Finite Group Databasebeta

← #11685773

Subgroups — #11685773

Order 768.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86137C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×#3102C211yesmaximal, characteristic, complemented
4#83123C211yesmaximal, characteristic, complemented
5#82531C211yesmaximal, characteristic, complemented
6#81507C212yesmaximal, complemented
7#81360C212yesmaximal, complemented
8#81225C212yesmaximal, complemented
9#81158C212yesmaximal, complemented
10#80584C212yesmaximal, complemented
11#80521C212yesmaximal, complemented
12#80219C212yesmaximal, complemented
13#80073C212yesmaximal, complemented
14#79708C211yesmaximal, characteristic, complemented
15#79703C211yesmaximal, characteristic, complemented
16#79632C211yesmaximal, characteristic, complemented
17SD16×Dic6C211yesmaximal, characteristic, complemented
18#79622C211yesmaximal, characteristic, complemented
19#79621C211yesmaximal, characteristic, complemented
20#79576C211yesmaximal, characteristic, complemented
21#79570C211yesmaximal, characteristic, complemented
22#79269C211yesmaximal, characteristic, complemented
23#79266C211yesmaximal, characteristic, complemented
24#61860—31nomaximal, Sylow
25C3×#529C2211yescharacteristic
26C3×C4×#41C2211yescharacteristic
27#5827C2212yes—
28#5707—22no—
29#5690C2212yes—
30#5681C2212yes—
31#5667—22no—
32#5643C2212yes—
33#5619C2212yes—
34#5585C2211yescharacteristic
35#5570C2211yescharacteristic
36#5570C2212yes—
37Q8×Dic6C2211yescharacteristic
38Q8×Dic6C2211yescharacteristic
39#5553C2211yescharacteristic
40#5552—21no—
41#5551—21no—
42#5543—21no—
43#5543—21no—
44#5543C2211yescharacteristic
45#5543C2211yescharacteristic
46D4×Dic6—22no—
47D4×Dic6C2212yes—
48D4×Dic6C2211yescharacteristic
49#5534—21no—
50#5526—21no—
51#5519—22no—
52#5519C2212yes—
53#5477C2211yescharacteristic
54#5470—21no—
55#5470C2211yescharacteristic
56C2×#869—21no—
57C2×#869C2211yescharacteristic
58C3×#485C2211yescharacteristic
59C3×#482C2211yescharacteristic
60C3×#479C2211yescharacteristic
61C3×#478C2211yescharacteristic
62C3×#464C2211yescharacteristic
63C3×#463C2211yescharacteristic
64C3×#452C2211yescharacteristic
65C3×#449C2211yescharacteristic
66C3×C4×Q16C2211yescharacteristic
67C3×C4×SD16C2211yescharacteristic
68C3×C4×SD16C2211yescharacteristic
69C3×C4×D8C2211yescharacteristic
70C3×#431C2211yescharacteristic
71#5238C2212yes—
72#5185C2212yes—
73#5184C2212yes—
74#5165C2212yes—
75#5163C2212yes—
76Dic3×SD16C2212yes—
77Dic3×SD16C2212yes—
78#5152C2212yes—
79#5150C2212yes—
80#5064C2212yes—
81#5055C2212yes—
82#5043C2212yes—
83#5033C2212yes—
84#5027C2211yescharacteristic
85#5026C2212yes—
86#5021C2211yescharacteristic
87#5021C2211yescharacteristic
88#5020C2211yescharacteristic
89#5015C2211yescharacteristic
90#5014C2212yes—
