Finite Group Databasebeta

← #7715528

Subgroups — #7715528

Order 512.

4146 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49800C214yesmaximal, complemented
2#49762C214yesmaximal
3#48249C214yesmaximal, complemented
4#48198C214yesmaximal, complemented
5#47519C214yesmaximal, complemented
6#47443C214yesmaximal, complemented
7#47294C214yesmaximal, complemented
8#46924C214yesmaximal, complemented
9#39682C212yesmaximal, complemented
10#39641C211yesmaximal, characteristic, complemented
11#39638C211yesmaximal, characteristic, complemented
12#39546C212yesmaximal, complemented
13#39514C211yesmaximal, characteristic, complemented
14#39510C211yesmaximal, characteristic, complemented
15#37961C212yesmaximal, complemented
16#37936C212yesmaximal, complemented
17#37888C211yesmaximal, characteristic, complemented
18#37888C211yesmaximal, characteristic, complemented
19#37883C211yesmaximal, characteristic, complemented
20#37882C211yesmaximal, characteristic, complemented
21#37592C212yesmaximal, complemented
22#37295C212yesmaximal, complemented
23#37279C212yesmaximal
24#35336C211yesmaximal, characteristic, complemented
25#35336C211yesmaximal, characteristic, complemented
26#35336C211yesmaximal, characteristic, complemented
27#35294C211yesmaximal, characteristic, complemented
28#35284C211yesmaximal, characteristic, complemented
29#35275C211yesmaximal, characteristic, complemented
30#34434C212yesmaximal, complemented
31#34081C211yesmaximal, characteristic
32C2×#544C2212yes—
33C2×#529C2211yescharacteristic
34#2868C2211yescharacteristic
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2857C2212yes—
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2851C2212yes—
45#2851C2212yes—
46#2839C2214yes—
47#2836C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2800C2214yes—
51#2794C2214yes—
52#2793C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2791C2214yes—
56#2788C2214yes—
57#2786C2214yes—
58#2781C2214yes—
59#2781C2214yes—
60#2777C2214yes—
61#2776C2214yes—
62#2776C2214yes—
63#2775C2214yes—
64#2774C2214yes—
65#2770C2214yes—
66#2770C2214yes—
67#2770C2214yes—
68#2769C2214yes—
69#2769C2214yes—
70#2767C2214yes—
71#2766C2214yes—
72#2765C2214yes—
73#2762C2214yes—
74#2761C2214yes—
75#2755C2214yes—
76#2755C2214yes—
77#2747C2214yes—
78#2744C2214yes—
79#2726C2214yes—
80#2722C2214yes—
81#2721C2214yes—
82#2719C2214yes—
83#2716C2214yes—
84#2716C2214yes—
85#2716C2214yes—
86#2713C2214yes—
87#2698C2214yes—
88#2698C2214yes—
89#2695C2214yes—
90#2694C2214yes—
91#2689C2214yes—
92#2687C2214yes—
93#2681C2214yes—
94#2677C2214yes—
95#2674C2214yes—
96#2666C2214yes—
97#2660C2212yes—
98#2660C2212yes—
99#2650C2214yes—
100#2647C2211yescharacteristic
101#2647C2211yescharacteristic
102#2647C2212yes—
103#2647C2212yes—
104#2647C2211yescharacteristic
105#2647C2211yescharacteristic
106#2637C2214yes—
107#2634C2214yes—
108#2629C2211yescharacteristic
109#2629C2211yescharacteristic
110#2629C2212yes—
111#2629C2211yescharacteristic
112#2629C2212yes—
113#2629C2212yes—
114#2629C2211yescharacteristic
115#2628C2212yes—
116#2601C2214yes—
117#2601C2214yes—
118#2599C2214yes—
119#2594C2214yes—
120#2590C2214yes—
121#2590C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2590C2214yes—
125#2590C2214yes—
126#2590C2214yes—
127#2590C2214yes—
128#2587C2214yes—
129#2587C2214yes—
130#2587C2214yes—
131#2587C2214yes—
132#2587C2214yes—
133#2587C2214yes—
134#2585C2214yes—
135#2585C2214yes—
136#2584C2212yes—
137#2573C2214yes—
138#2570C2214yes—
139#2570C2214yes—
140#2563C2212yes—
141#2562C2212yes—
142#2552C2214yes—
143#2551C2214yes—
144#2550C2214yes—
145#2550C2214yes—
146#2546C2212yes—
147#2546C2214yes—
148#2525C2214yes—
149#2525C2214yes—
150#2525C2214yes—
151#2524C2214yes—
152#2524C2214yes—
153#2524C2214yes—
154#2524C2214yes—
155#2520C2214yes—
156#2519C2214yes—
157#2519C2214yes—
158#2512C2214yes—
159#2509C2212yes—
160#2509C2214yes—
161#2508C2212yes—
162#2508C2212yes—
163#2508C2214yes—
164#2508C2212yes—
165#2507C2212yes—
166#2507C2212yes—
167#2507C2214yes—
168#2507C2212yes—
169#2506C2212yes—
