Finite Group Databasebeta

← #11701640

Subgroups — #11701640

Order 768.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86289C211yesmaximal, characteristic, complemented
2#86133C211yesmaximal, characteristic, complemented
3C3×#3172C211yesmaximal, characteristic, complemented
4#83324C211yesmaximal, characteristic, complemented
5#83145C211yesmaximal, characteristic, complemented
6#81988C212yesmaximal, complemented
7#81880C212yesmaximal, complemented
8#81738C212yesmaximal, complemented
9#81667C212yesmaximal, complemented
10#80918C212yesmaximal, complemented
11#80916C212yesmaximal, complemented
12#80842C212yesmaximal, complemented
13#80820C212yesmaximal, complemented
14#79740C211yesmaximal, characteristic, complemented
15#79735C211yesmaximal, characteristic, complemented
16#79703C211yesmaximal, characteristic, complemented
17#79699C211yesmaximal, characteristic, complemented
18#79685C211yesmaximal, characteristic, complemented
19#79681C211yesmaximal, characteristic, complemented
20#79628C211yesmaximal, characteristic, complemented
21#79621C211yesmaximal, characteristic, complemented
22#78528C211yesmaximal, characteristic, complemented
23#78511C211yesmaximal, characteristic, complemented
24#62619—31nomaximal, Sylow
25C3×#533C2211yescharacteristic
26C3×#529C2211yescharacteristic
27#5733C2212yes—
28#5724C2212yes—
29#5712—22no—
30#5692—22no—
31#5689C2212yes—
32#5682C2212yes—
33#5648—22no—
34#5647—22no—
35#5642C2212yes—
36#5633C2212yes—
37#5631C2212yes—
38#5611C2212yes—
39#5585—21no—
40#5585C2211yescharacteristic
41#5579—21no—
42#5579C2211yescharacteristic
43#5577C2211yescharacteristic
44Q8×D12C2211yescharacteristic
45#5567C2211yescharacteristic
46Q8×Dic6C2211yescharacteristic
47#5563C2211yescharacteristic
48#5555—21no—
49#5543C2211yescharacteristic
50#5541—21no—
51#5535—21no—
52#5534—21no—
53#5534—21no—
54#5519—21no—
55#5479C2211yescharacteristic
56#5477C2211yescharacteristic
57C2×#869C2211yescharacteristic
58C3×#501C2211yescharacteristic
59C3×#497C2211yescharacteristic
60C3×#491C2211yescharacteristic
61C3×#489C2211yescharacteristic
62C3×#470C2211yescharacteristic
63C3×#470C2211yescharacteristic
64C3×#468C2211yescharacteristic
65C3×#468C2211yescharacteristic
66C3×C4×Q16C2211yescharacteristic
67C3×C4×Q16C2211yescharacteristic
68C3×C4×SD16C2211yescharacteristic
69C3×C4×SD16C2211yescharacteristic
70C3×C4×M16C2211yescharacteristic
71#5187C2212yes—
72#5186C2212yes—
73#5185C2212yes—
74#5182C2212yes—
75#5172C2212yes—
76#5170C2212yes—
77#5165C2212yes—
78#5162C2212yes—
79#5133C2212yes—
80#5133C2212yes—
81#5128C2212yes—
82#5127C2212yes—
83#5079C2212yes—
84#5078C2212yes—
85#5068C2212yes—
86#5059C2212yes—
87#5047C2212yes—
88#5044C2212yes—
89#5044C2212yes—
90#5037C2212yes—
91#5031C2211yescharacteristic
92#5027C2211yescharacteristic
93#5021C2211yescharacteristic
