Finite Group Databasebeta

← #7698645

Subgroups — #7698645

Order 512.

4842 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59989C212yesmaximal, complemented
2#59629C211yesmaximal, characteristic, complemented
3#59615C214yesmaximal, complemented
4#59096C212yesmaximal, complemented
5#52289C212yesmaximal, complemented
6#52203C211yesmaximal, characteristic
7#45420C211yesmaximal, characteristic, complemented
8#45415C212yesmaximal, complemented
9#45321C211yesmaximal, characteristic
10#45184C212yesmaximal, complemented
11#44858C214yesmaximal, complemented
12#44829C212yesmaximal, complemented
13#44715C214yesmaximal, complemented
14#43877C212yesmaximal, complemented
15#40435C214yesmaximal, complemented
16#40143C214yesmaximal, complemented
17#39053C212yesmaximal, complemented
18#38518C214yesmaximal, complemented
19#38057C212yesmaximal, complemented
20#37783C212yesmaximal, complemented
21#36423C211yesmaximal, characteristic, complemented
22#36409C212yesmaximal, complemented
23#36080C211yesmaximal, characteristic
24#35949C211yesmaximal, characteristic, complemented
25#35901C212yesmaximal, complemented
26#35749C212yesmaximal, complemented
27#34291C212yesmaximal, complemented
28#34276C212yesmaximal, complemented
29#34231C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#552C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×#536C2212yes—
34C2×#533C2212yes—
35C2×#520C2211yescharacteristic
36C2×#519C2212yes—
37C22×C4×Q8C2211yescharacteristic
38#2863C2214yes—
39#2855C2212yes—
40#2855C2211yescharacteristic
41#2853C2212yes—
42#2807C2212yes—
43#2804C2212yes—
44#2802C2214yes—
45#2792C2214yes—
46#2790C2214yes—
47#2788C2214yes—
48#2782C2214yes—
49#2776C2214yes—
50#2770C2214yes—
51#2766C2214yes—
52#2766C2214yes—
53#2765C2214yes—
54#2764C2211yescharacteristic
55#2763C2212yes—
56#2763C2214yes—
57#2763C2211yescharacteristic
58#2762C2214yes—
59#2762C2214yes—
60#2762C2212yes—
61#2761C2212yes—
62#2760C2211yescharacteristic
63#2758C2214yes—
64#2758C2214yes—
65#2755C2214yes—
66#2755C2214yes—
67#2749C2212yes—
68#2743C2212yes—
69#2742C2212yes—
70#2737C2212yes—
71#2713C2214yes—
72#2713C2214yes—
73#2707C2214yes—
74#2706C2212yes—
75#2704C2214yes—
76#2700C2214yes—
77#2693C2211yescharacteristic
78#2687C2214yes—
79#2680C2212yes—
80#2677C2212yes—
81#2674C2214yes—
82#2664C2212yes—
83#2650C2214yes—
84#2645C2212yes—
85#2642C2211yescharacteristic
86#2634C2214yes—
87#2634C2212yes—
88#2621C2212yes—
89#2616C2211yescharacteristic
90#2611C2212yes—
91#2611C2214yes—
92#2608C2214yes—
93#2607C2212yes—
94#2604C2212yes—
95#2599C2214yes—
96#2598C2212yes—
97#2594C2214yes—
98#2589C2214yes—
99#2588C2214yes—
100#2587C2214yes—
101#2584C2211yescharacteristic
102#2581C2212yes—
103#2578C2214yes—
104#2577C2214yes—
105#2576C2214yes—
106#2573C2214yes—
107#2573C2214yes—
108#2572C2214yes—
109#2570C2214yes—
110#2569C2214yes—
111#2562C2212yes—
112#2558C2214yes—
113#2551C2212yes—
114#2549C2214yes—
115#2546C2212yes—
116#2542C2211yescharacteristic
117#2533C2214yes—
118#2533C2214yes—
119#2532C2214yes—
120#2529C2214yes—
121#2527C2214yes—
122#2527C2214yes—
123#2523C2212yes—
124#2522C2214yes—
125#2517C2212yes—
126#2515C2214yes—
127#2515C2214yes—
128#2514C2212yes—
129#2514C2214yes—
130#2511C2214yes—
131#2511C2214yes—
132#2509C2212yes—
133#2509C2214yes—
134#2508C2212yes—
135#2508C2214yes—
136#2506C2214yes—
137#2505C2214yes—
138#2503C2211yescharacteristic
139#2495C2212yes—
140#2493C2214yes—
141#2493C2214yes—
142#2492C2212yes—
143#2492C2212yes—
144#2487C2211yescharacteristic
145#2484C2212yes—
146#2475C2214yes—
