Finite Group Databasebeta

← #7692867

Subgroups — #7692867

Order 512.

5178 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#59767C213yesmaximal, complemented
2#59750C213yesmaximal, complemented
3#59564C213yesmaximal, complemented
4#59233C213yesmaximal, complemented
5#59230C213yesmaximal, complemented
6#45369C213yesmaximal, complemented
7#45133C213yesmaximal, complemented
8#44993C213yesmaximal, complemented
9#44925C213yesmaximal, complemented
10#38285C213yesmaximal, complemented
11#38284C213yesmaximal, complemented
12#37953C213yesmaximal, complemented
13#37952C213yesmaximal, complemented
14Q8×#124C211yesmaximal, characteristic, complemented
15#36467C211yesmaximal, characteristic, complemented
16#36457C211yesmaximal, characteristic, complemented
17#36434C211yesmaximal, characteristic, complemented
18#36430C211yesmaximal, characteristic, complemented
19#36385C213yesmaximal, complemented
20#36373C213yesmaximal, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35854C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35771C211yesmaximal, characteristic, complemented
25#34874C213yesmaximal, complemented
26#34294C211yesmaximal, characteristic, complemented
27#34293C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34262C211yesmaximal, characteristic, complemented
30#34129C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2862C2213yes—
45#2861C2213yes—
46#2858C2213yes—
47#2850C2213yes—
48#2850C2213yes—
49#2808C2216yes—
50#2803C2216yes—
51#2785C2216yes—
52#2785C2216yes—
53#2784C2216yes—
54#2784C2216yes—
55#2783C2216yes—
56#2781C2216yes—
57#2781C2216yes—
58#2775C2216yes—
59#2756C2216yes—
60#2744C2216yes—
61#2731C2216yes—
62#2686C2216yes—
63#2660C2213yes—
64#2640C2213yes—
65#2620C2213yes—
66#2620C2213yes—
67#2612C2213yes—
68#2610C2216yes—
69#2610C2213yes—
70#2610C2213yes—
71#2609C2216yes—
72#2609C2213yes—
73#2593C2216yes—
74#2593C2213yes—
75#2592C2213yes—
76#2592C2213yes—
77#2584C2213yes—
78#2574C2216yes—
79#2574C2213yes—
80#2574C2213yes—
81#2568C2213yes—
82#2563C2213yes—
83#2563C2213yes—
84#2563C2216yes—
85#2563C2213yes—
86#2562C2213yes—
87#2555C2213yes—
88#2551C2213yes—
89#2551C2213yes—
90#2550C2213yes—
91#2550C2213yes—
92#2548C2213yes—
93#2546C2213yes—
94#2545C2213yes—
95#2545C2213yes—
96#2544C2213yes—
97#2544C2213yes—
98#2538C2213yes—
99#2537C2213yes—
100#2536C2213yes—
101#2535C2213yes—
102#2532C2216yes—
103#2531C2213yes—
104#2531C2213yes—
105#2529C2213yes—
106#2529C2213yes—
107#2529C2216yes—
108#2526C2216yes—
109#2518C2216yes—
110#2508C2216yes—
111#2492C2213yes—
112#2492C2213yes—
113#2492C2213yes—
114#2492C2213yes—
115#2492C2213yes—
116#2491C2213yes—
117#2491C2213yes—
118#2491C2213yes—
119#2491C2213yes—
120#2491C2216yes—
121#2491C2213yes—
122#2490C2213yes—
123#2490C2213yes—
124#2490C2213yes—
125#2489C2213yes—
126#2489C2213yes—
127#2489C2213yes—
128#2476C2213yes—
129#2476C2213yes—
130#2476C2216yes—
131#2474C2216yes—
132#2474C2216yes—
133#2474C2213yes—
134#2474C2216yes—
135#2474C2211yescharacteristic
136#2459C2216yes—
137#2439C2216yes—
138#2429C2213yes—
139#2429C2213yes—
140#2428C2213yes—
141#2428C2213yes—
142#2427C2213yes—
143#2427C2213yes—
144#2426C2213yes—
145#2426C2213yes—
146#2417C2213yes—
147#2417C2213yes—
148#2416C2213yes—
149#2416C2213yes—
150#2415C2213yes—
151#2415C2213yes—
152#2414C2213yes—
153#2414C2216yes—
154#2414C2213yes—
155#2399C2213yes—
156#2398C2213yes—
157#2392C2213yes—
158#2392C2213yes—
159#2372C2216yes—
160#2367C2213yes—
161#2367C2213yes—
162#2363C2216yes—
163#2363C2213yes—
164#2362C2213yes—
165#2361C2213yes—
166#2360C2213yes—
167#2357C2213yes—
168#2356C2213yes—
169#2355C2213yes—
170#2355C2213yes—
171#2355C2213yes—
172#2354C2213yes—
173#2354C2213yes—
174#2354C2213yes—
175#2354C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182D4×C4⋊C4C2213yes—
183#2347C2213yes—
184#2346C2216yes—
185#2346C2213yes—
186#2346C2213yes—
187#2346C2213yes—
188#2345C2213yes—
189#2345C2213yes—
190#2345C2213yes—
191#2344C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2326C2213yes—
205#2326C2213yes—
206#2324C2213yes—
207#2323C2213yes—