91#5008C2211yescharacteristic
92#5008C2211yescharacteristic
93#5007C2211yescharacteristic
94#5003C2212yes—
95#4926C2211yescharacteristic
96#4891C2212yes—
97#4890C2212yes—
98#4876C2212yes—
99#4876C2212yes—
100#4871C2212yes—
101#4870C2212yes—
102#4858C2212yes—
103#4855C2212yes—
104#4842C2212yes—
105#4842C2212yes—
106#4828C2212yes—
107#4828C2212yes—
108#4817C2212yes—
109#4800C2212yes—
110#4799C2212yes—
111#4799C2212yes—
112#4794C2212yes—
113#4791C2212yes—
114#4791C2212yes—
115#4788C2212yes—
116#4785C2212yes—
117#4764C2212yes—
118#4763C2212yes—
119#4763C2212yes—
120#4761C2212yes—
121#4761C2212yes—
122#4760C2212yes—
123#4756C2212yes—
124#4735C2212yes—
125#4735C2212yes—
126#4720C2212yes—
127#4720C2212yes—
128#4694C2211yescharacteristic
129#4694C2211yescharacteristic
130#4680C2211yescharacteristic
131#4680C2211yescharacteristic
132#4679C2211yescharacteristic
133#4679C2211yescharacteristic
134C8×Dic6C2211yescharacteristic
135C8×Dic6C2211yescharacteristic
136#3554—31no—
137#3503—31no—
138#3388—32no—
139#3387—31no—
140#3384—32no—
141#3384—31no—
142#3381—31no—
143Q8×SD16—31no—
144#3375—31no—
145#3373—32no—
146#3371—32no—
147#3366—31no—
148#3362—31no—
149#3361—31no—
150#3244—32no—
151#3241—32no—
152#3238—31no—
153#3227—31no—
154#3125—32no—
155#3119—32no—
156#3115—31no—
157#3102D311yescharacteristic, complemented
158#2985—31no—
159C2×C3×#41C2311yescharacteristic
160C2×#235—21no—
161C2×#235—21no—
162C22×Dic6—21no—
163C22×Dic6—22no—
164C22×Dic6—21no—
165C2×C3×Q16C2311yescharacteristic
166C2×C3×SD16C2311yescharacteristic
167C2×C3×SD16C2311yescharacteristic
168C2×C3×D8C2311yescharacteristic
169C3×#126—21no—
170C3×#125C2311yescharacteristic
171C3×#124C2311yescharacteristic
172C3×#123—21no—
173C3×C22⋊Q8C2311yescharacteristic
174C3×#121C2311yescharacteristic
175C3×C4×Q8C2311yescharacteristic
176C3×C4×Q8C2311yescharacteristic
177C3×C4×Q8C2311yescharacteristic
178C3×C4×D4—21no—
179C3×C4×D4—21no—
180C3×C4×D4—21no—
181C3×C4×D4C2311yescharacteristic
182C3×C4×D4C2311yescharacteristic
183C3×C4×D4C2311yescharacteristic
184C3×#117—21no—
185C3×#117—21no—
186C3×#117C2311yescharacteristic
187C2×C3×C42—21no—
188C2×C3×C42C2311yescharacteristic
189#947C2312yes—
190Q8×Dic3C2312yes—
191Q8×Dic3C2312yes—
192Q8×Dic3C2312yes—
193C2×#215C2312yes—
194#940C2312yes—
195#939—22no—
196#938—22no—
197D4×Dic3—22no—
198D4×Dic3—22no—
199D4×Dic3C2312yes—
200D4×Dic3C2312yes—
201D4×Dic3C2312yes—
202C2×#213C2312yes—
203#930—21no—
204#930—21no—
205#930C2312yes—
206#926—22no—
207#926C2312yes—
208C2×C4⋊Dic3—21no—
209C2×C4⋊Dic3—22no—
210C2×C4⋊Dic3—21no—
211C2×C4⋊Dic3—21no—
212C2×C4⋊Dic3C2312yes—
213#924—21no—
214#924—21no—
215#924—22no—
216#924—21no—
217#924D412yes—
218#924D411yescharacteristic
219#924D411yescharacteristic
220#898—22no—
221#897—22no—
222#897—22no—