94#5021C2211yescharacteristic
95#5021C2211yescharacteristic
96#5021C2211yescharacteristic
97#5019C2211yescharacteristic
98#5015C2211yescharacteristic
99#4925C2211yescharacteristic
100#4890C2212yes—
101#4884C2212yes—
102#4882C2212yes—
103#4875C2212yes—
104#4871C2212yes—
105#4868C2212yes—
106#4866C2212yes—
107#4857C2212yes—
108#4817C2212yes—
109#4813C2212yes—
110#4812C2212yes—
111#4804C2212yes—
112#4803C2212yes—
113#4802C2212yes—
114D3×#103C2212yes—
115#4800C2212yes—
116#4797C2212yes—
117#4794C2212yes—
118#4792C2212yes—
119#4790C2212yes—
120#4780C2212yes—
121#4775C2212yes—
122#4757C2212yes—
123#4756C2212yes—
124#4714C2212yes—
125#4714C2212yes—
126#4709C2212yes—
127#4708C2212yes—
128#4694C2211yescharacteristic
129#4694C2211yescharacteristic
130#4688C2211yescharacteristic
131C8×D12C2211yescharacteristic
132#4681C2211yescharacteristic
133#4681C2211yescharacteristic
134#4679C2211yescharacteristic
135C8×Dic6C2211yescharacteristic
136#3554—31no—
137#3544—31no—
138#3375—31no—
139#3372—31no—
140#3363—31no—
141#3361—31no—
142#3333—31no—
143#3330—32no—
144#3329—31no—
145#3327—32no—
146#3315—32no—
147#3308—32no—
148#3305—31no—
149#3299—31no—
150#3243—32no—
151#3230—31no—
152#3225—32no—
153#3212—31no—
154#3175—32no—
155#3172D311yescharacteristic, complemented
156#3141—31no—
157#3137—32no—
158#2969—31no—
159C2×#239C2312yes—
160C2×D3×Q8C2312yes—
161C2×#237—22no—
162C2×#235C2312yes—
163C22×Dic6—21no—
164C2×C3×Q16C2311yescharacteristic
165C2×C3×Q16C2311yescharacteristic
166C2×C3×SD16C2311yescharacteristic
167C2×C3×SD16C2311yescharacteristic
168C2×C3×M16C2311yescharacteristic
169C2×C3×M16C2311yescharacteristic
170C3×C4⋊Q8C2311yescharacteristic
171C3×C4⋊Q8C2311yescharacteristic
172C3×#126—21no—
173C3×#125—21no—
174C3×#125C2311yescharacteristic
175C3×#124C2311yescharacteristic
176C3×#123—21no—
177C3×C22⋊Q8—21no—
178C3×C22⋊Q8C2311yescharacteristic
179C3×C22⋊Q8C2311yescharacteristic
180C3×C22⋊Q8C2311yescharacteristic
181C3×#121C2311yescharacteristic
182C3×C4×Q8—21no—
183C3×C4×Q8C2311yescharacteristic
184C3×C4×Q8C2311yescharacteristic
185C3×C4×Q8C2311yescharacteristic
186C3×C4×D4—21no—
187C3×C4×D4C2311yescharacteristic
188C3×#117—21no—
189C3×#117—21no—
190C2×C3×C42C2311yescharacteristic
191#947—22no—
192#947C2312yes—
193#946—22no—
194#946C2312yes—
195Q8×Dic3C2312yes—
196#944C2312yes—
197C2×#216C2312yes—
198C2×#215C2312yes—
199#938C2312yes—
200#935—22no—
201D4×Dic3C2312yes—
202C2×#214C2312yes—
203C2×#213C2312yes—
204#930—21no—
205#930—21no—
206#930—21no—
207#930D411yescharacteristic
208#929D412yes—
209C4×#67C2312yes—
210#926—21no—
211C2×C4⋊Dic3—21no—
212C2×C4⋊Dic3—21no—
213C2×C4⋊Dic3C2312yes—
214#924—21no—
215#924D411yescharacteristic
216C2×ΓL(1,𝔽25)C2312yes—
217C2×D3×C8C2312yes—
218#898—22no—
219#898—22no—
220#897—22no—
221#897—22no—
222#897C2312yes—
223#896—22no—
