Finite Group Databasebeta

← #31740253

Subgroups — #31740253

Order 17152.

1850 conjugacy classes of subgroups.

The subgroup lattice has 1730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574281C211yesmaximal, characteristic, complemented
2#22574153C211yesmaximal, characteristic, complemented
3#22573207C211yesmaximal, characteristic, complemented
4#22573077C211yesmaximal, characteristic, complemented
5#22573038C211yesmaximal, characteristic, complemented
6#22572964C211yesmaximal, characteristic, complemented
7#22572794C211yesmaximal, characteristic, complemented
8#22572771C211yesmaximal, characteristic, complemented
9#22572771C211yesmaximal, characteristic, complemented
10#22572352C211yesmaximal, characteristic, complemented
11#22572307C211yesmaximal, characteristic, complemented
12#22572247C211yesmaximal, characteristic, complemented
13#22572172C211yesmaximal, characteristic, complemented
14#22572061C211yesmaximal, characteristic, complemented
15#22572046C211yesmaximal, characteristic, complemented
16#22571821C211yesmaximal, characteristic, complemented
17#22571821C211yesmaximal, characteristic, complemented
18#22571811C211yesmaximal, characteristic, complemented
19#22570938C211yesmaximal, characteristic, complemented
20#22570848C211yesmaximal, characteristic, complemented
21#22570837C211yesmaximal, characteristic, complemented
22#22570488C211yesmaximal, characteristic, complemented
23#22570453C211yesmaximal, characteristic, complemented
24#22570425C211yesmaximal, characteristic, complemented
25#22570395C211yesmaximal, characteristic, complemented
26#22570258C211yesmaximal, characteristic, complemented
27#22570229C211yesmaximal, characteristic, complemented
28#22569043C211yesmaximal, characteristic, complemented
29#22569043C211yesmaximal, characteristic, complemented
30C4×#14524071C211yesmaximal, characteristic, complemented
31C67×#2969C211yesmaximal, characteristic, complemented
32C2×#14524071C2211yescharacteristic
33C2×#14524071C2211yescharacteristic
34C2×#14524071C2211yescharacteristic
35#16864131C2211yescharacteristic, complemented
36#16864119C2211yescharacteristic, complemented
37#16864116C2211yescharacteristic, complemented
38#16864106C2211yescharacteristic, complemented
39#16864106C2211yescharacteristic, complemented
40#16864097—21no—
41#16864092C2211yescharacteristic
42#16864092C2211yescharacteristic
43#16864091—21no—
44#16864086C2211yescharacteristic, complemented
45#16864086C2211yescharacteristic, complemented
46#16864078—21no—
47#16864076—21no—
48#16864074—21no—
49#16864073—21no—
50#16864071—21no—
51#16864051C2211yescharacteristic
52#16864050C2211yescharacteristic
53#16864042C2211yescharacteristic
54#16864042C2211yescharacteristic
55#16864042C2211yescharacteristic, complemented
56#16864042C2211yescharacteristic, complemented
57#16864035—21no—
58D4×D268C2211yescharacteristic, complemented
59#16864017C2211yescharacteristic, complemented
60#16864017C2211yescharacteristic, complemented
61#16864008C2211yescharacteristic, complemented
62#16864001C2211yescharacteristic
63#16863994—21no—
64#16863992—21no—
65#16863980—21no—
66#16863978—21no—
67#16863930C2211yescharacteristic, complemented
68#16863930C2211yescharacteristic, complemented
69#16863929—21no—
70#126×D67—21no—
71#16863904—21no—
72#123×D67—21no—
73#16863876C2211yescharacteristic
74#16863876C2211yescharacteristic, complemented
75#16863870C2211yescharacteristic, complemented
76#16863870C2211yescharacteristic, complemented
77C4×#11761628C2211yescharacteristic, complemented
78C2×C4×D268C2211yescharacteristic, complemented
79#16863801C2211yescharacteristic, complemented
80#16863798C2211yescharacteristic, complemented
81#16863798C2211yescharacteristic, complemented
82#16863780C2211yescharacteristic, complemented
83#16863780C2211yescharacteristic, complemented
84#16863769C2211yescharacteristic, complemented
85#16863765C2211yescharacteristic, complemented
86#16863761C2211yescharacteristic, complemented
87#16863756C2211yescharacteristic, complemented
88#16863756C2211yescharacteristic, complemented
89#16863751C2211yescharacteristic, complemented
90#16863751C2211yescharacteristic, complemented
91#16863738C2211yescharacteristic, complemented
92#16863738C2211yescharacteristic, complemented
93#16863732C2211yescharacteristic, complemented
94#16863732C2211yescharacteristic, complemented
95#16863727C2211yescharacteristic, complemented
96#16863727C2211yescharacteristic, complemented
97#16863721C2211yescharacteristic, complemented
98#16863721C2211yescharacteristic, complemented
99#16863721C2211yescharacteristic, complemented
100#16863721C2211yescharacteristic, complemented
101#16863715C2211yescharacteristic, complemented
102#16863715C2211yescharacteristic, complemented
103#16863704C2211yescharacteristic, complemented
104#16863704C2211yescharacteristic, complemented
105#16863697C2211yescharacteristic, complemented
106#16863697C2211yescharacteristic, complemented
107#16863697C2211yescharacteristic, complemented
108#16863697C2211yescharacteristic, complemented
109#16863697C2211yescharacteristic, complemented
110#16863697C2211yescharacteristic, complemented
111#16863687C2211yescharacteristic, complemented
112#16863687C2211yescharacteristic, complemented
113#16863682C2211yescharacteristic, complemented
114#16863677C2211yescharacteristic, complemented
115#16863654C2211yescharacteristic, complemented
116#16863649C2211yescharacteristic
117#16863642C2211yescharacteristic, complemented
118#16863642C2211yescharacteristic, complemented
119#16863642C2211yescharacteristic, complemented
120#16863642C2211yescharacteristic, complemented
121#16863642C2211yescharacteristic, complemented
122#16863642C2211yescharacteristic, complemented
123#16863637C2211yescharacteristic, complemented
