Finite Group Databasebeta

← #11685752

Subgroups — #11685752

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86215C211yesmaximal, characteristic, complemented
2#86138C211yesmaximal, characteristic, complemented
3C3×#3238C211yesmaximal, characteristic, complemented
4#83224C211yesmaximal, characteristic, complemented
5#83140C211yesmaximal, characteristic
6#81971C212yesmaximal, complemented
7#81966C212yesmaximal, complemented
8#81677C212yesmaximal, complemented
9#81670C212yesmaximal, complemented
10#81422C212yesmaximal, complemented
11#81416C212yesmaximal, complemented
12#81279C212yesmaximal, complemented
13#81273C212yesmaximal
14#81138C211yesmaximal, characteristic, complemented
15#81137C211yesmaximal, characteristic, complemented
16#81135C211yesmaximal, characteristic, complemented
17#81102C211yesmaximal, characteristic, complemented
18#81091C211yesmaximal, characteristic, complemented
19#81087C211yesmaximal, characteristic, complemented
20#81056C211yesmaximal, characteristic, complemented
21#81054C211yesmaximal, characteristic, complemented
22#79348C211yesmaximal, characteristic, complemented
23#79316C211yesmaximal, characteristic, complemented
24#61859—31nomaximal, Sylow
25C2×C3×C4⋊Q8C2211yescharacteristic
26C3×#529C2211yescharacteristic
27Q8×#67—22no—
28#5730C2211yescharacteristic
29#5730C2211yescharacteristic
30#5729—22no—
31#5728—21no—
32#5727C2212yes—
33D3×C4⋊Q8—21no—
34#5722C2211yescharacteristic
35#5722C2211yescharacteristic
36#5721C2212yes—
37#5701—22no—
38#5685C2212yes—
39#5671C2212yes—
40#5651—22no—
41#5625C2212yes—
42#5603C2212yes—
43#5567C2211yescharacteristic
44Q8×Dic6C2211yescharacteristic
45#5543C2211yescharacteristic
46#5542—21no—
47#5542C2211yescharacteristic
48#5541—21no—
49#5519—21no—
50#5518—21no—
51#5511—21no—
52#5511—21no—
53#5504C2212yes—
54#5500C2212yes—
55C4×#235C2211yescharacteristic
56#5470C2211yescharacteristic
57#5470C2211yescharacteristic
58C3×#501C2212yes—
59C3×#489C2212yes—
60C3×#483C2212yes—
61C3×#480C2212yes—
62C3×#477C2211yescharacteristic
63C3×#477C2211yescharacteristic
64C3×#476C2211yescharacteristic
65C3×#476C2211yescharacteristic
66C3×#432C2211yescharacteristic
67#5093C2211yescharacteristic
68#5093C2211yescharacteristic
69#5091C2212yes—
70#5091C2212yes—
71#5078C2211yescharacteristic
72#5078C2211yescharacteristic
73#5066C2211yescharacteristic
74#5063C2211yescharacteristic
75#5057C2211yescharacteristic
76#5054C2211yescharacteristic
77#5047C2211yescharacteristic
78#5045C2211yescharacteristic
79#5037C2211yescharacteristic
80#5035C2211yescharacteristic
81C4×#216C2211yescharacteristic
82C4×#215C2211yescharacteristic
83C4×#214C2211yescharacteristic
84C4×#213C2211yescharacteristic
85#4970C2212yes—
86#4970C2212yes—
87#4925C2211yescharacteristic
88#4890C2212yes—
89#4889C2212yes—
90#4877C2212yes—
91#4876C2212yes—
92#4875C2212yes—
93#4875C2212yes—
94#4874C2212yes—
95#4873C2212yes—
96#4871C2212yes—
97#4858C2212yes—
98#4857C2212yes—
99#4857C2212yes—
100#4856C2212yes—
101#4854C2212yes—
102#4853C2212yes—
103#4852C2212yes—