224#896—22no—
225#896—22no—
226#896—22no—
227#896—22no—
228#895—22no—
229#895C2312yes—
230#894—22no—
231#894—22no—
232#894—22no—
233#894—22no—
234#894—22no—
235#893—22no—
236#893C2312yes—
237#892C2312yes—
238D3×C4⋊C4—22no—
239D3×C4⋊C4C2312yes—
240#890—22no—
241#890C2312yes—
242#889—22no—
243#889—22no—
244#888—22no—
245#888—22no—
246#888C2312yes—
247#887C2312yes—
248#886—22no—
249#886—22no—
250#885—22no—
251#885—22no—
252#885—22no—
253#884—22no—
254#884—22no—
255#883—22no—
256#883—22no—
257#879—22no—
258#878—22no—
259#878—22no—
260#878—22no—
261#877—22no—
262#876D412yes—
263#875—21no—
264#875D411yescharacteristic
265#875C2312yes—
266#874—21no—
267#874C2311yescharacteristic
268C4×D12—21no—
269C4×D12—21no—
270C4×D12—21no—
271C4×D12—21no—
272C4×D12—21no—
273C4×D12—21no—
274C4×D12C2311yescharacteristic
275#872C2312yes—
276#870—21no—
277#870—21no—
278#870D411yescharacteristic
279#869—21no—
280#869—21no—
281#869—21no—
282#869—21no—
283#869C2311yescharacteristic
284#869C2312yes—
285#869C2311yescharacteristic
286#869C2311yescharacteristic
287C4×Dic6—21no—
288C4×Dic6—21no—
289C4×Dic6C2311yescharacteristic
290C3×#107C2311yescharacteristic
291C3×#107C2311yescharacteristic
292C3×#106C2311yescharacteristic
293C3×#106C2311yescharacteristic
294C3×#103C2311yescharacteristic
295C3×#103C2311yescharacteristic
296C3×#103C2311yescharacteristic
297C3×#103C2311yescharacteristic
298C3×#103C2311yescharacteristic
299C3×#103C2311yescharacteristic
300C3×#102C2311yescharacteristic
301C3×#102C2311yescharacteristic
302C3×#97C2311yescharacteristic
303C3×#97C2311yescharacteristic
304C3×C4×C8C2311yescharacteristic
305C3×C4×C8C2311yescharacteristic
306#835C2312yes—
307#835C2312yes—
308#835C2312yes—
309#835C2312yes—
310#830C2312yes—
311#821C2312yes—
312#821C2312yes—
313#821C2312yes—
314#821C2312yes—
315(C2×D3)⋊C8C2312yes—
316(C2×D3)⋊C8C2312yes—
317#816C2312yes—
318#816C2312yes—
319#816C2312yes—
320#816C2312yes—
321#815C2312yes—
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2312yes—
324C8×Dic3C2312yes—
325#810C2312yes—
326#810C2312yes—
327#809C2312yes—
328#809C2312yes—
329#807C2312yes—
330#807C2312yes—
331#807C2312yes—
332#807C2312yes—
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4×C3⋊C8C2312yes—
336#563—62no—
337#562—62no—
338#559—31no—
339#559—61no—
340Q82—31no—
341#557—31no—
342#555—31no—
343#554—31no—
344#554—31no—
345#554—61no—
346#552—32no—
347#552—61no—
348#550—31no—
349D4×Q8—31no—
350#548—32no—
351#547—32no—
352#547—32no—
353#547—61no—
354#544—32no—
355#544—61no—
356#542—32no—
357#542—32no—
358#542—61no—
359#542—61no—
360#540—61no—
361#539—62no—
362#536—32no—
363#536—62no—
364#533C2×D311yescharacteristic
365#532—31no—
366C2×C4⋊Q8—31no—
367#529—31no—
368#529C2×D311yescharacteristic
369#501C2×D311yescharacteristic
370#500—32no—
371#497C2×D311yescharacteristic