124#16863632C2211yescharacteristic
125#16863625C2211yescharacteristic, complemented
126#16863625C2211yescharacteristic, complemented
127#16863619C2211yescharacteristic, complemented
128#16863619C2211yescharacteristic, complemented
129#16863612C2211yescharacteristic
130#16863612C2211yescharacteristic
131#16863612C2211yescharacteristic, complemented
132#16863612C2211yescharacteristic, complemented
133#16863612C2211yescharacteristic, complemented
134#16863612C2211yescharacteristic, complemented
135#16863607C2211yescharacteristic, complemented
136#16863602C2211yescharacteristic, complemented
137#16863592C2211yescharacteristic
138#16863592C2211yescharacteristic
139#16863560C2211yescharacteristic
140#16863560C2211yescharacteristic
141#16863560C2211yescharacteristic, complemented
142#16863560C2211yescharacteristic, complemented
143#16863549C2211yescharacteristic, complemented
144#16863549C2211yescharacteristic, complemented
145#16863543C2211yescharacteristic
146#16863543C2211yescharacteristic
147#16863532C2211yescharacteristic
148#16863532C2211yescharacteristic
149#16863532C2211yescharacteristic, complemented
150#16863532C2211yescharacteristic, complemented
151#16863509C2211yescharacteristic
152#16863509C2211yescharacteristic
153#16863509C2211yescharacteristic, complemented
154#16863509C2211yescharacteristic, complemented
155#16863509C2211yescharacteristic, complemented
156#16863504C2211yescharacteristic, complemented
157#16863498C2211yescharacteristic, complemented
158#16863498C2211yescharacteristic, complemented
159#16863498C2211yescharacteristic, complemented
160#16863498C2211yescharacteristic, complemented
161#16863498C2211yescharacteristic, complemented
162#16863498C2211yescharacteristic, complemented
163C4×Dic268C2211yescharacteristic, complemented
164C4×#11761617C2211yescharacteristic, complemented
165C4×#11761617C2211yescharacteristic, complemented
166C4×#11761617C2211yescharacteristic, complemented
167C4×#11761617C2211yescharacteristic, complemented
168C4×#11761617C2211yescharacteristic, complemented
169C4×#11761617C2211yescharacteristic, complemented
170C4×#11761617C2211yescharacteristic, complemented
171C4×#11761617C2211yescharacteristic, complemented
172C4×D536C2211yescharacteristic
173C4×D536C2211yescharacteristic
174C4×D536C2211yescharacteristic
175C4×D536C2211yescharacteristic
176C4×D536C2211yescharacteristic, complemented
177C4×D536C2211yescharacteristic, complemented
178C4×D536C2211yescharacteristic, complemented
179#16863438C2211yescharacteristic, complemented
180#16863438C2211yescharacteristic, complemented
181#16863438C2211yescharacteristic, complemented
182#16863402C2211yescharacteristic, complemented
183#16863398C2211yescharacteristic, complemented
184#16863393C2211yescharacteristic
185#16863393C2211yescharacteristic, complemented
186C2×#14523965C2211yescharacteristic, complemented
187C2×#14523965C2211yescharacteristic, complemented
188#529×C67C2211yescharacteristic
189#446×C67C2211yescharacteristic, complemented
190C8×Q8×C67C2211yescharacteristic, complemented
191#436×C67C2211yescharacteristic, complemented
192#436×C67C2211yescharacteristic, complemented
193#436×C67C2211yescharacteristic, complemented
194#435×C67C2211yescharacteristic, complemented
195#435×C67C2211yescharacteristic, complemented
196C8×D4×C67C2211yescharacteristic, complemented
197#433×C67C2211yescharacteristic, complemented
198#433×C67C2211yescharacteristic, complemented
199#431×C67C2211yescharacteristic, complemented
200#405×C67C2211yescharacteristic, complemented
201#405×C67C2211yescharacteristic, complemented
202C4×M16×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761628C2311yescharacteristic
205C2×#11761628C2311yescharacteristic
206C2×#11761627—21no—
207C22×D268C2311yescharacteristic
208C22×D268C2311yescharacteristic
209C22×D268C2311yescharacteristic
210C2×D4×D67—21no—
211C22×C4×D67—21no—
212#14524071—24no—
213#14524071—24no—
214#14524071—24no—
215C2×Dic268C2311yescharacteristic
216C2×Dic268C2311yescharacteristic
217C2×#11761617C2311yescharacteristic
218C2×#11761617C2311yescharacteristic
219C2×#11761617C2311yescharacteristic
220C2×#11761617C2311yescharacteristic
221C2×#11761617C2311yescharacteristic
222C2×#11761617C2311yescharacteristic
223C2×#11761617C2311yescharacteristic
224C2×#11761617C2311yescharacteristic
225C2×D536C2311yescharacteristic
226C2×D536C2311yescharacteristic
227C2×D536C2311yescharacteristic
228C2×D536C2311yescharacteristic
229C2×D536C2311yescharacteristic
230C2×D536C2311yescharacteristic
231#14524043C2311yescharacteristic
232#14524043C2311yescharacteristic
233#14524043C2311yescharacteristic
234#14524040C2311yescharacteristic
235#14524038—21no—
236#14524038—21no—
237#14524038—21no—
238#14524038—21no—
239#14524038—21no—
240#14524038—21no—
241#14524037—21no—
242#14524037—21no—
243#14524036—21no—
244#14524036—21no—
245#14524036—21no—
246#14524036—21no—
247#14524036—21no—
248#14524036—21no—
249#14524035C2311yescharacteristic
250#14524035C2311yescharacteristic
251#14524035C2311yescharacteristic
252#14524035C2311yescharacteristic
253#14524033—21no—
254#14524033—21no—
255#14524033—21no—
256#14524033—21no—
257#14524032—21no—
258#14524031C2311yescharacteristic
259#14524031C2311yescharacteristic
260#14524031C2311yescharacteristic
261#14524031C2311yescharacteristic
262#14524030—21no—
263#14524029—21no—
264#14524029—21no—
265#14524028—21no—
266#14524028—21no—
267#14524028—21no—
268#14524028—21no—
269#14524028—21no—
270#14524028—21no—
271#14524028—21no—
272#14524028—21no—
273#14524027—21no—
274#14524027—21no—
275#14524026—21no—
276#14524026—21no—
277#14524025—21no—
278#14524025—21no—
279#14524025—21no—
280#14524025—21no—
281#14524025—21no—
282#14524025—21no—
283#14524024—21no—
284#14524024—21no—