104#4850C2211yescharacteristic
105#4849C2211yescharacteristic
106#4842C2211yescharacteristic
107#4841C2211yescharacteristic
108#4831C2211yescharacteristic
109#4831C2211yescharacteristic
110#4830C2211yescharacteristic
111#4830C2211yescharacteristic
112#4818C2212yes—
113#4817C2212yes—
114#4799C2212yes—
115#4797C2212yes—
116#4795C2212yes—
117#4793C2212yes—
118#4792C2212yes—
119#4790C2212yes—
120#4787C2212yes—
121#4768C2212yes—
122#4767C2212yes—
123#4765C2212yes—
124#4763C2212yes—
125#4759C2212yes—
126#4757C2212yes—
127#4756C2212yes—
128#4733C2212yes—
129#4723C2212yes—
130#4720C2212yes—
131#4720C2212yes—
132#4716C2212yes—
133#4710C2212yes—
134#4701C2212yes—
135#4701C2212yes—
136#3555—31no—
137#3503—31no—
138#3390—32no—
139#3386—32no—
140#3385—31no—
141#3385—31no—
142Q8×Q16—31no—
143#3380—31no—
144#3377—32no—
145#3372—31no—
146#3369—31no—
147#3367—32no—
148#3363—31no—
149#3360—31no—
150#3243—32no—
151#3242—32no—
152#3238D311yescharacteristic, complemented
153#3230—31no—
154#3124—32no—
155#3120—32no—
156#3116—31no—
157#3102—31no—
158#2985—31no—
159C22×C3×Q8—21no—
160C2×D3×Q8—22no—
161C2×#235C2311yescharacteristic
162C3×C4⋊Q8—21no—
163C3×C4⋊Q8—21no—
164C3×C4⋊Q8C2312yes—
165C3×C4⋊Q8C2311yescharacteristic
166C3×C4⋊Q8C2311yescharacteristic
167C3×#126—21no—
168C3×#125C2311yescharacteristic
169C3×#124C2311yescharacteristic
170C3×#123—21no—
171C3×C22⋊Q8C2311yescharacteristic
172C3×#121C2311yescharacteristic
173C3×C4×Q8C2311yescharacteristic
174C3×C4×D4—21no—
175C3×C4×D4C2311yescharacteristic
176C3×#117—21no—
177C2×C3×C4⋊C4—21no—
178C2×C3×C4⋊C4C2312yes—
179C2×C3×C42C2311yescharacteristic
180#946—22no—
181#946—22no—
182#946—22no—
183Q8×Dic3—22no—
184Q8×Dic3C2312yes—
185#944—22no—
186#944—22no—
187#944—22no—
188#944C2312yes—
189C2×#216C2311yescharacteristic
190C2×#215C2311yescharacteristic
191#936—22no—
192#936C2312yes—
193#935—22no—
194D4×Dic3C2312yes—
195C2×#214C2311yescharacteristic
196C2×#213C2311yescharacteristic
197C4×#67—21no—
198C4×#67—21no—
199C4×#67—22no—
200C4×#67—22no—
201#926—21no—
202#926—21no—
203#926C2311yescharacteristic
204#926C2312yes—
205C2×C4⋊Dic3—21no—
206#924—21no—
207#924—21no—
208#924—21no—
209#924—22no—
210#924—22no—
211#924D412yes—
212#924D411yescharacteristic
213#924D411yescharacteristic
214#924C2312yes—
215C2×Dic12C2312yes—
216C2×#204C2312yes—
217#897—21no—
218#897—21no—
219#896—22no—
220#896—22no—
221#893C2312yes—
222#893C2312yes—
223#892—22no—
224D3×C4⋊C4—22no—
225D3×C4⋊C4—21no—
226D3×C4⋊C4—21no—
227#890—22no—
228#890—22no—
229#890C2312yes—
230#890C2312yes—
231#890C2312yes—
232#889—22no—
233#889—22no—
234#889—22no—
235#889—22no—
236#889—22no—
237#889—22no—
238#888—22no—
239#888—21no—
240#888—21no—
241#888—22no—
242#888—22no—
243#888C2312yes—
244#888C2312yes—
245#888C2312yes—
246#887—21no—
247#887—21no—
248#887—22no—
249#887C2312yes—
250#887C2312yes—
251#887C2312yes—
252#887C2312yes—
253#879—22no—
254#879—22no—
255#879—22no—
256#879—22no—
257#879—22no—
258#879—22no—
259#878—22no—
260#878—22no—
261#878—22no—
262#877—22no—