147#2475C2214yes—
148#2474C2214yes—
149#2470C2214yes—
150#2470C2214yes—
151#2469C2214yes—
152#2468C2214yes—
153#2465C2214yes—
154#2462C2214yes—
155#2462C2214yes—
156#2462C2214yes—
157#2461C2214yes—
158#2458C2214yes—
159#2457C2214yes—
160#2455C2212yes—
161#2453C2212yes—
162#2451C2214yes—
163#2451C2214yes—
164#2451C2212yes—
165#2450C2214yes—
166#2446C2212yes—
167#2446C2212yes—
168#2446C2212yes—
169#2442C2212yes—
170#2439C2212yes—
171#2438C2214yes—
172#2434C2212yes—
173#2434C2211yescharacteristic
174#2434C2212yes—
175#2429C2212yes—
176#2429C2212yes—
177#2429C2212yes—
178#2429C2212yes—
179#2421C2212yes—
180#2417C2212yes—
181#2415C2212yes—
182#2413C2212yes—
183#2409C2211yescharacteristic
184#2402C2214yes—
185#2401C2212yes—
186#2399C2214yes—
187#2398C2211yescharacteristic
188#2396C2212yes—
189#2396C2212yes—
190#2396C2212yes—
191#2388C2211yescharacteristic
192#2374C2212yes—
193#2369C2212yes—
194#2369C2212yes—
195#2365C2212yes—
196#2365C2212yes—
197#2365C2212yes—
198#2365C2214yes—
199#2362C2212yes—
200#2362C2212yes—
201#2362C2214yes—
202#2362C2212yes—
203#2362C2212yes—
204#2362C2212yes—
205#2362C2212yes—
206#2362C2212yes—
207#2360C2214yes—
208#2360C2212yes—
209#2360C2212yes—
210#2360C2212yes—
211#2360C2212yes—
212#2360C2212yes—
213#2359C2214yes—
214#2359C2214yes—
215#2359C2214yes—
216#2359C2214yes—
217#2359C2214yes—
218#2356C2214yes—
219#2356C2212yes—
220#2356C2214yes—
221#2352C2212yes—
222#2352C2214yes—
223#2351C2212yes—
224#2347C2211yescharacteristic
225#2347C2214yes—
226#2346C2214yes—
227#2344C2211yescharacteristic
228Q8×C22⋊C4C2212yes—
229Q8×C22⋊C4C2212yes—
230#2332C2214yes—
231#2332C2214yes—
232#2327C2214yes—
233#2327C2214yes—
234#2327C2212yes—
235#2326C2214yes—
236#2323C2212yes—
237#2323C2214yes—
238#2320C2212yes—
239#2320C2212yes—
240#2317C2212yes—
241C4×C4⋊Q8C2214yes—
242C4×#125C2214yes—
243C4×#125C2214yes—
244C4×#124C2214yes—
245C4×C22⋊Q8C2214yes—
246C4×C22⋊Q8C2212yes—
247C4×#123C2212yes—
248C4×#123C2211yescharacteristic
249#2298C2214yes—
250#2297C2212yes—
251#2296C2212yes—
252C2×#391C2212yes—
253#2290C2214yes—
254#2290C2212yes—
255#2283C2212yes—
256#2276C2212yes—
257#2276C2211yescharacteristic
258C4×#117C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2312yes—
262#557—44no—
263#552—44no—
264D4×Q8—216no—
265#536—216no—
266#533—216no—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×#126C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2311yescharacteristic
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×#123C2311yescharacteristic
285C2×#123C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297#520—44no—
298#519—48no—
299C2×C4×Q8—44no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2311yescharacteristic
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2311yescharacteristic
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C2×#117C2314yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C42C2312yes—
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337#401C2314yes—
338#401C2312yes—
339#401C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2312yes—
369#399C2312yes—
370#399C2312yes—
371#399C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2311yescharacteristic
398#397C2311yescharacteristic
399#397C2312yes—
400#397C2312yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2312yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#395C2314yes—
411#395C2312yes—
412#395C2314yes—
413#395C2312yes—
414#395C2311yescharacteristic
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2312yes—
421#395C2314yes—