223#896—22no—
224#896—22no—
225#894—22no—
226#893C2312yes—
227#893C2312yes—
228D3×C4⋊C4—22no—
229#890—22no—
230#890—22no—
231#890—22no—
232#890C2312yes—
233#890C2312yes—
234#890C2312yes—
235#888—22no—
236#888—22no—
237#888C2312yes—
238#888C2312yes—
239#888C2312yes—
240#886—22no—
241#886—22no—
242#885—22no—
243#885—22no—
244#884—22no—
245#883—22no—
246#883—22no—
247#883—22no—
248#67⋊C4—22no—
249#878—22no—
250#878—22no—
251#878—22no—
252#878—22no—
253#878—22no—
254#878—22no—
255#878—22no—
256#875—21no—
257#875—21no—
258#874C2311yescharacteristic
259C4×D12—21no—
260C4×D12—21no—
261C4×D12C2312yes—
262#870—22no—
263#870D412yes—
264#869—22no—
265#869—21no—
266#869—21no—
267#869—21no—
268#869—22no—
269#869—21no—
270#869—21no—
271#869D411yescharacteristic
272#869D411yescharacteristic
273#869C2311yescharacteristic
274#869C2311yescharacteristic
275#869C2311yescharacteristic
276#869C2312yes—
277C4×Dic6—21no—
278C4×Dic6—21no—
279C4×Dic6—22no—
280C4×Dic6—21no—
281C4×Dic6C2312yes—
282C4×Dic6C2311yescharacteristic
283C4×Dic6C2311yescharacteristic
284C3×#107C2311yescharacteristic
285C3×#107C2311yescharacteristic
286C3×#106C2311yescharacteristic
287C3×#106C2311yescharacteristic
288C3×C4⋊C8C2311yescharacteristic
289C3×C4⋊C8C2311yescharacteristic
290C3×#103C2311yescharacteristic
291C3×#103C2311yescharacteristic
292C3×#103C2311yescharacteristic
293C3×#103C2311yescharacteristic
294C3×#102C2311yescharacteristic
295C3×#102C2311yescharacteristic
296C3×#102C2311yescharacteristic
297C3×#102C2311yescharacteristic
298C3×C22⋊C8C2311yescharacteristic
299C3×C22⋊C8C2311yescharacteristic
300C3×C4×C8C2311yescharacteristic
301C3×C4×C8C2311yescharacteristic
302#835C2312yes—
303#835C2312yes—
304#835C2312yes—
305#832C2312yes—
306#832C2312yes—
307#832C2312yes—
308#830C2312yes—
309#821C2312yes—
310#821C2312yes—
311#821C2312yes—
312#821C2312yes—
313#817C2312yes—
314#817C2312yes—
315#817C2312yes—
316#817C2312yes—
317#815C2312yes—
318#815C2312yes—
319Dic3⋊C8C2312yes—
320Dic3⋊C8C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323C8×Dic3C2312yes—
324C8×Dic3C2312yes—
325#809C2312yes—
326#809C2312yes—
327#808C2312yes—
328#808C2312yes—
329#808C2312yes—
330#807C2312yes—
331#807C2312yes—
332#807C2312yes—
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4⋊(C3⋊C8)C2311yescharacteristic
335#803C2312yes—
336#562—62no—
337#559—32no—
338#559—31no—
339Q82—31no—
340Q82—31no—
341#557—32no—
342#557—31no—
343#554—32no—
344#554—31no—
345#554—31no—
346#554—61no—
347#554—61no—
348#550—31no—
349D4×Q8—32no—
350D4×Q8—31no—
351D4×Q8—62no—
352#548—61no—
353#547—61no—
354#544—32no—
355#544—62no—
356#542—32no—
357#542—61no—
358#540—32no—
359#539—62no—
360#536—61no—
361#533—31no—
362#533—61no—
363#532—31no—
364C2×C4⋊Q8—31no—
365C2×C4⋊Q8—61no—
