Finite Group Databasebeta

← #31734485

Subgroups — #31734485

Order 17152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573767C211yesmaximal, characteristic, complemented
2#22572754C211yesmaximal, characteristic, complemented
3#22572748C211yesmaximal, characteristic, complemented
4#22572739C211yesmaximal, characteristic, complemented
5#22572733C211yesmaximal, characteristic, complemented
6#22572724C211yesmaximal, characteristic, complemented
7#22572718C211yesmaximal, characteristic, complemented
8#22572709C211yesmaximal, characteristic, complemented
9#22572703C211yesmaximal, characteristic, complemented
10#22572694C211yesmaximal, characteristic, complemented
11#22572688C211yesmaximal, characteristic, complemented
12#22572679C211yesmaximal, characteristic, complemented
13#22572673C211yesmaximal, characteristic, complemented
14#22572664C211yesmaximal, characteristic, complemented
15#22572658C211yesmaximal, characteristic, complemented
16#22572649C211yesmaximal, characteristic, complemented
17#22572643C211yesmaximal, characteristic, complemented
18#22570731C211yesmaximal, characteristic, complemented
19#22570122C211yesmaximal, characteristic, complemented
20#22570122C211yesmaximal, characteristic, complemented
21#22570118C211yesmaximal, characteristic, complemented
22#22570118C211yesmaximal, characteristic, complemented
23#22569997C211yesmaximal, characteristic, complemented
24#22569991C211yesmaximal, characteristic, complemented
25#22569815C211yesmaximal, characteristic, complemented
26#22569787C211yesmaximal, characteristic, complemented
27#22569007C211yesmaximal, characteristic, complemented
28C2×#16863468C211yesmaximal, characteristic, complemented
29#22568798C211yesmaximal, characteristic, complemented
30C2×#16863432C211yesmaximal, characteristic, complemented
31C67×#3475C211yesmaximal, characteristic, complemented
32C2×#14524063C2211yescharacteristic
33C22×#11761612C2211yescharacteristic
34C23×C67⋊C8C2211yescharacteristic
35#16864116C2211yescharacteristic
36#16864111C2211yescharacteristic
37#16864103C2211yescharacteristic
38#16864092C2211yescharacteristic
39#16864092C2211yescharacteristic
40#16864086C2211yescharacteristic
41#16864086C2211yescharacteristic
42#16864081—21no—
43#16864072—21no—
44#16864072—21no—
45#16864050C2211yescharacteristic
46#16864040—21no—
47#16863953C2211yescharacteristic
48#16863928—21no—
49#16863926—21no—
50#16863926—21no—
51#16863907C2211yescharacteristic
52#16863907C2211yescharacteristic
53C4×#11761628C2211yescharacteristic
54C4×#11761627—21no—
55C2×#14524002C2211yescharacteristic
56C2×#14524002C2211yescharacteristic
57#16863806C2211yescharacteristic, complemented
58#16863806C2211yescharacteristic, complemented
59#16863806C2211yescharacteristic, complemented
60#16863806C2211yescharacteristic, complemented
61#16863802C2211yescharacteristic, complemented
62#16863802C2211yescharacteristic, complemented
63#16863802C2211yescharacteristic, complemented
64#16863802C2211yescharacteristic, complemented
65#16863737C2211yescharacteristic, complemented
66#16863737C2211yescharacteristic, complemented
67#16863737C2211yescharacteristic, complemented
68#16863737C2211yescharacteristic, complemented
69#16863734C2211yescharacteristic, complemented
70#16863734C2211yescharacteristic, complemented
71#16863734C2211yescharacteristic, complemented
72#16863734C2211yescharacteristic, complemented
73#16863731C2211yescharacteristic, complemented
74#16863731C2211yescharacteristic, complemented
75#16863729C2211yescharacteristic, complemented
76#16863729C2211yescharacteristic, complemented
77#16863726C2211yescharacteristic, complemented
78#16863726C2211yescharacteristic, complemented
79#16863724C2211yescharacteristic, complemented
80#16863724C2211yescharacteristic, complemented
81#16863720C2211yescharacteristic, complemented
82#16863720C2211yescharacteristic, complemented
83#16863720C2211yescharacteristic, complemented
84#16863720C2211yescharacteristic, complemented
85#16863717C2211yescharacteristic, complemented
86#16863717C2211yescharacteristic, complemented
87#16863717C2211yescharacteristic, complemented
88#16863717C2211yescharacteristic, complemented
89#16863714C2211yescharacteristic, complemented
90#16863714C2211yescharacteristic, complemented
91#16863712C2211yescharacteristic, complemented
92#16863712C2211yescharacteristic, complemented
93#16863709C2211yescharacteristic, complemented
94#16863709C2211yescharacteristic, complemented
95#16863707C2211yescharacteristic, complemented
96#16863707C2211yescharacteristic, complemented
97#16863703C2211yescharacteristic, complemented
98#16863703C2211yescharacteristic, complemented
99#16863700C2211yescharacteristic, complemented
100#16863700C2211yescharacteristic, complemented
101#16863696C2211yescharacteristic, complemented
102#16863696C2211yescharacteristic, complemented
103#16863693C2211yescharacteristic, complemented
104#16863693C2211yescharacteristic, complemented
105#16863691C2211yescharacteristic, complemented
106#16863688C2211yescharacteristic, complemented
107#16863686C2211yescharacteristic, complemented
108#16863683C2211yescharacteristic, complemented
109#16863681C2211yescharacteristic, complemented
110#16863678C2211yescharacteristic, complemented
111#16863676C2211yescharacteristic, complemented
112#16863673C2211yescharacteristic, complemented
113#16863652C2211yescharacteristic, complemented
114#16863652C2211yescharacteristic, complemented
115#16863647C2211yescharacteristic, complemented
116#16863647C2211yescharacteristic, complemented
117#16863644C2211yescharacteristic, complemented