170#2497C2212yes—
171#2497C2214yes—
172#2496C2212yes—
173#2496C2212yes—
174#2496C2212yes—
175#2495C2212yes—
176#2495C2212yes—
177#2495C2212yes—
178#2494C2212yes—
179#2487C2212yes—
180#2486C2212yes—
181#2485C2212yes—
182#2485C2212yes—
183#2484C2214yes—
184#2481C2214yes—
185#2478C2214yes—
186#2475C2214yes—
187#2473C2214yes—
188#2470C2214yes—
189#2469C2214yes—
190#2446C2214yes—
191#2446C2214yes—
192#2441C2214yes—
193#2440C2214yes—
194#2440C2214yes—
195#2439C2214yes—
196#2429C2214yes—
197#2413C2214yes—
198#2381C2214yes—
199#2378C2214yes—
200#2370C2212yes—
201#2370C2212yes—
202#2369C2212yes—
203#2365C2214yes—
204#2365C2212yes—
205#2362C2214yes—
206#2347C2212yes—
207#2347C2212yes—
208#2345C2212yes—
209#2344C2212yes—
210#2337C2212yes—
211#2336C2212yes—
212#2336C2214yes—
213#2336C2214yes—
214#2335C2212yes—
215#2335C2212yes—
216#2334C2212yes—
217#2334C2212yes—
218#2333C2212yes—
219#2332C2212yes—
220#2332C2214yes—
221#2331C2212yes—
222#2330C2211yescharacteristic
223#2330C2211yescharacteristic
224#2330C2212yes—
225#2330C2212yes—
226#2330C2212yes—
227#2330C2211yescharacteristic
228#2330C2211yescharacteristic
229#2323C2214yes—
230#2317C2212yes—
231#2314C2211yescharacteristic
232#2314C2211yescharacteristic
233#2314C2212yes—
234#2314C2211yescharacteristic
235#2314C2212yes—
236#2314C2211yescharacteristic
237C4×C4⋊Q8C2212yes—
238C4×#125C2212yes—
239C4×#125C2211yescharacteristic
240C4×#125C2211yescharacteristic
241C4×#125C2212yes—
242#2298C2211yescharacteristic
243#2298C2211yescharacteristic
244#2295C2211yescharacteristic
245#2295C2211yescharacteristic
246#2293C2211yescharacteristic
247#2293C2211yescharacteristic
248#2290C2211yescharacteristic
249#2290C2211yescharacteristic
250#2290C2211yescharacteristic
251#2290C2211yescharacteristic
252#2285C2211yescharacteristic
253#2285C2212yes—
254C2×#384C2211yescharacteristic
255#2283C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259#544—216no—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266#529—28no—
267C2×#126C2311yescharacteristic
268C2×#126C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2311yescharacteristic
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2311yescharacteristic
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#123C2311yescharacteristic
283C2×#123C2311yescharacteristic
284C2×#123C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×#121C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2314yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2314yes—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310#401C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#390C2314yes—
417#390C2312yes—
418#390C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2312yes—
487#388C2314yes—
488#388C2312yes—
489#388C2314yes—
490#388C2312yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2312yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2312yes—
595#385C2314yes—
596#384C2312yes—
597#384C2311yescharacteristic
598#384C2312yes—
599#384C2311yescharacteristic
600#384C2311yescharacteristic
601#384C2311yescharacteristic
602#384C2314yes—
603#384C2314yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2314yes—
608#383C2314yes—
609#383C2312yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2314yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#381C2314yes—
628#381C2312yes—
629#381C2314yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2311yescharacteristic
699#376C2311yescharacteristic
700C43C2311yescharacteristic
701C43C2311yescharacteristic
702C43C2311yescharacteristic
703C43C2311yescharacteristic
704C22×Q8C2414yes—
705C22×Q8C2411yescharacteristic
706C22×Q8C2414yes—
707C22×D4C2411yescharacteristic
708C22×D4C2411yescharacteristic
709C22×D4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C23×C4C2414yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2411yescharacteristic
717C23×C4C2411yescharacteristic
718C4⋊Q8—216no—
719C4⋊Q8—28no—
720C4⋊Q8—28no—
721C4⋊Q8—84no—
722C4⋊Q8—84no—
723C4⋊Q8—84no—
724#126—24no—
725#126—24no—
726#126—84no—
727#126—84no—
