximal, characteristic, complemented
26#22570227C211yesmaximal, characteristic, complemented
27#22569214C211yesmaximal, characteristic, complemented
28#22569052C211yesmaximal, characteristic, complemented
29#22569037C211yesmaximal, characteristic, complemented
30C4×#14524068C211yesmaximal, characteristic, complemented
31C67×#3524C211yesmaximal, characteristic, complemented
32C2×#14524074C2211yescharacteristic
33C2×#14524068C2211yescharacteristic
34C2×#14524068C2211yescharacteristic
35#16864131C2211yescharacteristic
36#16864106C2211yescharacteristic
37#16864097—21no—
38#16864092C2211yescharacteristic
39#16864086C2211yescharacteristic
40#16864073—21no—
41#16864071—21no—
42#16864050C2211yescharacteristic
43#16864042C2211yescharacteristic
44#16864042C2211yescharacteristic
45#16864035—21no—
46D4×D268C2211yescharacteristic
47#16864017C2211yescharacteristic
48#16864001C2211yescharacteristic
49#16863994—21no—
50#16863980—21no—
51#16863930C2211yescharacteristic
52#16863904—21no—
53#123×D67—21no—
54#16863876C2211yescharacteristic
55#16863870C2211yescharacteristic
56C2×C4×D268C2211yescharacteristic
57#16863795C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863792C2211yescharacteristic, complemented
60#16863778C2211yescharacteristic, complemented
61#16863778C2211yescharacteristic, complemented
62#16863772C2211yescharacteristic
63#16863762C2211yescharacteristic
64#16863760C2211yescharacteristic, complemented
65#16863758C2211yescharacteristic, complemented
66#16863755C2211yescharacteristic, complemented
67#16863753C2211yescharacteristic, complemented
68#16863750C2211yescharacteristic, complemented
69#16863737C2211yescharacteristic, complemented
70#16863734C2211yescharacteristic, complemented
71#16863731C2211yescharacteristic, complemented
72#16863729C2211yescharacteristic, complemented
73#16863720C2211yescharacteristic
74#16863720C2211yescharacteristic, complemented
75#16863720C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic, complemented
77#16863712C2211yescharacteristic, complemented
78#16863712C2211yescharacteristic, complemented
79#16863709C2211yescharacteristic
80#16863707C2211yescharacteristic, complemented
81#16863703C2211yescharacteristic, complemented
82#16863703C2211yescharacteristic, complemented
83#16863703C2211yescharacteristic, complemented
84#16863700C2211yescharacteristic, complemented
85#16863696C2211yescharacteristic, complemented
86#16863693C2211yescharacteristic
87#16863693C2211yescharacteristic
88#16863693C2211yescharacteristic, complemented
89#16863691C2211yescharacteristic, complemented
90#16863683C2211yescharacteristic, complemented
91#16863676C2211yescharacteristic, complemented
92#16863673C2211yescharacteristic
93#16863652C2211yescharacteristic, complemented
94#16863652C2211yescharacteristic, complemented
95#16863647C2211yescharacteristic
96#16863647C2211yescharacteristic
97#16863647C2211yescharacteristic, complemented
98#16863647C2211yescharacteristic, complemented
99#16863644C2211yescharacteristic
100#16863640C2211yescharacteristic, complemented
101#16863630C2211yescharacteristic, complemented
102#16863630C2211yescharacteristic, complemented
103#16863627C2211yescharacteristic
104#16863623C2211yescharacteristic, complemented
105#16863618C2211yescharacteristic, complemented
106#16863618C2211yescharacteristic, complemented
107#16863611C2211yescharacteristic, complemented
108#16863611C2211yescharacteristic, complemented
109#16863608C2211yescharacteristic
110#16863608C2211yescharacteristic
111#16863608C2211yescharacteristic, complemented
112#16863608C2211yescharacteristic, complemented
113#16863596C2211yescharacteristic
114#16863596C2211yescharacteristic
115#16863593C2211yescharacteristic, complemented
116#16863588C2211yescharacteristic
117#16863558C2211yescharacteristic, complemented
118#16863558C2211yescharacteristic, complemented
119#16863546C2211yescharacteristic
120#16863546C2211yescharacteristic
121#16863541C2211yescharacteristic
122#16863541C2211yescharacteristic
123#16863539C2211yescharacteristic
124#16863539C2211yescharacteristic
125#16863535C2211yescharacteristic, complemented
126#16863535C2211yescharacteristic, complemented
127#16863529C2211yescharacteristic
128#16863529C2211yescharacteristic
129#16863527C2211yescharacteristic, complemented
130Q8×C67⋊C8C2211yescharacteristic, complemented
131#16863506C2211yescharacteristic
132#16863506C2211yescharacteristic
133#16863506C2211yescharacteristic, complemented
134#16863506C2211yescharacteristic, complemented
135#16863501C2211yescharacteristic, complemented
136#16863501C2211yescharacteristic, complemented
137#16863496C2211yescharacteristic, complemented
138#16863494C2211yescharacteristic
139#16863494C2211yescharacteristic
140#16863494C2211yescharacteristic, complemented
141#16863494C2211yescharacteristic, complemented
142#16863494C2211yescharacteristic, complemented
143C4×#11761618C2211yescharacteristic, complemented
144C4×#11761618C2211yescharacteristic, complemented
145C4×#11761615C2211yescharacteristic
146C4×#11761615C2211yescharacteristic
147C4×#11761615C2211yescharacteristic
148C4×#11761615C2211yescharacteristic
149C4×#11761615C2211yescharacteristic, complemented
150C4×#11761615C2211yescharacteristic, complemented
151C4×#11761615C2211yescharacteristic, complemented
152C4×#11761616C2211yescharacteristic, complemented
153C4×#11761613C2211yescharacteristic
154C4×#11761613C2211yescharacteristic
155C4×#11761613C2211yescharacteristic, complemented
156C4×#11761613C2211yescharacteristic, complemented
157C4×#11761613C2211yescharacteristic, complemented