118#16863644C2211yescharacteristic, complemented
119#16863640C2211yescharacteristic, complemented
120#16863640C2211yescharacteristic, complemented
121#16863635C2211yescharacteristic, complemented
122#16863635C2211yescharacteristic, complemented
123#16863630C2211yescharacteristic, complemented
124#16863630C2211yescharacteristic, complemented
125#16863627C2211yescharacteristic, complemented
126#16863627C2211yescharacteristic, complemented
127#16863623C2211yescharacteristic, complemented
128#16863623C2211yescharacteristic, complemented
129#16863506C2211yescharacteristic, complemented
130#16863506C2211yescharacteristic, complemented
131#16863501C2211yescharacteristic, complemented
132#16863501C2211yescharacteristic, complemented
133#16863496C2211yescharacteristic, complemented
134#16863496C2211yescharacteristic, complemented
135#16863494C2211yescharacteristic, complemented
136#16863494C2211yescharacteristic, complemented
137#16863468C2211yescharacteristic
138#16863468C2211yescharacteristic
139#16863468C2211yescharacteristic
140#16863468C2211yescharacteristic
141#16863468C2211yescharacteristic
142#16863468C2211yescharacteristic
143#16863468C2211yescharacteristic
144#16863468C2211yescharacteristic
145#16863439C2211yescharacteristic, complemented
146#16863439C2211yescharacteristic, complemented
147#16863439C2211yescharacteristic, complemented
148#16863439C2211yescharacteristic, complemented
149#16863436C2211yescharacteristic, complemented
150#16863436C2211yescharacteristic, complemented
151#16863436C2211yescharacteristic, complemented
152#16863436C2211yescharacteristic, complemented
153#16863432C2211yescharacteristic
154#16863432C2211yescharacteristic
155#16863432C2211yescharacteristic
156#16863432C2211yescharacteristic
157#16863432C2211yescharacteristic
158#16863432C2211yescharacteristic
159#16863432C2211yescharacteristic
160#16863432C2211yescharacteristic
161#16863432C2211yescharacteristic
162#16863432C2211yescharacteristic, complemented
163#16863432C2211yescharacteristic, complemented
164#16863432C2211yescharacteristic, complemented
165#16863432C2211yescharacteristic, complemented
166C2×#14523976C2211yescharacteristic, complemented
167C2×#14523976C2211yescharacteristic, complemented
168C2×#14523974C2211yescharacteristic, complemented
169C2×#14523974C2211yescharacteristic, complemented
170C2×C4⋊(C67⋊C8)C2211yescharacteristic
171#16863392C2211yescharacteristic
172#16863392C2211yescharacteristic
173#16863392C2211yescharacteristic
174#16863390C2211yescharacteristic
175#16863390C2211yescharacteristic
176#16863390C2211yescharacteristic
177C2×C22⋊(C67⋊C8)C2211yescharacteristic
178C2×C22⋊(C67⋊C8)C2211yescharacteristic
179C2×#14523954C2211yescharacteristic
180#556×C67C2211yescharacteristic
181#555×C67C2211yescharacteristic
182#554×C67C2211yescharacteristic
183#553×C67C2211yescharacteristic
184#553×C67C2211yescharacteristic
185#552×C67—21no—
186#552×C67C2211yescharacteristic
187#552×C67C2211yescharacteristic
188#551×C67—21no—
189#551×C67—21no—
190#547×C67C2211yescharacteristic
191#546×C67—21no—
192#533×C67C2211yescharacteristic
193#529×C67—21no—
194#529×C67—21no—
195#529×C67—21no—
196#525×C67C2211yescharacteristic
197#525×C67C2211yescharacteristic
198C4×#41×C67—21no—
199C4×#41×C67C2211yescharacteristic
200C2×C4×D4×C67C2211yescharacteristic
201C2×#117×C67C2211yescharacteristic
202C2×#117×C67C2211yescharacteristic
203C2×#11761628C2311yescharacteristic
204C2×#11761627—21no—
205#14524063—24no—
206C2×#11761618C2311yescharacteristic
207C2×#11761616C2311yescharacteristic
208C2×#11761615C2311yescharacteristic
209C2×#11761613C2311yescharacteristic
210C2×#11761612—24no—
211C2×#11761612C2311yescharacteristic
212C2×#11761612C2311yescharacteristic
213C2×#11761612C2311yescharacteristic
214C2×#11761612C2311yescharacteristic
215C22×C67⋊C8—24no—
216C22×C67⋊C8C2311yescharacteristic
217C22×C67⋊C8C2311yescharacteristic
218C22×C67⋊C8C2311yescharacteristic
219C22×C67⋊C8C2311yescharacteristic
220C22×C67⋊C8C2311yescharacteristic
221C22×C67⋊C8C2311yescharacteristic
222C22×C67⋊C8C2311yescharacteristic
223C22×C67⋊C8C2311yescharacteristic
224#14524043C2311yescharacteristic
225#14524043C2311yescharacteristic
226#14524038—21no—
227#14524038—21no—
228#14524036—21no—
229#14524036—21no—
230#14524036—21no—
231#14524036—21no—
232#14524035C2311yescharacteristic
233#14524035C2311yescharacteristic
234#14524034—21no—
235#14524033—21no—
236#14524033—21no—
237#14524030—21no—
238#14524029—21no—
239#14524029—21no—
240#14524027—21no—
241#14524027—21no—
242#14524026—21no—
243#14524026—21no—
244#14524025—21no—
245#14524025—21no—
246#14524024—21no—
247#14524024—21no—
248#14524023—21no—
249#14524022—21no—
250#14524022—21no—
251#14524022C2311yescharacteristic
252#14524022C2311yescharacteristic
253#14524022C2311yescharacteristic
254#14524022C2311yescharacteristic
255#14524020—21no—
256#14524020—21no—
257#14524017C2311yescharacteristic
258#14524017C2311yescharacteristic
259#14524017C2311yescharacteristic
260#14524017C2311yescharacteristic
261#14524015—21no—
262#14524015—21no—
263#14524014—21no—
264#14524012—21no—
265#14524012—21no—
266C4×Dic134—21no—
267C4×Dic134—21no—
268C4×Dic134C2311yescharacteristic
269C4×Dic134C2311yescharacteristic
270#14524008—21no—
271C4×D268C2311yescharacteristic
272C4×D268C2311yescharacteristic
273D4×Dic67—21no—
274C4×C22⋊D67—21no—
275C4×C22⋊D67—21no—
276C4×C22⋊D67—21no—
277C4×C22⋊D67—21no—
278C4×C22⋊D67—21no—
279C4×C22⋊D67—21no—
280(C22⋊D67)⋊C4—21no—
281(C22⋊D67)⋊C4—21no—
282#14524002—21no—
283#14524002—21no—
284#14524002—21no—
285#14524002—21no—
286#14524002C2311yescharacteristic