728#126—84no—
729#125—24no—
730#125—216no—
731#125—28no—
732#125—28no—
733#125—28no—
734#125—24no—
735#125—24no—
736#125—84no—
737#125—84no—
738#124—24no—
739#123—24no—
740#123—24no—
741#123—84no—
742C22⋊Q8—24no—
743C22⋊Q8—216no—
744C22⋊Q8—216no—
745C22⋊Q8—84no—
746#121—24no—
747C4×Q8—24no—
748C4×Q8—84no—
749C4×Q8—84no—
750C4×D4—24no—
751C4×D4—24no—
752C4×D4—24no—
753#117—28no—
754#117—24no—
755#117—24no—
756#117—24no—
757#117—24no—
758#117—24no—
759#117—84no—
760#117—84no—
761#117#4118yes—
762C2×C4⋊C4—28no—
763C2×C4⋊C4—84no—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2411yescharacteristic
867C2×C22⋊C4C2411yescharacteristic
868C2×C42—24no—
869C2×C42—24no—
870C2×C42—24no—
871C2×C42C2411yescharacteristic
872C2×C42C2414yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2511yescharacteristic
981C24C2511yescharacteristic
982C24C2511yescharacteristic
983C2×Q8—22no—
984C2×Q8—28no—
985C2×Q8—28no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—42no—
990C2×Q8—44no—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—28no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4C2×#4114yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4C2×#4114yes—
1119C4⋊C4C2×#4114yes—
1120C22⋊C4—28no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4C2×#4114yes—
1150C22⋊C4C2×#4114yes—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—28no—
1156C42—24no—
1157C42—24no—
1158C42—22no—
1159C42—22no—
1160C42—22no—
1161C42—22no—
1162C42—22no—
1163C42—22no—
1164C42—42no—
1165C42—44no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—42no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42—42no—
1182C42C2×#4114yes—
1183C42C2×#4114yes—
1184C422−1+414yes—
1185C422−1+414yes—
1186C23—21no—
1187C23—21no—
1188C23—22no—
1189C23—22no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23C22×#4112yes—
1201C23C2611yescharacteristic
1202Q8—88no—
1203Q8—82no—
1204Q8—88no—
1205D4—82no—
1206D4—82no—
1207D4—82no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—28no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—24no—
1224C2×C4—21no—
1225C2×C4—24no—
1226C2×C4—21no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—44no—
1278C2×C4—44no—
1279C2×C4—82no—
1280C2×C4—82no—
1281C2×C4—88no—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4112yes—
1287C2×C4C22×#4112yes—
1288C2×C4C2×2−1+414yes—
1289C2×C4C2×2−1+414yes—
1290C2×C4C2×2−1+412yes—
1291C2×C4C2×2−1+412yes—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22C23×#4111yescharacteristic
1308C22C22×2−1+411yescharacteristic
1309C22C22×2−1+411yescharacteristic
1310C22H(7,𝔽2)12yes—
1311C222−1+612yes—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—24no—
1318C4—24no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—44no—
1323C4—44no—
1324C4—41no—
1325C4—44no—
1326C4—44no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4#350914yes—
1340C2—42no—
1341C2—81no—
1342C2—81no—
1343C2C2×#350911yescharacteristic
1344C2#6285811yescharacteristic
1345C2#6286111yescharacteristic
1346C2#6287712yes—
1347C2#6287712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49800C2semidirect
3. #48249C2semidirect
4. #48198C2semidirect
5. #47519C2semidirect
6. #47443C2semidirect
7. #47294C2semidirect
8. #46924C2semidirect
9. #39682C2semidirect
10. #39641C2semidirect
11. #39638C2semidirect
12. #39546C2semidirect
13. #39514C2semidirect
14. #39510C2semidirect
15. #37961C2semidirect
16. #37936C2semidirect
17. #37888C2semidirect
18. #37888C2semidirect
19. #37883C2semidirect
20. #37882C2semidirect
21. #37592C2semidirect
22. #37295C2semidirect
24. #35336C2semidirect
25. #35336C2semidirect
26. #35336C2semidirect
27. #35294C2semidirect
28. #35284C2semidirect
29. #35275C2semidirect
30. #34434C2semidirect

Maximal subgroups

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

subgroupindex
#498002
#497622
#482492
#481982
#475192
#474432
#472942
#469242
#396822
#396412
#396382
#395462
#395142
#395102
#379612
#379362
#378882
#378832
#378822
#375922
#372952
#372792
#353362
#352942
#352842
#352752
#344342
#340812