158C4×#11761613C2211yescharacteristic, complemented
159#16863474C2211yescharacteristic
160#16863474C2211yescharacteristic, complemented
161#16863474C2211yescharacteristic, complemented
162#16863468C2211yescharacteristic
163#16863468C2211yescharacteristic, complemented
164D4×C67⋊C8C2211yescharacteristic, complemented
165#16863457C2211yescharacteristic, complemented
166#16863457C2211yescharacteristic, complemented
167#16863449C2211yescharacteristic, complemented
168#16863439C2211yescharacteristic, complemented
169#16863439C2211yescharacteristic, complemented
170#16863436C2211yescharacteristic, complemented
171#16863400C2211yescharacteristic
172#16863397C2211yescharacteristic, complemented
173#16863392C2211yescharacteristic, complemented
174#16863390C2211yescharacteristic
175C2×#14523967C2211yescharacteristic, complemented
176C2×#14523963C2211yescharacteristic
177#16863352C2211yescharacteristic, complemented
178#16863352C2211yescharacteristic, complemented
179C4×#11761612C2211yescharacteristic, complemented
180#559×C67—21no—
181#559×C67C2211yescharacteristic, complemented
182#557×C67C2211yescharacteristic, complemented
183#555×C67—21no—
184#555×C67C2211yescharacteristic, complemented
185#553×C67—21no—
186#553×C67C2211yescharacteristic, complemented
187#552×C67—21no—
188#552×C67C2211yescharacteristic
189#550×C67C2211yescharacteristic
190#548×C67C2211yescharacteristic, complemented
191#548×C67C2211yescharacteristic, complemented
192#542×C67—21no—
193#542×C67C2211yescharacteristic, complemented
194#540×C67—21no—
195#540×C67C2211yescharacteristic, complemented
196#529×C67—21no—
197#529×C67—21no—
198#529×C67C2211yescharacteristic
199#529×C67C2211yescharacteristic, complemented
200#520×C67C2211yescharacteristic, complemented
201#519×C67C2211yescharacteristic, complemented
202C4×#41×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761627—21no—
205C22×D268C2311yescharacteristic
206C22×D268C2311yescharacteristic
207C2×D4×D67—21no—
208C22×C4×D67—21no—
209#14524074—24no—
210#14524068—24no—
211#14524068—24no—
212C2×#11761618C2311yescharacteristic
213C2×#11761618C2311yescharacteristic
214C2×#11761616C2311yescharacteristic
215C2×#11761616C2311yescharacteristic
216C2×#11761615C2311yescharacteristic
217C2×#11761615C2311yescharacteristic
218C2×#11761615C2311yescharacteristic
219C2×#11761615C2311yescharacteristic
220C2×#11761615C2311yescharacteristic
221C2×#11761615C2311yescharacteristic
222C2×#11761613C2311yescharacteristic
223C2×#11761613C2311yescharacteristic
224C2×#11761613C2311yescharacteristic
225C2×#11761613C2311yescharacteristic
226C2×#11761613C2311yescharacteristic
227C2×#11761613C2311yescharacteristic
228C2×#11761612C2311yescharacteristic
229C2×#11761612C2311yescharacteristic
230C2×#11761612C2311yescharacteristic
231C2×#11761612C2311yescharacteristic
232C22×C67⋊C8C2311yescharacteristic
233C22×C67⋊C8C2311yescharacteristic
234#14524043C2311yescharacteristic
235#14524040C2311yescharacteristic
236#14524038—21no—
237#14524038—21no—
238#14524037—21no—
239#14524036—21no—
240#14524035C2311yescharacteristic
241#14524035C2311yescharacteristic
242#14524033—21no—
243#14524032—21no—
244#14524031C2311yescharacteristic
245#14524031C2311yescharacteristic
246#14524029—21no—
247#14524028—21no—
248#14524028—21no—
249#14524028—21no—
250#14524028—21no—
251#14524028—21no—
252#14524028—21no—
253#14524027—21no—
254#14524027—21no—
255#14524026—21no—
256#14524025—21no—
257#14524025—21no—
258#14524024—21no—
259#14524023—21no—
260#14524022C2311yescharacteristic
261#14524022C2311yescharacteristic
262#14524021—21no—
263#14524021—21no—
264#14524021—21no—
265#14524019—21no—
266#14524018—21no—
267#14524017C2311yescharacteristic
268#14524017C2311yescharacteristic
269#14524017C2311yescharacteristic
270#14524017C2311yescharacteristic
271#14524016—21no—
272#14524016—21no—
273#14524016—21no—
274#14524016—21no—
275#14524015—21no—
276#14524013—21no—
277#14524013—21no—
278#14524011—21no—
279#14524011—21no—
280C4×Dic134C2311yescharacteristic
281C4×Dic134C2311yescharacteristic
282C4×D268—21no—
283C4×D268—21no—
284C4×D268C2311yescharacteristic
285C4×D268C2311yescharacteristic
286C4×D268C2311yescharacteristic
287C4×D268C2311yescharacteristic
288C4×D268C2311yescharacteristic
289C4×D268C2311yescharacteristic
290C4×D268C2311yescharacteristic
291C4×D268C2311yescharacteristic
292#14524005—21no—
293#14524005—21no—
294#14524005—21no—
295C4×C22⋊D67—21no—
296(C22⋊D67)⋊C4—21no—
297(C22⋊D67)⋊C4—21no—
298(C22⋊D67)⋊C4—21no—
299#14524002C2311yescharacteristic
300#14524001—21no—
301#14524000—21no—
302#14523999—21no—
303C2×C4⋊Dic67C2311yescharacteristic
304C2×C4⋊Dic67C2311yescharacteristic
305C4⋊C4×D67—21no—
306C4⋊C4×D67—21no—
307C2×(C2×D67)⋊C4—21no—
308C22⋊C4×D67—21no—
309C22⋊C4×D67—21no—
310C22⋊C4×D67—21no—
311C22⋊C4×D67—21no—
312#14523976C2311yescharacteristic
313#14523976C2311yescharacteristic
314#14523976C2311yescharacteristic
315#14523976C2311yescharacteristic
316#14523976C2311yescharacteristic
317#14523976C2311yescharacteristic
318#14523976C2311yescharacteristic
319#14523976C2311yescharacteristic
320#14523974C2311yescharacteristic
321#14523974C2311yescharacteristic
322#14523974C2311yescharacteristic
323#14523974C2311yescharacteristic
324#14523974C2311yescharacteristic
325#14523974C2311yescharacteristic
326#14523974C2311yescharacteristic
327#14523974C2311yescharacteristic
328C4⋊(C67⋊C8)C2311yescharacteristic
329C4⋊(C67⋊C8)C2311yescharacteristic
330C4⋊(C67⋊C8)C2311yescharacteristic
331C4⋊(C67⋊C8)C2311yescharacteristic
332C4⋊(C67⋊C8)C2311yescharacteristic
333C4⋊(C67⋊C8)C2311yescharacteristic
334#14523967C2311yescharacteristic