263C4×D12C2311yescharacteristic
264C4×D12C2311yescharacteristic
265#872—21no—
266C42×D3—21no—
267#870—21no—
268#870—21no—
269#870D412yes—
270#869—21no—
271#869D411yescharacteristic
272#869D411yescharacteristic
273#869C2311yescharacteristic
274#869C2311yescharacteristic
275C4×Dic6—21no—
276C4×Dic6—21no—
277C4×Dic6—21no—
278C4×Dic6C2312yes—
279C4×Dic6C2311yescharacteristic
280C4×Dic6C2311yescharacteristic
281C4×Dic6C2312yes—
282C4×Dic6C2311yescharacteristic
283C4×Dic6C2311yescharacteristic
284C3×#107C2312yes—
285C3×#107C2312yes—
286C3×#106C2312yes—
287C3×#106C2312yes—
288C3×C4⋊C8C2311yescharacteristic
289C3×C4⋊C8C2311yescharacteristic
290C3×#103C2312yes—
291C3×#103C2312yes—
292C3×#102C2312yes—
293C3×#102C2312yes—
294C3×C22⋊C8C2312yes—
295C3×#97C2312yes—
296#835C2311yescharacteristic
297#835C2311yescharacteristic
298#832C2311yescharacteristic
299#832C2311yescharacteristic
300#830C2311yescharacteristic
301#830C2311yescharacteristic
302#821C2312yes—
303#818C2312yes—
304#817C2312yes—
305#816C2312yes—
306#816C2312yes—
307#816C2312yes—
308#815C2312yes—
309#815C2312yes—
310Dic3⋊C8C2312yes—
311Dic3⋊C8C2312yes—
312Dic3⋊C8C2312yes—
313Dic3⋊C8C2312yes—
314C8×Dic3C2312yes—
315C8×Dic3C2312yes—
316#810C2311yescharacteristic
317#810C2312yes—
318#810C2312yes—
319#810C2312yes—
320#810C2312yes—
321#810C2311yescharacteristic
322#809C2311yescharacteristic
323#809C2311yescharacteristic
324#808C2311yescharacteristic
325#808C2311yescharacteristic
326#807C2312yes—
327#807C2311yescharacteristic
328#807C2312yes—
329#807C2312yes—
330#807C2312yes—
331#807C2311yescharacteristic
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4×C3⋊C8C2311yescharacteristic
335C4×C3⋊C8C2311yescharacteristic
336#563—62no—
337Q82—31no—
338Q82—31no—
339Q82—31no—
340#557—32no—
341#557—32no—
342#557—31no—
343#556—32no—
344#556—31no—
345#556—61no—
346#554—31no—
347#554—31no—
348#554—31no—
349#554—61no—
350#554—61no—
351#552—61no—
352D4×Q8—32no—
353D4×Q8—62no—
354#544—32no—
355#544—61no—
356#544—62no—
357#542—32no—
358#541—32no—
359#541—61no—
360#541—62no—
361#533—31no—
362#533—31no—
363#533—61no—
364C2×C4⋊Q8—61no—
365C2×C4⋊Q8C2×D311yescharacteristic
366#529C2×D311yescharacteristic
367#520—32no—
368C4×#41—31no—
369#501—32no—
370#501—32no—
371#501C2×D312yes—
372#500—31no—
373#500—31no—
374#500—32no—
375#499—32no—
376#491—32no—
377#489—32no—
378#489C2×D312yes—
379#488—32no—
380#487—31no—
381#487—31no—
382#487—32no—
383#485—31no—
384#485—32no—
385#484—32no—
386#484—32no—
387#483C2×D312yes—
388#482—31no—
389#480C2×D312yes—
390#479—31no—
391#479—32no—
392#479—32no—
393#479—32no—
394#479—32no—
395#478—31no—
396#478—32no—
397#478—32no—
398#477—32no—
399#477—32no—
400#477—32no—
401#477—32no—
402#477—31no—
403#477—32no—
404#477C2×D311yescharacteristic
405#477C2×D311yescharacteristic
406#476—31no—
407#476C2×D311yescharacteristic
408#476C2×D311yescharacteristic
409#475—32no—
410#474—32no—
411#474—32no—
412#464—31no—
413#464—32no—
414#463—31no—
415#463—32no—
416#462—31no—
417#462—32no—
418#461—31no—
419#461—32no—