287#14524002C2311yescharacteristic
288#14524002C2311yescharacteristic
289#14524002C2311yescharacteristic
290#14524002C2311yescharacteristic
291#14524002C2311yescharacteristic
292#14524002C2311yescharacteristic
293#14524001—21no—
294#14524000—21no—
295#14523999—21no—
296#14523999—21no—
297C2×C4⋊Dic67C2311yescharacteristic
298C2×C4⋊Dic67C2311yescharacteristic
299C2×C4⋊Dic67C2311yescharacteristic
300C2×C4⋊Dic67C2311yescharacteristic
301C2×C22⋊Dic67—21no—
302C2×C22⋊Dic67—21no—
303C2×C4×Dic67—21no—
304C2×C4×Dic67—21no—
305C42×D67—21no—
306#14523976C2311yescharacteristic
307#14523976C2311yescharacteristic
308#14523976C2311yescharacteristic
309#14523976C2311yescharacteristic
310#14523976C2311yescharacteristic
311#14523976C2311yescharacteristic
312#14523976C2311yescharacteristic
313#14523976C2311yescharacteristic
314#14523976C2311yescharacteristic
315#14523976C2311yescharacteristic
316#14523976C2311yescharacteristic
317#14523976C2311yescharacteristic
318#14523976C2311yescharacteristic
319#14523976C2311yescharacteristic
320#14523976C2311yescharacteristic
321#14523976C2311yescharacteristic
322#14523976C2311yescharacteristic
323#14523976C2311yescharacteristic
324#14523974C2311yescharacteristic
325#14523974C2311yescharacteristic
326#14523974C2311yescharacteristic
327#14523974C2311yescharacteristic
328#14523974C2311yescharacteristic
329#14523974C2311yescharacteristic
330#14523974C2311yescharacteristic
331#14523974C2311yescharacteristic
332#14523974C2311yescharacteristic
333#14523974C2311yescharacteristic
334#14523974C2311yescharacteristic
335#14523974C2311yescharacteristic
336#14523974C2311yescharacteristic
337#14523974C2311yescharacteristic
338#14523974C2311yescharacteristic
339#14523974C2311yescharacteristic
340#14523974C2311yescharacteristic
341#14523974C2311yescharacteristic
342C4⋊(C67⋊C8)C2311yescharacteristic
343C4⋊(C67⋊C8)C2311yescharacteristic
344C4⋊(C67⋊C8)C2311yescharacteristic
345C4⋊(C67⋊C8)C2311yescharacteristic
346#14523967C2311yescharacteristic
347#14523967C2311yescharacteristic
348#14523967C2311yescharacteristic
349#14523967C2311yescharacteristic
350#14523967C2311yescharacteristic
351#14523967C2311yescharacteristic
352#14523966C2311yescharacteristic
353#14523966C2311yescharacteristic
354#14523966C2311yescharacteristic
355#14523966C2311yescharacteristic
356#14523966C2311yescharacteristic
357#14523966C2311yescharacteristic
358#14523964C2311yescharacteristic
359#14523964C2311yescharacteristic
360#14523964C2311yescharacteristic
361#14523964C2311yescharacteristic
362#14523964C2311yescharacteristic
363#14523964C2311yescharacteristic
364#14523963C2311yescharacteristic
365#14523963C2311yescharacteristic
366#14523963C2311yescharacteristic
367#14523963C2311yescharacteristic
368#14523963C2311yescharacteristic
369#14523963C2311yescharacteristic
370C22⋊(C67⋊C8)C2311yescharacteristic
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
378#14523954C2311yescharacteristic
379#14523954C2311yescharacteristic
380#14523954C2311yescharacteristic
381#14523954C2311yescharacteristic
382C2×#41×C67—21no—
383C2×#41×C67C2311yescharacteristic
384C22×D4×C67D411yescharacteristic
385C23×C4×C67C2311yescharacteristic
386C23×C4×C67C2311yescharacteristic
387C4⋊Q8×C67C2311yescharacteristic
388C4⋊Q8×C67C2311yescharacteristic
389#126×C67—21no—
390#126×C67—21no—
391#126×C67—21no—
392#126×C67—21no—
393#126×C67—21no—
394#126×C67—21no—
395#125×C67—21no—
396#125×C67—21no—
397#125×C67—21no—
398#125×C67C2311yescharacteristic
399#125×C67C2311yescharacteristic
400#124×C67—21no—
401#124×C67—21no—
402#124×C67—21no—
403#123×C67—21no—
404#123×C67—21no—
405#123×C67—21no—
406#123×C67—21no—
407#123×C67—21no—
408#123×C67—21no—
409#123×C67—21no—
410#123×C67—21no—
411C22⋊Q8×C67—21no—
412C22⋊Q8×C67—21no—
413C22⋊Q8×C67—21no—
414C22⋊Q8×C67—21no—
415C22⋊Q8×C67—21no—
416C22⋊Q8×C67C2311yescharacteristic
417C22⋊Q8×C67C2311yescharacteristic
418C22⋊Q8×C67C2311yescharacteristic
419C22⋊Q8×C67C2311yescharacteristic
420#121×C67—21no—
421#121×C67—21no—
422#121×C67—21no—
423#121×C67C2311yescharacteristic
424#121×C67C2311yescharacteristic
425#121×C67C2311yescharacteristic
426#121×C67C2311yescharacteristic
427#120×C67—21no—
428#120×C67—21no—
429C4×Q8×C67—21no—
430C4×Q8×C67—21no—
431C4×Q8×C67—21no—
432C4×Q8×C67C2311yescharacteristic
433C4×Q8×C67C2311yescharacteristic
434C4×D4×C67—21no—
435C4×D4×C67—21no—
436C4×D4×C67—21no—
437C4×D4×C67—21no—
438C4×D4×C67—21no—
439C4×D4×C67—21no—
440C4×D4×C67—21no—
441C4×D4×C67—21no—
442C4×D4×C67—21no—
443C4×D4×C67D411yescharacteristic
444C4×D4×C67D411yescharacteristic
445C4×D4×C67D411yescharacteristic
446C4×D4×C67D411yescharacteristic
447C4×D4×C67C2311yescharacteristic
448C4×D4×C67C2311yescharacteristic
449C4×D4×C67C2311yescharacteristic
450C4×D4×C67C2311yescharacteristic
451C4×D4×C67C2311yescharacteristic
452C4×D4×C67C2311yescharacteristic
453#117×C67—21no—
454#117×C67—21no—
455#117×C67—21no—
456#117×C67—21no—
457#117×C67—21no—
458#117×C67—21no—
459#117×C67—21no—
460#117×C67—21no—
461#117×C67C2311yescharacteristic
462#117×C67C2311yescharacteristic
463#117×C67C2311yescharacteristic
464#117×C67C2311yescharacteristic
465#117×C67C2311yescharacteristic
466#117×C67C2311yescharacteristic
467#117×C67C2311yescharacteristic
468C2×C4⋊C4×C67D411yescharacteristic
469C2×C4⋊C4×C67C2311yescharacteristic
470C2×C4⋊C4×C67C2311yescharacteristic
471C2×C4⋊C4×C67C2311yescharacteristic
472C2×C4⋊C4×C67C2311yescharacteristic
473C2×C22⋊C4×C67—21no—
474C2×C22⋊C4×C67—21no—
475C2×C22⋊C4×C67D411yescharacteristic
476C2×C22⋊C4×C67D411yescharacteristic
477C2×C42×C67—21no—
478C2×C42×C67—21no—
479C2×C42×C67—21no—