366#529C2×D311yescharacteristic
367#520—32no—
368C4×#41C2×D311yescharacteristic
369#501—32no—
370#501—32no—
371#501—32no—
372#499—32no—
373#498—32no—
374#498—31no—
375#498—31no—
376#490—32no—
377#489—32no—
378#489—32no—
379#488—32no—
380#486—32no—
381#486—31no—
382#486—31no—
383#485C2×D311yescharacteristic
384#483—32no—
385#482—32no—
386#482C2×D311yescharacteristic
387#481—32no—
388#481—32no—
389#480—32no—
390#479—32no—
391#479—32no—
392#479C2×D311yescharacteristic
393#478—32no—
394#478—32no—
395#478—32no—
396#478—32no—
397#478C2×D311yescharacteristic
398#477—31no—
399#477—31no—
400#476—31no—
401#476—31no—
402#476—32no—
403#476—32no—
404#476—32no—
405#476—32no—
406#476—32no—
407#475—31no—
408#475—32no—
409#475—32no—
410#474—31no—
411#474—32no—
412#464—32no—
413#464C2×D311yescharacteristic
414#463—32no—
415#463C2×D311yescharacteristic
416#460—32no—
417#460—31no—
418#459—32no—
419#459—31no—
420#452C2×D311yescharacteristic
421#449—32no—
422#449C2×D311yescharacteristic
423#446—32no—
424#446—32no—
425#446—31no—
426#446—31no—
427C8×Q8—31no—
428C8×Q8—31no—
429#442—32no—
430#442—32no—
431#442—32no—
432#441—32no—
433#440—32no—
434#440—32no—
435C4×Q16C2×D311yescharacteristic
436C4×SD16—32no—
437C4×SD16—32no—
438C4×SD16—32no—
439C4×SD16C2×D311yescharacteristic
440C4×SD16C2×D311yescharacteristic
441C4×D8—32no—
442C4×D8C2×D311yescharacteristic
443#433—32no—
444#433—32no—
445#432—31no—
446#431C2×D311yescharacteristic
447C3×#41—22no—
448C3×#41—22no—
449C2×C3×Q8C2411yescharacteristic
450C2×C3×Q8C2411yescharacteristic
451C2×C3×D4—21no—
452C2×C3×D4—21no—
453C2×C3×D4C2411yescharacteristic
454C2×C3×D4C2411yescharacteristic
455C22×C3×C4—21no—
456C22×C3×C4—21no—
457C22×C3×C4—21no—
458C22×C3×C4—21no—
459C22×C3×C4C2×D411yescharacteristic
460C22×C3×C4C2×D411yescharacteristic
461C22×C3×C4C2411yescharacteristic
462C2×#67—22no—
463C2×#67—22no—
464C2×#67—22no—
465C22×Dic3—22no—
466C22×Dic3—22no—
467C22×Dic3—22no—
468C22×Dic3—22no—
469#235—82no—
470#235—82no—
471C2×D12—21no—
472C2×D12—21no—
473C2×D12C2412yes—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×Dic6—22no—
478C2×Dic6—21no—
479C2×Dic6—21no—
480C2×Dic6—21no—
481C2×Dic6—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6—82no—
485C2×Dic6—84no—
486C2×Dic6—82no—
487C2×Dic6C2×D411yescharacteristic
488C2×Dic6C2×D411yescharacteristic
489C2×Dic6C2×D412yes—
490C3×Q16—22no—
491C3×SD16—22no—
492C3×SD16—22no—
493C3×D8—22no—
494C2×C3×C8C2411yescharacteristic
495C2×C3×C8C2411yescharacteristic
496C2×C3×C8C2411yescharacteristic
497C2×C3×C8C2411yescharacteristic
498C3×C4⋊C4—21no—
499C3×C4⋊C4—21no—
500C3×C4⋊C4—21no—
501C3×C4⋊C4—21no—
502C3×C4⋊C4—21no—
503C3×C4⋊C4—21no—
504C3×C4⋊C4C2411yescharacteristic
505C3×C4⋊C4C2411yescharacteristic
506C3×C4⋊C4C2411yescharacteristic
507C3×C4⋊C4C2411yescharacteristic