285#14524023—21no—
286#14524022C2311yescharacteristic
287#14524022C2311yescharacteristic
288#14524022C2311yescharacteristic
289#14524022C2311yescharacteristic
290#14524022C2311yescharacteristic
291#14524022C2311yescharacteristic
292#14524021—21no—
293#14524021—21no—
294#14524021—21no—
295#14524021—21no—
296#14524021—21no—
297#14524021—21no—
298#14524019—21no—
299#14524019—21no—
300#14524019—21no—
301#14524018—21no—
302#14524017C2311yescharacteristic
303#14524017C2311yescharacteristic
304#14524017C2311yescharacteristic
305#14524017C2311yescharacteristic
306#14524017C2311yescharacteristic
307#14524017C2311yescharacteristic
308#14524016—21no—
309#14524016—21no—
310#14524016—21no—
311#14524016—21no—
312#14524016—21no—
313#14524016—21no—
314#14524015—21no—
315#14524015—21no—
316#14524014—21no—
317#14524013—21no—
318#14524013—21no—
319#14524011—21no—
320#14524011—21no—
321#14524011—21no—
322#14524011—21no—
323C4×Dic134C2311yescharacteristic
324C4×Dic134C2311yescharacteristic
325C4×Dic134C2311yescharacteristic
326C4×Dic134C2311yescharacteristic
327C4×Dic134C2311yescharacteristic
328C4×Dic134C2311yescharacteristic
329#14524008—21no—
330C4×D268—21no—
331C4×D268—21no—
332C4×D268C2311yescharacteristic
333C4×D268C2311yescharacteristic
334C4×D268C2311yescharacteristic
335C4×D268C2311yescharacteristic
336C4×D268C2311yescharacteristic
337C4×D268C2311yescharacteristic
338C4×D268C2311yescharacteristic
339C4×D268C2311yescharacteristic
340C4×D268C2311yescharacteristic
341C4×D268C2311yescharacteristic
342C4×D268C2311yescharacteristic
343C4×D268C2311yescharacteristic
344C4×D268C2311yescharacteristic
345C4×D268C2311yescharacteristic
346#14524005—21no—
347#14524005—21no—
348#14524005—21no—
349#14524005—21no—
350#14524005—21no—
351C4×C22⋊D67—21no—
352C4×C22⋊D67—21no—
353C4×C22⋊D67—21no—
354C4×C22⋊D67—21no—
355(C22⋊D67)⋊C4—21no—
356(C22⋊D67)⋊C4—21no—
357(C22⋊D67)⋊C4—21no—
358(C22⋊D67)⋊C4—21no—
359(C22⋊D67)⋊C4—21no—
360(C22⋊D67)⋊C4—21no—
361#14524002C2311yescharacteristic
362#14524002C2311yescharacteristic
363#14524002C2311yescharacteristic
364#14524001—21no—
365#14524001—21no—
366#14524001—21no—
367#14524000—21no—
368#14524000—21no—
369#14524000—21no—
370#14523999—21no—
371#14523999—21no—
372C2×C4⋊Dic67C2311yescharacteristic
373C2×C4⋊Dic67C2311yescharacteristic
374C2×C4⋊Dic67C2311yescharacteristic
375C4⋊C4×D67—21no—
376C4⋊C4×D67—21no—
377C4⋊C4×D67—21no—
378C4⋊C4×D67—21no—
379C4⋊C4×D67—21no—
380C2×(C2×D67)⋊C4—21no—
381C22⋊C4×D67—21no—
382C22⋊C4×D67—21no—
383C22⋊C4×D67—21no—
384C22⋊C4×D67—21no—
385C22⋊C4×D67—21no—
386C22⋊C4×D67—21no—
387C22⋊C4×D67—21no—
388C22⋊C4×D67—21no—
389C42×D67—21no—
390#14523977C2311yescharacteristic
391#14523977C2311yescharacteristic
392#14523977C2311yescharacteristic
393#14523977C2311yescharacteristic
394#14523977C2311yescharacteristic
395#14523977C2311yescharacteristic
396#14523977C2311yescharacteristic
397#14523977C2311yescharacteristic
398#14523975C2311yescharacteristic
399#14523975C2311yescharacteristic
400#14523975C2311yescharacteristic
401#14523975C2311yescharacteristic
402#14523975C2311yescharacteristic
403#14523975C2311yescharacteristic
404#14523975C2311yescharacteristic
405#14523975C2311yescharacteristic
406#14523968C2311yescharacteristic
407#14523968C2311yescharacteristic
408#14523968C2311yescharacteristic
409#14523968C2311yescharacteristic
410#14523968C2311yescharacteristic
411#14523968C2311yescharacteristic
412#14523968C2311yescharacteristic
413#14523968C2311yescharacteristic
414#14523968C2311yescharacteristic
415#14523968C2311yescharacteristic
416#14523968C2311yescharacteristic
417#14523968C2311yescharacteristic
418#14523965C2311yescharacteristic
419#14523965C2311yescharacteristic
420#14523965C2311yescharacteristic
421#14523965C2311yescharacteristic
422#14523965C2311yescharacteristic
423#14523965C2311yescharacteristic
424#14523965C2311yescharacteristic
425#14523965C2311yescharacteristic
426#14523965C2311yescharacteristic
427#14523965C2311yescharacteristic
428#14523965C2311yescharacteristic
429#14523965C2311yescharacteristic
430#14523965C2311yescharacteristic
431#14523965C2311yescharacteristic
432#14523965C2311yescharacteristic
433#14523965C2311yescharacteristic
434#14523965C2311yescharacteristic
435#14523965C2311yescharacteristic
436#14523965C2311yescharacteristic
437#14523965C2311yescharacteristic
438C2×M16×C67C2311yescharacteristic
439C2×M16×C67C2311yescharacteristic
440C2×M16×C67C2311yescharacteristic
441C2×M16×C67C2311yescharacteristic
442C22×C8×C67C2311yescharacteristic
443C22×C8×C67C2311yescharacteristic
444#126×C67D411yescharacteristic
445#126×C67D411yescharacteristic
446#125×C67D411yescharacteristic
447#124×C67D411yescharacteristic
448#123×C67D411yescharacteristic
449#123×C67D411yescharacteristic
450C22⋊Q8×C67D411yescharacteristic
451#121×C67D411yescharacteristic
452C4×Q8×C67C2311yescharacteristic
453C4×D4×C67C2311yescharacteristic
454C4×D4×C67C2311yescharacteristic
455C4×D4×C67C2311yescharacteristic
456#117×C67C2311yescharacteristic
457#117×C67C2311yescharacteristic
458C2×C42×C67C2311yescharacteristic
459C4⋊C8×C67C2311yescharacteristic
460C4⋊C8×C67C2311yescharacteristic
461C4⋊C8×C67C2311yescharacteristic
462C4⋊C8×C67C2311yescharacteristic
463C4⋊C8×C67C2311yescharacteristic
464C4⋊C8×C67C2311yescharacteristic
465C22⋊C8×C67C2311yescharacteristic
466C22⋊C8×C67C2311yescharacteristic
467C22⋊C8×C67C2311yescharacteristic
468C22⋊C8×C67C2311yescharacteristic
469C22⋊C8×C67C2311yescharacteristic
470C22⋊C8×C67C2311yescharacteristic
471#97×C67C2311yescharacteristic
472#97×C67C2311yescharacteristic
473#97×C67C2311yescharacteristic
474#97×C67C2311yescharacteristic
475C4×C8×C67C2311yescharacteristic
476C4×C8×C67C2311yescharacteristic
477C4×C8×C67C2311yescharacteristic
478C4×C8×C67C2311yescharacteristic
