Finite Group Databasebeta

← #7848984

Subgroups — #7848984

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C212yesmaximal, complemented
2#59925C212yesmaximal, complemented
3#59695C212yesmaximal, complemented
4#59681C212yesmaximal, complemented
5#59477C212yesmaximal, complemented
6#52248C211yesmaximal, characteristic
7#51724C214yesmaximal, complemented
8#49632C214yesmaximal, complemented
9#48908C214yesmaximal, complemented
10#47544C212yesmaximal, complemented
11#46969C212yesmaximal, complemented
12#46268C212yesmaximal, complemented
13#45348C212yesmaximal, complemented
14#45343C212yesmaximal, complemented
15#45322C212yesmaximal, complemented
16#45149C212yesmaximal, complemented
17#43945C214yesmaximal
18#43587C214yesmaximal, complemented
19#42941C211yesmaximal, characteristic, complemented
20#42937C211yesmaximal, characteristic
21#40471C214yesmaximal, complemented
22#39593C212yesmaximal, complemented
23#37383C211yesmaximal, characteristic, complemented
24#36506C212yesmaximal, complemented
25#35845C211yesmaximal, characteristic, complemented
26#35700C211yesmaximal, characteristic
27#35671C212yesmaximal, complemented
28#34487C212yesmaximal, complemented
29#34209C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#541C2212yes—
34C22×C4⋊Q8C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37#2865C2214yes—
38#2855C2212yes—
39#2833C2212yes—
40#2832C2212yes—
41#2802C2214yes—
42#2802C2214yes—
43#2801C2214yes—
44#2795C2211yescharacteristic
45#2795C2214yes—
46#2794C2212yes—
47#2792C2212yes—
48#2792C2211yescharacteristic
49#2789C2212yes—
50#2785C2211yescharacteristic
51#2783C2212yes—
52#2777C2214yes—
53#2776C2214yes—
54#2771C2212yes—
55#2771C2212yes—
56#2769C2212yes—
57#2769C2211yescharacteristic
58#2767C2214yes—
59#2766C2214yes—
60#2765C2214yes—
61#2764C2212yes—
62#2762C2214yes—
63#2758C2214yes—
64#2755C2214yes—
65#2752C2212yes—
66#2751C2214yes—
67#2745C2214yes—
68#2745C2214yes—
69#2744C2212yes—
70#2742C2214yes—
71#2739C2214yes—
72#2738C2214yes—
73#2737C2212yes—
74#2734C2214yes—
75#2734C2214yes—
76#2729C2214yes—
77#2729C2214yes—
78#2725C2214yes—
79#2725C2214yes—
80#2721C2212yes—
81#2719C2214yes—
82#2719C2214yes—
83#2719C2214yes—
84#2716C2214yes—
85#2713C2214yes—
86#2705C2212yes—
87#2698C2214yes—
88#2694C2212yes—
89#2690C2214yes—
90#2689C2214yes—
91#2666C2214yes—
92#2650C2214yes—
93#2628C2211yescharacteristic
94#2628C2212yes—
95#2627C2214yes—
96#2621C2211yescharacteristic
97#2621C2212yes—
98#2611C2214yes—
99#2606C2214yes—
100#2605C2214yes—
101#2604C2214yes—
102#2601C2214yes—
103#2596C2214yes—
104#2594C2214yes—
105#2590C2214yes—
106#2590C2214yes—
107#2590C2214yes—
108#2588C2214yes—
109#2586C2214yes—
110#2586C2214yes—
111#2586C2212yes—
112#2586C2212yes—
113#2585C2214yes—
114#2584C2214yes—
115#2583C2214yes—
116#2581C2211yescharacteristic
117#2581C2212yes—
118#2579C2214yes—
119#2575C2214yes—
120#2575C2214yes—
121#2574C2214yes—
122#2570C2214yes—
123#2568C2212yes—
124#2567C2212yes—
125#2567C2211yescharacteristic
126#2558C2214yes—
127#2556C2214yes—
128#2550C2214yes—
129#2550C2214yes—
130#2546C2212yes—
131#2546C2212yes—
132#2546C2212yes—
133#2546C2211yescharacteristic
134#2546C2212yes—
135#2536C2211yescharacteristic
136#2536C2212yes—
137#2533C2214yes—
138#2533C2214yes—
139#2533C2214yes—
140#2529C2214yes—
141#2529C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2525C2214yes—
145#2525C2214yes—
146#2525C2214yes—
147#2522C2214yes—
148#2520C2214yes—
149#2519C2214yes—
150#2516C2214yes—
151#2515C2214yes—
152#2515C2214yes—
153#2514C2212yes—
154#2514C2212yes—
155#2511C2212yes—
156#2511C2212yes—
157#2509C2212yes—
158#2509C2214yes—
159#2507C2214yes—
160#2507C2214yes—
161#2506C2212yes—
162#2499C2212yes—
163#2497C2212yes—
164#2492C2212yes—
165#2489C2212yes—
166#2479C2214yes—
167#2475C2214yes—
168#2469C2214yes—
169#2469C2214yes—
170#2468C2214yes—
171#2466C2214yes—
172#2462C2214yes—
173#2453C2212yes—
174#2453C2214yes—
175#2453C2212yes—
176#2453C2214yes—