335#14523967C2311yescharacteristic
336#14523967C2311yescharacteristic
337#14523967C2311yescharacteristic
338#14523967C2311yescharacteristic
339#14523967C2311yescharacteristic
340#14523967C2311yescharacteristic
341#14523967C2311yescharacteristic
342#14523966C2311yescharacteristic
343#14523966C2311yescharacteristic
344#14523966C2311yescharacteristic
345#14523966C2311yescharacteristic
346#14523964C2311yescharacteristic
347#14523964C2311yescharacteristic
348#14523964C2311yescharacteristic
349#14523964C2311yescharacteristic
350#14523964C2311yescharacteristic
351#14523964C2311yescharacteristic
352#14523964C2311yescharacteristic
353#14523964C2311yescharacteristic
354#14523963C2311yescharacteristic
355#14523963C2311yescharacteristic
356#14523963C2311yescharacteristic
357#14523963C2311yescharacteristic
358#14523963C2311yescharacteristic
359#14523963C2311yescharacteristic
360#14523963C2311yescharacteristic
361#14523963C2311yescharacteristic
362#14523963C2311yescharacteristic
363#14523963C2311yescharacteristic
364#14523963C2311yescharacteristic
365#14523963C2311yescharacteristic
366C22⋊(C67⋊C8)C2311yescharacteristic
367C22⋊(C67⋊C8)C2311yescharacteristic
368C22⋊(C67⋊C8)C2311yescharacteristic
369C22⋊(C67⋊C8)C2311yescharacteristic
370C22⋊(C67⋊C8)C2311yescharacteristic
371C22⋊(C67⋊C8)C2311yescharacteristic
372#14523954C2311yescharacteristic
373#14523954C2311yescharacteristic
374#14523954C2311yescharacteristic
375#14523954C2311yescharacteristic
376C4×C67⋊C8C2311yescharacteristic
377C4×C67⋊C8C2311yescharacteristic
378C4×C67⋊C8C2311yescharacteristic
379C4×C67⋊C8C2311yescharacteristic
380C4×C67⋊C8C2311yescharacteristic
381C4×C67⋊C8C2311yescharacteristic
382C2×#41×C67C2311yescharacteristic
383C2×#41×C67C2311yescharacteristic
384C22×Q8×C67C2311yescharacteristic
385C4⋊Q8×C67—21no—
386C4⋊Q8×C67C2311yescharacteristic
387#127×C67—21no—
388#127×C67C2311yescharacteristic
389#126×C67—21no—
390#126×C67—21no—
391#126×C67—21no—
392#126×C67—21no—
393#126×C67D411yescharacteristic
394#126×C67D411yescharacteristic
395#125×C67—21no—
396#125×C67—21no—
397#125×C67—21no—
398#125×C67D411yescharacteristic
399#125×C67C2311yescharacteristic
400#125×C67C2311yescharacteristic
401#124×C67—21no—
402#124×C67—21no—
403#124×C67—21no—
404#124×C67—21no—
405#124×C67—21no—
406#124×C67—21no—
407#124×C67D411yescharacteristic
408#124×C67C2311yescharacteristic
409#124×C67C2311yescharacteristic
410#123×C67—21no—
411#123×C67—21no—
412#123×C67—21no—
413#123×C67—21no—
414#123×C67—21no—
415#123×C67—21no—
416#123×C67—21no—
417#123×C67—21no—
418#123×C67D411yescharacteristic
419#123×C67D411yescharacteristic
420C22⋊Q8×C67—21no—
421C22⋊Q8×C67—21no—
422C22⋊Q8×C67—21no—
423C22⋊Q8×C67D411yescharacteristic
424C22⋊Q8×C67C2311yescharacteristic
425C22⋊Q8×C67C2311yescharacteristic
426#121×C67—21no—
427#121×C67—21no—
428#121×C67—21no—
429#121×C67—21no—
430#121×C67—21no—
431#121×C67—21no—
432#121×C67—21no—
433#121×C67—21no—
434#121×C67D411yescharacteristic
435#121×C67C2311yescharacteristic
436#121×C67C2311yescharacteristic
437#121×C67C2311yescharacteristic
438#121×C67C2311yescharacteristic
439C4×Q8×C67—21no—
440C4×Q8×C67—21no—
441C4×Q8×C67—21no—
442C4×Q8×C67C2311yescharacteristic
443C4×Q8×C67C2311yescharacteristic
444C4×Q8×C67C2311yescharacteristic
445C4×Q8×C67C2311yescharacteristic
446C4×Q8×C67C2311yescharacteristic
447C4×Q8×C67C2311yescharacteristic
448C4×Q8×C67C2311yescharacteristic
449C4×D4×C67—21no—
450C4×D4×C67—21no—
451C4×D4×C67—21no—
452C4×D4×C67—21no—
453C4×D4×C67—21no—
454C4×D4×C67—21no—
455C4×D4×C67—21no—
456C4×D4×C67—21no—
457C4×D4×C67—21no—
458C4×D4×C67—21no—
459C4×D4×C67C2311yescharacteristic
460C4×D4×C67C2311yescharacteristic
461C4×D4×C67C2311yescharacteristic
462C4×D4×C67C2311yescharacteristic
463C4×D4×C67C2311yescharacteristic
464C4×D4×C67C2311yescharacteristic
465C4×D4×C67C2311yescharacteristic
466#117×C67—21no—
467#117×C67—21no—
468#117×C67—21no—
469#117×C67—21no—
470#117×C67—21no—
471#117×C67—21no—
472#117×C67—21no—
473#117×C67C2311yescharacteristic
474#117×C67C2311yescharacteristic
475#117×C67C2311yescharacteristic
476#117×C67C2311yescharacteristic
477C2×C4⋊C4×C67—21no—
478C2×C4⋊C4×C67C2311yescharacteristic
479C2×C42×C67—21no—
480C2×C42×C67C2311yescharacteristic
481C23×D67—21no—
482C23×D67—21no—
483#11761628—22no—
484#11761628—41no—
485#11761627—82no—
486C2×Dic134—21no—
487C2×Dic134C2411yescharacteristic
488C2×D268—22no—
489C2×D268—22no—
490C2×D268—21no—
491C2×D268—21no—
492C2×D268—21no—
493C2×D268—21no—
494C2×D268—41no—
495C2×D268—41no—
496C2×D268C2411yescharacteristic
497C2×D268C2411yescharacteristic
498C2×D268C2411yescharacteristic
499C2×C22⋊D67—21no—
500C2×C22⋊D67—21no—
501C2×C22⋊D67—21no—
502C2×C22⋊D67—21no—
503C2×C22⋊D67—21no—
504D4×D67—82no—
505C22×Dic67—21no—
506C22×Dic67—21no—
507C2×C4×D67—21no—
508C2×C4×D67—21no—
509C2×C4×D67—21no—
510C2×C4×D67—21no—
511C2×C4×D67—21no—
512C2×C4×D67—21no—
513C2×C4×D67—21no—
514C2×C4×D67—21no—
515C2×C4×D67—21no—
516C2×C4×D67—82no—
517#11761618—22no—
518#11761618—22no—
519#11761616—41no—
520#11761616—41no—
521#11761615—22no—
522#11761615—22no—
523#11761615—22no—
524#11761615—41no—
525#11761615—41no—
526#11761615#4114yescomplemented
527#11761613—22no—
528#11761613—22no—
529#11761613—22no—
530#11761613—22no—
531#11761613—41no—
532#11761613—41no—
533#11761612—22no—
534#11761612—22no—
535#11761612—22no—
536#11761612—41no—
537C2×C67⋊C8—41no—
538C2×C67⋊C8—41no—
539C2×C67⋊C8C2411yescharacteristic
540C2×C67⋊C8C2411yescharacteristic
541C2×C67⋊C8C2411yescharacteristic
542C2×C67⋊C8C2411yescharacteristic
543C2×C67⋊C8C2411yescharacteristic
544C2×C67⋊C8C2411yescharacteristic
