Finite Group Databasebeta

← #7698907

Subgroups — #7698907

Order 512.

5186 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59750C213yesmaximal, complemented
2#59232C213yesmaximal, complemented
3#59217C213yesmaximal, complemented
4#52228C213yesmaximal, complemented
5#45382C213yesmaximal, complemented
6#45378C213yesmaximal, complemented
7#45228C213yesmaximal, complemented
8#45009C213yesmaximal, complemented
9#44963C213yesmaximal, complemented
10#44925C213yesmaximal, complemented
11#38942C213yesmaximal, complemented
12#38936C213yesmaximal, complemented
13#38290C213yesmaximal, complemented
14#38288C213yesmaximal, complemented
15#37954C213yesmaximal, complemented
16#37953C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18#36467C211yesmaximal, characteristic, complemented
19#36430C211yesmaximal, characteristic, complemented
20#36049C211yesmaximal, characteristic, complemented
21#36049C211yesmaximal, characteristic, complemented
22#36029C211yesmaximal, characteristic, complemented
23#35957C211yesmaximal, characteristic, complemented
24#35854C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#34295C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34263C211yesmaximal, characteristic, complemented
30#34193C211yesmaximal, characteristic, complemented
31#34192C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2861C2213yes—
45#2856C2213yes—
46#2850C2213yes—
47#2808C2216yes—
48#2803C2216yes—
49#2795C2216yes—
50#2785C2213yes—
51#2784C2213yes—
52#2784C2216yes—
53#2783C2216yes—
54#2781C2213yes—
55#2781C2213yes—
56#2781C2216yes—
57#2775C2213yes—
58#2775C2213yes—
59#2769C2213yes—
60#2756C2213yes—
61#2756C2213yes—
62#2756C2216yes—
63#2756C2216yes—
64#2756C2216yes—
65#2744C2211yescharacteristic
66#2744C2213yes—
67#2737C2213yes—
68#2737C2213yes—
69#2737C2216yes—
70#2699C2213yes—
71#2699C2216yes—
72#2686C2213yes—
73#2686C2213yes—
74#2686C2216yes—
75#2686C2216yes—
76#2660C2213yes—
77#2641C2213yes—
78#2641C2213yes—
79#2640C2213yes—
80#2620C2213yes—
81#2619C2213yes—
82#2610C2216yes—
83#2610C2216yes—
84#2609C2216yes—
85#2592C2213yes—
86#2592C2213yes—
87#2584C2213yes—
88#2572C2216yes—
89#2567C2213yes—
90#2563C2213yes—
91#2562C2213yes—
92#2562C2213yes—
93#2562C2213yes—
94#2555C2216yes—
95#2552C2213yes—
96#2552C2213yes—
97#2550C2213yes—
98#2550C2213yes—
99#2548C2213yes—
100#2548C2213yes—
101#2548C2213yes—
102#2544C2213yes—
103#2544C2213yes—
104#2541C2213yes—
105#2538C2213yes—
106#2537C2216yes—
107#2537C2213yes—
108#2535C2213yes—
109#2535C2213yes—
110#2531C2216yes—
111#2529C2216yes—
112#2518C2216yes—
113#2518C2216yes—
114#2500C2216yes—
115#2497C2216yes—
116#2492C2213yes—
117#2491C2213yes—
118#2491C2213yes—
119#2491C2213yes—
120#2491C2213yes—
121#2491C2213yes—
122#2490C2213yes—
123#2490C2213yes—
124#2490C2213yes—
125#2490C2213yes—
126#2490C2213yes—
127#2490C2213yes—
128#2490C2213yes—
129#2489C2213yes—
130#2489C2213yes—
131#2489C2213yes—
132#2485C2216yes—
133#2476C2216yes—
134#2476C2216yes—
135#2476C2216yes—
136#2474C2216yes—
137#2459C2216yes—
138#2459C2216yes—
139#2428C2213yes—
140#2428C2213yes—
141#2428C2213yes—
142#2428C2213yes—
143#2427C2213yes—
144#2427C2213yes—
145#2426C2213yes—
146#2426C2213yes—
147#2420C2216yes—
148#2417C2213yes—
149#2416C2213yes—
150#2416C2213yes—
151#2416C2213yes—
152#2416C2213yes—
153#2416C2213yes—
154#2415C2213yes—
155#2414C2216yes—
156#2414C2213yes—
157#2399C2213yes—
158#2398C2213yes—
159#2398C2213yes—
160#2398C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2367C2213yes—
164#2366C2213yes—
165#2363C2216yes—
166#2363C2213yes—
167#2361C2213yes—
168#2361C2213yes—
169#2360C2213yes—
170#2357C2213yes—
171#2357C2213yes—
172#2356C2213yes—
173#2356C2213yes—
174#2354C2213yes—
175#2354C2213yes—
176#2354C2213yes—
177#2354C2213yes—
178#2352C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185D4×C4⋊C4C2213yes—
186#2347C2213yes—
187#2347C2213yes—
188#2345C2213yes—
189#2345C2213yes—
190#2345C2213yes—
191#2345C2213yes—
192#2344C2213yes—
193#2344C2213yes—