372#495—32no—
373#491—32no—
374#491C2×D311yescharacteristic
375#489—32no—
376#489—32no—
377#489—32no—
378#489C2×D311yescharacteristic
379#488—32no—
380#488—32no—
381#487—32no—
382#487—32no—
383#487—31no—
384#487—31no—
385#486—31no—
386#486—31no—
387#485—32no—
388#484—32no—
389#484—32no—
390#484—32no—
391#482—32no—
392#480—32no—
393#479—32no—
394#478—32no—
395#477—31no—
396#477—31no—
397#477—31no—
398#477—31no—
399#477—32no—
400#474—32no—
401#470C2×D311yescharacteristic
402#470C2×D311yescharacteristic
403#468—32no—
404#468—32no—
405#468C2×D311yescharacteristic
406#468C2×D311yescharacteristic
407#467—32no—
408#466—32no—
409#464—32no—
410#463—32no—
411#462—32no—
412#462—31no—
413#461—32no—
414#461—31no—
415#460—31no—
416#459—31no—
417#452—32no—
418#452—32no—
419#451—32no—
420#449—32no—
421#449—32no—
422#448—32no—
423#446—31no—
424C8×Q8—31no—
425#440—32no—
426#440—32no—
427C4×Q16—32no—
428C4×Q16C2×D311yescharacteristic
429C4×Q16C2×D311yescharacteristic
430C4×SD16C2×D311yescharacteristic
431C4×SD16C2×D311yescharacteristic
432C4×D8—32no—
433#436—32no—
434#436—31no—
435#435—32no—
436C8×D4—31no—
437#433—32no—
438#431—31no—
439#419—32no—
440#417—32no—
441#417—32no—
442#417—32no—
443#416—32no—
444C2×#103—32no—
445#405—32no—
446C4×M16C2×D311yescharacteristic
447C2×C3×Q8—21no—
448C2×C3×Q8C2411yescharacteristic
449C2×C3×Q8C2411yescharacteristic
450C2×C3×Q8C2411yescharacteristic
451C2×C3×D4—21no—
452C2×C3×D4C2411yescharacteristic
453C22×C3×C4—21no—
454C22×C3×C4C2×D411yescharacteristic
455C22×C3×C4C2×D411yescharacteristic
456C22×C3×C4C2411yescharacteristic
457C2×#67—22no—
458C2×#67—22no—
459C2×#67C2×D412yes—
460C22×Dic3—22no—
461C22×Dic3—22no—
462#239—42no—
463#239—42no—
464D3×Q8—42no—
465D3×Q8—42no—
466#237—84no—
467#235—42no—
468#235—42no—
469C2×D12—21no—
470C2×D12—22no—
471C2×D12—22no—
472C2×D12—21no—
473C2×D12C2×D411yescharacteristic
474C2×D12C2412yes—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3C2412yes—
481C2×Dic6—21no—
482C2×Dic6—22no—
483C2×Dic6—21no—
484C2×Dic6—22no—
485C2×Dic6—22no—
486C2×Dic6—82no—
487C2×Dic6C2×D411yescharacteristic
488C2×Dic6C2412yes—
489C3×Q16—41no—
490C3×Q16—41no—
491C3×SD16—41no—
492C3×SD16—41no—
493C3×M16—41no—
494C3×M16—41no—
495C2×C3×C8C2411yescharacteristic
496C2×C3×C8C2411yescharacteristic
497C2×C3×C8C2411yescharacteristic
498C2×C3×C8C2411yescharacteristic
499C3×C4⋊C4—21no—
500C3×C4⋊C4—21no—
501C3×C4⋊C4—21no—
502C3×C4⋊C4—21no—
503C3×C4⋊C4—21no—
504C3×C4⋊C4—21no—
505C3×C4⋊C4—21no—
506C3×C4⋊C4—21no—
507C3×C4⋊C4—21no—
508C3×C4⋊C4—21no—
509C3×C4⋊C4—21no—
510C3×C4⋊C4C2411yescharacteristic
511C3×C4⋊C4C2411yescharacteristic
512C3×C4⋊C4C2411yescharacteristic
513C3×C4⋊C4C2411yescharacteristic
514C3×C22⋊C4—21no—
515C3×C22⋊C4—21no—
516C3×C22⋊C4—21no—
517C3×C22⋊C4—21no—
518C3×C22⋊C4—21no—
519C3×C22⋊C4—21no—
520C3×C22⋊C4—21no—