208#2320C2213yes—
209#2319C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×#124C2213yes—
213C4×#124C2213yes—
214C4×#124C2213yes—
215C4×C22⋊Q8C2213yes—
216C4×#121C2213yes—
217C4×#121C2213yes—
218C4×#121C2213yes—
219#2298C2213yes—
220#2298C2213yes—
221#2295C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2290C2213yes—
228#2290C2213yes—
229#2285C2213yes—
230#2285C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242Q82—44no—
243#557—44no—
244#550—44no—
245D4×Q8—44no—
246#548—28no—
247#548—28no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2316yes—
256C2×#127C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2311yescharacteristic
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2316yes—
283#520—28no—
284#519—28no—
285C4×#41—28no—
286C2×C4×Q8—28no—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
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×#117C2313yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2311yescharacteristic
320C2×#117C2316yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2316yes—
325C22×C4⋊C4C2313yes—
326C22×C4⋊C4C2313yes—
327C22×C42C2313yes—
328C22×C42C2313yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#397C2313yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2313yes—
347#397C2313yes—
348#397C2311yescharacteristic
349#397C2316yes—
350#396C2313yes—
351#396C2313yes—
352#396C2316yes—
353#396C2313yes—
354#396C2316yes—
355#396C2316yes—
356#396C2316yes—
357#396C2311yescharacteristic
358#396C2316yes—
359#395C2313yes—
360#395C2313yes—
361#395C2316yes—
362#395C2313yes—
363#395C2316yes—
364#395C2311yescharacteristic
365#394C2316yes—
366#394C2313yes—
367#394C2313yes—
368#394C2313yes—
369#394C2316yes—
370#394C2313yes—
371#394C2316yes—
372#394C2316yes—
373#394C2316yes—
374#394C2316yes—
375#394C2311yescharacteristic
376#394C2313yes—
377#394C2313yes—
378#394C2313yes—
379#394C2316yes—
380#394C2316yes—
381#394C2316yes—
382#393C2313yes—
383#393C2316yes—
384#393C2316yes—
385#393C2316yes—
386#393C2316yes—
387#393C2316yes—
388#393C2316yes—
389#393C2313yes—
390#392C2313yes—
391#392C2313yes—
392#392C2316yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2316yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2316yes—
409#391C2311yescharacteristic
410#391C2316yes—
411#390C2313yes—
412#390C2313yes—
413#390C2316yes—
414#390C2316yes—
415#390C2316yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2316yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#388C2313yes—
451#388C2316yes—
452#388C2313yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2311yescharacteristic
457#388C2313yes—
458#388C2316yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2316yes—
468#388C2316yes—
469#388C2313yes—
470#388C2316yes—
471#388C2316yes—
472#388C2311yescharacteristic
473#388C2316yes—
474#388C2316yes—
475#388C2313yes—
476#388C2316yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2311yescharacteristic
496#388C2313yes—
497#388C2313yes—
498#388C2311yescharacteristic
499#388C2313yes—
500#387C2313yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2311yescharacteristic
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2313yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#386C2313yes—
520#386C2313yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2316yes—
525#386C2313yes—
526#386C2311yescharacteristic
527#386C2313yes—
528#386C2313yes—
529#386C2313yes—
530#386C2313yes—
531#386C2316yes—
532#385C2316yes—
533#385C2313yes—
534#385C2313yes—
535#385C2316yes—
536#385C2313yes—
537#385C2316yes—
538#385C2311yescharacteristic
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#383C2316yes—
544#382C2313yes—
545#382C2316yes—
546#382C2316yes—
547#382C2316yes—
548#382C2316yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2316yes—
554#381C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2316yes—
565#380C2316yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2316yes—
571#380C2313yes—
572#380C2316yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2311yescharacteristic