545C2×C67⋊C8C2411yescharacteristic
546C2×C67⋊C8C2411yescharacteristic
547C4⋊Dic67—21no—
548C4⋊Dic67—21no—
549C4⋊Dic67—21no—
550C4⋊Dic67C2411yescharacteristic
551C4⋊Dic67C2411yescharacteristic
552C4⋊Dic67C2411yescharacteristic
553C4⋊Dic67C2411yescharacteristic
554Dic67⋊C4—21no—
555Dic67⋊C4—21no—
556Dic67⋊C4—21no—
557Dic67⋊C4—21no—
558Dic67⋊C4—21no—
559Dic67⋊C4—21no—
560Dic67⋊C4—21no—
561Dic67⋊C4—21no—
562C22⋊Dic67—21no—
563C22⋊Dic67—21no—
564C22⋊Dic67—21no—
565(C2×D67)⋊C4—21no—
566(C2×D67)⋊C4—21no—
567(C2×D67)⋊C4—21no—
568(C2×D67)⋊C4—21no—
569(C2×D67)⋊C4—21no—
570(C2×D67)⋊C4—21no—
571(C2×D67)⋊C4—21no—
572(C2×D67)⋊C4—21no—
573(C2×D67)⋊C4—21no—
574(C2×D67)⋊C4—21no—
575(C2×D67)⋊C4—21no—
576(C2×D67)⋊C4—21no—
577(C2×D67)⋊C4—21no—
578(C2×D67)⋊C4—21no—
579(C2×D67)⋊C4—21no—
580(C2×D67)⋊C4—21no—
581C4×Dic67—21no—
582C4×Dic67—21no—
583C4×Dic67—21no—
584#41×C67—22no—
585#41×C67—22no—
586#41×C67—41no—
587#41×C67—41no—
588C2×Q8×C67—21no—
589C2×Q8×C67—21no—
590C2×Q8×C67—22no—
591C2×Q8×C67—41no—
592C2×Q8×C67C2×D411yescharacteristic
593C2×Q8×C67C2411yescharacteristic
594C2×Q8×C67C2411yescharacteristic
595C2×D4×C67—21no—
596C2×D4×C67—21no—
597C2×D4×C67—21no—
598C2×D4×C67—21no—
599C2×D4×C67—21no—
600C2×D4×C67—21no—
601C2×D4×C67—21no—
602C2×D4×C67—21no—
603C2×D4×C67C2×D411yescharacteristic
604C2×D4×C67C2×D411yescharacteristic
605C2×D4×C67C2×D411yescharacteristic
606C2×D4×C67C2411yescharacteristic
607C2×D4×C67C2411yescharacteristic
608C22×C4×C67—21no—
609C22×C4×C67—21no—
610C22×C4×C67—21no—
611C22×C4×C67—21no—
612C22×C4×C67—21no—
613C22×C4×C67—21no—
614C22×C4×C67—21no—
615C22×C4×C67—21no—
616C22×C4×C67C2×D411yescharacteristic
617C22×C4×C67C2×D411yescharacteristic
618C22×C4×C67C2411yescharacteristic
619C22×C4×C67C2411yescharacteristic
620C22×C4×C67C2411yescharacteristic
621C4⋊C4×C67—21no—
622C4⋊C4×C67—21no—
623C4⋊C4×C67—21no—
624C4⋊C4×C67—21no—
625C4⋊C4×C67—21no—
626C4⋊C4×C67—21no—
627C4⋊C4×C67—21no—
628C4⋊C4×C67—21no—
629C4⋊C4×C67—21no—
630C4⋊C4×C67—21no—
631C4⋊C4×C67—21no—
632C4⋊C4×C67—21no—
633C4⋊C4×C67—21no—
634C4⋊C4×C67—21no—
635C4⋊C4×C67C2×D411yescharacteristic
636C4⋊C4×C67C2×D411yescharacteristic
637C4⋊C4×C67C2×D411yescharacteristic
638C4⋊C4×C67C2×D411yescharacteristic
639C4⋊C4×C67C2×D411yescharacteristic
640C4⋊C4×C67C2×D411yescharacteristic
641C4⋊C4×C67C2×D411yescharacteristic
642C4⋊C4×C67C2×D411yescharacteristic
643C4⋊C4×C67C2×D411yescharacteristic
644C4⋊C4×C67C2×D411yescharacteristic
645C4⋊C4×C67C2411yescharacteristic
646C4⋊C4×C67C2411yescharacteristic
647C4⋊C4×C67C2411yescharacteristic
648C4⋊C4×C67C2411yescharacteristic
649C22⋊C4×C67—21no—
650C22⋊C4×C67—21no—
651C22⋊C4×C67—21no—
652C22⋊C4×C67—21no—
653C22⋊C4×C67—21no—
654C22⋊C4×C67—21no—
655C22⋊C4×C67—21no—
656C22⋊C4×C67—21no—
657C22⋊C4×C67—21no—
658C22⋊C4×C67—21no—
659C22⋊C4×C67—21no—
660C22⋊C4×C67—21no—
661C22⋊C4×C67—21no—
662C22⋊C4×C67—21no—
663C22⋊C4×C67—21no—
664C22⋊C4×C67—21no—
665C22⋊C4×C67C2×D411yescharacteristic
666C22⋊C4×C67C2×D411yescharacteristic
667C22⋊C4×C67C2×D411yescharacteristic
668C22⋊C4×C67C2×D411yescharacteristic
669C22⋊C4×C67C2×D411yescharacteristic
670C22⋊C4×C67C2×D411yescharacteristic
671C22⋊C4×C67C2×D411yescharacteristic
672C22⋊C4×C67C2×D411yescharacteristic
673C22⋊C4×C67C2×D411yescharacteristic
674C22⋊C4×C67C2×D411yescharacteristic
675C42×C67—21no—
676C42×C67—21no—
677C42×C67—21no—
678C42×C67—21no—
679C42×C67—21no—
680C42×C67—21no—
681C42×C67—21no—
682C42×C67—21no—
683C42×C67C2×D411yescharacteristic
684C42×C67C2×D411yescharacteristic
685C42×C67C2411yescharacteristic
686C42×C67C2411yescharacteristic
687C42×C67C2411yescharacteristic
688C42×C67C2411yescharacteristic
689C23×C67—21no—
690C23×C67—21no—
691C23×C67C22×D411yescharacteristic
692C23×C67C22×D411yescharacteristic
693C23×C67C22×D411yescharacteristic
694C22×D67—21no—
695C22×D67—21no—
696C22×D67—21no—
697C22×D67—42no—
698C22×D67—42no—
699C22×D67—42no—
700C22×D67—81no—
701C22×D67—81no—
702C22×D67—81no—
703Q8×C67—21no—
704Q8×C67—21no—
705Q8×C67—21no—
706Q8×C67—41no—
707Q8×C67—42no—
708Q8×C67—81no—
709Q8×C67C2×#4112yes—
710D4×C67—21no—
711D4×C67—21no—
712D4×C67—21no—
713D4×C67—21no—
714D4×C67—41no—
715D4×C67—41no—
716D4×C67—41no—
717D4×C67—42no—
718D4×C67—42no—
719D4×C67—81no—
720D4×C67—81no—
721D4×C67—81no—
722D4×C67—81no—
723D4×C67—81no—
724D4×C67—81no—
725C2×C4×C67—21no—
726C2×C4×C67—21no—
727C2×C4×C67—21no—
728C2×C4×C67—21no—
729C2×C4×C67—21no—
730C2×C4×C67—21no—
731C2×C4×C67—21no—
732C2×C4×C67—21no—
733C2×C4×C67—21no—
734C2×C4×C67—21no—
735C2×C4×C67—21no—
736C2×C4×C67—21no—
737C2×C4×C67—41no—
738C2×C4×C67—41no—
739C2×C4×C67—42no—
740C2×C4×C67—42no—
741C2×C4×C67—42no—
742C2×C4×C67—81no—
743C2×C4×C67—81no—
744C2×C4×C67—81no—
745C2×C4×C67—81no—
746C2×C4×C67—81no—
747C2×C4×C67C22×D411yescharacteristic
748C2×C4×C67C22×D411yescharacteristic
749C2×C4×C67C22×D411yescharacteristic
750C2×C4×C67C22×D411yescharacteristic
751C2×C4×C67C22×D411yescharacteristic
752C2×C4×C67C22×D411yescharacteristic
753C2×C4×C67C22×D411yescharacteristic
754C2×C4×C67C22×D411yescharacteristic
755C2×C4×C67C22×D411yescharacteristic
756C2×C4×C67C22×D411yescharacteristic
757C2×C4×C67C22×D411yescharacteristic
758C2×C4×C67C2511yescharacteristic
759C22⋊D67—42no—
760C22⋊D67—42no—
761C22⋊D67—81no—
762C22⋊D67—81no—
763C22⋊D67—81no—
764C2×Dic67—21no—
765C2×Dic67—21no—
766C2×Dic67—21no—
767C2×Dic67—21no—
768C2×Dic67—21no—
769C2×Dic67—42no—
770C2×Dic67—81no—
771D268—21no—
772D268—21no—
773D268—21no—
774D268—21no—
775D268—21no—
776D268—42no—
777D268—42no—
778D268—81no—
779D268—81no—
780D268C2×#4112yes—
781C4×D67—42no—
782C4×D67—81no—
783C4×D67—81no—
784C4×D67—81no—