480C2×C42×C67C2311yescharacteristic
481#11761628—22no—
482#11761628—22no—
483#11761627—44no—
484C2×Dic134—21no—
485C2×Dic134—21no—
486C2×Dic134C2411yescharacteristic
487C2×D268C2411yescharacteristic
488C2×C22⋊D67—21no—
489C2×C22⋊D67—21no—
490C2×C22⋊D67—21no—
491C2×C22⋊D67—21no—
492C2×C22⋊D67—21no—
493C22×Dic67—21no—
494C22×Dic67—21no—
495C22×Dic67—21no—
496C22×Dic67—21no—
497C2×C4×D67—21no—
498C2×C4×D67—21no—
499C2×C4×D67—21no—
500#11761618—22no—
501#11761616—22no—
502#11761615—22no—
503#11761613—22no—
504#11761612—22no—
505#11761612—22no—
506#11761612—22no—
507#11761612—22no—
508C2×C67⋊C8—22no—
509C2×C67⋊C8—22no—
510C2×C67⋊C8—22no—
511C2×C67⋊C8—22no—
512C2×C67⋊C8—22no—
513C2×C67⋊C8—22no—
514C2×C67⋊C8—22no—
515C2×C67⋊C8#4114yescomplemented
516C2×C67⋊C8C2411yescharacteristic
517C2×C67⋊C8C2411yescharacteristic
518C2×C67⋊C8C2411yescharacteristic
519C2×C67⋊C8C2411yescharacteristic
520C2×C67⋊C8C2411yescharacteristic
521C2×C67⋊C8C2411yescharacteristic
522C2×C67⋊C8C2411yescharacteristic
523C2×C67⋊C8C2411yescharacteristic
524C4⋊Dic67—21no—
525C4⋊Dic67—21no—
526C4⋊Dic67—21no—
527C4⋊Dic67—21no—
528C4⋊Dic67—21no—
529C4⋊Dic67—21no—
530C4⋊Dic67C2411yescharacteristic
531C4⋊Dic67C2411yescharacteristic
532C4⋊Dic67C2411yescharacteristic
533C4⋊Dic67C2411yescharacteristic
534C4⋊Dic67C2411yescharacteristic
535C4⋊Dic67C2411yescharacteristic
536Dic67⋊C4—21no—
537Dic67⋊C4—21no—
538Dic67⋊C4—21no—
539Dic67⋊C4—21no—
540Dic67⋊C4—21no—
541Dic67⋊C4—21no—
542Dic67⋊C4—21no—
543Dic67⋊C4—21no—
544Dic67⋊C4—21no—
545Dic67⋊C4—21no—
546C22⋊Dic67—21no—
547C22⋊Dic67—21no—
548C22⋊Dic67—21no—
549C22⋊Dic67—21no—
550C22⋊Dic67—21no—
551C22⋊Dic67—21no—
552C22⋊Dic67—21no—
553C22⋊Dic67—21no—
554C22⋊Dic67—21no—
555C22⋊Dic67—21no—
556C22⋊Dic67—21no—
557(C2×D67)⋊C4—21no—
558(C2×D67)⋊C4—21no—
559(C2×D67)⋊C4—21no—
560(C2×D67)⋊C4—21no—
561(C2×D67)⋊C4—21no—
562(C2×D67)⋊C4—21no—
563C4×Dic67—21no—
564C4×Dic67—21no—
565C4×Dic67—21no—
566C4×Dic67—21no—
567C4×Dic67—21no—
568C4×Dic67—21no—
569C4×Dic67—21no—
570C4×Dic67—21no—
571C4×Dic67—21no—
572C24×C67C2×D411yescharacteristic
573C24×C67C2×D411yescharacteristic
574#41×C67—22no—
575#41×C67—22no—
576#41×C67—44no—
577C2×Q8×C67—21no—
578C2×Q8×C67—21no—
579C2×Q8×C67C2411yescharacteristic
580C2×D4×C67—21no—
581C2×D4×C67—21no—
582C2×D4×C67—21no—
583C2×D4×C67—21no—
584C2×D4×C67—21no—
585C2×D4×C67—42no—
586C2×D4×C67C2×D411yescharacteristic
587C2×D4×C67C2×D411yescharacteristic
588C2×D4×C67C2×D411yescharacteristic
589C2×D4×C67C2×D411yescharacteristic
590C2×D4×C67C2411yescharacteristic
591C22×C4×C67—22no—
592C22×C4×C67—22no—
593C22×C4×C67—22no—
594C22×C4×C67—22no—
595C22×C4×C67—21no—
596C22×C4×C67—21no—
597C22×C4×C67—21no—
598C22×C4×C67—21no—
599C22×C4×C67—21no—
600C22×C4×C67—21no—
601C22×C4×C67—21no—
602C22×C4×C67C2×D411yescharacteristic
603C22×C4×C67C2×D411yescharacteristic
604C22×C4×C67C2×D411yescharacteristic
605C22×C4×C67C2×D411yescharacteristic
606C22×C4×C67C2×D411yescharacteristic
607C22×C4×C67C2×D411yescharacteristic
608C22×C4×C67C2×D411yescharacteristic
609C22×C4×C67C2×D411yescharacteristic
610C22×C4×C67C2411yescharacteristic
611C22×C4×C67C2411yescharacteristic
612C22×C4×C67C2411yescharacteristic
613C22×C4×C67C2411yescharacteristic
614C22×C4×C67C2411yescharacteristic
615C4⋊C4×C67—21no—
616C4⋊C4×C67—21no—
617C4⋊C4×C67—21no—
618C4⋊C4×C67—21no—
619C4⋊C4×C67—21no—
620C4⋊C4×C67—21no—
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×C67C2×D411yescharacteristic
632C4⋊C4×C67C2×D411yescharacteristic
633C4⋊C4×C67C2×D411yescharacteristic
634C4⋊C4×C67C2×D411yescharacteristic
635C4⋊C4×C67C2411yescharacteristic
636C4⋊C4×C67C2411yescharacteristic
637C4⋊C4×C67C2411yescharacteristic
638C4⋊C4×C67C2411yescharacteristic
639C4⋊C4×C67C2411yescharacteristic
640C4⋊C4×C67C2411yescharacteristic
641C22⋊C4×C67—21no—
642C22⋊C4×C67—21no—
643C22⋊C4×C67—21no—
644C22⋊C4×C67—21no—
645C22⋊C4×C67—21no—
646C22⋊C4×C67—21no—
647C22⋊C4×C67—21no—
648C22⋊C4×C67—21no—
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×C67C2×D411yescharacteristic
659C22⋊C4×C67C2×D411yescharacteristic
660C22⋊C4×C67C2×D411yescharacteristic
661C22⋊C4×C67C2×D411yescharacteristic
662C22⋊C4×C67C2×D411yescharacteristic
663C22⋊C4×C67C2×D411yescharacteristic
664C22⋊C4×C67C2×D411yescharacteristic
665C22⋊C4×C67C2×D411yescharacteristic
666C42×C67—21no—
667C42×C67—21no—
668C42×C67—21no—
669C42×C67—21no—
670C42×C67—21no—
671C42×C67—21no—
672C42×C67—21no—
673C42×C67—21no—
674C42×C67—21no—
675C42×C67C2×D411yescharacteristic
676C42×C67C2×D411yescharacteristic
677C42×C67C2411yescharacteristic
678C42×C67C2411yescharacteristic
679C23×C67—22no—
680C23×C67—22no—
681C23×C67—22no—
682C23×C67—21no—
683C23×C67—41no—
684C23×C67—41no—
685C23×C67—41no—
686C23×C67C22×D411yescharacteristic
687C23×C67C22×D411yescharacteristic
688C23×C67C22×D411yescharacteristic
689C23×C67C22×D411yescharacteristic
690C23×C67C22×D411yescharacteristic
691C22×D67—21no—
692Q8×C67—21no—
693Q8×C67—21no—
694Q8×C67—42no—
695Q8×C67—81no—
696D4×C67—22no—
697D4×C67—22no—
698D4×C67—21no—
699D4×C67—21no—
700D4×C67—41no—
701D4×C67—41no—
702D4×C67—42no—
703D4×C67—42no—
704D4×C67—42no—
705D4×C67—81no—
706D4×C67—81no—
707C2×C4×C67—22no—
708C2×C4×C67—22no—
709C2×C4×C67—22no—
710C2×C4×C67—22no—
711C2×C4×C67—22no—
712C2×C4×C67—22no—
713C2×C4×C67—21no—
714C2×C4×C67—21no—
715C2×C4×C67—21no—
716C2×C4×C67—21no—
717C2×C4×C67—21no—
718C2×C4×C67—21no—
719C2×C4×C67—21no—
720C2×C4×C67—21no—
721C2×C4×C67—21no—
722C2×C4×C67—21no—
723C2×C4×C67—21no—
724C2×C4×C67—21no—
725C2×C4×C67—21no—
726C2×C4×C67—21no—
727C2×C4×C67—21no—
728C2×C4×C67—41no—
729C2×C4×C67—41no—
730C2×C4×C67—42no—
731C2×C4×C67—42no—