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2328C2213yes—
207#2326C2213yes—
208#2324C2213yes—
209#2323C2213yes—
210#2320C2213yes—
211#2320C2213yes—
212#2319C2213yes—
213#2319C2213yes—
214#2319C2213yes—
215#2319C2213yes—
216#2314C2213yes—
217#2314C2213yes—
218C4×#124C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221C4×#121C2213yes—
222C4×#121C2213yes—
223#2298C2213yes—
224#2298C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2290C2213yes—
228#2290C2213yes—
229#2285C2213yes—
230#2283C2213yes—
231#2283C2213yes—
232#2283C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#557—44no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247#548—28no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×#127C2313yes—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×#124C2316yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2316yes—
281C2×#121C2316yes—
282C2×#121C2316yes—
283#520—28no—
284#520—28no—
285C4×#41—28no—
286C2×C4×Q8—28no—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2316yes—
315C2×C4×D4C2316yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2316yes—
320C2×#117C2316yes—
321C2×#117C2316yes—
322C22×C4⋊C4C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C4⋊C4C2313yes—
325C22×C42C2313yes—
326C22×C42C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2316yes—
330#400C2311yescharacteristic
331#400C2311yescharacteristic
332#400C2313yes—
333#400C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2311yescharacteristic
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#397C2313yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2313yes—
347#397C2313yes—
348#397C2311yescharacteristic
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#396C2313yes—
355#396C2316yes—
356#396C2316yes—
357#396C2311yescharacteristic
358#396C2313yes—
359#396C2313yes—
360#396C2316yes—
361#395C2313yes—
362#395C2316yes—
363#395C2313yes—
364#395C2313yes—
365#395C2313yes—
366#394C2316yes—
367#394C2316yes—
368#394C2316yes—
369#394C2316yes—
370#394C2316yes—
371#394C2316yes—
372#394C2316yes—
373#394C2313yes—
374#394C2316yes—
375#394C2316yes—
376#394C2313yes—
377#394C2313yes—
378#394C2316yes—
379#394C2316yes—
380#394C2313yes—
381#394C2313yes—
382#394C2313yes—
383#394C2313yes—
384#394C2313yes—
385#394C2313yes—
386#394C2313yes—
387#394C2313yes—
388#394C2313yes—
389#394C2316yes—
390#394C2316yes—
391#394C2316yes—
392#393C2313yes—
393#393C2316yes—
394#393C2313yes—
395#393C2316yes—
396#393C2313yes—
397#393C2313yes—
398#393C2313yes—
399#393C2313yes—
400#392C2316yes—
401#392C2316yes—
402#392C2313yes—
403#392C2313yes—
404#392C2316yes—
405#391C2316yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#390C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2316yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2316yes—
434#390C2316yes—
435#390C2313yes—
436#390C2316yes—
437#390C2316yes—
438#390C2313yes—
439#390C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#388C2313yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2313yes—
468#388C2316yes—
469#388C2313yes—
470#388C2313yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2311yescharacteristic
495#388C2311yescharacteristic
496#388C2313yes—
497#388C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2311yescharacteristic
514#387C2311yescharacteristic
515#387C2311yescharacteristic
516#386C2316yes—
517#386C2316yes—
518#386C2316yes—
519#386C2313yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2316yes—
525#386C2313yes—
526#386C2313yes—
527#386C2313yes—
528#386C2313yes—
529#386C2316yes—
530#386C2313yes—
531#386C2313yes—
532#386C2313yes—
533#385C2313yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2313yes—
538#385C2311yescharacteristic
539#384C2316yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#383C2313yes—
544#383C2316yes—
545#383C2313yes—
546#383C2313yes—
547#383C2313yes—
548#382C2316yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2311yescharacteristic
555#382C2313yes—
556#382C2313yes—
557#381C2316yes—
558#381C2316yes—