785C4×D67—81no—
786C4×D67—81no—
787C4×D67—81no—
788C4×D67—81no—
789C4×D67—81no—
790Dic134—21no—
791Dic134—21no—
792Dic134—81no—
793C67⋊C8—21no—
794C67⋊C8—21no—
795C67⋊C8—21no—
796C67⋊C8—21no—
797C67⋊C8—21no—
798C67⋊C8—21no—
799C67⋊C8—21no—
800C67⋊C8C2×#4112yes—
801C22×C67—21no—
802C22×C67—21no—
803C22×C67—21no—
804C22×C67—21no—
805C22×C67—21no—
806C22×C67—21no—
807C22×C67—21no—
808C22×C67—21no—
809C22×C67—21no—
810C22×C67—41no—
811C22×C67—41no—
812C22×C67—41no—
813C22×C67—41no—
814C22×C67—41no—
815C22×C67—41no—
816C22×C67C23×D411yescharacteristic
817C2×D67—22no—
818C2×D67—41no—
819C2×D67—41no—
820C2×D67—41no—
821C2×D67—41no—
822C2×D67—41no—
823C2×D67—41no—
824C2×D67—41no—
825C2×D67—41no—
826C2×D67—84no—
827C2×D67—162no—
828C4×C67—21no—
829C4×C67—21no—
830C4×C67—21no—
831C4×C67—21no—
832C4×C67—21no—
833C4×C67—21no—
834C4×C67—21no—
835C4×C67—21no—
836C4×C67—21no—
837C4×C67—21no—
838C4×C67—21no—
839C4×C67—22no—
840C4×C67—41no—
841C4×C67—41no—
842C4×C67—41no—
843C4×C67—41no—
844C4×C67—41no—
845C4×C67C22×#4111yescharacteristic
846C4×C67#58511yescharacteristic
847Dic67—41no—
848Dic67—41no—
849Dic67—41no—
850Dic67—41no—
851Dic67—41no—
852#61547—671nomaximal, Sylow
853C2×C67—41no—
854C2×C67—41no—
855C2×C67—41no—
856C2×C67—81no—
857C2×C67—81no—
858C2×C67D4×#4111yescharacteristic
859C2×C67#358411yescharacteristic
860C2×C67#358511yescharacteristic
861D67—42no—
862D67—81no—
863D67—81no—
864#3524D6711yescharacteristic, complemented
865#3513—671no—
866#3396—671no—
867#3381—671no—
868#3371—671no—
869#3370—671no—
870#3355—671no—
871#3354—671no—
872#3352—671no—
873#3319—671no—
874#3317—671no—
875#3310—671no—
876#3308—671no—
877#3301—671no—
878#3297—671no—
879#3275—671no—
880#3275—671no—
881#3274—671no—
882#3183—671no—
883#3176—671no—
884#3173—671no—
885#3126—671no—
886#3124—671no—
887#3119—671no—
888#3118—671no—
889#3105—671no—
890#3102—671no—
891#2969—671no—
892#2947—671no—
893#2946—671no—
894C4×AGL(1,ℤ/8)—671no—
895C67#6154711yescharacteristic, complemented, Sylow
896C2×#137—671no—
897C2×AGL(1,ℤ/8)—671no—
898C2×AGL(1,ℤ/8)—671no—
899#559—21no—
900#559—671no—
901#559C2×D6711yescharacteristic, complemented
902#557C2×D6711yescharacteristic, complemented
903#555—21no—
904#555C2×D6711yescharacteristic, complemented
905#554—671no—
906#553—21no—
907#553—671no—
908#553—1341no—
909#553C2×D6711yescharacteristic, complemented
910#552—21no—
911#552—671no—
912#552C2×D6711yescharacteristic
913#551—1341no—
914#551—1341no—
915#550C2×D6711yescharacteristic
916#548C2×D6711yescharacteristic, complemented
917#548C2×D6711yescharacteristic, complemented
918#547—671no—
919#546—671no—
920#546—671no—
921#546—1341no—
922D42—671no—
923#542—21no—
924#542—671no—
925#542C2×D6711yescharacteristic, complemented
926#540—21no—
927#540—671no—
928#540C2×D6711yescharacteristic, complemented
929#539—1341no—
930#538—1341no—
931#529—21no—
932#529—21no—
933#529—671no—
934#529C2×D6711yescharacteristic
935#529C2×D6711yescharacteristic, complemented
936#525—1341no—
937C2×#123—1341no—
938#520—671no—
939#520C2×D6711yescharacteristic, complemented
940#519C2×D6711yescharacteristic, complemented
941#518—671no—
942C4×#41C2×D6711yescharacteristic, complemented
943C2×C4×D4—671no—
944#499—671no—
945#499—671no—
946#498—671no—
947#495—671no—
948#495—671no—
949#493—671no—
950#490—671no—
951#490—671no—
952#489—671no—
953#489—671no—
954#488—671no—
955#488—671no—
956#485—671no—
957#485—671no—
958#484—671no—
959#484—671no—
960#482—671no—
961#482—671no—
962#482—671no—
963#482—671no—
964#481—671no—
965#481—671no—
966#480—671no—
967#480—671no—
968#479—671no—
969#479—671no—
970#479—671no—
971#479—671no—
972#478—671no—
973#478—671no—
974#478—671no—
975#478—671no—
976#477—671no—
977#476—671no—
978#474—671no—
979#474—671no—
980#470—671no—
981#470—671no—
982#469—671no—
983#469—671no—
984#469—671no—
985#469—671no—
986#468—671no—
987#468—671no—
988#466—671no—
989#466—671no—
990#465—671no—
991#465—671no—
992#464—671no—
993#464—671no—
994#463—671no—
995#463—671no—
996#463—671no—
997#463—671no—
998#463—671no—
999#463—671no—
1000#460—671no—
1001#460—671no—
1002#460—671no—
1003#459—671no—
1004#452—671no—
1005#452—671no—
1006#450—671no—
1007#450—671no—
1008#449—671no—
1009#449—671no—
1010#449—671no—
1011#449—671no—
1012#448—671no—
1013#448—671no—
1014#447—671no—
1015#447—671no—
1016#446—671no—
1017C8×Q8—671no—
1018#442—671no—
1019#442—671no—
1020#442—671no—
1021#442—671no—
1022#441—671no—
1023#441—671no—
1024#440—671no—
1025#440—671no—
1026#440—671no—
1027#440—671no—
1028#440—671no—
1029#440—671no—
1030C4×Q16—671no—
1031C4×Q16—671no—
1032C4×SD16—671no—
1033C4×SD16—671no—
1034C4×SD16—671no—
1035C4×SD16—671no—
1036C4×SD16—671no—
1037C4×SD16—671no—
1038C4×SD16—671no—
1039C4×SD16—671no—
1040C4×D8—671no—
1041C4×D8—671no—
1042C4×D8—671no—
1043C4×D8—671no—
1044C4×D8—671no—
1045C4×D8—671no—
1046#436—671no—
1047#436—671no—
1048#436—671no—
1049#435—671no—
1050#435—671no—
1051C8×D4—671no—
1052#433—671no—
1053#433—671no—
1054#431—671no—
1055#428—671no—
1056#428—671no—
1057#428—671no—
1058#418—671no—
1059#417—671no—
1060#416—671no—
1061#416—671no—
1062C2×#103—671no—
1063C2×#102—671no—
1064#405—671no—
1065#405—671no—
1066C4×M16—671no—
1067C2×#41—671no—
1068C2×#41—1341no—
1069C2×#41C22×D6711yescharacteristic
1070C2×#41C22×D6711yescharacteristic
1071C22×Q8C22×D6711yescharacteristic
1072C22×D4—671no—
1073C22×D4—671no—
1074C22×D4—1341no—
1075C23×C4—1341no—
1076#137—1344no—
1077AGL(1,ℤ/8)—1344no—
1078AGL(1,ℤ/8)—1344no—
1079C2×Q16—671no—
1080C2×Q16—671no—
1081C2×SD16—671no—
1082C2×SD16—671no—
1083C2×SD16—671no—
1084C2×SD16—671no—
1085C2×SD16—671no—
1086C2×SD16—671no—