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2316yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
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⋊C4C2316yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620#376C2313yes—
621#376C2313yes—
622#376C2313yes—
623#376C2316yes—
624#376C2313yes—
625#376C2313yes—
626#376C2313yes—
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2411yescharacteristic
645C22×Q8C2413yes—
646C22×Q8C2416yes—
647C22×Q8C2411yescharacteristic
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2411yescharacteristic
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2411yescharacteristic
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2416yes—
665C23×C4C2413yes—
666C4⋊Q8—46no—
667C4⋊Q8—46no—
668C4⋊Q8—46no—
669C4⋊Q8—46no—
670C4⋊Q8—46no—
671C4⋊Q8—86no—
672#127—46no—
673#125—46no—
674#125—46no—
675#124—24no—
676#124—212no—
677#124—212no—
678#124—46no—
679#124—412no—
680#124—46no—
681#124—46no—
682#124—46no—
683#124—86no—
684C22⋊Q8—212no—
685C22⋊Q8—212no—
686C22⋊Q8—46no—
687C22⋊Q8—46no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690#121—212no—
691#121—212no—
692#121—212no—
693#121—46no—
694#121—46no—
695#121—46no—
696#121—46no—
697#121—46no—
698#121—86no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—212no—
709C4×Q8—212no—
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—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—86no—
727#117—212no—
728#117—212no—
729#117—24no—
730#117—212no—
731#117—212no—
732#117—46no—
733#117—412no—
734#117—46no—
735#117—46no—
736#117—86no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4—212no—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2416yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2411yescharacteristic
836C2×C42—212no—
837C2×C42—212no—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2416yes—
844C2×C42C2413yes—
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2416yes—
863C2×C42C2416yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868#95C2413yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2413yes—
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2416yes—
906#95C2413yes—
907#95C2416yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2416yes—
913#95C2416yes—
914#95C2416yes—
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2416yes—
918#95C2416yes—
919#95C2416yes—
920#95C2416yes—
921#95C2413yes—
922#95C2413yes—
923C24C2511yescharacteristic
924C24C2513yes—
925C24C2513yes—
926C24C2511yescharacteristic
927#41—416no—
928#41—416no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—22no—
936C2×Q8—22no—
937C2×Q8—41no—
938C2×Q8—43no—
939C2×Q8—43no—
940C2×Q8—43no—
941C2×Q8—46no—
942C2×Q8—46no—
943C2×Q8—46no—
944C2×Q8—416no—
945C2×Q8—416no—
946C2×Q8C2×#4114yes—
947C2×Q8C2×#4114yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—26no—
950C2×D4—22no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—22no—
962C2×D4—41no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—46no—
974C2×D4—46no—
975C2×D4—46no—
976C22×C4—22no—
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—26no—
995C22×C4—212no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—43no—
999C22×C4—46no—
1000C22×C4—43no—
1001C22×C4—46no—
1002C22×C4—43no—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2513yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—212no—
1034C4⋊C4—22no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—26no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—26no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—46no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—41no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—41no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4C2×#41112yes—
1075C4⋊C4C2×#41112yes—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—26no—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—212no—
1082C22⋊C4—26no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—212no—
1088C22⋊C4—212no—
1089C22⋊C4—26no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—26no—
1095C22⋊C4—22no—