732C2×C4×C67—42no—
733C2×C4×C67—42no—
734C2×C4×C67—81no—
735C2×C4×C67—81no—
736C2×C4×C67—81no—
737C2×C4×C67C22×D411yescharacteristic
738C2×C4×C67C22×D411yescharacteristic
739C2×C4×C67C22×D411yescharacteristic
740C2×C4×C67C22×D411yescharacteristic
741C2×C4×C67C22×D411yescharacteristic
742C2×C4×C67C22×D411yescharacteristic
743C2×C4×C67C22×D411yescharacteristic
744C2×C4×C67C22×D411yescharacteristic
745C2×C4×C67C22×D411yescharacteristic
746C2×C4×C67C2×#4112yes—
747C2×C4×C672−1+412yes—
748C2×C4×C67C2511yescharacteristic
749C22⋊D67—42no—
750C22⋊D67—42no—
751C22⋊D67—42no—
752C22⋊D67—81no—
753C22⋊D67—81no—
754C2×Dic67—21no—
755C2×Dic67—21no—
756C2×Dic67—21no—
757C2×Dic67—21no—
758C2×Dic67—21no—
759C2×Dic67—21no—
760C2×Dic67—21no—
761C2×Dic67—42no—
762C2×Dic67—42no—
763C2×Dic67—81no—
764C2×Dic67—81no—
765D268—21no—
766D268—21no—
767C4×D67—42no—
768C4×D67—42no—
769C4×D67—81no—
770Dic134—21no—
771Dic134—21no—
772Dic134—42no—
773Dic134—81no—
774C67⋊C8—21no—
775C67⋊C8—21no—
776C67⋊C8—21no—
777C67⋊C8—21no—
778C67⋊C8—21no—
779C67⋊C8—21no—
780C67⋊C8C2×#4112yes—
781C67⋊C8C2×#4112yes—
782C22×C67—21no—
783C22×C67—21no—
784C22×C67—21no—
785C22×C67—21no—
786C22×C67—21no—
787C22×C67—21no—
788C22×C67—21no—
789C22×C67—21no—
790C22×C67—21no—
791C22×C67—21no—
792C22×C67—21no—
793C22×C67—21no—
794C22×C67—21no—
795C22×C67—44no—
796C22×C67—41no—
797C22×C67—41no—
798C22×C67—41no—
799C22×C67—82no—
800C22×C67#54712yes—
801C22×C67#57512yes—
802C22×C67C23×D411yescharacteristic
803C2×D67—41no—
804C2×D67—41no—
805C2×D67—41no—
806C4×C67—21no—
807C4×C67—21no—
808C4×C67—21no—
809C4×C67—21no—
810C4×C67—21no—
811C4×C67—21no—
812C4×C67—21no—
813C4×C67—21no—
814C4×C67—41no—
815C4×C67—41no—
816C4×C67—41no—
817C4×C67—41no—
818C4×C67—41no—
819C4×C67—41no—
820C4×C67—41no—
821C4×C67#54712yes—
822C4×C67C22×#4111yescharacteristic
823C4×C67C2×2−1+411yescharacteristic
824Dic67—41no—
825Dic67—41no—
826Dic67—41no—
827Dic67—41no—
828Dic67—41no—
829Dic67—41no—
830Dic67—41no—
831#61243—671nomaximal, Sylow
832C2×C67—22no—
833C2×C67—22no—
834C2×C67—41no—
835C2×C67—41no—
836C2×C67—41no—
837C2×C67—81no—
838C2×C67C2×#54711yescharacteristic
839C2×C67C2×#57511yescharacteristic
840C2×C67#358411yescharacteristic
841D67—81no—
842#3475—671no—
843#3475D6711yescharacteristic, complemented
844#3350—671no—
845#3350—671no—
846#3349—671no—
847#3349—671no—
848#3348—671no—
849#3348—671no—
850#3347—671no—
851#3347—671no—
852#3346—671no—
853#3346—671no—
854#3345—671no—
855#3345—671no—
856#3344—671no—
857#3344—671no—
858#3343—671no—
859#3343—671no—
860#3162—671no—
861#3091—671no—
862#3091—671no—
863#3091—671no—
864#3091—671no—
865#3076—671no—
866#3076—671no—
867#3054—671no—
868#3050—671no—
869#2943—671no—
870C2×#435—671no—
871#2911—671no—
872C2×#427—671no—
873C67#6124311yescharacteristic, complemented, Sylow
874C2×#135—671no—
875C22×M16—671no—
876C23×C8—671no—
877#556—671no—
878#556C2×D6711yescharacteristic
879#555—671no—
880#555C2×D6711yescharacteristic
881#554—671no—
882#554C2×D6711yescharacteristic
883#553—671no—
884#553—671no—
885#553C2×D6711yescharacteristic
886#553C2×D6711yescharacteristic
887#552—21no—
888#552—671no—
889#552—671no—
890#552—1341no—
891#552C2×D6711yescharacteristic
892#552C2×D6711yescharacteristic
893#551—21no—
894#551—21no—
895#551—1341no—
896#551—1341no—
897#547—671no—
898#547C2×D6711yescharacteristic
899#546—21no—
900#546—1341no—
901#533—671no—
902#533C2×D6711yescharacteristic
903#529—21no—
904#529—21no—
905#529—21no—
906#529—1341no—
907#529—1341no—
908#529—1341no—
909#525—671no—
910#525—671no—
911#525C2×D6711yescharacteristic
912#525C2×D6711yescharacteristic
913C4×#41—21no—
914C4×#41—671no—
915C4×#41—1341no—
916C4×#41C2×D6711yescharacteristic
917C2×C4×D4C2×D6711yescharacteristic
918C2×#117—671no—
919C2×#117—671no—
920C2×#117C2×D6711yescharacteristic
921C2×#117C2×D6711yescharacteristic
922#501—671no—
923#501—671no—
924#501—671no—
925#501—671no—
926#501—671no—
927#501—671no—
928#501—671no—
929#501—671no—
930#485—671no—
931#485—671no—
932#485—671no—
933#485—671no—
934#485—671no—
935#485—671no—
936#485—671no—
937#485—671no—
938#484—671no—
939#484—671no—
940#484—671no—
941#484—671no—
942#483—671no—
943#483—671no—
944#483—671no—
945#483—671no—
946#482—671no—
947#482—671no—
948#482—671no—
949#482—671no—
950#482—671no—
951#482—671no—
952#482—671no—
953#482—671no—
954#481—671no—
955#481—671no—
956#481—671no—
957#481—671no—
958#480—671no—
959#480—671no—
960#480—671no—
961#480—671no—
962#479—671no—
963#479—671no—
964#479—671no—
965#479—671no—
966#478—671no—
967#478—671no—
968#478—671no—
969#478—671no—
970#477—671no—
971#477—671no—
972#476—671no—
973#476—671no—
974#475—671no—
975#475—671no—
976#474—671no—
977#474—671no—
978#470—671no—
979#470—671no—
980#469—671no—
981#469—671no—
982#468—671no—
983#468—671no—
984#468—671no—
985#468—671no—
986#467—671no—
987#467—671no—
988#466—671no—
989#466—671no—
990#465—671no—
991#465—671no—
992#465—671no—
993#465—671no—
994#442—671no—
995#442—671no—
996#441—671no—
997#441—671no—
998#440—671no—
999#440—671no—
1000#440—671no—
1001#440—671no—
1002#435—671no—
1003#435—671no—
1004#435—671no—
1005#435—671no—
1006#435—671no—
1007#435—671no—
1008#435—671no—
1009#435—671no—
1010#428—671no—
1011#428—671no—
1012#428—671no—
1013#428—671no—
1014#428—671no—
1015#428—671no—
1016#428—671no—
1017#428—671no—
1018#427—671no—
1019#427—671no—
1020#427—671no—
1021#427—671no—
1022#427—671no—
1023#427—671no—
1024#427—671no—
1025#427—671no—
1026#427—671no—
1027#427—671no—
1028#427—671no—
1029#427—671no—
1030#427—671no—
1031C2×#107—671no—
1032C2×#107—671no—
1033C2×#106—671no—
1034C2×#106—671no—
1035C2×C4⋊C8—671no—