1087C2×SD16—671no—
1088C2×SD16—671no—
1089C2×D8—671no—
1090C2×D8—671no—
1091C2×D8—671no—
1092C2×D8—671no—
1093C2×D8—671no—
1094C2×D8—671no—
1095C2×M16—671no—
1096C2×M16—671no—
1097C2×M16—671no—
1098C2×M16—671no—
1099C22×C8—671no—
1100C22×C8—671no—
1101C4⋊Q8—21no—
1102C4⋊Q8—671no—
1103C4⋊Q8C22×D6711yescharacteristic
1104#127—21no—
1105#127—671no—
1106#127C22×D6711yescharacteristic
1107#126—21no—
1108#126—21no—
1109#126—21no—
1110#126—21no—
1111#126—1341no—
1112#126—1341no—
1113#126—1341no—
1114#126—1341no—
1115#126C22⋊D6711yescharacteristic
1116#126C22⋊D6711yescharacteristic
1117#125—21no—
1118#125—21no—
1119#125—21no—
1120#125—671no—
1121#125—671no—
1122#125—1341no—
1123#125C22⋊D6711yescharacteristic
1124#125C22×D6711yescharacteristic
1125#125C22×D6711yescharacteristic
1126#124—21no—
1127#124—21no—
1128#124—21no—
1129#124—21no—
1130#124—21no—
1131#124—21no—
1132#124—671no—
1133#124—671no—
1134#124—1341no—
1135#124—1341no—
1136#124C22⋊D6711yescharacteristic
1137#124C22×D6711yescharacteristic
1138#124C22×D6711yescharacteristic
1139#123—21no—
1140#123—21no—
1141#123—21no—
1142#123—21no—
1143#123—21no—
1144#123—21no—
1145#123—21no—
1146#123—21no—
1147#123—1341no—
1148#123—1341no—
1149#123—1341no—
1150#123—1341no—
1151#123—1341no—
1152#123—1341no—
1153#123—1341no—
1154#123—1341no—
1155#123—1341no—
1156#123—1341no—
1157#123—1341no—
1158#123—1341no—
1159#123C22⋊D6711yescharacteristic
1160#123C22⋊D6711yescharacteristic
1161C22⋊Q8—21no—
1162C22⋊Q8—21no—
1163C22⋊Q8—21no—
1164C22⋊Q8—671no—
1165C22⋊Q8—671no—
1166C22⋊Q8—1341no—
1167C22⋊Q8—1341no—
1168C22⋊Q8—1341no—
1169C22⋊Q8—1341no—
1170C22⋊Q8—1341no—
1171C22⋊Q8C22⋊D6711yescharacteristic
1172C22⋊Q8C22×D6711yescharacteristic
1173C22⋊Q8C22×D6711yescharacteristic
1174#121—21no—
1175#121—21no—
1176#121—21no—
1177#121—21no—
1178#121—21no—
1179#121—21no—
1180#121—21no—
1181#121—21no—
1182#121—671no—
1183#121—671no—
1184#121—671no—
1185#121—671no—
1186#121—1341no—
1187#121—1341no—
1188#121—1341no—
1189#121—1341no—
1190#121—1341no—
1191#121—1341no—
1192#121C22⋊D6711yescharacteristic
1193#121C22×D6711yescharacteristic
1194#121C22×D6711yescharacteristic
1195#121C22×D6711yescharacteristic
1196#121C22×D6711yescharacteristic
1197#120—1341no—
1198#120—1341no—
1199#120—1341no—
1200#120—1341no—
1201C4×Q8—21no—
1202C4×Q8—21no—
1203C4×Q8—21no—
1204C4×Q8—671no—
1205C4×Q8—671no—
1206C4×Q8C22×D6711yescharacteristic
1207C4×Q8C22×D6711yescharacteristic
1208C4×Q8C22×D6711yescharacteristic
1209C4×Q8C22×D6711yescharacteristic
1210C4×Q8C22×D6711yescharacteristic
1211C4×Q8C22×D6711yescharacteristic
1212C4×Q8C22×D6711yescharacteristic
1213C4×D4—21no—
1214C4×D4—21no—
1215C4×D4—21no—
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—21no—
1219C4×D4—21no—
1220C4×D4—21no—
1221C4×D4—21no—
1222C4×D4—21no—
1223C4×D4—671no—
1224C4×D4—671no—
1225C4×D4—671no—
1226C4×D4—671no—
1227C4×D4—671no—
1228C4×D4—671no—
1229C4×D4—671no—
1230C4×D4—671no—
1231C4×D4—1341no—
1232C4×D4—1341no—
1233C4×D4—1341no—
1234C4×D4—1341no—
1235C4×D4—1341no—
1236C4×D4—1341no—
1237C4×D4—1341no—
1238C4×D4—1341no—
1239C4×D4—1341no—
1240C4×D4C22×D6711yescharacteristic
1241C4×D4C22×D6711yescharacteristic
1242C4×D4C22×D6711yescharacteristic
1243C4×D4C22×D6711yescharacteristic
1244C4×D4C22×D6711yescharacteristic
1245C4×D4C22×D6711yescharacteristic
1246C4×D4C22×D6711yescharacteristic
1247#117—21no—
1248#117—21no—
1249#117—21no—
1250#117—21no—
1251#117—21no—
1252#117—21no—
1253#117—21no—
1254#117—671no—
1255#117—1341no—
1256#117—1341no—
1257#117—1341no—
1258#117C22×D6711yescharacteristic
1259#117C22×D6711yescharacteristic
1260#117C22×D6711yescharacteristic
1261#117C22×D6711yescharacteristic
1262C2×C4⋊C4—21no—
1263C2×C4⋊C4—671no—
1264C2×C4⋊C4—671no—
1265C2×C4⋊C4—1341no—
1266C2×C4⋊C4—1341no—
1267C2×C4⋊C4C22×D6711yescharacteristic
1268C2×C22⋊C4—1341no—
1269C2×C22⋊C4—1341no—
1270C2×C22⋊C4—1341no—
1271C2×C22⋊C4—1341no—
1272C2×C22⋊C4—1341no—
1273C2×C42—21no—
1274C2×C42C22×D6711yescharacteristic
1275#107—671no—
1276#107—671no—
1277#107—671no—
1278#107—671no—
1279#107—671no—
1280#107—671no—
1281#107—671no—
1282#107—671no—
1283#106—671no—
1284#106—671no—
1285#106—671no—
1286#106—671no—
1287#106—671no—
1288#106—671no—
1289#106—671no—
1290#106—671no—
1291C4⋊C8—671no—
1292C4⋊C8—671no—
1293C4⋊C8—671no—
1294C4⋊C8—671no—
1295C4⋊C8—671no—
1296C4⋊C8—671no—
1297#103—671no—
1298#103—671no—
1299#103—671no—
1300#103—671no—
1301#103—671no—
1302#103—671no—
1303#103—671no—
1304#103—671no—
1305#103—671no—
1306#103—671no—
1307#103—671no—
1308#103—671no—
1309#102—671no—
1310#102—671no—
1311#102—671no—
1312#102—671no—
1313#102—671no—
1314#102—671no—
1315#102—671no—
1316#102—671no—
1317#102—671no—
1318#102—671no—
1319#102—671no—
1320#102—671no—
1321#102—671no—
1322#102—671no—
1323#102—671no—
1324#102—671no—
1325#102—671no—
1326#102—671no—
1327#102—671no—
1328#102—671no—
1329C22⋊C8—671no—
1330C22⋊C8—671no—
1331C22⋊C8—671no—
1332C22⋊C8—671no—
1333C22⋊C8—671no—
1334C22⋊C8—671no—
1335#97—671no—
1336#97—671no—
1337#97—671no—
1338#97—671no—
1339C4×C8—671no—
1340C4×C8—671no—
1341C4×C8—671no—
1342C4×C8—671no—
1343C4×C8—671no—
1344C4×C8—671no—
1345C24—1341no—
1346C24—1341no—
1347#41—22no—
1348#41—22no—
1349#41—41no—
1350#41—41no—
1351#41—2681no—
1352#41—5362no—
1353#41—1342no—
1354C2×Q8—21no—
1355C2×Q8—21no—
1356C2×Q8—22no—
1357C2×Q8—41no—
1358C2×Q8—671no—
1359C2×Q8—1341no—
1360C2×Q8C2×C22⋊D6711yescharacteristic
1361C2×Q8C23×D6711yescharacteristic
1362C2×Q8C23×D6711yescharacteristic
1363C2×D4—21no—
1364C2×D4—21no—
1365C2×D4—21no—
1366C2×D4—21no—
1367C2×D4—21no—
1368C2×D4—21no—
1369C2×D4—21no—
1370C2×D4—21no—