1096C22⋊C4—26no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—46no—
1103C22⋊C4—46no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—46no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—46no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—46no—
1121C22⋊C4—46no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C42−1+414yes—
1127C42—22no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—212no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—22no—
1142C42—22no—
1143C42—22no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—46no—
1148C42—43no—
1149C42—43no—
1150C42—43no—
1151C42—43no—
1152C42—46no—
1153C42—43no—
1154C42—43no—
1155C42C2×#41112yes—
1156C42C2×#41112yes—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—23no—
1165C23—23no—
1166C23—23no—
1167C23—23no—
1168C23—21no—
1169C23—21no—
1170C23—23no—
1171C23—23no—
1172C23—21no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—21no—
1178C23—23no—
1179C23—23no—
1180C23—21no—
1181C23—23no—
1182C23—23no—
1183C23—21no—
1184C23C2×2−1+412yes—
1185C23C2611yescharacteristic
1186Q8—44no—
1187Q8—412no—
1188Q8—412no—
1189Q8—86no—
1190Q8—166no—
1191Q8#555116yes—
1192D4—412no—
1193D4—44no—
1194D4—412no—
1195D4—412no—
1196D4—86no—
1197D4—86no—
1198D4—86no—
1199D4—86no—
1200D4—166no—
1201C2×C4—28no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—412no—
1273C2×C4—412no—
1274C2×C4—412no—
1275C2×C4—412no—
1276C2×C4—412no—
1277C2×C4—412no—
1278C2×C4—86no—
1279C2×C4—812no—
1280C2×C4C22×#4112yes—
1281C2×C4C22×#4116yes—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4116yes—
1284C2×C4C22×#4116yes—
1285C2×C4C22×#4116yes—
1286C2×C4C2×H(5,𝔽2)16yes—
1287C2×C4C2×2−1+412yes—
1288C2×C4C2×2−1+412yes—
1289C2×C4#58512yes—
1290C2×C4#58512yes—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—43no—
1299C22—41no—
1300C22—43no—
1301C22—43no—
1302C22—43no—
1303C22—41no—
1304C22—41no—
1305C22—43no—
1306C22—43no—
1307C22—43no—
1308C22—43no—
1309C22—41no—
1310C22—43no—
1311C22—41no—
1312C22—43no—
1313C22—41no—
1314C22—43no—
1315C22—43no—
1316C22—41no—
1317C22—43no—
1318C22—43no—
1319C22C23×#4111yescharacteristic
1320C22C23×#4111yescharacteristic
1321C22C22×H(5,𝔽2)11yescharacteristic
1322C22C22×2−1+411yescharacteristic
1323C22C2×#58511yescharacteristic
1324C22C2×#58511yescharacteristic
1325C22H(7,𝔽2)11yescharacteristic
1326C4—26no—
1327C4—22no—
1328C4—26no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—43no—
1335C4—43no—
1336C4—41no—
1337C4—41no—
1338C4—43no—
1339C4—41no—
1340C4—41no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—41no—
1346C4—43no—
1347C4—43no—
1348C4—41no—
1349C4—41no—
1350C4—43no—
1351C4—43no—
1352C4C2×#555112yes—
1353C2—42no—
1354C2—83no—
1355C2—81no—
1356C2—83no—
1357C2C22×#55511yescharacteristic
1358C2#6278811yescharacteristic
1359C2#6279311yescharacteristic
1360C2#6292311yescharacteristic
1361C2#6299411yescharacteristic
1362C2#6300011yescharacteristic
1363C2#6301511yescharacteristic
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. #59767C2semidirect
2. #59750C2semidirect
3. #59564C2semidirect
4. #59233C2semidirect
5. #59230C2semidirect
6. #45369C2semidirect
7. #45133C2semidirect
8. #44993C2semidirect
9. #44925C2semidirect
10. #38285C2semidirect
11. #38284C2semidirect
12. #37953C2semidirect
13. #37952C2semidirect
14. Q8×#124C2semidirect
15. #36467C2semidirect
16. #36457C2semidirect
17. #36434C2semidirect
18. #36430C2semidirect
19. #36385C2semidirect
20. #36373C2semidirect
21. #35937C2semidirect
22. #35854C2semidirect
23. #35831C2semidirect
24. #35771C2semidirect
25. #34874C2semidirect
26. #34294C2semidirect
27. #34293C2semidirect
28. #34263C2semidirect
29. #34262C2semidirect
30. #34129C2semidirect
31. Q8×#117C2semidirect

Maximal subgroups

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

subgroupindex
#597672
#597502
#595642
#592332
#592302
#453692
#451332
#449932
#449252
#382852
#382842
#379532
#379522
Q8×#1242
#364672
#364572
#364342
#364302
#363852
#363732
#359372
#358542
#358312
#357712
#348742
#342942
#342932
#342632
#342622
#341292
Q8×#1172