508C3×C22⋊C4—21no—
509C3×C22⋊C4—21no—
510C3×C22⋊C4—21no—
511C3×C22⋊C4—21no—
512C3×C22⋊C4—21no—
513C3×C22⋊C4—21no—
514C3×C22⋊C4—21no—
515C3×C22⋊C4—21no—
516C3×C42—21no—
517C3×C42—21no—
518C3×C42—21no—
519C3×C42—21no—
520C3×C42C2×D411yescharacteristic
521C3×C42C2×D411yescharacteristic
522C3×C42C2411yescharacteristic
523C3×C42C2411yescharacteristic
524#217—22no—
525#217—22no—
526#217—22no—
527#217C2×D412yes—
528#217C2×D412yes—
529#215—24no—
530#213—24no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537C4⋊Dic3—21no—
538C4⋊Dic3—21no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—21no—
542C4⋊Dic3—22no—
543C4⋊Dic3—22no—
544C4⋊Dic3—22no—
545C4⋊Dic3—22no—
546C4⋊Dic3—22no—
547C4⋊Dic3—22no—
548C4⋊Dic3C2×D411yescharacteristic
549C4⋊Dic3C2×D412yes—
550C4⋊Dic3C2×D411yescharacteristic
551C4⋊Dic3C2×D412yes—
552C4⋊Dic3C2×D412yes—
553C4⋊Dic3C2412yes—
554C4⋊Dic3C2412yes—
555C4⋊Dic3C2412yes—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561Dic3⋊C4—22no—
562Dic3⋊C4C2×D412yes—
563Dic3⋊C4C2×D412yes—
564Dic3⋊C4C2×D412yes—
565Dic3⋊C4C2×D412yes—
566C4×Dic3—22no—
567C4×Dic3—22no—
568C4×Dic3—22no—
569C4×Dic3C2412yes—
570C4×Dic3C2412yes—
571C2×C3⋊C8C2412yes—
572C2×C3⋊C8C2412yes—
573C2×#41—61no—
574C2×#41—61no—
575C2×#41C22×D311yescharacteristic
576C22×Q8—62no—
577C22×Q8—61no—
578C22×Q8—61no—
579C2×Q16C22×D311yescharacteristic
580C2×SD16—32no—
581C2×SD16C22×D311yescharacteristic
582C2×SD16C22×D311yescharacteristic
583C2×D8—32no—
584C2×D8C22×D311yescharacteristic
585C4⋊Q8—32no—
586C4⋊Q8—32no—
587C4⋊Q8—32no—
588C4⋊Q8—31no—
589C4⋊Q8—31no—
590C4⋊Q8—32no—
591C4⋊Q8—31no—
592C4⋊Q8—31no—
593C4⋊Q8—31no—
594C4⋊Q8—62no—
595C4⋊Q8—61no—
596C4⋊Q8—61no—
597C4⋊Q8—62no—
598C4⋊Q8—61no—
599C4⋊Q8—62no—
600C4⋊Q8—62no—
601C4⋊Q8—61no—
602C4⋊Q8—61no—
603#127—32no—
604#127—31no—
605#126—21no—
606#126—62no—
607#125—32no—
608#125—32no—
609#125—32no—
610#125—32no—
611#125—62no—
612#125—62no—
613#125—62no—
614#125—62no—
615#125C22×D311yescharacteristic
616#124—32no—
617#124—61no—
618#124—62no—
619#124—62no—
620#124—61no—
621#124C22×D311yescharacteristic
622#123—21no—
623#123—62no—
624#123—62no—
625#123—62no—
626#123—62no—
627#123—62no—
628#123—62no—
629C22⋊Q8—31no—
630C22⋊Q8—31no—
631C22⋊Q8—32no—
632C22⋊Q8—62no—
633C22⋊Q8—62no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—61no—
645C22⋊Q8—61no—
646C22⋊Q8—61no—
647C22⋊Q8C22×D311yescharacteristic
648#121—32no—
649#121—62no—
650#121—62no—
651#121—62no—
652#121—61no—
653#121—61no—
654#121C22×D311yescharacteristic
655C4×Q8—32no—
656C4×Q8—31no—
657C4×Q8—31no—
658C4×Q8—32no—
659C4×Q8—32no—
660C4×Q8—32no—
661C4×Q8—62no—
662C4×Q8—61no—
663C4×Q8—61no—
664C4×Q8—61no—
665C4×Q8C22×D311yescharacteristic
666C4×Q8C22×D311yescharacteristic
667C4×Q8C22×D311yescharacteristic