1371C2×D4—2681no—
1372C2×D4—2681no—
1373C2×D4—5362no—
1374C2×D4—671no—
1375C2×D4—671no—
1376C2×D4—671no—
1377C2×D4—1342no—
1378C2×D4—1342no—
1379C2×D4—1341no—
1380C2×D4—1341no—
1381C2×D4—1341no—
1382C2×D4—1341no—
1383C2×D4—1341no—
1384C2×D4—1341no—
1385C2×D4—1341no—
1386C2×D4—1341no—
1387C2×D4—1341no—
1388C2×D4C2×C22⋊D6711yescharacteristic
1389C2×D4C2×C22⋊D6711yescharacteristic
1390C2×D4C2×C22⋊D6711yescharacteristic
1391C2×D4C23×D6711yescharacteristic
1392C2×D4C23×D6711yescharacteristic
1393C22×C4—21no—
1394C22×C4—21no—
1395C22×C4—21no—
1396C22×C4—21no—
1397C22×C4—21no—
1398C22×C4—21no—
1399C22×C4—21no—
1400C22×C4—21no—
1401C22×C4—5362no—
1402C22×C4—1341no—
1403C22×C4—1341no—
1404C22×C4—1341no—
1405C22×C4—1341no—
1406C22×C4—1341no—
1407C22×C4—1341no—
1408C22×C4—1341no—
1409C22×C4—1341no—
1410C22×C4—1341no—
1411C22×C4—1341no—
1412C22×C4—1341no—
1413C22×C4C2×C22⋊D6711yescharacteristic
1414C22×C4C2×C22⋊D6711yescharacteristic
1415C22×C4C23×D6711yescharacteristic
1416C22×C4C23×D6711yescharacteristic
1417C22×C4C23×D6711yescharacteristic
1418Q16—1342no—
1419Q16—1342no—
1420SD16—2681no—
1421SD16—2681no—
1422SD16—2681no—
1423SD16—2681no—
1424SD16—674no—
1425SD16—1342no—
1426SD16—1342no—
1427SD16—1342no—
1428D8—2681no—
1429D8—2681no—
1430D8—1342no—
1431D8—1342no—
1432D8—1342no—
1433D8—1342no—
1434M16—2681no—
1435M16—1342no—
1436M16—1342no—
1437M16—1342no—
1438C2×C8—2681no—
1439C2×C8—2681no—
1440C2×C8—671no—
1441C2×C8—671no—
1442C2×C8—671no—
1443C2×C8—671no—
1444C2×C8—671no—
1445C2×C8—671no—
1446C2×C8—671no—
1447C2×C8—671no—
1448C4⋊C4—21no—
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—21no—
1455C4⋊C4—21no—
1456C4⋊C4—21no—
1457C4⋊C4—21no—
1458C4⋊C4—21no—
1459C4⋊C4—21no—
1460C4⋊C4—21no—
1461C4⋊C4—21no—
1462C4⋊C4—671no—
1463C4⋊C4—671no—
1464C4⋊C4—671no—
1465C4⋊C4—671no—
1466C4⋊C4—1341no—
1467C4⋊C4—1341no—
1468C4⋊C4—1341no—
1469C4⋊C4—1341no—
1470C4⋊C4—1341no—
1471C4⋊C4—1341no—
1472C4⋊C4—1341no—
1473C4⋊C4—1341no—
1474C4⋊C4—1341no—
1475C4⋊C4—1341no—
1476C4⋊C4—1341no—
1477C4⋊C4C2×C22⋊D6711yescharacteristic
1478C4⋊C4C2×C22⋊D6711yescharacteristic
1479C4⋊C4C2×C22⋊D6711yescharacteristic
1480C4⋊C4C2×C22⋊D6711yescharacteristic
1481C4⋊C4C2×C22⋊D6711yescharacteristic
1482C4⋊C4C2×C22⋊D6711yescharacteristic
1483C4⋊C4C2×C22⋊D6711yescharacteristic
1484C4⋊C4C2×C22⋊D6711yescharacteristic
1485C4⋊C4C2×C22⋊D6711yescharacteristic
1486C4⋊C4C2×C22⋊D6711yescharacteristic
1487C4⋊C4C23×D6711yescharacteristic
1488C4⋊C4C23×D6711yescharacteristic
1489C4⋊C4C23×D6711yescharacteristic
1490C4⋊C4C23×D6711yescharacteristic
1491C22⋊C4—21no—
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4—21no—
1507C22⋊C4—1341no—
1508C22⋊C4—1341no—
1509C22⋊C4—1341no—
1510C22⋊C4—1341no—
1511C22⋊C4—1341no—
1512C22⋊C4—1341no—
1513C22⋊C4—1341no—
1514C22⋊C4—1341no—
1515C22⋊C4—1341no—
1516C22⋊C4—1341no—
1517C22⋊C4—1341no—
1518C22⋊C4—1341no—
1519C22⋊C4—1341no—
1520C22⋊C4—1341no—
1521C22⋊C4—1341no—
1522C22⋊C4—1341no—
1523C22⋊C4—1341no—
1524C22⋊C4—1341no—
1525C22⋊C4—1341no—
1526C22⋊C4C2×C22⋊D6711yescharacteristic
1527C22⋊C4C2×C22⋊D6711yescharacteristic
1528C22⋊C4C2×C22⋊D6711yescharacteristic
1529C22⋊C4C2×C22⋊D6711yescharacteristic
1530C22⋊C4C2×C22⋊D6711yescharacteristic
1531C22⋊C4C2×C22⋊D6711yescharacteristic
1532C22⋊C4C2×C22⋊D6711yescharacteristic
1533C22⋊C4C2×C22⋊D6711yescharacteristic
1534C22⋊C4C2×C22⋊D6711yescharacteristic
1535C22⋊C4C2×C22⋊D6711yescharacteristic
1536C42—21no—
1537C42—21no—
1538C42—21no—
1539C42—21no—
1540C42—21no—
1541C42—21no—
1542C42—21no—
1543C42—21no—
1544C42—1341no—
1545C42—1341no—
1546C42—1341no—
1547C42C2×C22⋊D6711yescharacteristic
1548C42C2×C22⋊D6711yescharacteristic
1549C42C23×D6711yescharacteristic
1550C42C23×D6711yescharacteristic
1551C42C23×D6711yescharacteristic
1552C42C23×D6711yescharacteristic
1553C23—21no—
1554C23—21no—
1555C23—2682no—
1556C23—2682no—
1557C23—2682no—
1558C23—5361no—
1559C23—5361no—
1560C23—5361no—
1561C23—1341no—
1562C23—1341no—
1563C23—1341no—
1564C23C22×C22⋊D6711yescharacteristic
1565C23C22×C22⋊D6711yescharacteristic
1566C23C22×C22⋊D6711yescharacteristic
1567Q8—21no—
1568Q8—21no—
1569Q8—21no—
1570Q8—41no—
1571Q8—42no—
1572Q8—81no—
1573Q8—5361no—
1574Q8—1341no—
1575Q8—1341no—
1576Q8#41×D6712yes—
1577D4—21no—
1578D4—21no—
1579D4—21no—
1580D4—21no—
1581D4—41no—
1582D4—41no—
1583D4—41no—
1584D4—42no—
1585D4—42no—
1586D4—81no—
1587D4—81no—
1588D4—81no—
1589D4—81no—
1590D4—81no—
1591D4—81no—
1592D4—2682no—
1593D4—2682no—
1594D4—2682no—
1595D4—2682no—
1596D4—5361no—
1597D4—5361no—
1598D4—5361no—
1599D4—5361no—
1600D4—5361no—
1601D4—672no—
1602D4—1341no—
1603D4—1341no—
1604D4—1341no—
1605D4—1341no—
1606D4—1341no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—41no—
1620C2×C4—41no—
1621C2×C4—42no—
1622C2×C4—42no—
1623C2×C4—42no—
1624C2×C4—81no—
1625C2×C4—81no—
1626C2×C4—81no—
1627C2×C4—81no—
1628C2×C4—81no—
1629C2×C4—2682no—
1630C2×C4—2682no—
1631C2×C4—5361no—
1632C2×C4—5361no—
1633C2×C4—5361no—
1634C2×C4—5361no—
1635C2×C4—5361no—
1636C2×C4—5361no—
1637C2×C4—5361no—
1638C2×C4—5361no—
1639C2×C4—5361no—
1640C2×C4—1341no—
1641C2×C4—1341no—
1642C2×C4—1341no—
1643C2×C4—1341no—
1644C2×C4—1341no—
1645C2×C4C22×C22⋊D6711yescharacteristic
1646C2×C4C22×C22⋊D6711yescharacteristic
1647C2×C4C22×C22⋊D6711yescharacteristic
1648C2×C4C22×C22⋊D6711yescharacteristic
1649C2×C4C22×C22⋊D6711yescharacteristic
1650C2×C4C22×C22⋊D6711yescharacteristic
1651C2×C4C22×C22⋊D6711yescharacteristic
1652C2×C4C22×C22⋊D6711yescharacteristic
1653C2×C4C22×C22⋊D6711yescharacteristic
1654C2×C4C22×C22⋊D6711yescharacteristic
1655C2×C4C22×C22⋊D6711yescharacteristic
1656C2×C4C24×D6711yescharacteristic