1036#416—671no—
1037#416—671no—
1038#416—671no—
1039#416—671no—
1040#416—671no—
1041#416—671no—
1042C2×C22⋊C8—671no—
1043C2×C22⋊C8—671no—
1044C2×#97—671no—
1045C2×#41—21no—
1046C2×#41—671no—
1047C2×#41—1341no—
1048C2×#41C22×D6711yescharacteristic
1049C22×D4C22⋊D6711yescharacteristic
1050C23×C4C22×D6711yescharacteristic
1051C23×C4C22×D6711yescharacteristic
1052#135—1344no—
1053C2×Q16—671no—
1054C2×SD16—671no—
1055C2×SD16—671no—
1056C2×D8—671no—
1057C2×M16—671no—
1058C2×M16—671no—
1059C2×M16—671no—
1060C2×M16—671no—
1061C2×M16—1344no—
1062C22×C8—671no—
1063C22×C8—671no—
1064C22×C8—671no—
1065C22×C8—671no—
1066C22×C8—671no—
1067C22×C8—671no—
1068C22×C8—671no—
1069C22×C8—671no—
1070C22×C8—1344no—
1071C4⋊Q8—671no—
1072C4⋊Q8—671no—
1073C4⋊Q8C22×D6711yescharacteristic
1074C4⋊Q8C22×D6711yescharacteristic
1075#126—21no—
1076#126—21no—
1077#126—21no—
1078#126—21no—
1079#126—21no—
1080#126—21no—
1081#126—1341no—
1082#126—1341no—
1083#126—1341no—
1084#126—1341no—
1085#126—1341no—
1086#126—1341no—
1087#125—21no—
1088#125—21no—
1089#125—21no—
1090#125—671no—
1091#125—671no—
1092#125—1341no—
1093#125—1341no—
1094#125—1341no—
1095#125C22×D6711yescharacteristic
1096#125C22×D6711yescharacteristic
1097#124—21no—
1098#124—21no—
1099#124—21no—
1100#124—1341no—
1101#124—1341no—
1102#124—1341no—
1103#123—21no—
1104#123—21no—
1105#123—21no—
1106#123—21no—
1107#123—21no—
1108#123—21no—
1109#123—21no—
1110#123—21no—
1111#123—1341no—
1112#123—1341no—
1113#123—1341no—
1114#123—1341no—
1115#123—1341no—
1116#123—1341no—
1117#123—1341no—
1118#123—1341no—
1119C22⋊Q8—21no—
1120C22⋊Q8—21no—
1121C22⋊Q8—21no—
1122C22⋊Q8—21no—
1123C22⋊Q8—21no—
1124C22⋊Q8—671no—
1125C22⋊Q8—671no—
1126C22⋊Q8—671no—
1127C22⋊Q8—671no—
1128C22⋊Q8—1341no—
1129C22⋊Q8—1341no—
1130C22⋊Q8—1341no—
1131C22⋊Q8—1341no—
1132C22⋊Q8—1341no—
1133C22⋊Q8C22×D6711yescharacteristic
1134C22⋊Q8C22×D6711yescharacteristic
1135C22⋊Q8C22×D6711yescharacteristic
1136C22⋊Q8C22×D6711yescharacteristic
1137#121—21no—
1138#121—21no—
1139#121—21no—
1140#121—671no—
1141#121—671no—
1142#121—671no—
1143#121—671no—
1144#121—1341no—
1145#121—1341no—
1146#121—1341no—
1147#121C22×D6711yescharacteristic
1148#121C22×D6711yescharacteristic
1149#121C22×D6711yescharacteristic
1150#121C22×D6711yescharacteristic
1151#120—21no—
1152#120—21no—
1153#120—1341no—
1154#120—1341no—
1155C4×Q8—21no—
1156C4×Q8—21no—
1157C4×Q8—21no—
1158C4×Q8—671no—
1159C4×Q8—671no—
1160C4×Q8—1341no—
1161C4×Q8—1341no—
1162C4×Q8—1341no—
1163C4×Q8C22×D6711yescharacteristic
1164C4×Q8C22×D6711yescharacteristic
1165C4×D4—21no—
1166C4×D4—21no—
1167C4×D4—21no—
1168C4×D4—21no—
1169C4×D4—21no—
1170C4×D4—21no—
1171C4×D4—21no—
1172C4×D4—21no—
1173C4×D4—21no—
1174C4×D4—671no—
1175C4×D4—671no—
1176C4×D4—1341no—
1177C4×D4—1341no—
1178C4×D4—1341no—
1179C4×D4—1341no—
1180C4×D4—1341no—
1181C4×D4—1341no—
1182C4×D4—1341no—
1183C4×D4—1341no—
1184C4×D4—1341no—
1185C4×D4C22⋊D6711yescharacteristic
1186C4×D4C22⋊D6711yescharacteristic
1187C4×D4C22⋊D6711yescharacteristic
1188C4×D4C22⋊D6711yescharacteristic
1189C4×D4C22×D6711yescharacteristic
1190C4×D4C22×D6711yescharacteristic
1191C4×D4C22×D6711yescharacteristic
1192C4×D4C22×D6711yescharacteristic
1193C4×D4C22×D6711yescharacteristic
1194C4×D4C22×D6711yescharacteristic
1195#117—21no—
1196#117—21no—
1197#117—21no—
1198#117—21no—
1199#117—21no—
1200#117—21no—
1201#117—21no—
1202#117—21no—
1203#117—671no—
1204#117—671no—
1205#117—671no—
1206#117—671no—
1207#117—671no—
1208#117—671no—
1209#117—671no—
1210#117—1341no—
1211#117—1341no—
1212#117—1341no—
1213#117—1341no—
1214#117—1341no—
1215#117—1341no—
1216#117—1341no—
1217#117—1341no—
1218#117C22×D6711yescharacteristic
1219#117C22×D6711yescharacteristic
1220#117C22×D6711yescharacteristic
1221#117C22×D6711yescharacteristic
1222#117C22×D6711yescharacteristic
1223#117C22×D6711yescharacteristic
1224#117C22×D6711yescharacteristic
1225C2×C4⋊C4—671no—
1226C2×C4⋊C4—671no—
1227C2×C4⋊C4—671no—
1228C2×C4⋊C4—671no—
1229C2×C4⋊C4C22⋊D6711yescharacteristic
1230C2×C4⋊C4C22×D6711yescharacteristic
1231C2×C4⋊C4C22×D6711yescharacteristic
1232C2×C4⋊C4C22×D6711yescharacteristic
1233C2×C4⋊C4C22×D6711yescharacteristic
1234C2×C22⋊C4—21no—
1235C2×C22⋊C4—21no—
1236C2×C22⋊C4—1341no—
1237C2×C22⋊C4—1341no—
1238C2×C22⋊C4C22⋊D6711yescharacteristic
1239C2×C22⋊C4C22⋊D6711yescharacteristic
1240C2×C42—21no—
1241C2×C42—21no—
1242C2×C42—21no—
1243C2×C42—1341no—
1244C2×C42—1341no—
1245C2×C42—1341no—
1246C2×C42C22×D6711yescharacteristic
1247#107—671no—
1248#107—671no—
1249#107—671no—
1250#107—671no—
1251#107—671no—
1252#107—671no—
1253#107—671no—
1254#107—671no—
1255#107—671no—
1256#107—671no—
1257#107—671no—
1258#107—671no—
1259#107—671no—
1260#107—671no—
1261#107—671no—
1262#107—671no—
1263#107—671no—
1264#107—671no—
1265#106—671no—
1266#106—671no—
1267#106—671no—
1268#106—671no—
1269#106—671no—
1270#106—671no—
1271#106—671no—
1272#106—671no—
1273#106—671no—
1274#106—671no—
1275#106—671no—
1276#106—671no—
1277#106—671no—
1278#106—671no—
1279#106—671no—
1280#106—671no—
1281#106—671no—
1282#106—671no—
1283C4⋊C8—671no—
1284C4⋊C8—671no—
1285C4⋊C8—671no—
1286C4⋊C8—671no—
1287#103—671no—
1288#103—671no—
1289#103—671no—
1290#103—671no—
1291#103—671no—
1292#103—671no—
1293#103—671no—
1294#103—671no—
1295#103—671no—
1296#103—671no—
1297#103—671no—
1298#103—671no—
1299#102—671no—
1300#102—671no—
1301#102—671no—
1302#102—671no—
1303#102—671no—
1304#102—671no—
1305#102—671no—
1306#102—671no—
1307#102—671no—
1308#102—671no—
1309#102—671no—
1310#102—671no—
1311C22⋊C8—671no—
1312C22⋊C8—671no—
1313C22⋊C8—671no—
1314C22⋊C8—671no—
1315C22⋊C8—671no—
1316C22⋊C8—671no—