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—32no—
672C4×D4—32no—
673C4×D4—32no—
674C4×D4—32no—
675C4×D4—32no—
676C4×D4—32no—
677C4×D4—61no—
678C4×D4—62no—
679C4×D4—62no—
680C4×D4—62no—
681C4×D4—61no—
682C4×D4C22×D311yescharacteristic
683C4×D4C22×D311yescharacteristic
684C4×D4C22×D311yescharacteristic
685#117—21no—
686#117—21no—
687#117—32no—
688#117—62no—
689#117C22×D311yescharacteristic
690C2×C4⋊C4—32no—
691C2×C4⋊C4—62no—
692C2×C4⋊C4—62no—
693C2×C4⋊C4—61no—
694C2×C4⋊C4—61no—
695C2×C4⋊C4—61no—
696C2×C42—21no—
697C2×C42C22×D311yescharacteristic
698#107—32no—
699#107—32no—
700#107—32no—
701#107C22×D311yescharacteristic
702#107C22×D311yescharacteristic
703#106—32no—
704#106—32no—
705#106—32no—
706#106—32no—
707#106—32no—
708#106—32no—
709#106—32no—
710#106C22×D311yescharacteristic
711#106C22×D311yescharacteristic
712C4⋊C8—32no—
713C4⋊C8—32no—
714C4⋊C8—32no—
715C4⋊C8—32no—
716C4⋊C8—31no—
717C4⋊C8—31no—
718C4⋊C8C22×D311yescharacteristic
719C4⋊C8C22×D311yescharacteristic
720#103—32no—
721#103—32no—
722#103—32no—
723#103C22×D311yescharacteristic
724#103C22×D311yescharacteristic
725#103C22×D311yescharacteristic
726#103C22×D311yescharacteristic
727#102—32no—
728#102—32no—
729#102—32no—
730#102—32no—
731#102—32no—
732#102—32no—
733#102—32no—
734#102—32no—
735#102—32no—
736#102C22×D311yescharacteristic
737#102C22×D311yescharacteristic
738#102C22×D311yescharacteristic
739#102C22×D311yescharacteristic
740C22⋊C8—32no—
741C22⋊C8C22×D311yescharacteristic
742C22⋊C8C22×D311yescharacteristic
743#97—32no—
744#97—32no—
745#97—32no—
746C4×C8—32no—
747C4×C8—32no—
748C4×C8C22×D311yescharacteristic
749C4×C8C22×D311yescharacteristic
750C23×C3—21no—
751C23×C3—21no—
752C23×C3C22×D411yescharacteristic
753C22×D3—22no—
754C3×Q8—21no—
755C3×Q8—21no—
756C3×Q8—21no—
757C3×Q82−1+412yes—
758C3×D4—24no—
759C3×D4—21no—
760C3×D4—21no—
761C3×D4—21no—
762C3×D4—81no—
763C3×D42−1+412yes—
764C2×C3×C4—24no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—41no—
775C2×C3×C4—42no—
776C2×C3×C4—42no—
777C2×C3×C4—42no—
778C2×C3×C4C22×D411yescharacteristic
779C2×C3×C4C22×D411yescharacteristic
780C2×C3×C4C22×D411yescharacteristic
781C2×C3×C4C22×D411yescharacteristic
782C2×C3×C4C22×D411yescharacteristic
783C2×C3×C4C2511yescharacteristic
784#67—82no—
785#67—82no—
786#67—82no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—82no—
791C2×Dic3—82no—
792C2×Dic3—82no—
793C2×Dic3—82no—
794C2×Dic3C22×D412yes—
795C2×Dic3C22×D412yes—
796C2×Dic3C22×D412yes—
797C2×Dic3C22×D412yes—
798D12—22no—
799D12—22no—
800D12—42no—
801D12—81no—
802C4×D3—82no—
803C4×D3—82no—
804C4×D3—82no—
805Dic6—22no—
806Dic6—22no—
807Dic6—42no—
808Dic6—44no—
809Dic6—42no—
810Dic6—82no—
811Dic6—82no—
812Dic6—82no—
813Dic6—81no—
814Dic6—81no—
815C3×C8—21no—
816C3×C8—21no—
817C3×C8—21no—