521C3×C42—21no—
522C3×C42—21no—
523C3×C42—21no—
524C3×C42C2×D411yescharacteristic
525C3×C42C2×D411yescharacteristic
526C3×C42C2411yescharacteristic
527C3×C42C2411yescharacteristic
528#217—22no—
529#217—22no—
530#217C2×D412yes—
531#216—42no—
532#215—42no—
533#214—42no—
534#213—42no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—22no—
538(C2×D3)⋊C4—22no—
539(C2×D3)⋊C4—22no—
540(C2×D3)⋊C4—22no—
541(C2×D3)⋊C4—22no—
542(C2×D3)⋊C4—22no—
543(C2×D3)⋊C4—22no—
544(C2×D3)⋊C4C2×D412yes—
545(C2×D3)⋊C4C2×D412yes—
546(C2×D3)⋊C4C2×D412yes—
547(C2×D3)⋊C4C2×D412yes—
548C4⋊Dic3—21no—
549C4⋊Dic3—21no—
550C4⋊Dic3—22no—
551C4⋊Dic3—21no—
552C4⋊Dic3—22no—
553C4⋊Dic3—21no—
554C4⋊Dic3—22no—
555C4⋊Dic3—22no—
556C4⋊Dic3—22no—
557C4⋊Dic3C2×D411yescharacteristic
558C4⋊Dic3C2×D411yescharacteristic
559C4⋊Dic3C2412yes—
560C4⋊Dic3C2412yes—
561Dic3⋊C4—22no—
562Dic3⋊C4—22no—
563Dic3⋊C4—22no—
564Dic3⋊C4—22no—
565Dic3⋊C4—22no—
566Dic3⋊C4—22no—
567Dic3⋊C4—22no—
568Dic3⋊C4C2×D412yes—
569Dic3⋊C4C2×D412yes—
570Dic3⋊C4C2×D412yes—
571Dic3⋊C4C2×D412yes—
572C4×Dic3—22no—
573C4×Dic3—22no—
574C4×Dic3—22no—
575C4×Dic3C2412yes—
576C2×C3⋊C8C2412yes—
577C2×C3⋊C8C2412yes—
578ΓL(1,𝔽25)—42no—
579D3×C8—42no—
580C2×#41—32no—
581C2×#41—32no—
582C2×#41—62no—
583C22×Q8—32no—
584C22×Q8—61no—
585C2×Q16—32no—
586C2×Q16C22×D311yescharacteristic
587C2×Q16C22×D311yescharacteristic
588C2×SD16—32no—
589C2×SD16—32no—
590C2×SD16C22×D311yescharacteristic
591C2×SD16C22×D311yescharacteristic
592C2×D8—32no—
593C2×M16—32no—
594C2×M16C22×D311yescharacteristic
595C2×M16C22×D311yescharacteristic
596C22×C8—32no—
597C4⋊Q8—32no—
598C4⋊Q8—32no—
599C4⋊Q8—32no—
600C4⋊Q8—31no—
601C4⋊Q8—31no—
602C4⋊Q8—31no—
603C4⋊Q8—61no—
604C4⋊Q8—61no—
605C4⋊Q8—62no—
606C4⋊Q8—62no—
607C4⋊Q8—61no—
608C4⋊Q8—61no—
609C4⋊Q8C22×D311yescharacteristic
610C4⋊Q8C22×D311yescharacteristic
611#127—31no—
612#127—61no—
613#126—21no—
614#126—32no—
615#126—62no—
616#126—62no—
617#126—62no—
618#125—21no—
619#125—32no—
620#125—31no—
621#125—61no—
622#125—61no—
623#125—62no—
624#125—62no—
625#125—62no—
626#125C22×D311yescharacteristic
627#124—32no—
628#124—31no—
629#124—32no—
630#124—61no—
631#124—62no—
632#124—62no—
633#124—62no—
634#124—62no—
635#124C22×D311yescharacteristic
636#123—21no—
637#123—32no—
638#123—62no—
639#123—62no—
640#123—62no—
641#123—62no—
642#123—62no—
643#123—62no—
644#123—62no—
645#123—62no—
646#123—62no—
647#123—62no—
648C22⋊Q8—21no—
649C22⋊Q8—31no—
650C22⋊Q8—32no—
651C22⋊Q8—32no—
652C22⋊Q8—62no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—62no—
659C22⋊Q8—62no—
660C22⋊Q8—62no—
661C22⋊Q8—62no—
662C22⋊Q8—62no—
663C22⋊Q8—61no—
664C22⋊Q8C22×D311yescharacteristic
665C22⋊Q8C22×D311yescharacteristic
666C22⋊Q8C22×D311yescharacteristic
667#121—31no—
668#121—32no—
669#121—32no—
670#121—62no—
671#121—62no—
672#121—62no—
673#121—61no—
674#121—61no—