479C4×C8×C67C2311yescharacteristic
480C4×C8×C67C2311yescharacteristic
481C23×D67—21no—
482C23×D67—21no—
483C23×D67—21no—
484#11761628—22no—
485#11761628—22no—
486#11761628—22no—
487#11761628—41no—
488#11761628—41no—
489#11761628—41no—
490#11761627—82no—
491C2×Dic134—21no—
492C2×Dic134—21no—
493C2×Dic134C2411yescharacteristic
494C2×Dic134C2411yescharacteristic
495C2×Dic134C2411yescharacteristic
496C2×D268—22no—
497C2×D268—22no—
498C2×D268—22no—
499C2×D268—21no—
500C2×D268—21no—
501C2×D268—21no—
502C2×D268—21no—
503C2×D268—21no—
504C2×D268—41no—
505C2×D268—41no—
506C2×D268—41no—
507C2×D268C2411yescharacteristic
508C2×D268C2411yescharacteristic
509C2×D268C2411yescharacteristic
510C2×D268C2411yescharacteristic
511C2×D268C2411yescharacteristic
512C2×C22⋊D67—21no—
513C2×C22⋊D67—21no—
514C2×C22⋊D67—21no—
515C2×C22⋊D67—21no—
516C2×C22⋊D67—21no—
517C2×C22⋊D67—21no—
518C2×C22⋊D67—21no—
519C2×C22⋊D67—21no—
520C2×C22⋊D67—21no—
521D4×D67—82no—
522C22×Dic67—21no—
523C22×Dic67—21no—
524C22×Dic67—21no—
525C2×C4×D67—21no—
526C2×C4×D67—21no—
527C2×C4×D67—21no—
528C2×C4×D67—21no—
529C2×C4×D67—21no—
530C2×C4×D67—21no—
531C2×C4×D67—21no—
532C2×C4×D67—21no—
533C2×C4×D67—21no—
534C2×C4×D67—21no—
535C2×C4×D67—21no—
536C2×C4×D67—21no—
537C2×C4×D67—21no—
538C2×C4×D67—21no—
539C2×C4×D67—21no—
540C2×C4×D67—21no—
541C2×C4×D67—21no—
542C2×C4×D67—82no—
543Dic268—41no—
544Dic268—41no—
545#11761617—22no—
546#11761617—22no—
547#11761617—22no—
548#11761617—22no—
549#11761617—22no—
550#11761617—22no—
551#11761617—41no—
552#11761617—41no—
553D536—22no—
554D536—22no—
555D536—22no—
556D536—41no—
557D536—41no—
558D536#4114yescomplemented
559C4⋊Dic67—21no—
560C4⋊Dic67—21no—
561C4⋊Dic67—21no—
562C4⋊Dic67—21no—
563C4⋊Dic67—21no—
564C4⋊Dic67—21no—
565C4⋊Dic67—21no—
566C4⋊Dic67C2411yescharacteristic
567C4⋊Dic67C2411yescharacteristic
568C4⋊Dic67C2411yescharacteristic
569C4⋊Dic67C2411yescharacteristic
570C4⋊Dic67C2411yescharacteristic
571C4⋊Dic67C2411yescharacteristic
572C4⋊Dic67C2411yescharacteristic
573C4⋊Dic67C2411yescharacteristic
574Dic67⋊C4—21no—
575Dic67⋊C4—21no—
576Dic67⋊C4—21no—
577Dic67⋊C4—21no—
578Dic67⋊C4—21no—
579Dic67⋊C4—21no—
580Dic67⋊C4—21no—
581Dic67⋊C4—21no—
582Dic67⋊C4—21no—
583Dic67⋊C4—21no—
584Dic67⋊C4—21no—
585Dic67⋊C4—21no—
586Dic67⋊C4—21no—
587Dic67⋊C4—21no—
588Dic67⋊C4—21no—
589Dic67⋊C4—21no—
590Dic67⋊C4—21no—
591Dic67⋊C4—21no—
592Dic67⋊C4—21no—
593Dic67⋊C4—21no—
594C22⋊Dic67—21no—
595C22⋊Dic67—21no—
596C22⋊Dic67—21no—
597C22⋊Dic67—21no—
598C22⋊Dic67—21no—
599C22⋊Dic67—21no—
600C22⋊Dic67—21no—
601C22⋊Dic67—21no—
602C22⋊Dic67—21no—
603(C2×D67)⋊C4—21no—
604(C2×D67)⋊C4—21no—
605(C2×D67)⋊C4—21no—
606(C2×D67)⋊C4—21no—
607(C2×D67)⋊C4—21no—
608(C2×D67)⋊C4—21no—
609(C2×D67)⋊C4—21no—
610(C2×D67)⋊C4—21no—
611(C2×D67)⋊C4—21no—
612(C2×D67)⋊C4—21no—
613(C2×D67)⋊C4—21no—
614(C2×D67)⋊C4—21no—
615(C2×D67)⋊C4—21no—
616(C2×D67)⋊C4—21no—
617(C2×D67)⋊C4—21no—
618(C2×D67)⋊C4—21no—
619(C2×D67)⋊C4—21no—
620(C2×D67)⋊C4—21no—
621(C2×D67)⋊C4—21no—
622(C2×D67)⋊C4—21no—
623(C2×D67)⋊C4—21no—
624(C2×D67)⋊C4—21no—
625(C2×D67)⋊C4—21no—
626(C2×D67)⋊C4—21no—
627(C2×D67)⋊C4—21no—
628(C2×D67)⋊C4—21no—
629(C2×D67)⋊C4—21no—
630(C2×D67)⋊C4—21no—
631C4×Dic67—21no—
632C4×Dic67—21no—
633C4×Dic67—21no—
634C4×Dic67—21no—
635C4×Dic67—21no—
636C4×Dic67—21no—
637C4×Dic67—21no—
638C4×Dic67—21no—
639C4×Dic67—21no—
640C2×Q8×C67C2×D411yescharacteristic
641C2×D4×C67C2×D411yescharacteristic
642C2×D4×C67C2×D411yescharacteristic
643C2×D4×C67C2×D411yescharacteristic
644C22×C4×C67C2×D411yescharacteristic
645C22×C4×C67C2×D411yescharacteristic
646C22×C4×C67C2411yescharacteristic
647C22×C4×C67C2411yescharacteristic
648C22×C4×C67C2411yescharacteristic
649M16×C67—22no—
650M16×C67—22no—
651M16×C67—22no—
652M16×C67—41no—
653C2×C8×C67—41no—
654C2×C8×C67—41no—
655C2×C8×C67C2411yescharacteristic
656C2×C8×C67C2411yescharacteristic
657C2×C8×C67C2411yescharacteristic
658C2×C8×C67C2411yescharacteristic
659C2×C8×C67C2411yescharacteristic
660C2×C8×C67C2411yescharacteristic
661C2×C8×C67C2411yescharacteristic
662C2×C8×C67C2411yescharacteristic
663C4⋊C4×C67C2×D411yescharacteristic
664C4⋊C4×C67C2×D411yescharacteristic
665C4⋊C4×C67C2×D411yescharacteristic
666C4⋊C4×C67C2×D411yescharacteristic
667C4⋊C4×C67C2×D411yescharacteristic
668C4⋊C4×C67C2×D411yescharacteristic
669C4⋊C4×C67C2×D411yescharacteristic
670C4⋊C4×C67C2×D411yescharacteristic
671C4⋊C4×C67C2×D411yescharacteristic
672C4⋊C4×C67C2×D411yescharacteristic
673C22⋊C4×C67C2×D411yescharacteristic
674C22⋊C4×C67C2×D411yescharacteristic
675C22⋊C4×C67C2×D411yescharacteristic
676C22⋊C4×C67C2×D411yescharacteristic
677C22⋊C4×C67C2×D411yescharacteristic
678C22⋊C4×C67C2×D411yescharacteristic
679C22⋊C4×C67C2×D411yescharacteristic
680C22⋊C4×C67C2×D411yescharacteristic
681C22⋊C4×C67C2×D411yescharacteristic
682C22⋊C4×C67C2×D411yescharacteristic
683C42×C67C2×D411yescharacteristic
684C42×C67C2×D411yescharacteristic
685C42×C67C2411yescharacteristic
686C42×C67C2411yescharacteristic
687C42×C67C2411yescharacteristic
688C42×C67C2411yescharacteristic
689C23×C67C22×D411yescharacteristic
690C23×C67C22×D411yescharacteristic
691C23×C67C22×D411yescharacteristic
692C22×D67—21no—
693C22×D67—21no—
694C22×D67—21no—
695C22×D67—21no—
696C22×D67—21no—
697C22×D67—42no—
698C22×D67—42no—
699C22×D67—42no—
700C22×D67—42no—
701C22×D67—81no—
702C22×D67—81no—
703C22×D67—81no—
704C22×D67—81no—
705C22×D67—81no—
706Q8×C67—41no—
707D4×C67—41no—
708D4×C67—41no—
709D4×C67—41no—
710C2×C4×C67—21no—
711C2×C4×C67—21no—
712C2×C4×C67—21no—
713C2×C4×C67—21no—
714C2×C4×C67—21no—
715C2×C4×C67—21no—
716C2×C4×C67—41no—
717C2×C4×C67—41no—
718C2×C4×C67C22×D411yescharacteristic
719C2×C4×C67C22×D411yescharacteristic
720C2×C4×C67C22×D411yescharacteristic
721C2×C4×C67C22×D411yescharacteristic