559#381C2313yes—
560#381C2313yes—
561#381C2313yes—
562#381C2311yescharacteristic
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2316yes—
576#380C2316yes—
577#380C2316yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2316yes—
583#380C2313yes—
584#380C2311yescharacteristic
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2316yes—
623C4×C22⋊C4C2316yes—
624#376C2313yes—
625#376C2313yes—
626#376C2313yes—
627#376C2313yes—
628#376C2316yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2411yescharacteristic
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2413yes—
652C22×D4C2416yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C22×D4C2416yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2411yescharacteristic
663C23×C4C2413yes—
664C23×C4C2416yes—
665C23×C4C2416yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C4⋊Q8—46no—
669C4⋊Q8—46no—
670#127—212no—
671#127—46no—
672#127—46no—
673#125—46no—
674#125—46no—
675#125—46no—
676#125—46no—
677#124—212no—
678#124—46no—
679#124—46no—
680#124—46no—
681#124—86no—
682#124—86no—
683C22⋊Q8—212no—
684C22⋊Q8—46no—
685C22⋊Q8—46no—
686#121—212no—
687#121—212no—
688#121—212no—
689#121—46no—
690#121—412no—
691#121—46no—
692#121—46no—
693#121—46no—
694#121—46no—
695#121—46no—
696#121—46no—
697#121—46no—
698#121—86no—
699#121—86no—
700#121—86no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—212no—
711C4×Q8—212no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8#4118yes—
715C4×Q8#4118yes—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—212no—
723C4×D4—212no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—86no—
729C4×D4—86no—
730#117—212no—
731#117—212no—
732#117—212no—
733#117—86no—
734#117—86no—
735#117—86no—
736C2×C4⋊C4—212no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4—212no—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2416yes—
836C2×C22⋊C4C2413yes—
837C2×C42—212no—
838C2×C42—212no—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2411yescharacteristic
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2416yes—
855C2×C42C2416yes—
856C2×C42C2416yes—
857C2×C42C2416yes—
858C2×C42C2413yes—
859C2×C42C2411yescharacteristic
860C2×C42C2413yes—
861C2×C42C2413yes—
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2416yes—
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2416yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2416yes—
906#95C2416yes—
907#95C2413yes—
908#95C2416yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2416yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921C24C2513yes—
922C24C2513yes—
923C24C2513yes—
924C24C2511yescharacteristic
925#41—416no—
926#41—416no—
927#41—416no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—43no—
932C2×Q8—43no—
933C2×Q8—43no—
934C2×Q8—43no—
935C2×Q8—43no—
936C2×Q8—43no—
937C2×Q8—416no—
938C2×Q8C2×#4114yes—
939C2×Q8C2×#4114yes—
940C2×Q8H(5,𝔽2)14yes—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—26no—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—212no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—43no—
957C2×D4—43no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—43no—
961C2×D4—46no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—46no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—46no—
972C2×D4—46no—
973C2×D4—46no—
974C2×D4—46no—
975C2×D4—46no—
976C2×D4—46no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—212no—
995C22×C4—212no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—41no—
999C22×C4—46no—
1000C22×C4—46no—
1001C22×C4—43no—
1002C22×C4—43no—
1003C22×C4—46no—
1004C22×C4—46no—
1005C22×C4—43no—
1006C22×C4—43no—
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2513yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—212no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—26no—
1043C4⋊C4—22no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—46no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4C2×#41112yes—