1317C22⋊C8—671no—
1318C22⋊C8—671no—
1319#97—671no—
1320#97—671no—
1321#97—671no—
1322#97—671no—
1323C24C2×C22⋊D6711yescharacteristic
1324C24C2×C22⋊D6711yescharacteristic
1325#41—22no—
1326#41—22no—
1327#41—44no—
1328#41—2684no—
1329#41—1342no—
1330#41—1342no—
1331C2×Q8—21no—
1332C2×Q8—21no—
1333C2×Q8—671no—
1334C2×Q8—1341no—
1335C2×Q8—1341no—
1336C2×Q8C23×D6711yescharacteristic
1337C2×D4—21no—
1338C2×D4—21no—
1339C2×D4—21no—
1340C2×D4—21no—
1341C2×D4—21no—
1342C2×D4—42no—
1343C2×D4—671no—
1344C2×D4—1341no—
1345C2×D4—1341no—
1346C2×D4—1341no—
1347C2×D4—1341no—
1348C2×D4—1341no—
1349C2×D4C2×C22⋊D6711yescharacteristic
1350C2×D4C2×C22⋊D6711yescharacteristic
1351C2×D4C2×C22⋊D6711yescharacteristic
1352C2×D4C2×C22⋊D6711yescharacteristic
1353C2×D4C23×D6711yescharacteristic
1354C22×C4—22no—
1355C22×C4—22no—
1356C22×C4—22no—
1357C22×C4—22no—
1358C22×C4—21no—
1359C22×C4—21no—
1360C22×C4—21no—
1361C22×C4—21no—
1362C22×C4—21no—
1363C22×C4—21no—
1364C22×C4—21no—
1365C22×C4—1341no—
1366C22×C4—1341no—
1367C22×C4—1341no—
1368C22×C4—1341no—
1369C22×C4—1341no—
1370C22×C4—1341no—
1371C22×C4—1341no—
1372C22×C4C2×C22⋊D6711yescharacteristic
1373C22×C4C2×C22⋊D6711yescharacteristic
1374C22×C4C2×C22⋊D6711yescharacteristic
1375C22×C4C2×C22⋊D6711yescharacteristic
1376C22×C4C2×C22⋊D6711yescharacteristic
1377C22×C4C2×C22⋊D6711yescharacteristic
1378C22×C4C2×C22⋊D6711yescharacteristic
1379C22×C4C2×C22⋊D6711yescharacteristic
1380C22×C4C23×D6711yescharacteristic
1381C22×C4C23×D6711yescharacteristic
1382C22×C4C23×D6711yescharacteristic
1383C22×C4C23×D6711yescharacteristic
1384C22×C4C23×D6711yescharacteristic
1385Q16—1342no—
1386SD16—1342no—
1387SD16—1342no—
1388D8—1342no—
1389M16—1342no—
1390M16—1342no—
1391M16—1342no—
1392M16—1342no—
1393C2×C8—674no—
1394C2×C8—671no—
1395C2×C8—671no—
1396C2×C8—671no—
1397C2×C8—671no—
1398C2×C8—671no—
1399C2×C8—671no—
1400C2×C8—671no—
1401C2×C8—671no—
1402C2×C8—1342no—
1403C2×C8—1342no—
1404C2×C8—1342no—
1405C2×C8—1342no—
1406C2×C8—1342no—
1407C2×C8—1342no—
1408C2×C8—1342no—
1409C4⋊C4—21no—
1410C4⋊C4—21no—
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—21no—
1416C4⋊C4—21no—
1417C4⋊C4—21no—
1418C4⋊C4—21no—
1419C4⋊C4—21no—
1420C4⋊C4—21no—
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—671no—
1426C4⋊C4—671no—
1427C4⋊C4—671no—
1428C4⋊C4—671no—
1429C4⋊C4—671no—
1430C4⋊C4—671no—
1431C4⋊C4—1341no—
1432C4⋊C4—1341no—
1433C4⋊C4—1341no—
1434C4⋊C4—1341no—
1435C4⋊C4—1341no—
1436C4⋊C4—1341no—
1437C4⋊C4—1341no—
1438C4⋊C4—1341no—
1439C4⋊C4—1341no—
1440C4⋊C4—1341no—
1441C4⋊C4—1341no—
1442C4⋊C4—1341no—
1443C4⋊C4—1341no—
1444C4⋊C4—1341no—
1445C4⋊C4—1341no—
1446C4⋊C4—1341no—
1447C4⋊C4C2×C22⋊D6711yescharacteristic
1448C4⋊C4C2×C22⋊D6711yescharacteristic
1449C4⋊C4C2×C22⋊D6711yescharacteristic
1450C4⋊C4C2×C22⋊D6711yescharacteristic
1451C4⋊C4C23×D6711yescharacteristic
1452C4⋊C4C23×D6711yescharacteristic
1453C4⋊C4C23×D6711yescharacteristic
1454C4⋊C4C23×D6711yescharacteristic
1455C4⋊C4C23×D6711yescharacteristic
1456C4⋊C4C23×D6711yescharacteristic
1457C22⋊C4—21no—
1458C22⋊C4—21no—
1459C22⋊C4—21no—
1460C22⋊C4—21no—
1461C22⋊C4—21no—
1462C22⋊C4—21no—
1463C22⋊C4—21no—
1464C22⋊C4—21no—
1465C22⋊C4—21no—
1466C22⋊C4—21no—
1467C22⋊C4—21no—
1468C22⋊C4—21no—
1469C22⋊C4—21no—
1470C22⋊C4—21no—
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—1341no—
1475C22⋊C4—1341no—
1476C22⋊C4—1341no—
1477C22⋊C4—1341no—
1478C22⋊C4—1341no—
1479C22⋊C4—1341no—
1480C22⋊C4—1341no—
1481C22⋊C4—1341no—
1482C22⋊C4—1341no—
1483C22⋊C4—1341no—
1484C22⋊C4—1341no—
1485C22⋊C4—1341no—
1486C22⋊C4—1341no—
1487C22⋊C4—1341no—
1488C22⋊C4—1341no—
1489C22⋊C4—1341no—
1490C22⋊C4—1341no—
1491C22⋊C4C2×C22⋊D6711yescharacteristic
1492C22⋊C4C2×C22⋊D6711yescharacteristic
1493C22⋊C4C2×C22⋊D6711yescharacteristic
1494C22⋊C4C2×C22⋊D6711yescharacteristic
1495C22⋊C4C2×C22⋊D6711yescharacteristic
1496C22⋊C4C2×C22⋊D6711yescharacteristic
1497C22⋊C4C2×C22⋊D6711yescharacteristic
1498C22⋊C4C2×C22⋊D6711yescharacteristic
1499C42—21no—
1500C42—21no—
1501C42—21no—
1502C42—21no—
1503C42—21no—
1504C42—21no—
1505C42—21no—
1506C42—21no—
1507C42—21no—
1508C42—1341no—
1509C42—1341no—
1510C42—1341no—
1511C42—1341no—
1512C42—1341no—
1513C42—1341no—
1514C42—1341no—
1515C42—1341no—
1516C42—1341no—
1517C42C2×C22⋊D6711yescharacteristic
1518C42C2×C22⋊D6711yescharacteristic
1519C42C23×D6711yescharacteristic
1520C42C23×D6711yescharacteristic
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—21no—
1525C23—41no—
1526C23—41no—
1527C23—41no—
1528C23—1341no—
1529C23C22×C22⋊D6711yescharacteristic
1530C23C22×C22⋊D6711yescharacteristic
1531C23C22×C22⋊D6711yescharacteristic
1532C23C22×C22⋊D6711yescharacteristic
1533C23C22×C22⋊D6711yescharacteristic
1534Q8—21no—
1535Q8—21no—
1536Q8—42no—
1537Q8—81no—
1538Q8—2682no—
1539Q8—5361no—
1540Q8—1341no—
1541Q8—1341no—
1542D4—22no—
1543D4—22no—
1544D4—21no—
1545D4—21no—
1546D4—41no—
1547D4—41no—
1548D4—42no—
1549D4—42no—
1550D4—42no—
1551D4—81no—
1552D4—81no—
1553D4—2682no—
1554D4—2682no—
1555D4—2682no—
1556D4—5361no—
1557D4—5361no—
1558D4—1341no—
1559D4—1341no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—41no—
1582C2×C4—41no—
1583C2×C4—42no—
1584C2×C4—42no—
1585C2×C4—42no—
1586C2×C4—42no—
1587C2×C4—81no—
1588C2×C4—81no—
1589C2×C4—81no—
1590C2×C4—2682no—
1591C2×C4—2682no—
1592C2×C4—2682no—
1593C2×C4—2682no—
1594C2×C4—5361no—
1595C2×C4—5361no—
1596C2×C4—5361no—
1597C2×C4—1341no—
1598C2×C4—1341no—
1599C2×C4—1341no—
1600C2×C4—1341no—
1601C2×C4—1341no—
1602C2×C4—1341no—
1603C2×C4—1341no—
1604C2×C4C22×C22⋊D6711yescharacteristic
1605C2×C4C22×C22⋊D6711yescharacteristic
1606C2×C4C22×C22⋊D6711yescharacteristic