722C2×C4×C67C22×D411yescharacteristic
723C2×C4×C67C22×D411yescharacteristic
724C2×C4×C67C22×D411yescharacteristic
725C2×C4×C67C22×D411yescharacteristic
726C2×C4×C67C22×D411yescharacteristic
727C2×C4×C67C22×D411yescharacteristic
728C2×C4×C67C22×D411yescharacteristic
729C2×C4×C67C2511yescharacteristic
730C22⋊D67—42no—
731C22⋊D67—42no—
732C22⋊D67—42no—
733C22⋊D67—42no—
734C22⋊D67—81no—
735C22⋊D67—81no—
736C22⋊D67—81no—
737C22⋊D67—81no—
738C22⋊D67—81no—
739C2×Dic67—21no—
740C2×Dic67—21no—
741C2×Dic67—21no—
742C2×Dic67—21no—
743C2×Dic67—21no—
744C2×Dic67—21no—
745C2×Dic67—21no—
746C2×Dic67—21no—
747C2×Dic67—21no—
748C2×Dic67—21no—
749C2×Dic67—21no—
750C2×Dic67—42no—
751C2×Dic67—81no—
752C2×Dic67—81no—
753D268—21no—
754D268—21no—
755D268—21no—
756D268—21no—
757D268—21no—
758D268—21no—
759D268—21no—
760D268—21no—
761D268—42no—
762D268—42no—
763D268—42no—
764D268—81no—
765D268—81no—
766D268C2×#4112yes—
767D268C2×#4112yes—
768C4×D67—42no—
769C4×D67—42no—
770C4×D67—42no—
771C4×D67—81no—
772C4×D67—81no—
773C4×D67—81no—
774C4×D67—81no—
775C4×D67—81no—
776C4×D67—81no—
777C4×D67—81no—
778C4×D67—81no—
779C4×D67—81no—
780C4×D67—81no—
781C4×D67—81no—
782C4×D67—81no—
783C4×D67—81no—
784C4×D67—81no—
785Dic134—21no—
786Dic134—21no—
787Dic134—21no—
788Dic134—21no—
789Dic134—21no—
790Dic134—21no—
791Dic134—81no—
792Dic134—81no—
793C8×C67—21no—
794C8×C67—21no—
795C8×C67—21no—
796C8×C67—21no—
797C8×C67—21no—
798C8×C67—21no—
799C8×C67—21no—
800C8×C67C2×#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×C67C23×D411yescharacteristic
811C2×D67—22no—
812C2×D67—22no—
813C2×D67—41no—
814C2×D67—41no—
815C2×D67—41no—
816C2×D67—41no—
817C2×D67—41no—
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—
828C2×D67—162no—
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—21no—
840C4×C67C22×#4111yescharacteristic
841C4×C67#58511yescharacteristic
842Dic67—41no—
843Dic67—41no—
844Dic67—41no—
845Dic67—41no—
846Dic67—41no—
847Dic67—41no—
848Dic67—41no—
849Dic67—41no—
850Dic67—41no—
851Dic67—41no—
852Dic67—41no—
853#61548—671nomaximal, Sylow
854C2×C67—41no—
855C2×C67—41no—
856C2×C67—41no—
857C2×C67D4×#4111yescharacteristic
858C2×C67#358411yescharacteristic
859C2×C67#358511yescharacteristic
860D67—42no—
861D67—42no—
862D67—81no—
863D67—81no—
864D67—81no—
865#3521—671no—
866#3513—671no—
867#3394—671no—
868#3380—671no—
869#3376—671no—
870#3370—671no—
871#3353—671no—
872#3351—671no—
873#3351—671no—
874#3318—671no—
875#3315—671no—
876#3311—671no—
877#3306—671no—
878#3297—671no—
879#3296—671no—
880#3273—671no—
881#3273—671no—
882#3272—671no—
883#3183—671no—
884#3175—671no—
885#3174—671no—
886#3125—671no—
887#3122—671no—
888#3120—671no—
889#3118—671no—
890#3105—671no—
891#3102—671no—
892#2969D6711yescharacteristic, complemented
893#2946—671no—
894#2946—671no—
895C4×AGL(1,ℤ/8)—671no—
896C67#6154811yescharacteristic, complemented, Sylow
897C2×AGL(1,ℤ/8)—671no—
898C2×AGL(1,ℤ/8)—671no—
899C2×AGL(1,ℤ/8)—671no—
900#559—671no—
901#556—671no—
902#556—671no—
903#554—671no—
904#554—671no—
905#553—671no—
906#553—671no—
907#553—1341no—
908#553—1341no—
909#552—671no—
910#552—671no—
911#552—1341no—
912#551—1341no—
913#551—1341no—
914#551—1341no—
915#551—1341no—
916#547—671no—
917#547—671no—
918#546—671no—
919#546—671no—
920#546—671no—
921#546—671no—
922#546—1341no—
923D42—671no—
924#542—671no—
925#542—671no—
926#541—671no—
927#540—671no—
928#539—1341no—
929#539—1341no—
930#538—1341no—
931#538—1341no—
932#529—671no—
933#529—671no—
934#529—1341no—
935#529C2×D6711yescharacteristic
936C2×#126—1341no—
937#525—1341no—
938C2×#123—1341no—
939#520—671no—
940#520—671no—
941#518—671no—
942#518—671no—
943C4×#41—671no—
944C2×C4×D4—671no—
945#500—671no—
946#499—671no—
947#499—671no—
948#495—671no—
949#495—671no—
950#492—671no—
951#491—671no—
952#490—671no—
953#489—671no—
954#489—671no—
955#488—671no—
956#488—671no—
957#485—671no—
958#485—671no—
959#484—671no—
960#484—671no—
961#483—671no—
962#483—671no—
963#482—671no—
964#482—671no—
965#482—671no—
966#482—671no—
967#481—671no—
968#481—671no—
969#479—671no—
970#479—671no—
971#478—671no—
972#478—671no—
973#478—671no—
974#478—671no—
975#478—671no—
976#478—671no—
977#476—671no—
978#476—671no—
979#475—671no—
980#474—671no—
981#470—671no—
982#469—671no—
983#468—671no—
984#468—671no—
985#468—671no—
986#468—671no—
987#468—671no—
988#468—671no—
989#467—671no—
990#466—671no—
991#465—671no—
992#465—671no—
993#464—671no—
994#464—671no—
995#463—671no—
996#463—671no—
997#463—671no—
998#463—671no—
999#463—671no—
1000#463—671no—
1001#462—671no—
1002#461—671no—
1003#459—671no—
1004#459—671no—
1005#452—671no—
1006#452—671no—
1007#452—671no—
1008#452—671no—
1009#450—671no—
1010#450—671no—
1011#449—671no—
1012#449—671no—
1013#447—671no—
1014#447—671no—
1015#447—671no—
1016#447—671no—
1017#446C2×D6711yescharacteristic, complemented
1018C8×Q8C2×D6711yescharacteristic, complemented
1019#442—671no—
1020#442—671no—
1021#442—671no—
1022#442—671no—
1023#442—671no—
1024#441—671no—
1025#440—671no—
1026#440—671no—
1027#440—671no—
1028#440—671no—
1029#440—671no—
1030#440—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—
1046C4×D8—671no—
1047#436C2×D6711yescharacteristic, complemented
1048#436C2×D6711yescharacteristic, complemented
1049#436C2×D6711yescharacteristic, complemented
1050#435C2×D6711yescharacteristic, complemented
1051#435C2×D6711yescharacteristic, complemented
1052C8×D4C2×D6711yescharacteristic, complemented
1053#433C2×D6711yescharacteristic, complemented
1054#433C2×D6711yescharacteristic, complemented
1055#431C2×D6711yescharacteristic, complemented
1056#428—671no—
1057#428—671no—
1058#428—671no—
1059#418—671no—
1060#417—671no—
1061#416—671no—
1062#416—671no—
1063C2×#102—671no—
1064C2×#102—671no—
1065#405C2×D6711yescharacteristic, complemented