422#394C2311yescharacteristic
423#394C2312yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2311yescharacteristic
433#393C2311yescharacteristic
434#393C2311yescharacteristic
435#393C2312yes—
436#392C2311yescharacteristic
437#392C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
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#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#386C2312yes—
590#386C2314yes—
591#386C2312yes—
592#386C2314yes—
593#386C2312yes—
594#386C2312yes—
595#386C2311yescharacteristic
596#386C2312yes—
597#386C2312yes—
598#386C2312yes—
599#386C2312yes—
600#386C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2312yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2312yes—
620#385C2312yes—
621#385C2311yescharacteristic
622#385C2312yes—
623#385C2314yes—
624#384C2314yes—
625#384C2312yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#383C2312yes—
632#383C2312yes—
633#383C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#381C2312yes—
644#381C2314yes—
645#381C2314yes—
646#381C2312yes—
647#381C2312yes—
648#381C2312yes—
649#381C2311yescharacteristic
650#381C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2312yes—
660#380C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2311yescharacteristic
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2314yes—
720C2×#41—28no—
721C2×#41—42no—
722C22×Q8—28no—
723C22×Q8—28no—
724C22×Q8—28no—
725C22×Q8—42no—
726C22×Q8—44no—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C4⋊Q8—28no—
752C4⋊Q8—28no—
753C4⋊Q8—28no—
754C4⋊Q8—216no—
755C4⋊Q8—216no—
756C4⋊Q8—44no—
757C4⋊Q8—42no—
758#126—44no—
759#125—216no—
760#125—44no—
761#125—42no—
762#125—48no—
763#125—44no—
764#124—216no—
765#123—216no—
766#123—216no—
767#123—28no—
768#123—24no—
769#123—44no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—216no—
775C22⋊Q8—28no—
776C22⋊Q8—216no—
777C22⋊Q8—216no—
778C22⋊Q8—42no—
779C22⋊Q8—42no—
780C22⋊Q8#41116yes—
781C4×Q8—28no—
782C4×Q8—28no—
783C4×Q8—216no—
784C4×Q8—28no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—48no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—42no—
792C4×Q8—48no—
793C4×Q8—48no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×D4—28no—
798C4×D4—216no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—42no—
802#117—28no—
803#117—28no—
804#117—24no—
805#117—216no—
806#117—28no—
807#117—44no—
808#117—44no—
809#117—48no—
810#117—48no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2411yescharacteristic
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C42—28no—
914C2×C42—44no—
915C2×C42—42no—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2411yescharacteristic
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2411yescharacteristic
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2411yescharacteristic
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023C24C2511yescharacteristic
1024C24C2512yes—
1025C24C2511yescharacteristic
1026#41—416no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—28no—
1032C2×Q8—24no—
1033C2×Q8—28no—
1034C2×Q8—24no—
1035C2×Q8—28no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—22no—
1039C2×Q8—41no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—41no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—432no—
1047C2×Q8—416no—
1048C2×Q8C2×#4118yes—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—22no—
1054C2×D4—24no—
1055C2×D4—42no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—41no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—28no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—41no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—41no—