1657C8—672no—
1658C8—1341no—
1659C8—1341no—
1660C8—1341no—
1661C8—1341no—
1662C8—1341no—
1663C8—1341no—
1664C8—1341no—
1665C22—21no—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—21no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—2681no—
1681C22—2681no—
1682C22—2681no—
1683C22—2681no—
1684C22—2681no—
1685C22—2681no—
1686C22—2681no—
1687C22—2681no—
1688C22—5364no—
1689C22—10722no—
1690C22—1342no—
1691C22C23×C22⋊D6711yescharacteristic
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—22no—
1696C4—21no—
1697C4—21no—
1698C4—21no—
1699C4—21no—
1700C4—21no—
1701C4—21no—
1702C4—21no—
1703C4—21no—
1704C4—41no—
1705C4—41no—
1706C4—41no—
1707C4—41no—
1708C4—41no—
1709C4—2681no—
1710C4—2681no—
1711C4—2681no—
1712C4—2681no—
1713C4—2681no—
1714C4C2×#41×D6711yescharacteristic
1715C4#1686423211yescharacteristic
1716C2—41no—
1717C2—41no—
1718C2—41no—
1719C2—81no—
1720C2—81no—
1721C2—2682no—
1722C2—5361no—
1723C2—5361no—
1724C2#41×C22⋊D6711yescharacteristic
1725C2#2257498011yescharacteristic
1726C2#2257498811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3524C2
socleC22×C67C23×D4
hypercenter#3524D67
hypocenterC67#61547
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #529 ◁ #3524

Complements

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

NH ≅ G/Ntype
1. #22574153C2semidirect
2. #22573217C2semidirect
3. #22573080C2semidirect
4. #22572977C2semidirect
5. #22572956C2semidirect
6. #22572809C2semidirect
7. #22572798C2semidirect
8. #22572778C2semidirect
9. #22572359C2semidirect
10. #22572335C2semidirect
11. #22572224C2semidirect
12. #22572200C2semidirect
13. #22572111C2semidirect
14. #22572053C2semidirect
15. #22571841C2semidirect
16. #22571841C2semidirect
17. #22571829C2semidirect
18. #22570932C2semidirect
19. #22570853C2semidirect
20. #22570820C2semidirect
21. #22570500C2semidirect
22. #22570471C2semidirect
23. #22570402C2semidirect
24. #22570387C2semidirect
25. #22570252C2semidirect
26. #22570227C2semidirect
27. #22569214C2semidirect
28. #22569052C2semidirect
29. #22569037C2semidirect
30. C4×#14524068C2semidirect
31. C67×#3524C2semidirect
57. #16863795C22semidirect
58. #16863795C22semidirect
59. #16863792C22semidirect
60. #16863778C22semidirect
61. #16863778C22semidirect
64. #16863760C22semidirect
65. #16863758C22semidirect
66. #16863755C22semidirect
67. #16863753C22semidirect
68. #16863750C22semidirect
69. #16863737C22semidirect
70. #16863734C22semidirect
71. #16863731C22semidirect
72. #16863729C22semidirect
74. #16863720C22semidirect
75. #16863720C22semidirect
76. #16863717C22semidirect
77. #16863712C22semidirect
78. #16863712C22semidirect
80. #16863707C22semidirect
81. #16863703C22semidirect
82. #16863703C22semidirect
83. #16863703C22semidirect
84. #16863700C22semidirect
85. #16863696C22semidirect
88. #16863693C22semidirect
89. #16863691C22semidirect
90. #16863683C22semidirect
91. #16863676C22semidirect
93. #16863652C22semidirect
94. #16863652C22semidirect
97. #16863647C22semidirect
98. #16863647C22semidirect
100. #16863640C22semidirect
101. #16863630C22semidirect
102. #16863630C22semidirect
104. #16863623C22semidirect
105. #16863618C22semidirect
106. #16863618C22semidirect
107. #16863611C22semidirect
108. #16863611C22semidirect
111. #16863608C22semidirect
112. #16863608C22semidirect
115. #16863593C22semidirect
117. #16863558C22semidirect
118. #16863558C22semidirect
125. #16863535C22semidirect
126. #16863535C22semidirect
129. #16863527C22semidirect
130. Q8×C67⋊C8C22semidirect
133. #16863506C22semidirect
134. #16863506C22semidirect
135. #16863501C22semidirect
136. #16863501C22semidirect
137. #16863496C22semidirect
140. #16863494C22semidirect
141. #16863494C22semidirect
142. #16863494C22semidirect
143. C4×#11761618C22semidirect
144. C4×#11761618C22semidirect
149. C4×#11761615C22semidirect
150. C4×#11761615C22semidirect
151. C4×#11761615C22semidirect
152. C4×#11761616C22semidirect
155. C4×#11761613C22semidirect
156. C4×#11761613C22semidirect
157. C4×#11761613C22semidirect
158. C4×#11761613C22semidirect
160. #16863474C22semidirect
161. #16863474C22semidirect
163. #16863468C22semidirect
164. D4×C67⋊C8C22semidirect
165. #16863457C22semidirect
166. #16863457C22semidirect
167. #16863449C22semidirect
168. #16863439C22semidirect
169. #16863439C22semidirect
170. #16863436C22semidirect
172. #16863397C22semidirect
173. #16863392C22semidirect
175. C2×#14523967C22semidirect
177. #16863352C22semidirect
178. #16863352C22semidirect
179. C4×#11761612C22semidirect
181. #559×C67C22semidirect
182. #557×C67C22semidirect
184. #555×C67C22semidirect
186. #553×C67C22semidirect
190. #548×C67C22semidirect
191. #548×C67C22semidirect
193. #542×C67C22semidirect
195. #540×C67C22semidirect
199. #529×C67C22semidirect
200. #520×C67C22semidirect
201. #519×C67C22semidirect
202. C4×#41×C67C22semidirect
526. #11761615#41semidirect
864. #3524D67semidirect
895. C67#61547semidirect
901. #559C2×D67semidirect
902. #557C2×D67semidirect
904. #555C2×D67semidirect
909. #553C2×D67semidirect
916. #548C2×D67semidirect
917. #548C2×D67semidirect
925. #542C2×D67semidirect
928. #540C2×D67semidirect
935. #529C2×D67semidirect
939. #520C2×D67semidirect
940. #519C2×D67semidirect
942. C4×#41C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225741532
#225732172
#225730802
#225729772
#225729562
#225728092
#225727982
#225727782
#225723592
#225723352
#225722242
#225722002
#225721112
#225720532
#225718412
#225718292
#225709322
#225708532
#225708202
#225705002
#225704712
#225704022
#225703872
#225702522
#225702272
#225692142
#225690522
#225690372
C4×#145240682
C67×#35242
#6154767