1066#405C2×D6711yescharacteristic, complemented
1067C4×M16C2×D6711yescharacteristic, complemented
1068C2×#41—671no—
1069C2×#41—671no—
1070C2×#41—671no—
1071C2×#41—1341no—
1072C22×D4—671no—
1073C22×D4—671no—
1074C22×D4—671no—
1075C22×D4—1341no—
1076C23×C4—1341no—
1077AGL(1,ℤ/8)—1344no—
1078AGL(1,ℤ/8)—1344no—
1079AGL(1,ℤ/8)—1344no—
1080C2×Q16—671no—
1081C2×Q16—671no—
1082C2×SD16—671no—
1083C2×SD16—671no—
1084C2×SD16—671no—
1085C2×SD16—671no—
1086C2×SD16—671no—
1087C2×SD16—671no—
1088C2×SD16—671no—
1089C2×SD16—671no—
1090C2×D8—671no—
1091C2×D8—671no—
1092C2×D8—671no—
1093C2×D8—671no—
1094C2×D8—671no—
1095C2×D8—671no—
1096C2×M16C22×D6711yescharacteristic
1097C2×M16C22×D6711yescharacteristic
1098C2×M16C22×D6711yescharacteristic
1099C2×M16C22×D6711yescharacteristic
1100C22×C8C22×D6711yescharacteristic
1101C22×C8C22×D6711yescharacteristic
1102C4⋊Q8—671no—
1103C4⋊Q8—671no—
1104C4⋊Q8—671no—
1105#127—671no—
1106#126—1341no—
1107#126—1341no—
1108#126—1341no—
1109#126—1341no—
1110#126—1341no—
1111#126—1341no—
1112#126—1341no—
1113#126—1341no—
1114#126—1341no—
1115#126—1341no—
1116#126—1341no—
1117#126—1341no—
1118#126—1341no—
1119#126—1341no—
1120#126D26811yescharacteristic
1121#126D26811yescharacteristic
1122#125—671no—
1123#125—671no—
1124#125—671no—
1125#125—671no—
1126#125—1341no—
1127#125—1341no—
1128#125—1341no—
1129#125—1341no—
1130#125D26811yescharacteristic
1131#124—671no—
1132#124—671no—
1133#124—671no—
1134#124—671no—
1135#124—1341no—
1136#124—1341no—
1137#124—1341no—
1138#124—1341no—
1139#124D26811yescharacteristic
1140#123—1341no—
1141#123—1341no—
1142#123—1341no—
1143#123—1341no—
1144#123—1341no—
1145#123—1341no—
1146#123—1341no—
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#123—1341no—
1160#123D26811yescharacteristic
1161#123D26811yescharacteristic
1162C22⋊Q8—671no—
1163C22⋊Q8—671no—
1164C22⋊Q8—671no—
1165C22⋊Q8—671no—
1166C22⋊Q8—671no—
1167C22⋊Q8—671no—
1168C22⋊Q8—1341no—
1169C22⋊Q8—1341no—
1170C22⋊Q8—1341no—
1171C22⋊Q8—1341no—
1172C22⋊Q8—1341no—
1173C22⋊Q8—1341no—
1174C22⋊Q8—1341no—
1175C22⋊Q8—1341no—
1176C22⋊Q8—1341no—
1177C22⋊Q8—1341no—
1178C22⋊Q8D26811yescharacteristic
1179#121—671no—
1180#121—671no—
1181#121—671no—
1182#121—671no—
1183#121—671no—
1184#121—671no—
1185#121—1341no—
1186#121—1341no—
1187#121—1341no—
1188#121—1341no—
1189#121—1341no—
1190#121—1341no—
1191#121—1341no—
1192#121—1341no—
1193#121—1341no—
1194#121—1341no—
1195#121D26811yescharacteristic
1196#120—1341no—
1197#120—1341no—
1198#120—1341no—
1199#120—1341no—
1200#120—1341no—
1201#120—1341no—
1202C4×Q8—671no—
1203C4×Q8—671no—
1204C4×Q8—671no—
1205C4×Q8—671no—
1206C4×Q8—671no—
1207C4×Q8—671no—
1208C4×Q8—1341no—
1209C4×Q8C22×D6711yescharacteristic
1210C4×D4—671no—
1211C4×D4—671no—
1212C4×D4—671no—
1213C4×D4—671no—
1214C4×D4—671no—
1215C4×D4—671no—
1216C4×D4—671no—
1217C4×D4—671no—
1218C4×D4—671no—
1219C4×D4—671no—
1220C4×D4—671no—
1221C4×D4—671no—
1222C4×D4—671no—
1223C4×D4—671no—
1224C4×D4—1341no—
1225C4×D4—1341no—
1226C4×D4—1341no—
1227C4×D4—1341no—
1228C4×D4—1341no—
1229C4×D4—1341no—
1230C4×D4—1341no—
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×D4—1341no—
1241C4×D4C22×D6711yescharacteristic
1242C4×D4C22×D6711yescharacteristic
1243C4×D4C22×D6711yescharacteristic
1244#117—671no—
1245#117—671no—
1246#117—671no—
1247#117—1341no—
1248#117—1341no—
1249#117—1341no—
1250#117—1341no—
1251#117—1341no—
1252#117—1341no—
1253#117—1341no—
1254#117—1341no—
1255#117C22×D6711yescharacteristic
1256#117C22×D6711yescharacteristic
1257C2×C4⋊C4—671no—
1258C2×C4⋊C4—671no—
1259C2×C4⋊C4—671no—
1260C2×C4⋊C4—1341no—
1261C2×C4⋊C4—1341no—
1262C2×C4⋊C4—1341no—
1263C2×C4⋊C4—1341no—
1264C2×C4⋊C4—1341no—
1265C2×C22⋊C4—1341no—
1266C2×C22⋊C4—1341no—
1267C2×C22⋊C4—1341no—
1268C2×C22⋊C4—1341no—
1269C2×C22⋊C4—1341no—
1270C2×C22⋊C4—1341no—
1271C2×C22⋊C4—1341no—
1272C2×C22⋊C4—1341no—
1273C2×C22⋊C4—1341no—
1274C2×C42—1341no—
1275C2×C42C22×D6711yescharacteristic
1276#107—671no—
1277#107—671no—
1278#107—671no—
1279#107—671no—
1280#107—671no—
1281#107—671no—
1282#107—671no—
1283#107—671no—
1284#106—671no—
1285#106—671no—
1286#106—671no—
1287#106—671no—
1288#106—671no—
1289#106—671no—
1290#106—671no—
1291#106—671no—
1292C4⋊C8C22×D6711yescharacteristic
1293C4⋊C8C22×D6711yescharacteristic
1294C4⋊C8C22×D6711yescharacteristic
1295C4⋊C8C22×D6711yescharacteristic
1296C4⋊C8C22×D6711yescharacteristic
1297C4⋊C8C22×D6711yescharacteristic
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#103—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—
1329#102—671no—
1330C22⋊C8C22×D6711yescharacteristic
1331C22⋊C8C22×D6711yescharacteristic
1332C22⋊C8C22×D6711yescharacteristic
1333C22⋊C8C22×D6711yescharacteristic
1334C22⋊C8C22×D6711yescharacteristic
1335C22⋊C8C22×D6711yescharacteristic
1336#97C22×D6711yescharacteristic
1337#97C22×D6711yescharacteristic
1338#97C22×D6711yescharacteristic
1339#97C22×D6711yescharacteristic
1340C4×C8C22×D6711yescharacteristic
1341C4×C8C22×D6711yescharacteristic
1342C4×C8C22×D6711yescharacteristic
1343C4×C8C22×D6711yescharacteristic
1344C4×C8C22×D6711yescharacteristic
1345C4×C8C22×D6711yescharacteristic
1346C24—1341no—
1347C24—1341no—
1348C24—1341no—
1349#41—2681no—
1350#41—2681no—
1351#41—2681no—
1352#41—5362no—
1353#41—1342no—
1354#41—1342no—
1355#41—1342no—
1356C2×Q8—671no—
1357C2×Q8—671no—
1358C2×Q8—671no—
1359C2×Q8—1341no—
1360C2×Q8—1341no—
1361C2×Q8C2×D26811yescharacteristic
1362C2×D4—2681no—
1363C2×D4—2681no—
1364C2×D4—2681no—
1365C2×D4—5362no—
1366C2×D4—671no—
1367C2×D4—671no—
1368C2×D4—671no—
1369C2×D4—671no—
1370C2×D4—671no—
1371C2×D4—1342no—
1372C2×D4—1342no—
1373C2×D4—1342no—
1374C2×D4—1341no—
1375C2×D4—1341no—
1376C2×D4—1341no—
1377C2×D4—1341no—
1378C2×D4—1341no—
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×D26811yescharacteristic