1078C4⋊C4C2×#41112yes—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—212no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—22no—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—212no—
1092C22⋊C4—43no—
1093C22⋊C4—41no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—46no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—46no—
1102C22⋊C4—46no—
1103C22⋊C4—46no—
1104C22⋊C4—46no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—46no—
1117C22⋊C4—46no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—46no—
1122C22⋊C4—46no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—46no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C42—22no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—41no—
1146C42—46no—
1147C42—43no—
1148C42—43no—
1149C42—46no—
1150C42—46no—
1151C42—46no—
1152C42—43no—
1153C42C2×#41112yes—
1154C42C2×#41112yes—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—23no—
1162C23—23no—
1163C23—23no—
1164C23—23no—
1165C23—23no—
1166C23—23no—
1167C23—23no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—23no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23#58512yes—
1183C23C2611yescharacteristic
1184Q8—412no—
1185Q8—86no—
1186Q8—86no—
1187Q8#555116yes—
1188D4—412no—
1189D4—412no—
1190D4—412no—
1191D4—412no—
1192D4—86no—
1193D4—812no—
1194D4—86no—
1195D4—86no—
1196D4—86no—
1197D4—86no—
1198D4—166no—
1199D4—166no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—44no—
1275C2×C4—412no—
1276C2×C4—412no—
1277C2×C4—412no—
1278C2×C4—412no—
1279C2×C4—412no—
1280C2×C4—812no—
1281C2×C4—86no—
1282C2×C4—86no—
1283C2×C4—812no—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4116yes—
1287C2×C4C22×#4116yes—
1288C2×C4C22×#4116yes—
1289C2×C4C22×#4116yes—
1290C2×C4C2×H(5,𝔽2)16yes—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—43no—
1299C22—43no—
1300C22—43no—
1301C22—43no—
1302C22—43no—
1303C22—43no—
1304C22—43no—
1305C22—43no—
1306C22—43no—
1307C22—43no—
1308C22—43no—
1309C22—43no—
1310C22—43no—
1311C22—43no—
1312C22—43no—
1313C22—43no—
1314C22—43no—
1315C22—43no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22C23×#4111yescharacteristic
1320C22C23×#4111yescharacteristic
1321C22C22×H(5,𝔽2)11yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22H(7,𝔽2)11yescharacteristic
1324C22H(7,𝔽2)11yescharacteristic
1325C222−1+611yescharacteristic
1326C4—22no—
1327C4—26no—
1328C4—22no—
1329C4—26no—
1330C4—41no—
1331C4—41no—
1332C4—43no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—43no—
1337C4—43no—
1338C4—41no—
1339C4—41no—
1340C4—43no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—41no—
1345C4—43no—
1346C4—43no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—43no—
1352C4C2×#555112yes—
1353C2—42no—
1354C2—83no—
1355C2—83no—
1356C2—83no—
1357C2C22×#55511yescharacteristic
1358C2#6285111yescharacteristic
1359C2#6285811yescharacteristic
1360C2#6289911yescharacteristic
1361C2#6300511yescharacteristic
1362C2#6300811yescharacteristic
1363C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59750C2semidirect
2. #59232C2semidirect
3. #59217C2semidirect
4. #52228C2semidirect
5. #45382C2semidirect
6. #45378C2semidirect
7. #45228C2semidirect
8. #45009C2semidirect
9. #44963C2semidirect
10. #44925C2semidirect
11. #38942C2semidirect
12. #38936C2semidirect
13. #38290C2semidirect
14. #38288C2semidirect
15. #37954C2semidirect
16. #37953C2semidirect
17. #36576C2semidirect
18. #36467C2semidirect
19. #36430C2semidirect
20. #36049C2semidirect
21. #36049C2semidirect
22. #36029C2semidirect
23. #35957C2semidirect
24. #35854C2semidirect
25. #35831C2semidirect
26. #34295C2semidirect
27. #34294C2semidirect
28. #34263C2semidirect
29. #34263C2semidirect
30. #34193C2semidirect
31. #34192C2semidirect

Maximal subgroups

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

subgroupindex
#597502
#592322
#592172
#522282
#453822
#453782
#452282
#450092
#449632
#449252
#389422
#389362
#382902
#382882
#379542
#379532
#365762
#364672
#364302
#360492
#360292
#359572
#358542
#358312
#342952
#342942
#342632
#341932
#341922