675#121—61no—
676#121C22×D311yescharacteristic
677C4×Q8—21no—
678C4×Q8—31no—
679C4×Q8—32no—
680C4×Q8—32no—
681C4×Q8—61no—
682C4×Q8—61no—
683C4×Q8C22×D311yescharacteristic
684C4×Q8C22×D311yescharacteristic
685C4×Q8C22×D311yescharacteristic
686C4×D4—21no—
687C4×D4—32no—
688C4×D4—32no—
689C4×D4—32no—
690C4×D4—31no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4—61no—
694C4×D4—61no—
695C4×D4—62no—
696C4×D4—61no—
697C4×D4—61no—
698C4×D4C22×D311yescharacteristic
699#117—21no—
700#117—21no—
701#117—32no—
702#117—32no—
703#117—62no—
704#117—61no—
705C2×C4⋊C4—32no—
706C2×C4⋊C4—32no—
707C2×C4⋊C4—62no—
708C2×C4⋊C4—61no—
709C2×C4⋊C4—61no—
710C2×C42C22×D311yescharacteristic
711#107—32no—
712#107—32no—
713#107—32no—
714#107—32no—
715#107C22×D311yescharacteristic
716#107C22×D311yescharacteristic
717#106C22×D311yescharacteristic
718#106C22×D311yescharacteristic
719C4⋊C8—32no—
720C4⋊C8—32no—
721C4⋊C8—31no—
722C4⋊C8—31no—
723#103—32no—
724#103—32no—
725#103—32no—
726#103—32no—
727#103—32no—
728#103—32no—
729#103—32no—
730#103—32no—
731#103—32no—
732#103—32no—
733#103C22×D311yescharacteristic
734#103C22×D311yescharacteristic
735#103C22×D311yescharacteristic
736#103C22×D311yescharacteristic
737#103C22×D311yescharacteristic
738#103C22×D311yescharacteristic
739#102—32no—
740#102—32no—
741#102—32no—
742#102—32no—
743#102—32no—
744#102—32no—
745#102C22×D311yescharacteristic
746#102C22×D311yescharacteristic
747C22⋊C8—32no—
748C22⋊C8—32no—
749C22⋊C8—32no—
750#97—32no—
751#97C22×D311yescharacteristic
752#97C22×D311yescharacteristic
753C4×C8—32no—
754C4×C8—32no—
755C4×C8C22×D311yescharacteristic
756C4×C8C22×D311yescharacteristic
757C23×C3—21no—
758C23×C3C22×D411yescharacteristic
759C22×D3—22no—
760C22×D3C22×D412yes—
761C3×Q8—21no—
762C3×Q8—21no—
763C3×Q8—21no—
764C3×Q8—21no—
765C3×Q8—21no—
766C3×Q8—21no—
767C3×Q8—81no—
768C3×D4—21no—
769C3×D4—21no—
770C3×D4—42no—
771C2×C3×C4—22no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—41no—
782C2×C3×C4—42no—
783C2×C3×C4C22×D411yescharacteristic
784C2×C3×C4C22×D411yescharacteristic
785C2×C3×C4C22×D411yescharacteristic
786C2×C3×C4C22×D411yescharacteristic
787C2×C3×C4C22×D411yescharacteristic
788C2×C3×C4C2511yescharacteristic
789#67—42no—
790#67—82no—
791#67—82no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—44no—
796C2×Dic3—82no—
797C2×Dic3C22×D412yes—
798C2×Dic3C22×D412yes—
799C2×Dic3C22×D412yes—
800D12—22no—
801D12—22no—
802D12—22no—
803D12—42no—
804D12—81no—
805D12—82no—
806D12—82no—
807C4×D3—22no—
808C4×D3—22no—
809C4×D3—82no—
810C4×D3—82no—
811C4×D3—82no—
812C4×D3—82no—
813C4×D3—82no—
814Dic6—22no—
815Dic6—22no—
816Dic6—22no—
817Dic6—82no—
818Dic6—82no—
819Dic6—81no—
820Dic6—82no—
821Dic6—81no—
822C3×C8—21no—
823C3×C8—21no—
824C3×C8—21no—
825C3×C8—21no—
826C3⋊C8—22no—
827C3⋊C8—22no—
828#41—122no—
829#41—122no—