1389C2×D4C2×D26811yescharacteristic
1390C2×D4C2×D26811yescharacteristic
1391C22×C4—5362no—
1392C22×C4—1341no—
1393C22×C4—1341no—
1394C22×C4—1341no—
1395C22×C4—1341no—
1396C22×C4—1341no—
1397C22×C4—1341no—
1398C22×C4—1341no—
1399C22×C4—1341no—
1400C22×C4—1341no—
1401C22×C4—1341no—
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×C4C2×D26811yescharacteristic
1413C22×C4C2×D26811yescharacteristic
1414C22×C4C23×D6711yescharacteristic
1415C22×C4C23×D6711yescharacteristic
1416C22×C4C23×D6711yescharacteristic
1417Q16—2681no—
1418Q16—2681no—
1419SD16—2681no—
1420SD16—2681no—
1421SD16—1342no—
1422SD16—1342no—
1423SD16—1342no—
1424SD16—1342no—
1425SD16—1342no—
1426SD16—1342no—
1427D8—2681no—
1428D8—2681no—
1429D8—674no—
1430D8—1342no—
1431D8—1342no—
1432D8—1342no—
1433M16—22no—
1434M16—22no—
1435M16—22no—
1436M16—41no—
1437C2×C8—41no—
1438C2×C8—41no—
1439C2×C8C23×D6711yescharacteristic
1440C2×C8C23×D6711yescharacteristic
1441C2×C8C23×D6711yescharacteristic
1442C2×C8C23×D6711yescharacteristic
1443C2×C8C23×D6711yescharacteristic
1444C2×C8C23×D6711yescharacteristic
1445C2×C8C23×D6711yescharacteristic
1446C2×C8C23×D6711yescharacteristic
1447C4⋊C4—671no—
1448C4⋊C4—671no—
1449C4⋊C4—671no—
1450C4⋊C4—671no—
1451C4⋊C4—671no—
1452C4⋊C4—671no—
1453C4⋊C4—671no—
1454C4⋊C4—671no—
1455C4⋊C4—1341no—
1456C4⋊C4—1341no—
1457C4⋊C4—1341no—
1458C4⋊C4—1341no—
1459C4⋊C4—1341no—
1460C4⋊C4—1341no—
1461C4⋊C4—1341no—
1462C4⋊C4—1341no—
1463C4⋊C4—1341no—
1464C4⋊C4—1341no—
1465C4⋊C4—1341no—
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⋊C4—1341no—
1478C4⋊C4—1341no—
1479C4⋊C4—1341no—
1480C4⋊C4—1341no—
1481C4⋊C4—1341no—
1482C4⋊C4C2×D26811yescharacteristic
1483C4⋊C4C2×D26811yescharacteristic
1484C4⋊C4C2×D26811yescharacteristic
1485C4⋊C4C2×D26811yescharacteristic
1486C4⋊C4C2×D26811yescharacteristic
1487C4⋊C4C2×D26811yescharacteristic
1488C4⋊C4C2×D26811yescharacteristic
1489C4⋊C4C2×D26811yescharacteristic
1490C4⋊C4C2×D26811yescharacteristic
1491C4⋊C4C2×D26811yescharacteristic
1492C22⋊C4—1341no—
1493C22⋊C4—1341no—
1494C22⋊C4—1341no—
1495C22⋊C4—1341no—
1496C22⋊C4—1341no—
1497C22⋊C4—1341no—
1498C22⋊C4—1341no—
1499C22⋊C4—1341no—
1500C22⋊C4—1341no—
1501C22⋊C4—1341no—
1502C22⋊C4—1341no—
1503C22⋊C4—1341no—
1504C22⋊C4—1341no—
1505C22⋊C4—1341no—
1506C22⋊C4—1341no—
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⋊C4—1341no—
1527C22⋊C4—1341no—
1528C22⋊C4—1341no—
1529C22⋊C4C2×D26811yescharacteristic
1530C22⋊C4C2×D26811yescharacteristic
1531C22⋊C4C2×D26811yescharacteristic
1532C22⋊C4C2×D26811yescharacteristic
1533C22⋊C4C2×D26811yescharacteristic
1534C22⋊C4C2×D26811yescharacteristic
1535C22⋊C4C2×D26811yescharacteristic
1536C22⋊C4C2×D26811yescharacteristic
1537C22⋊C4C2×D26811yescharacteristic
1538C22⋊C4C2×D26811yescharacteristic
1539C42—1341no—
1540C42—1341no—
1541C42—1341no—
1542C42—1341no—
1543C42—1341no—
1544C42—1341no—
1545C42—1341no—
1546C42—1341no—
1547C42—1341no—
1548C42C2×D26811yescharacteristic
1549C42C2×D26811yescharacteristic
1550C42C23×D6711yescharacteristic
1551C42C23×D6711yescharacteristic
1552C42C23×D6711yescharacteristic
1553C42C23×D6711yescharacteristic
1554C23—2682no—
1555C23—2682no—
1556C23—2682no—
1557C23—2682no—
1558C23—5361no—
1559C23—5361no—
1560C23—5361no—
1561C23—5361no—
1562C23—5361no—
1563C23—1341no—
1564C23—1341no—
1565C23—1341no—
1566C23—1341no—
1567C23—1341no—
1568C23C22×D26811yescharacteristic
1569C23C22×D26811yescharacteristic
1570C23C22×D26811yescharacteristic
1571Q8—41no—
1572Q8—5361no—
1573Q8—5361no—
1574Q8—1341no—
1575Q8—1341no—
1576Q8—1341no—
1577Q8—1341no—
1578Q8—1341no—
1579Q8—1341no—
1580D4—41no—
1581D4—41no—
1582D4—41no—
1583D4—2682no—
1584D4—2682no—
1585D4—2682no—
1586D4—2682no—
1587D4—2682no—
1588D4—2682no—
1589D4—2682no—
1590D4—5361no—
1591D4—5361no—
1592D4—5361no—
1593D4—5361no—
1594D4—5361no—
1595D4—5361no—
1596D4—5361no—
1597D4—672no—
1598D4—672no—
1599D4—1341no—
1600D4—1341no—
1601D4—1341no—
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—41no—
1614C2×C4—41no—
1615C2×C4—2682no—
1616C2×C4—2682no—
1617C2×C4—2682no—
1618C2×C4—2682no—
1619C2×C4—5361no—
1620C2×C4—5361no—
1621C2×C4—5361no—
1622C2×C4—5361no—
1623C2×C4—5361no—
1624C2×C4—5361no—
1625C2×C4—5361no—
1626C2×C4—5361no—
1627C2×C4—5361no—
1628C2×C4—5361no—
1629C2×C4—5361no—
1630C2×C4—5361no—
1631C2×C4—5361no—
1632C2×C4—5361no—
1633C2×C4—5361no—
1634C2×C4—5361no—
1635C2×C4—1341no—
1636C2×C4—1341no—
1637C2×C4—1341no—
1638C2×C4—1341no—
1639C2×C4—1341no—
1640C2×C4—1341no—
1641C2×C4—1341no—
1642C2×C4—1341no—
1643C2×C4—1341no—
1644C2×C4—1341no—
1645C2×C4—1341no—
1646C2×C4C22×D26811yescharacteristic
1647C2×C4C22×D26811yescharacteristic
1648C2×C4C22×D26811yescharacteristic
1649C2×C4C22×D26811yescharacteristic
1650C2×C4C22×D26811yescharacteristic
1651C2×C4C22×D26811yescharacteristic
1652C2×C4C22×D26811yescharacteristic
1653C2×C4C22×D26811yescharacteristic
1654C2×C4C22×D26811yescharacteristic
1655C2×C4C22×D26811yescharacteristic
1656C2×C4C22×D26811yescharacteristic
1657C2×C4C24×D6711yescharacteristic
1658C8—21no—
1659C8—21no—
1660C8—21no—
1661C8—21no—
1662C8—21no—
1663C8—21no—
1664C8—21no—
1665C8#41×D6712yes—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—21no—
1670C22—21no—
1671C22—21no—
1672C22—21no—
1673C22—21no—
1674C22—21no—
1675C22—2681no—
1676C22—2681no—
1677C22—2681no—
1678C22—2681no—
1679C22—2681no—
1680C22—2681no—
1681C22—2681no—
1682C22—2681no—
1683C22—2681no—
1684C22—2681no—
1685C22—2681no—
1686C22—2681no—
1687C22—2681no—
1688C22—5364no—
1689C22—10722no—
1690C22—10722no—
1691C22—1342no—
1692C22—1342no—
1693C22C23×D26811yescharacteristic
1694C4—21no—
1695C4—21no—
1696C4—21no—
1697C4—21no—
1698C4—21no—
1699C4—21no—
1700C4—21no—
1701C4—21no—
1702C4—21no—
1703C4—21no—
1704C4—21no—
1705C4—2681no—
1706C4—2681no—
1707C4—2681no—