420#452—31no—
421#452—32no—
422#449—31no—
423#446—31no—
424#446—31no—
425#446—32no—
426#446—32no—
427C8×Q8—31no—
428C8×Q8—31no—
429#441—32no—
430#441—32no—
431#440—32no—
432#440—32no—
433#440—32no—
434#440—32no—
435C4×Q16—31no—
436C4×Q16—32no—
437C4×Q16—32no—
438C4×SD16—31no—
439C4×SD16—31no—
440C4×SD16—32no—
441C4×D8—31no—
442C4×D8—32no—
443#433—32no—
444#433—32no—
445#432C2×D311yescharacteristic
446#431—31no—
447C2×C3×Q8—22no—
448C2×C3×Q8—21no—
449C2×C3×Q8—21no—
450C2×C3×Q8—82no—
451C2×C3×Q8C2411yescharacteristic
452C2×C3×D4—21no—
453C2×C3×D4C2411yescharacteristic
454C22×C3×C4—22no—
455C22×C3×C4—21no—
456C22×C3×C4C2×D411yescharacteristic
457C22×C3×C4C2×D411yescharacteristic
458C22×C3×C4C2411yescharacteristic
459C2×#67—21no—
460C22×Dic3—22no—
461D3×Q8—84no—
462#235—22no—
463#235—22no—
464C2×D12C2411yescharacteristic
465C2×C4×D3—21no—
466C2×C4×D3—21no—
467C2×C4×D3—21no—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×Dic6—21no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6C2×D411yescharacteristic
475C2×Dic6C2×D411yescharacteristic
476C2×Dic6C2×D412yes—
477C2×Dic6C2412yes—
478C2×Dic6C2411yescharacteristic
479C2×C3×C8C2412yes—
480C2×C3×C8C2412yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—21no—
483C3×C4⋊C4—21no—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—21no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—21no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4C2412yes—
490C3×C4⋊C4C2412yes—
491C3×C4⋊C4C2411yescharacteristic
492C3×C4⋊C4C2411yescharacteristic
493C3×C22⋊C4—21no—
494C3×C22⋊C4—21no—
495C3×C22⋊C4—21no—
496C3×C22⋊C4—21no—
497C3×C22⋊C4—21no—
498C3×C42—21no—
499C3×C42C2×D411yescharacteristic
500C3×C42C2×D411yescharacteristic
501C3×C42C2411yescharacteristic
502C3×C42C2411yescharacteristic
503#217—22no—
504#217—21no—
505#217—22no—
506#217—22no—
507#217—22no—
508#217C2×D412yes—
509#217C2×D412yes—
510#216—22no—
511#215—22no—
512#214—22no—
513#213—22no—
514(C2×D3)⋊C4—21no—
515(C2×D3)⋊C4—21no—
516(C2×D3)⋊C4—22no—
517(C2×D3)⋊C4—22no—
518C4⋊Dic3—21no—
519C4⋊Dic3—21no—
520C4⋊Dic3—21no—
521C4⋊Dic3—22no—
522C4⋊Dic3—22no—
523C4⋊Dic3—22no—
524C4⋊Dic3—22no—
525C4⋊Dic3C2×D411yescharacteristic
526C4⋊Dic3C2×D411yescharacteristic
527C4⋊Dic3C2×D412yes—
528C4⋊Dic3C2×D412yes—
529C4⋊Dic3C2×D412yes—
530C4⋊Dic3C2412yes—
531C4⋊Dic3C2411yescharacteristic
532C4⋊Dic3C2411yescharacteristic
533Dic3⋊C4—22no—
534Dic3⋊C4—22no—
535Dic3⋊C4—21no—
536Dic3⋊C4—21no—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4C2×D412yes—
550Dic3⋊C4C2×D412yes—
551Dic3⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553C4×Dic3—22no—
554C4×Dic3—21no—
555C4×Dic3—21no—
556C4×Dic3—21no—
557C4×Dic3—22no—
558C4×Dic3—22no—
559C4×Dic3—22no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3C2412yes—
563C4×Dic3C2412yes—
564C2×C3⋊C8C2411yescharacteristic
565C2×C3⋊C8C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2411yescharacteristic
568Dic12—24no—
569#204—24no—
570C2×#41—31no—
571C22×Q8—21no—
572C22×Q8—62no—
573C2×Q16—31no—
574C2×Q16—32no—
575C2×SD16—31no—