830#41—122no—
831#41—122no—
832#41—244no—
833C2×Q8—21no—
834C2×Q8—31no—
835C2×Q8—32no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—61no—
839C2×Q8—62no—
840C2×Q8—61no—
841C2×Q8—122no—
842C2×Q8—122no—
843C2×Q8—242no—
844C2×Q8C23×D311yescharacteristic
845C2×Q8C23×D311yescharacteristic
846C2×Q8C23×D311yescharacteristic
847C2×D4—21no—
848C2×D4—32no—
849C2×D4—31no—
850C2×D4—32no—
851C2×D4—62no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—61no—
856C2×D4—61no—
857C2×D4C23×D311yescharacteristic
858C22×C4—21no—
859C22×C4—32no—
860C22×C4—62no—
861C22×C4—62no—
862C22×C4—62no—
863C22×C4—62no—
864C22×C4—62no—
865C22×C4—62no—
866C22×C4—62no—
867C22×C4D3×D411yescharacteristic
868C22×C4D3×D411yescharacteristic
869C22×C4C23×D311yescharacteristic
870Q16—41no—
871Q16—41no—
872Q16—122no—
873SD16—41no—
874SD16—41no—
875SD16—122no—
876SD16—122no—
877D8—122no—
878M16—41no—
879M16—41no—
880M16—122no—
881C2×C8—32no—
882C2×C8—32no—
883C2×C8—122no—
884C2×C8C23×D311yescharacteristic
885C2×C8C23×D311yescharacteristic
886C2×C8C23×D311yescharacteristic
887C2×C8C23×D311yescharacteristic
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—32no—
900C4⋊C4—31no—
901C4⋊C4—32no—
902C4⋊C4—32no—
903C4⋊C4—31no—
904C4⋊C4—32no—
905C4⋊C4—32no—
906C4⋊C4—32no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—62no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—62no—
914C4⋊C4—62no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4—61no—
919C4⋊C4—61no—
920C4⋊C4—62no—
921C4⋊C4—61no—
922C4⋊C4—61no—
923C4⋊C4C23×D311yescharacteristic
924C4⋊C4C23×D311yescharacteristic
925C4⋊C4C23×D311yescharacteristic
926C4⋊C4C23×D311yescharacteristic
927C22⋊C4—21no—
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—21no—
931C22⋊C4—21no—
932C22⋊C4—21no—
933C22⋊C4—21no—
934C22⋊C4—32no—
935C22⋊C4—32no—
936C22⋊C4—32no—
937C22⋊C4—32no—
938C22⋊C4—32no—
939C22⋊C4—62no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4—62no—
943C22⋊C4—62no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C22⋊C4—62no—
947C22⋊C4—62no—
948C22⋊C4—62no—
949C22⋊C4—62no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—32no—
954C42—62no—
955C42—62no—
956C42—62no—
957C42D3×D411yescharacteristic
958C42D3×D411yescharacteristic
959C42C23×D311yescharacteristic
960C42C23×D311yescharacteristic
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—41no—
965C22×C3—41no—
966C22×C3—41no—
967C22×C3C23×D411yescharacteristic
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—22no—
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—21no—
977C3×C4—21no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—41no—
981C3×C4—41no—
982C3×C4—41no—
983C3×C4—41no—
984C3×C4—41no—
985C3×C4#57812yes—
986C3×C4#58511yescharacteristic
987C3×C4#58511yescharacteristic
988Dic3—22no—
989Dic3—22no—
990Dic3—22no—
991Dic3—42no—