1082C22×C4—42no—
1083C22×C4—41no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4C2×#4118yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4C2×#4118yes—
1177C4⋊C4C2×#41116yes—
1178C4⋊C4H(5,𝔽2)14yes—
1179C22⋊C4—28no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—41no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—41no—
1210C22⋊C4—42no—
1211C22⋊C4—41no—
1212C22⋊C4—42no—
1213C22⋊C4C2×#41116yes—
1214C22⋊C42−1+414yes—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—28no—
1220C42—28no—
1221C42—28no—
1222C42—28no—
1223C42—24no—
1224C42—28no—
1225C42—24no—
1226C42—24no—
1227C42—28no—
1228C42—28no—
1229C42—24no—
1230C42—24no—
1231C42—22no—
1232C42—28no—
1233C42—44no—
1234C42—42no—
1235C42—44no—
1236C42—44no—
1237C42—42no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—21no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—21no—
1253C23—22no—
1254C23—21no—
1255C23—21no—
1256C23—21no—
1257C23—22no—
1258C23C22×#4114yes—
1259C23C2×2−1+412yes—
1260C23C2611yescharacteristic
1261Q8—216no—
1262Q8—416no—
1263Q8—48no—
1264Q8—44no—
1265Q8—44no—
1266Q8—44no—
1267Q8—48no—
1268Q8—88no—
1269D4—48no—
1270D4—48no—
1271D4—44no—
1272D4—82no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—216no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—48no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—416no—
1343C2×C4—44no—
1344C2×C4—44no—
1345C2×C4—44no—
1346C2×C4—84no—
1347C2×C4—82no—
1348C2×C4—164no—
1349C2×C4—162no—
1350C2×C4C22×#4118yes—
1351C2×C4C22×#4114yes—
1352C2×C4C22×#4118yes—
1353C2×C4C22×#4114yes—
1354C2×C4C2×H(5,𝔽2)14yes—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4C2×2−1+414yes—
1357C22—24no—
1358C22—24no—
1359C22—24no—
1360C22—22no—
1361C22—24no—
1362C22—42no—
1363C22—41no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—42no—
1372C22—41no—
1373C22—41no—
1374C22C23×#4112yes—
1375C22C22×H(5,𝔽2)11yescharacteristic
1376C22C22×2−1+411yescharacteristic
1377C222−1+612yes—
1378C222−1+611yescharacteristic
1379C4—24no—
1380C4—28no—
1381C4—24no—
1382C4—24no—
1383C4—28no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—42no—
1390C4—41no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—41no—
1400C4—41no—
1401C4—44no—
1402C4—41no—
1403C4—42no—
1404C4#348114yes—
1405C2—44no—
1406C2—42no—
1407C2—81no—
1408C2C2×#348111yescharacteristic
1409C2#6286112yes—
1410C2#6291511yescharacteristic
1411C2#6299812yes—
1412C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2388C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59989C2semidirect
2. #59629C2semidirect
3. #59615C2semidirect
4. #59096C2semidirect
5. #52289C2semidirect
7. #45420C2semidirect
8. #45415C2semidirect
10. #45184C2semidirect
11. #44858C2semidirect
12. #44829C2semidirect
13. #44715C2semidirect
14. #43877C2semidirect
15. #40435C2semidirect
16. #40143C2semidirect
17. #39053C2semidirect
18. #38518C2semidirect
19. #38057C2semidirect
20. #37783C2semidirect
21. #36423C2semidirect
22. #36409C2semidirect
24. #35949C2semidirect
25. #35901C2semidirect
26. #35749C2semidirect
27. #34291C2semidirect
28. #34276C2semidirect
29. #34231C2semidirect

Maximal subgroups

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

subgroupindex
#599892
#596292
#596152
#590962
#522892
#522032
#454202
#454152
#453212
#451842
#448582
#448292
#447152
#438772
#404352
#401432
#390532
#385182
#380572
#377832
#364232
#364092
#360802
#359492
#359012
#357492
#342912
#342762
#342312