177#2451C2212yes—
178#2446C2212yes—
179#2446C2212yes—
180#2446C2212yes—
181#2446C2212yes—
182#2446C2212yes—
183#2441C2214yes—
184#2441C2212yes—
185#2434C2212yes—
186#2434C2212yes—
187#2434C2212yes—
188#2429C2212yes—
189#2429C2214yes—
190#2429C2212yes—
191#2429C2212yes—
192#2429C2212yes—
193#2423C2212yes—
194#2415C2212yes—
195#2415C2214yes—
196#2415C2212yes—
197#2409C2212yes—
198#2396C2211yescharacteristic
199#2396C2212yes—
200#2396C2212yes—
201#2395C2212yes—
202#2392C2211yescharacteristic
203#2392C2212yes—
204#2378C2214yes—
205#2378C2214yes—
206#2373C2214yes—
207#2370C2214yes—
208#2370C2214yes—
209#2370C2214yes—
210#2370C2212yes—
211#2369C2214yes—
212#2365C2212yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2365C2212yes—
217#2362C2212yes—
218#2362C2212yes—
219#2362C2212yes—
220#2357C2214yes—
221#2355C2212yes—
222#2355C2212yes—
223#2354C2212yes—
224#2351C2211yescharacteristic
225#2351C2211yescharacteristic
226Q8×C4⋊C4C2212yes—
227#2347C2212yes—
228#2344C2214yes—
229#2344C2214yes—
230Q8×C22⋊C4C2212yes—
231Q8×C22⋊C4C2212yes—
232Q8×C22⋊C4C2212yes—
233#2332C2214yes—
234#2332C2214yes—
235#2331C2214yes—
236#2327C2212yes—
237#2327C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2323C2212yes—
241#2322C2214yes—
242#2319C2214yes—
243#2310C2212yes—
244#2310C2211yescharacteristic
245#2310C2211yescharacteristic
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×#125C2214yes—
251C4×#125C2212yes—
252C4×#126C2212yes—
253C4×#123C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256#2293C2212yes—
257#2285C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#557—44no—
263D4×Q8—216no—
264D4×Q8—44no—
265#541—48no—
266C2×C4⋊Q8—28no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#123C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297#519—44no—
298#519—44no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2311yescharacteristic
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2314yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2311yescharacteristic
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2312yes—
364#399C2311yescharacteristic
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2311yescharacteristic
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2312yes—
416#395C2312yes—
417#395C2311yescharacteristic
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#394C2311yescharacteristic
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2312yes—
435#394C2312yes—
436#394C2312yes—
437#393C2314yes—
438#393C2314yes—
439#393C2311yescharacteristic
440#393C2312yes—
441#393C2312yes—
442#392C2311yescharacteristic
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2312yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#386C2314yes—
625#386C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2312yes—
638#384C2312yes—
639#384C2314yes—
640#383C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2311yescharacteristic
650#382C2312yes—
651#382C2311yescharacteristic
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2312yes—
658#381C2312yes—
659#381C2314yes—
660#381C2312yes—
661#381C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2314yes—
715#376C2312yes—
716#376C2314yes—
717C43C2312yes—
718C43C2312yes—
719C22×Q8—28no—
720C22×Q8—24no—
721C22×Q8—42no—
722C22×Q8—42no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8—44no—
726C22×Q8—44no—
727C22×Q8#4118yes—
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2411yescharacteristic
735C22×Q8C2412yes—
736C22×Q8C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C4⋊Q8—28no—
746C4⋊Q8—28no—
747C4⋊Q8—28no—
748C4⋊Q8—28no—
749C4⋊Q8—28no—
750C4⋊Q8—216no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—44no—
754C4⋊Q8—44no—
755C4⋊Q8—44no—
756C4⋊Q8—42no—
757#126—28no—
758#126—48no—
759#126—48no—
760#125—28no—
761#125—28no—
762#125—216no—
763#125—48no—
764#125—48no—
765#125—48no—
766#123—28no—
767C22⋊Q8—28no—
768C22⋊Q8—216no—
769C22⋊Q8—28no—