818C3×C8—21no—
819C3⋊C8—22no—
820C3⋊C8—22no—
821#41—22no—
822#41—22no—
823#41—242no—
824#41—242no—
825C2×Q8—31no—
826C2×Q8—31no—
827C2×Q8—32no—
828C2×Q8—62no—
829C2×Q8—62no—
830C2×Q8—62no—
831C2×Q8—61no—
832C2×Q8—62no—
833C2×Q8—61no—
834C2×Q8—61no—
835C2×Q8—242no—
836C2×Q8—242no—
837C2×Q8—244no—
838C2×Q8C23×D311yescharacteristic
839C2×Q8C23×D311yescharacteristic
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—32no—
843C2×D4—62no—
844C2×D4—62no—
845C2×D4—62no—
846C2×D4—61no—
847C2×D4—61no—
848C2×D4C23×D311yescharacteristic
849C2×D4C23×D311yescharacteristic
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—62no—
855C22×C4—62no—
856C22×C4—62no—
857C22×C4—62no—
858C22×C4—62no—
859C22×C4—62no—
860C22×C4—62no—
861C22×C4D3×D411yescharacteristic
862C22×C4D3×D411yescharacteristic
863C22×C4C23×D311yescharacteristic
864Q16—22no—
865SD16—22no—
866SD16—22no—
867SD16—64no—
868D8—22no—
869D8—64no—
870C2×C8—32no—
871C2×C8—32no—
872C2×C8C23×D311yescharacteristic
873C2×C8C23×D311yescharacteristic
874C2×C8C23×D311yescharacteristic
875C2×C8C23×D311yescharacteristic
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—32no—
883C4⋊C4—31no—
884C4⋊C4—31no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—32no—
888C4⋊C4—32no—
889C4⋊C4—32no—
890C4⋊C4—32no—
891C4⋊C4—32no—
892C4⋊C4—32no—
893C4⋊C4—32no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—62no—
898C4⋊C4—62no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4—61no—
908C4⋊C4—61no—
909C4⋊C4—62no—
910C4⋊C4—61no—
911C4⋊C4C23×D311yescharacteristic
912C4⋊C4C23×D311yescharacteristic
913C4⋊C4C23×D311yescharacteristic
914C4⋊C4C23×D311yescharacteristic
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—21no—
920C22⋊C4—21no—
921C22⋊C4—21no—
922C22⋊C4—21no—
923C22⋊C4—32no—
924C22⋊C4—32no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C22⋊C4—62no—
928C22⋊C4—62no—
929C22⋊C4—62no—
930C22⋊C4—62no—
931C22⋊C4—62no—
932C22⋊C4—62no—
933C22⋊C4—62no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—32no—
939C42—32no—
940C42—62no—
941C42—62no—
942C42—62no—
943C42D3×D411yescharacteristic
944C42D3×D411yescharacteristic
945C42C23×D311yescharacteristic
946C42C23×D311yescharacteristic
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—22no—
950C22×C3—21no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3C23×D411yescharacteristic
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C3×C4—21no—
961C3×C4—21no—
962C3×C4—21no—
963C3×C4—22no—
964C3×C4—21no—
965C3×C4—41no—
966C3×C4—41no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4#57712yes—
971C3×C4C2×2−1+411yescharacteristic
972C3×C4C2×2−1+411yescharacteristic
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—22no—
977Dic3—42no—
978Dic3—42no—
979Dic3—42no—
980C23—21no—
981C23—21no—
982C23—62no—