576C2×SD16—31no—
577C2×SD16—32no—
578C2×D8—31no—
579C4⋊Q8—21no—
580C4⋊Q8—21no—
581C4⋊Q8—32no—
582C4⋊Q8—32no—
583C4⋊Q8—32no—
584C4⋊Q8—32no—
585C4⋊Q8—31no—
586C4⋊Q8—31no—
587C4⋊Q8—31no—
588C4⋊Q8—31no—
589C4⋊Q8—61no—
590C4⋊Q8—62no—
591C4⋊Q8—61no—
592C4⋊Q8—61no—
593C4⋊Q8—62no—
594C4⋊Q8—62no—
595C4⋊Q8—62no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8C22×D312yes—
599C4⋊Q8C22×D311yescharacteristic
600C4⋊Q8C22×D311yescharacteristic
601#126—21no—
602#126—62no—
603#126—62no—
604#126—62no—
605#126—62no—
606#126—62no—
607#126—62no—
608#125—32no—
609#125—32no—
610#125—32no—
611#125—32no—
612#125—61no—
613#125—62no—
614#125—62no—
615#125—62no—
616#125—62no—
617#125—62no—
618#125—62no—
619#125—62no—
620#125—62no—
621#125—61no—
622#125C22×D311yescharacteristic
623#124—32no—
624#124—62no—
625#124C22×D311yescharacteristic
626#123—21no—
627#123—62no—
628C22⋊Q8—32no—
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—61no—
640C22⋊Q8—61no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—61no—
645C22⋊Q8—61no—
646C22⋊Q8—61no—
647C22⋊Q8C22×D311yescharacteristic
648#121C22×D311yescharacteristic
649C4×Q8—32no—
650C4×Q8—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—32no—
655C4×Q8—32no—
656C4×Q8—32no—
657C4×Q8—31no—
658C4×Q8—31no—
659C4×Q8—32no—
660C4×Q8—61no—
661C4×Q8—61no—
662C4×Q8—62no—
663C4×Q8—61no—
664C4×Q8—61no—
665C4×Q8—62no—
666C4×Q8—61no—
667C4×Q8C22×D311yescharacteristic
668C4×D4—21no—
669C4×D4—32no—
670C4×D4—32no—
671C4×D4—32no—
672C4×D4—31no—
673C4×D4—31no—
674C4×D4—62no—
675C4×D4—62no—
676C4×D4—61no—
677C4×D4—61no—
678C4×D4C22×D311yescharacteristic
679#117—21no—
680#117—32no—
681#117—31no—
682#117—62no—
683#117—62no—
684#117—61no—
685#117—61no—
686#117—61no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—62no—
689C2×C4⋊C4—61no—
690C2×C4⋊C4—61no—
691C2×C4⋊C4—61no—
692C2×C4⋊C4C22×D312yes—
693C2×C42—61no—
694C2×C42C22×D311yescharacteristic
695#107—32no—
696#107—32no—
697#107—31no—
698#107—31no—
699#107—32no—
700#107—32no—
701#107—32no—
702#107C22×D312yes—
703#107C22×D312yes—
704#106—32no—
705#106—31no—
706#106—31no—
707#106C22×D312yes—
708#106C22×D312yes—
709C4⋊C8—32no—
710C4⋊C8—32no—
711C4⋊C8—32no—
712C4⋊C8—32no—
713C4⋊C8—31no—
714C4⋊C8—31no—
715C4⋊C8C22×D311yescharacteristic
716C4⋊C8C22×D311yescharacteristic
717#103—31no—
718#103—31no—
719#103—32no—
720#103—32no—
721#103—32no—
722#103—31no—
723#103—32no—
724#103—31no—
725#103—32no—
726#103—32no—
727#103—32no—
728#103C22×D312yes—
729#103C22×D312yes—
730#102—31no—
731#102—31no—
732#102—32no—
733#102—31no—
734#102—31no—
735#102C22×D312yes—
736#102C22×D312yes—
737C22⋊C8—31no—
738C22⋊C8—31no—
739C22⋊C8C22×D312yes—
740#97—32no—
741#97—32no—
742#97C22×D312yes—
743C4×C8—32no—
744C4×C8—32no—
745C4×C8—31no—
746C4×C8—31no—
747C23×C3—21no—
748C23×C3C22×D411yescharacteristic
749C22×D3—21no—
750C3×Q8—21no—
751C3×Q8—21no—
752C3×Q8—44no—
753C3×Q8—81no—
754C3×Q8—81no—
755C3×D4—21no—
756C3×D4—21no—
757C3×D4—81no—
758C2×C3×C4—22no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—41no—