770C22⋊Q8—216no—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—42no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—42no—
789C4×Q8—42no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×D4—28no—
793C4×D4—216no—
794C4×D4—44no—
795C4×D4—42no—
796#117—24no—
797#117—42no—
798#117—42no—
799#117—44no—
800#117—44no—
801#117—44no—
802#117—48no—
803#117—42no—
804#117—44no—
805C2×C4⋊C4—216no—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C42—24no—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2411yescharacteristic
993#95C2411yescharacteristic
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2512yes—
1020C24C2511yescharacteristic
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—28no—
1025C2×Q8—22no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—416no—
1044C2×Q8—416no—
1045C2×Q8—816no—
1046C2×Q8C2×#4114yes—
1047C2×Q8C2×#4114yes—
1048C2×Q8C2×#4118yes—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—28no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4C2×#4114yes—
1071C22×C4C2×#4118yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—22no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4H(5,𝔽2)14yes—
1171C4⋊C42−1+418yes—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—41no—
1195C22⋊C4—41no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C42—22no—
1202C42—24no—
1203C42—22no—
1204C42—28no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—22no—
1210C42—24no—
1211C42—22no—
1212C42—28no—
1213C42—24no—
1214C42—28no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—42no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C23—21no—
1234C23—22no—
1235C23—21no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23C22×#4112yes—
1245C23C2611yescharacteristic
1246Q8—28no—
1247Q8—28no—
1248Q8—48no—
1249Q8—48no—
1250Q8—48no—
1251Q8—48no—
1252Q8—88no—
1253Q8—82no—
1254Q8—84no—
1255D4—48no—
1256D4—44no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—28no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—48no—
1324C2×C4—48no—
1325C2×C4—48no—
1326C2×C4—48no—
1327C2×C4—88no—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4114yes—
1330C2×C4C22×#4114yes—
1331C2×C4C22×#4112yes—
1332C2×C4C2×H(5,𝔽2)14yes—
1333C2×C4C2×H(5,𝔽2)12yes—
1334C2×C4C2×2−1+414yes—
1335C2×C4C2×2−1+414yes—
1336C2×C4C2×2−1+414yes—
1337C2×C4#58512yes—
1338C22—24no—
1339C22—22no—
1340C22—41no—
1341C22—41no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22C23×#4111yescharacteristic
1351C22C22×H(5,𝔽2)11yescharacteristic
1352C22C22×2−1+412yes—
1353C22C2×#58511yescharacteristic
1354C222−1+612yes—
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—24no—
1359C4—24no—
1360C4—24no—
1361C4—24no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—42no—
1369C4—41no—
1370C4—42no—
1371C4—41no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—42no—
1376C4—44no—
1377C4—41no—
1378C4—42no—
1379C4—44no—
1380C4—44no—
1381C4#350514yes—
1382C2—42no—
1383C2—82no—
1384C2C2×#350511yescharacteristic
1385C2#6295612yes—
1386C2#6299812yes—
1387C2#6303711yescharacteristic
1388C2#6304411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59963C2semidirect
2. #59925C2semidirect
3. #59695C2semidirect
4. #59681C2semidirect
5. #59477C2semidirect
7. #51724C2semidirect
8. #49632C2semidirect
9. #48908C2semidirect
10. #47544C2semidirect
11. #46969C2semidirect
12. #46268C2semidirect
13. #45348C2semidirect
14. #45343C2semidirect
15. #45322C2semidirect
16. #45149C2semidirect
18. #43587C2semidirect
19. #42941C2semidirect
21. #40471C2semidirect
22. #39593C2semidirect
23. #37383C2semidirect
24. #36506C2semidirect
25. #35845C2semidirect
27. #35671C2semidirect
28. #34487C2semidirect
29. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#599632
#599252
#596952
#596812
#594772
#522482
#517242
#496322
#489082
#475442
#469692
#462682
#453482
#453432
#453222
#451492
#439452
#435872
#429412
#429372
#404712
#395932
#373832
#365062
#358452
#357002
#356712
#344872
#342092