Finite Group Databasebeta

← #8726634

Subgroups — #8726634

Order 512.

4423 conjugacy classes of subgroups.

The subgroup lattice has 1446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C212yesmaximal, complemented
2#59946C211yesmaximal, characteristic, complemented
3#59656C212yesmaximal, complemented
4#59642C212yesmaximal, complemented
5#59434C212yesmaximal, complemented
6#56481C214yesmaximal, complemented
7#54561C214yesmaximal, complemented
8#54317C214yesmaximal, complemented
9#53900C212yesmaximal, complemented
10#53045C212yesmaximal, complemented
11#52958C211yesmaximal, characteristic, complemented
12#52307C211yesmaximal, characteristic
13#47543C214yesmaximal, complemented
14#46969C212yesmaximal, complemented
15#45364C212yesmaximal, complemented
16#45330C211yesmaximal, characteristic, complemented
17#45237C212yesmaximal, complemented
18#44068C214yesmaximal, complemented
19#42911C211yesmaximal, characteristic, complemented
20#42446C212yesmaximal, complemented
21#42382C212yesmaximal, complemented
22#42123C214yesmaximal, complemented
23#40212C212yesmaximal, complemented
24#40083C212yesmaximal, complemented
25#39744C211yesmaximal, characteristic, complemented
26#39654C212yesmaximal, complemented
27#39633C212yesmaximal, complemented
28#36089C211yesmaximal, characteristic, complemented
29#35686C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#552C2212yes—
33C2×#536C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2868C2211yescharacteristic
36#2863C2212yes—
37#2838C2214yes—
38#2837C2214yes—
39#2835C2212yes—
40#2832C2214yes—
41#2832C2212yes—
42#2829C2214yes—
43#2829C2214yes—
44#2827C2214yes—
45#2821C2212yes—
46#2811C2211yescharacteristic
47#2811C2212yes—
48#2807C2214yes—
49#2807C2214yes—
50#2806C2214yes—
51#2806C2214yes—
52#2803C2214yes—
53#2801C2214yes—
54#2800C2214yes—
55#2795C2214yes—
56#2792C2214yes—
57#2790C2214yes—
58#2790C2214yes—
59#2789C2212yes—
60#2788C2214yes—
61#2785C2212yes—
62#2785C2212yes—
63#2785C2211yescharacteristic
64#2785C2211yescharacteristic
65#2780C2214yes—
66#2777C2214yes—
67#2777C2214yes—
68#2772C2214yes—
69#2769C2214yes—
70#2768C2214yes—
71#2767C2214yes—
72#2766C2214yes—
73#2764C2212yes—
74#2764C2214yes—
75#2759C2214yes—
76#2757C2214yes—
77#2754C2214yes—
78#2745C2214yes—
79#2733C2212yes—
80#2733C2212yes—
81#2733C2211yescharacteristic
82#2733C2212yes—
83#2733C2212yes—
84#2731C2214yes—
85#2731C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2728C2212yes—
89#2721C2214yes—
90#2721C2214yes—
91#2719C2214yes—
92#2718C2214yes—
93#2717C2212yes—
94#2716C2214yes—
95#2712C2214yes—
96#2712C2212yes—
97#2710C2214yes—
98#2710C2214yes—
99#2710C2214yes—
100#2706C2214yes—
101#2694C2214yes—
102#2674C2214yes—
103#2674C2214yes—
104#2666C2214yes—
105#2662C2212yes—
106#2658C2212yes—
107#2654C2214yes—
108#2653C2214yes—
109#2651C2214yes—
110#2647C2214yes—
111#2637C2212yes—
112#2633C2214yes—
113#2632C2212yes—
114#2630C2214yes—
115#2616C2211yescharacteristic
116#2616C2212yes—
117#2616C2211yescharacteristic
118#2603C2212yes—
119#2600C2212yes—
120#2599C2214yes—
121#2594C2214yes—
122#2594C2214yes—
123#2593C2214yes—
124#2589C2214yes—
125#2589C2214yes—
126#2587C2214yes—
127#2586C2212yes—
128#2586C2212yes—
129#2584C2214yes—
130#2582C2214yes—
131#2582C2212yes—
132#2581C2212yes—
133#2580C2214yes—
134#2574C2214yes—
135#2570C2214yes—
136#2568C2212yes—
137#2567C2212yes—
138#2558C2214yes—
139#2554C2214yes—
140#2550C2214yes—
141#2550C2214yes—
142#2547C2211yescharacteristic
143#2547C2212yes—
144#2546C2211yescharacteristic
145#2546C2212yes—
146#2546C2212yes—
147#2545C2212yes—
148#2545C2214yes—
149#2542C2212yes—
150#2538C2212yes—
151#2536C2212yes—
152#2536C2212yes—
153#2532C2214yes—
154#2532C2214yes—
155#2532C2214yes—
156#2530C2214yes—
157#2529C2214yes—
158#2529C2214yes—
159#2527C2214yes—
160#2525C2214yes—
161#2519C2214yes—
162#2514C2214yes—
163#2502C2212yes—
164#2502C2212yes—
165#2502C2211yescharacteristic
166#2497C2212yes—
167#2497C2212yes—
168#2497C2212yes—
169#2494C2212yes—
170#2494C2212yes—
171#2492C2212yes—