1708C4—2681no—
1709C4—2681no—
1710C4—2681no—
1711C4—2681no—
1712C4—2681no—
1713C4—2681no—
1714C4—2681no—
1715C4—2681no—
1716C4C2×#41×D6711yescharacteristic
1717C4#1686423211yescharacteristic
1718C2—41no—
1719C2—41no—
1720C2—41no—
1721C2—2682no—
1722C2—2682no—
1723C2—5361no—
1724C2—5361no—
1725C2—5361no—
1726C2#41×D26811yescharacteristic
1727C2#2257498311yescharacteristic
1728C2#2257499011yescharacteristic
subgroupG/H
centerC22C23×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#2969C2
socleC22×C67C23×D4
hypercenter#2969D67
hypocenterC67#61548
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #529 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #22574281C2semidirect
2. #22574153C2semidirect
3. #22573207C2semidirect
4. #22573077C2semidirect
5. #22573038C2semidirect
6. #22572964C2semidirect
7. #22572794C2semidirect
8. #22572771C2semidirect
9. #22572771C2semidirect
10. #22572352C2semidirect
11. #22572307C2semidirect
12. #22572247C2semidirect
13. #22572172C2semidirect
14. #22572061C2semidirect
15. #22572046C2semidirect
16. #22571821C2semidirect
17. #22571821C2semidirect
18. #22571811C2semidirect
19. #22570938C2semidirect
20. #22570848C2semidirect
21. #22570837C2semidirect
22. #22570488C2semidirect
23. #22570453C2semidirect
24. #22570425C2semidirect
25. #22570395C2semidirect
26. #22570258C2semidirect
27. #22570229C2semidirect
28. #22569043C2semidirect
29. #22569043C2semidirect
30. C4×#14524071C2semidirect
31. C67×#2969C2semidirect
35. #16864131C22semidirect
36. #16864119C22semidirect
37. #16864116C22semidirect
38. #16864106C22semidirect
39. #16864106C22semidirect
44. #16864086C22semidirect
45. #16864086C22semidirect
55. #16864042C22semidirect
56. #16864042C22semidirect
58. D4×D268C22semidirect
59. #16864017C22semidirect
60. #16864017C22semidirect
61. #16864008C22semidirect
67. #16863930C22semidirect
68. #16863930C22semidirect
74. #16863876C22semidirect
75. #16863870C22semidirect
76. #16863870C22semidirect
77. C4×#11761628C22semidirect
78. C2×C4×D268C22semidirect
79. #16863801C22semidirect
80. #16863798C22semidirect
81. #16863798C22semidirect
82. #16863780C22semidirect
83. #16863780C22semidirect
84. #16863769C22semidirect
85. #16863765C22semidirect
86. #16863761C22semidirect
87. #16863756C22semidirect
88. #16863756C22semidirect
89. #16863751C22semidirect
90. #16863751C22semidirect
91. #16863738C22semidirect
92. #16863738C22semidirect
93. #16863732C22semidirect
94. #16863732C22semidirect
95. #16863727C22semidirect
96. #16863727C22semidirect
97. #16863721C22semidirect
98. #16863721C22semidirect
99. #16863721C22semidirect
100. #16863721C22semidirect
101. #16863715C22semidirect
102. #16863715C22semidirect
103. #16863704C22semidirect
104. #16863704C22semidirect
105. #16863697C22semidirect
106. #16863697C22semidirect
107. #16863697C22semidirect
108. #16863697C22semidirect
109. #16863697C22semidirect
110. #16863697C22semidirect
111. #16863687C22semidirect
112. #16863687C22semidirect
113. #16863682C22semidirect
114. #16863677C22semidirect
115. #16863654C22semidirect
117. #16863642C22semidirect
118. #16863642C22semidirect
119. #16863642C22semidirect
120. #16863642C22semidirect
121. #16863642C22semidirect
122. #16863642C22semidirect
123. #16863637C22semidirect
125. #16863625C22semidirect
126. #16863625C22semidirect
127. #16863619C22semidirect
128. #16863619C22semidirect
131. #16863612C22semidirect
132. #16863612C22semidirect
133. #16863612C22semidirect
134. #16863612C22semidirect
135. #16863607C22semidirect
136. #16863602C22semidirect
141. #16863560C22semidirect
142. #16863560C22semidirect
143. #16863549C22semidirect
144. #16863549C22semidirect
149. #16863532C22semidirect
150. #16863532C22semidirect
153. #16863509C22semidirect
154. #16863509C22semidirect
155. #16863509C22semidirect
156. #16863504C22semidirect
157. #16863498C22semidirect
158. #16863498C22semidirect
159. #16863498C22semidirect
160. #16863498C22semidirect
161. #16863498C22semidirect
162. #16863498C22semidirect
163. C4×Dic268C22semidirect
164. C4×#11761617C22semidirect
165. C4×#11761617C22semidirect
166. C4×#11761617C22semidirect
167. C4×#11761617C22semidirect
168. C4×#11761617C22semidirect
169. C4×#11761617C22semidirect
170. C4×#11761617C22semidirect
171. C4×#11761617C22semidirect
176. C4×D536C22semidirect
177. C4×D536C22semidirect
178. C4×D536C22semidirect
179. #16863438C22semidirect
180. #16863438C22semidirect
181. #16863438C22semidirect
182. #16863402C22semidirect
183. #16863398C22semidirect
185. #16863393C22semidirect
186. C2×#14523965C22semidirect
187. C2×#14523965C22semidirect
189. #446×C67C22semidirect
190. C8×Q8×C67C22semidirect
191. #436×C67C22semidirect
192. #436×C67C22semidirect
193. #436×C67C22semidirect
194. #435×C67C22semidirect
195. #435×C67C22semidirect
196. C8×D4×C67C22semidirect
197. #433×C67C22semidirect
198. #433×C67C22semidirect
199. #431×C67C22semidirect
200. #405×C67C22semidirect
201. #405×C67C22semidirect
202. C4×M16×C67C22semidirect
558. D536#41semidirect
892. #2969D67semidirect
896. C67#61548semidirect
1017. #446C2×D67semidirect
1018. C8×Q8C2×D67semidirect
1047. #436C2×D67semidirect
1048. #436C2×D67semidirect
1049. #436C2×D67semidirect
1050. #435C2×D67semidirect
1051. #435C2×D67semidirect
1052. C8×D4C2×D67semidirect
1053. #433C2×D67semidirect
1054. #433C2×D67semidirect
1055. #431C2×D67semidirect
1065. #405C2×D67semidirect
1066. #405C2×D67semidirect
1067. C4×M16C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225742812
#225741532
#225732072
#225730772
#225730382
#225729642
#225727942
#225727712
#225723522
#225723072
#225722472
#225721722
#225720612
#225720462
#225718212
#225718112
#225709382
#225708482
#225708372
#225704882
#225704532
#225704252
#225703952
#225702582
#225702292
#225690432
C4×#145240712
C67×#29692
#6154867