992Dic3—42no—
993Dic3—42no—
994C23—21no—
995C23—32no—
996C23—62no—
997C23C2×D3×D411yescharacteristic
998Q8—21no—
999Q8—21no—
1000Q8—21no—
1001Q8—21no—
1002Q8—21no—
1003Q8—21no—
1004Q8—62no—
1005Q8—62no—
1006Q8—62no—
1007Q8—81no—
1008Q8—241no—
1009Q8—241no—
1010Q8—242no—
1011Q8—242no—
1012Q8—242no—
1013D4—21no—
1014D4—21no—
1015D4—42no—
1016D4—62no—
1017D4—62no—
1018D4—62no—
1019D4—122no—
1020D4—122no—
1021D4—241no—
1022D4—242no—
1023D4—242no—
1024D4—242no—
1025D4—242no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—32no—
1037C2×C4—32no—
1038C2×C4—32no—
1039C2×C4—41no—
1040C2×C4—42no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—124no—
1047C2×C4—242no—
1048C2×C4—242no—
1049C2×C4—242no—
1050C2×C4—242no—
1051C2×C4—242no—
1052C2×C4—242no—
1053C2×C4C2×D3×D411yescharacteristic
1054C2×C4C2×D3×D411yescharacteristic
1055C2×C4C2×D3×D411yescharacteristic
1056C2×C4C2×D3×D411yescharacteristic
1057C2×C4C2×D3×D411yescharacteristic
1058C2×C4C24×D311yescharacteristic
1059C8—21no—
1060C8—21no—
1061C8—21no—
1062C8—21no—
1063C8—62no—
1064C8—62no—
1065C2×C3—41no—
1066C2×C3—81no—
1067C2×C3#350011yescharacteristic
1068C2×C3C2×#57811yescharacteristic
1069C2×C3#358511yescharacteristic
1070D3—42no—
1071D3—82no—
1072C22—21no—
1073C22—21no—
1074C22—21no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22C22×D3×D411yescharacteristic
1085C4—21no—
1086C4—21no—
1087C4—21no—
1088C4—21no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—62no—
1097C4—62no—
1098C4—62no—
1099C4—122no—
1100C4—122no—
1101C4—122no—
1102C4#577912yes—
1103C4#596411yescharacteristic
1104C4#596411yescharacteristic
1105C3#6261911yescharacteristic, complemented, Sylow
1106C2—41no—
1107C2—81no—
1108C2—122no—
1109C2—242no—
1110C2#8624411yescharacteristic
1111C2C2×#577911yescharacteristic
1112C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3172C2
socleC22×C3C23×D4
hypercenter#3172D3
hypocenterC3#62619
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
1. #86289C2semidirect
2. #86133C2semidirect
3. C3×#3172C2semidirect
4. #83324C2semidirect
5. #83145C2semidirect
6. #81988C2semidirect
7. #81880C2semidirect
8. #81738C2semidirect
9. #81667C2semidirect
10. #80918C2semidirect
11. #80916C2semidirect
12. #80842C2semidirect
13. #80820C2semidirect
14. #79740C2semidirect
15. #79735C2semidirect
16. #79703C2semidirect
17. #79699C2semidirect
18. #79685C2semidirect
19. #79681C2semidirect
20. #79628C2semidirect
21. #79621C2semidirect
22. #78528C2semidirect
23. #78511C2semidirect
155. #3172D3semidirect
1105. C3#62619semidirect

Maximal subgroups

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

subgroupindex
#862892
#861332
C3×#31722
#833242
#831452
#819882
#818802
#817382
#816672
#809182
#809162
#808422
#808202
#797402
#797352
#797032
#796992
#796852
#796812
#796282
#796212
#785282
#785112
#626193