172#2492C2212yes—
173#2492C2212yes—
174#2492C2212yes—
175#2492C2212yes—
176#2489C2212yes—
177#2486C2211yescharacteristic
178#2486C2212yes—
179#2485C2212yes—
180#2475C2214yes—
181#2474C2214yes—
182#2470C2214yes—
183#2469C2214yes—
184#2468C2214yes—
185#2466C2214yes—
186#2466C2214yes—
187#2461C2214yes—
188#2461C2214yes—
189#2459C2214yes—
190#2458C2214yes—
191#2455C2214yes—
192#2455C2214yes—
193#2452C2214yes—
194#2451C2214yes—
195#2451C2214yes—
196#2448C2214yes—
197#2441C2212yes—
198#2441C2212yes—
199#2441C2212yes—
200#2440C2212yes—
201#2440C2212yes—
202#2439C2212yes—
203#2434C2211yescharacteristic
204#2429C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2423C2212yes—
210#2421C2212yes—
211#2417C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2415C2212yes—
216#2409C2211yescharacteristic
217#2409C2212yes—
218#2399C2212yes—
219#2392C2214yes—
220#2388C2211yescharacteristic
221#2388C2212yes—
222#2388C2212yes—
223#2388C2211yescharacteristic
224#2374C2212yes—
225#2369C2214yes—
226#2367C2214yes—
227#2365C2214yes—
228#2362C2214yes—
229#2362C2212yes—
230#2362C2212yes—
231#2360C2212yes—
232#2360C2212yes—
233#2360C2212yes—
234#2354C2212yes—
235Q8×C4⋊C4C2212yes—
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2212yes—
238#2347C2212yes—
239#2347C2211yescharacteristic
240#2347C2212yes—
241#2346C2211yescharacteristic
242Q8×C22⋊C4C2212yes—
243#2337C2214yes—
244#2332C2214yes—
245#2331C2214yes—
246#2327C2212yes—
247#2326C2214yes—
248#2311C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×#125C2212yes—
252C4×#124C2212yes—
253C4×#124C2212yes—
254C4×#124C2211yescharacteristic
255C4×#124C2212yes—
256C4×#124C2212yes—
257#2295C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#557—44no—
263#556—44no—
264#552—48no—
265#536—44no—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306#520—44no—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2312yes—
335#401C2314yes—
336#401C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2311yescharacteristic
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2314yes—
420#395C2311yescharacteristic
421#395C2312yes—
422#395C2314yes—
423#394C2312yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2311yescharacteristic
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2312yes—
439#394C2311yescharacteristic
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#393C2311yescharacteristic
447#393C2312yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2311yescharacteristic
453#393C2314yes—
454#393C2312yes—
455#393C2314yes—
456#393C2312yes—
457#393C2314yes—
458#392C2312yes—
459#392C2312yes—
460#392C2311yescharacteristic
461#392C2311yescharacteristic
462#392C2312yes—
463#392C2312yes—
464#392C2312yes—
465#392C2312yes—
466#392C2312yes—
467#392C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2314yes—
495#391C2314yes—
496#391C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2311yescharacteristic
504#390C2312yes—
505#390C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2312yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
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#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#384C2312yes—
646#384C2312yes—
647#384C2314yes—
648#384C2314yes—
649#384C2312yes—
650#384C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2312yes—
656#382C2314yes—
657#382C2312yes—
658#382C2311yescharacteristic
659#382C2314yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#381C2314yes—
665#381C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2314yes—
713#376C2312yes—
714#376C2312yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—42no—
718C2×#41—44no—
719C2×#41—42no—
720C2×#41—44no—
721C22×Q8—42no—
722C22×Q8—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C4⋊Q8—216no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758C4⋊Q8—82no—
759C4⋊Q8—82no—
760#126—44no—
761#126—44no—
762#126—48no—
763#125—28no—
764#125—48no—
765#125—48no—
766#124—28no—
767#124—28no—
768#124—28no—
769#124—44no—
770#124—44no—
771#124—42no—
772#124—44no—