767C2×C3×C4—42no—
768C2×C3×C4—82no—
769C2×C3×C4C22×D411yescharacteristic
770C2×C3×C4C22×D411yescharacteristic
771C2×C3×C4C22×D411yescharacteristic
772C2×C3×C4C22×D411yescharacteristic
773C2×C3×C4C22×D411yescharacteristic
774C2×C3×C4C2511yescharacteristic
775#67—24no—
776C2×Dic3—21no—
777C2×Dic3—22no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—22no—
781C2×Dic3—82no—
782C2×Dic3C22×D412yes—
783C2×Dic3C22×D412yes—
784C2×Dic3C22×D412yes—
785C2×Dic3C22×D412yes—
786D12—21no—
787D122−1+412yes—
788C4×D3—24no—
789C4×D3—42no—
790C4×D3—42no—
791C4×D3—82no—
792C4×D3—82no—
793Dic6—22no—
794Dic6—22no—
795Dic6—21no—
796Dic6—22no—
797Dic6—22no—
798Dic6—42no—
799Dic6—82no—
800Dic6—82no—
801Dic6—82no—
802Dic6—81no—
803Dic62−1+412yes—
804C3×C8—22no—
805C3×C8—22no—
806C3⋊C8—21no—
807C3⋊C8—21no—
808C3⋊C8—21no—
809C3⋊C8—21no—
810#41—62no—
811#41—62no—
812C2×Q8—22no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—31no—
816C2×Q8—31no—
817C2×Q8—32no—
818C2×Q8—31no—
819C2×Q8—32no—
820C2×Q8—62no—
821C2×Q8—62no—
822C2×Q8—62no—
823C2×Q8—61no—
824C2×Q8—82no—
825C2×Q8—244no—
826C2×Q8C23×D311yescharacteristic
827C2×D4—21no—
828C2×D4—31no—
829C2×D4—61no—
830C2×D4C23×D311yescharacteristic
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—62no—
834C22×C4—62no—
835C22×C4—62no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4D3×D411yescharacteristic
840C22×C4D3×D411yescharacteristic
841C22×C4C23×D311yescharacteristic
842Q16—64no—
843Q16—62no—
844SD16—64no—
845SD16—62no—
846SD16—62no—
847D8—62no—
848C2×C8—31no—
849C2×C8—31no—
850C2×C8—31no—
851C2×C8—31no—
852C2×C8C23×D312yes—
853C2×C8C23×D312yes—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—31no—
863C4⋊C4—32no—
864C4⋊C4—31no—
865C4⋊C4—32no—
866C4⋊C4—32no—
867C4⋊C4—32no—
868C4⋊C4—32no—
869C4⋊C4—32no—
870C4⋊C4—32no—
871C4⋊C4—31no—
872C4⋊C4—31no—
873C4⋊C4—32no—
874C4⋊C4—62no—
875C4⋊C4—62no—
876C4⋊C4—62no—
877C4⋊C4—62no—
878C4⋊C4—62no—
879C4⋊C4—62no—
880C4⋊C4—62no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—62no—
890C4⋊C4—61no—
891C4⋊C4—61no—
892C4⋊C4—61no—
893C4⋊C4—61no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—61no—
897C4⋊C4C23×D311yescharacteristic
898C4⋊C4C23×D311yescharacteristic
899C4⋊C4C23×D312yes—
900C4⋊C4C23×D312yes—
901C22⋊C4—21no—
902C22⋊C4—21no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—32no—
907C22⋊C4—32no—
908C22⋊C4—62no—
909C22⋊C4—62no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—62no—
913C22⋊C4—61no—
914C22⋊C4—62no—
915C22⋊C4—61no—
916C22⋊C4—61no—
917C42—21no—
918C42—32no—
919C42—32no—
920C42—62no—
921C42—62no—
922C42—62no—
923C42—62no—
924C42—62no—
925C42—61no—
926C42—61no—
927C42—61no—
928C42—62no—
929C42D3×D411yescharacteristic
930C42D3×D411yescharacteristic
931C42C23×D311yescharacteristic
932C42C23×D311yescharacteristic
933C22×C3—21no—
934C22×C3—21no—
935C22×C3—21no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3C23×D411yescharacteristic
940C2×D3—22no—
941C2×D3—41no—
942C2×D3—41no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—41no—
948C3×C4—42no—