1607C2×C4C22×C22⋊D6711yescharacteristic
1608C2×C4C22×C22⋊D6711yescharacteristic
1609C2×C4C22×C22⋊D6711yescharacteristic
1610C2×C4C22×C22⋊D6711yescharacteristic
1611C2×C4C22×C22⋊D6711yescharacteristic
1612C2×C4C22×C22⋊D6711yescharacteristic
1613C2×C4#41×D6712yes—
1614C2×C4#1452409012yes—
1615C2×C4C24×D6711yescharacteristic
1616C8—672no—
1617C8—672no—
1618C8—1341no—
1619C8—1341no—
1620C8—1341no—
1621C8—1341no—
1622C8—1341no—
1623C8—1341no—
1624C22—21no—
1625C22—21no—
1626C22—21no—
1627C22—21no—
1628C22—21no—
1629C22—21no—
1630C22—21no—
1631C22—21no—
1632C22—21no—
1633C22—21no—
1634C22—21no—
1635C22—21no—
1636C22—21no—
1637C22—44no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—82no—
1642C22—2681no—
1643C22—2681no—
1644C22—2681no—
1645C22#1686404512yes—
1646C22#1686419412yes—
1647C22C23×C22⋊D6711yescharacteristic
1648C4—21no—
1649C4—21no—
1650C4—21no—
1651C4—21no—
1652C4—21no—
1653C4—21no—
1654C4—21no—
1655C4—21no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C4—41no—
1660C4—41no—
1661C4—41no—
1662C4—41no—
1663C4—2681no—
1664C4—2681no—
1665C4—2681no—
1666C4—2681no—
1667C4—2681no—
1668C4—2681no—
1669C4—2681no—
1670C4#1686404512yes—
1671C4C2×#41×D6711yescharacteristic
1672C4C2×#1452409011yescharacteristic
1673C2—22no—
1674C2—22no—
1675C2—41no—
1676C2—41no—
1677C2—41no—
1678C2—81no—
1679C2—5361no—
1680C2C2×#1686404511yescharacteristic
1681C2C2×#1686419411yescharacteristic
1682C2#2257498011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3475C2
socleC22×C67C23×D4
hypercenter#3475D67
hypocenterC67#61243
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #22573767C2semidirect
2. #22572754C2semidirect
3. #22572748C2semidirect
4. #22572739C2semidirect
5. #22572733C2semidirect
6. #22572724C2semidirect
7. #22572718C2semidirect
8. #22572709C2semidirect
9. #22572703C2semidirect
10. #22572694C2semidirect
11. #22572688C2semidirect
12. #22572679C2semidirect
13. #22572673C2semidirect
14. #22572664C2semidirect
15. #22572658C2semidirect
16. #22572649C2semidirect
17. #22572643C2semidirect
18. #22570731C2semidirect
19. #22570122C2semidirect
20. #22570122C2semidirect
21. #22570118C2semidirect
22. #22570118C2semidirect
23. #22569997C2semidirect
24. #22569991C2semidirect
25. #22569815C2semidirect
26. #22569787C2semidirect
27. #22569007C2semidirect
28. C2×#16863468C2semidirect
29. #22568798C2semidirect
30. C2×#16863432C2semidirect
31. C67×#3475C2semidirect
57. #16863806C22semidirect
58. #16863806C22semidirect
59. #16863806C22semidirect
60. #16863806C22semidirect
61. #16863802C22semidirect
62. #16863802C22semidirect
63. #16863802C22semidirect
64. #16863802C22semidirect
65. #16863737C22semidirect
66. #16863737C22semidirect
67. #16863737C22semidirect
68. #16863737C22semidirect
69. #16863734C22semidirect
70. #16863734C22semidirect
71. #16863734C22semidirect
72. #16863734C22semidirect
73. #16863731C22semidirect
74. #16863731C22semidirect
75. #16863729C22semidirect
76. #16863729C22semidirect
77. #16863726C22semidirect
78. #16863726C22semidirect
79. #16863724C22semidirect
80. #16863724C22semidirect
81. #16863720C22semidirect
82. #16863720C22semidirect
83. #16863720C22semidirect
84. #16863720C22semidirect
85. #16863717C22semidirect
86. #16863717C22semidirect
87. #16863717C22semidirect
88. #16863717C22semidirect
89. #16863714C22semidirect
90. #16863714C22semidirect
91. #16863712C22semidirect
92. #16863712C22semidirect
93. #16863709C22semidirect
94. #16863709C22semidirect
95. #16863707C22semidirect
96. #16863707C22semidirect
97. #16863703C22semidirect
98. #16863703C22semidirect
99. #16863700C22semidirect
100. #16863700C22semidirect
101. #16863696C22semidirect
102. #16863696C22semidirect
103. #16863693C22semidirect
104. #16863693C22semidirect
105. #16863691C22semidirect
106. #16863688C22semidirect
107. #16863686C22semidirect
108. #16863683C22semidirect
109. #16863681C22semidirect
110. #16863678C22semidirect
111. #16863676C22semidirect
112. #16863673C22semidirect
113. #16863652C22semidirect
114. #16863652C22semidirect
115. #16863647C22semidirect
116. #16863647C22semidirect
117. #16863644C22semidirect
118. #16863644C22semidirect
119. #16863640C22semidirect
120. #16863640C22semidirect
121. #16863635C22semidirect
122. #16863635C22semidirect
123. #16863630C22semidirect
124. #16863630C22semidirect
125. #16863627C22semidirect
126. #16863627C22semidirect
127. #16863623C22semidirect
128. #16863623C22semidirect
129. #16863506C22semidirect
130. #16863506C22semidirect
131. #16863501C22semidirect
132. #16863501C22semidirect
133. #16863496C22semidirect
134. #16863496C22semidirect
135. #16863494C22semidirect
136. #16863494C22semidirect
145. #16863439C22semidirect
146. #16863439C22semidirect
147. #16863439C22semidirect
148. #16863439C22semidirect
149. #16863436C22semidirect
150. #16863436C22semidirect
151. #16863436C22semidirect
152. #16863436C22semidirect
162. #16863432C22semidirect
163. #16863432C22semidirect
164. #16863432C22semidirect
165. #16863432C22semidirect
166. C2×#14523976C22semidirect
167. C2×#14523976C22semidirect
168. C2×#14523974C22semidirect
169. C2×#14523974C22semidirect
515. C2×C67⋊C8#41semidirect
843. #3475D67semidirect
873. C67#61243semidirect

Maximal subgroups

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

subgroupindex
#225737672
#225727542
#225727482
#225727392
#225727332
#225727242
#225727182
#225727092
#225727032
#225726942
#225726882
#225726792
#225726732
#225726642
#225726582
#225726492
#225726432
#225707312
#225701222
#225701182
#225699972
#225699912
#225698152
#225697872
#225690072
C2×#168634682
#225687982
C2×#168634322
C67×#34752
#6124367