983C23C2×D3×D411yescharacteristic
984Q8—21no—
985Q8—21no—
986Q8—21no—
987Q8—62no—
988Q8—62no—
989Q8—122no—
990Q8—124no—
991Q8—122no—
992Q8—241no—
993Q8—241no—
994Q8—242no—
995Q8—242no—
996Q8—242no—
997Q8#101012yes—
998D4—24no—
999D4—21no—
1000D4—21no—
1001D4—21no—
1002D4—62no—
1003D4—62no—
1004D4—81no—
1005D4—122no—
1006D4—241no—
1007D4—242no—
1008D4—242no—
1009D4—242no—
1010D4#101012yes—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—41no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—242no—
1033C2×C4—242no—
1034C2×C4—242no—
1035C2×C4—242no—
1036C2×C4—242no—
1037C2×C4—242no—
1038C2×C4—242no—
1039C2×C4C2×D3×D411yescharacteristic
1040C2×C4C2×D3×D411yescharacteristic
1041C2×C4C2×D3×D411yescharacteristic
1042C2×C4C2×D3×D411yescharacteristic
1043C2×C4C2×D3×D411yescharacteristic
1044C2×C4C24×D311yescharacteristic
1045C8—21no—
1046C8—21no—
1047C8—21no—
1048C8—21no—
1049C8—62no—
1050C8—62no—
1051C2×C3—41no—
1052C2×C3—42no—
1053C2×C3—81no—
1054C2×C3#348611yescharacteristic
1055C2×C3C2×#57711yescharacteristic
1056C2×C3#358511yescharacteristic
1057D3—82no—
1058C22—21no—
1059C22—22no—
1060C22—21no—
1061C22—21no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—122no—
1068C22—122no—
1069C22—122no—
1070C22C22×D3×D411yescharacteristic
1071C4—21no—
1072C4—22no—
1073C4—21no—
1074C4—21no—
1075C4—21no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—62no—
1082C4—62no—
1083C4—62no—
1084C4—62no—
1085C4—122no—
1086C4—122no—
1087C4—122no—
1088C4#577012yes—
1089C4C2×#101011yescharacteristic
1090C4C2×#101011yescharacteristic
1091C3#6186011yescharacteristic, complemented, Sylow
1092C2—41no—
1093C2—42no—
1094C2—81no—
1095C2—242no—
1096C2#8602211yescharacteristic
1097C2C2×#577011yescharacteristic
1098C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3102C2
socleC22×C3C23×D4
hypercenter#3102D3
hypocenterC3#61860
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #86137C2semidirect
2. #85828C2semidirect
3. C3×#3102C2semidirect
4. #83123C2semidirect
5. #82531C2semidirect
6. #81507C2semidirect
7. #81360C2semidirect
8. #81225C2semidirect
9. #81158C2semidirect
10. #80584C2semidirect
11. #80521C2semidirect
12. #80219C2semidirect
13. #80073C2semidirect
14. #79708C2semidirect
15. #79703C2semidirect
16. #79632C2semidirect
17. SD16×Dic6C2semidirect
18. #79622C2semidirect
19. #79621C2semidirect
20. #79576C2semidirect
21. #79570C2semidirect
22. #79269C2semidirect
23. #79266C2semidirect
157. #3102D3semidirect
1091. C3#61860semidirect

Maximal subgroups

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

subgroupindex
#861372
#858282
C3×#31022
#831232
#825312
#815072
#813602
#812252
#811582
#805842
#805212
#802192
#800732
#797082
#797032
#796322
SD16×Dic62
#796222
#796212
#795762
#795702
#792692
#792662
#618603