949C3×C4—42no—
950C3×C4—41no—
951C3×C4—41no—
952C3×C4#57812yes—
953C3×C4C2×2−1+411yescharacteristic
954C3×C4C2×2−1+411yescharacteristic
955Dic3—22no—
956Dic3—22no—
957Dic3—22no—
958Dic3—22no—
959Dic3—22no—
960Dic3—41no—
961Dic3—42no—
962Dic3—42no—
963Dic3—41no—
964C23—21no—
965C23—61no—
966C23C2×D3×D411yescharacteristic
967Q8—21no—
968Q8—21no—
969Q8—32no—
970Q8—44no—
971Q8—61no—
972Q8—62no—
973Q8—62no—
974Q8—62no—
975Q8—62no—
976Q8—81no—
977Q8—81no—
978Q8—122no—
979Q8—241no—
980Q8—242no—
981Q8—242no—
982Q8—242no—
983D4—21no—
984D4—21no—
985D4—32no—
986D4—64no—
987D4—61no—
988D4—81no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—32no—
998C2×C4—32no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—41no—
1002C2×C4—42no—
1003C2×C4—64no—
1004C2×C4—61no—
1005C2×C4—62no—
1006C2×C4—61no—
1007C2×C4—62no—
1008C2×C4—61no—
1009C2×C4—82no—
1010C2×C4—122no—
1011C2×C4—122no—
1012C2×C4—242no—
1013C2×C4—242no—
1014C2×C4—242no—
1015C2×C4C2×D3×D411yescharacteristic
1016C2×C4C2×D3×D411yescharacteristic
1017C2×C4C2×D3×D411yescharacteristic
1018C2×C4C2×D3×D411yescharacteristic
1019C2×C4C2×D3×D411yescharacteristic
1020C2×C4C24×D311yescharacteristic
1021C8—22no—
1022C8—22no—
1023C8—61no—
1024C8—61no—
1025C8—61no—
1026C8—61no—
1027C2×C3—41no—
1028C2×C3—81no—
1029C2×C3#348611yescharacteristic
1030C2×C3C2×#57811yescharacteristic
1031C2×C3#358511yescharacteristic
1032D3—42no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—62no—
1040C22—121no—
1041C22—121no—
1042C22C22×D3×D411yescharacteristic
1043C4—21no—
1044C4—21no—
1045C4—21no—
1046C4—21no—
1047C4—41no—
1048C4—42no—
1049C4—42no—
1050C4—41no—
1051C4—41no—
1052C4—62no—
1053C4—62no—
1054C4—62no—
1055C4—62no—
1056C4—62no—
1057C4—122no—
1058C4—121no—
1059C4—122no—
1060C4—121no—
1061C4#577912yes—
1062C4D3×2−1+411yescharacteristic
1063C4D3×2−1+411yescharacteristic
1064C3#6185911yescharacteristic, complemented, Sylow
1065C2—41no—
1066C2—81no—
1067C2—122no—
1068C2#8635511yescharacteristic
1069C2#8719211yescharacteristic
1070C2C2×#577911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3238C2
socleC22×C3C23×D4
prime radical#5037C22
hypercenter#3238D3
hypocenterC3#61859
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
1. #86215C2semidirect
2. #86138C2semidirect
3. C3×#3238C2semidirect
4. #83224C2semidirect
6. #81971C2semidirect
7. #81966C2semidirect
8. #81677C2semidirect
9. #81670C2semidirect
10. #81422C2semidirect
11. #81416C2semidirect
12. #81279C2semidirect
14. #81138C2semidirect
15. #81137C2semidirect
16. #81135C2semidirect
17. #81102C2semidirect
18. #81091C2semidirect
19. #81087C2semidirect
20. #81056C2semidirect
21. #81054C2semidirect
22. #79348C2semidirect
23. #79316C2semidirect
152. #3238D3semidirect
1064. C3#61859semidirect

Maximal subgroups

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

subgroupindex
#862152
#861382
C3×#32382
#832242
#831402
#819712
#819662
#816772
#816702
#814222
#814162
#812792
#812732
#811382
#811372
#811352
#811022
#810912
#810872
#810562
#810542
#793482
#793162
#618593