773#124—84no—
774#124—82no—
775#123—48no—
776#123—48no—
777#123—44no—
778#123—84no—
779C22⋊Q8—28no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—42no—
789C22⋊Q8—42no—
790C4×Q8—24no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—42no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—84no—
800C4×Q8—84no—
801C4×D4—48no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—84no—
809C4×D4—84no—
810#117—28no—
811#117—24no—
812#117—24no—
813#117—48no—
814#117—44no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955#95C2411yescharacteristic
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2411yescharacteristic
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2411yescharacteristic
974#95C2411yescharacteristic
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020C24C2512yes—
1021C24C2512yes—
1022C24C2511yescharacteristic
1023C24C2511yescharacteristic
1024#41—416no—
1025#41—88no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—28no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—22no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—41no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—42no—
1051C2×Q8—88no—
1052C2×Q82−1+418yes—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—22no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—41no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4H(5,𝔽2)14yes—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—41no—
1210C22⋊C4—41no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C42—28no—
1236C42—24no—
1237C42—24no—
1238C42—22no—
1239C42—24no—
1240C42—24no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—22no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—42no—
1256C42—44no—
1257C42—44no—
1258C42—42no—
1259C42—42no—
1260C42—41no—
1261C23—21no—
1262C23—22no—
1263C23—21no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—21no—
1274C23—21no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—21no—
1282C23—22no—
1283C23—21no—
1284C23—22no—
1285C23C2611yescharacteristic
1286Q8—48no—
1287Q8—44no—
1288Q8—44no—
1289Q8—48no—
1290Q8—84no—
1291Q8—84no—
1292Q8—82no—
1293Q8—88no—
1294Q8—84no—
1295Q8—82no—
1296D4—48no—
1297D4—48no—
1298D4—48no—
1299D4—44no—
1300D4—82no—
1301D4—84no—
1302D4—84no—
1303D4—84no—
1304D4—82no—
1305C2×C4—21no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—44no—
1368C2×C4—48no—
1369C2×C4—44no—
1370C2×C4—48no—
1371C2×C4—88no—
1372C2×C4—84no—
1373C2×C4—162no—
1374C2×C4—164no—
1375C2×C4C2×H(5,𝔽2)14yes—
1376C2×C4C2×H(5,𝔽2)12yes—
1377C2×C4C2×2−1+414yes—
1378C2×C4C2×2−1+414yes—
1379C2×C4C2×2−1+414yes—
1380C2×C4#58512yes—
1381C2×C4#58514yes—
1382C22—41no—
1383C22—41no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—41no—
1393C22—41no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—41no—
1398C22—42no—
1399C22—41no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22C22×H(5,𝔽2)11yescharacteristic
1407C22C22×2−1+412yes—
1408C22C2×#58512yes—
1409C22C2×#58511yescharacteristic
1410C22H(7,𝔽2)11yescharacteristic
1411C4—24no—
1412C4—22no—
1413C4—24no—
1414C4—24no—
1415C4—24no—
1416C4—42no—
1417C4—41no—
1418C4—42no—
1419C4—41no—
1420C4—44no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—41no—
1428C4—44no—
1429C4—44no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—44no—
1435C4#354014yes—
1436C2—81no—
1437C2—81no—
1438C2—82no—
1439C2—82no—
1440C2C2×#354011yescharacteristic
1441C2#6289911yescharacteristic
1442C2#6290212yes—
1443C2#6303412yes—
1444C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52307C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59951C2semidirect
2. #59946C2semidirect
3. #59656C2semidirect
4. #59642C2semidirect
5. #59434C2semidirect
6. #56481C2semidirect
7. #54561C2semidirect
8. #54317C2semidirect
9. #53900C2semidirect
10. #53045C2semidirect
11. #52958C2semidirect
13. #47543C2semidirect
14. #46969C2semidirect
15. #45364C2semidirect
16. #45330C2semidirect
17. #45237C2semidirect
18. #44068C2semidirect
19. #42911C2semidirect
20. #42446C2semidirect
21. #42382C2semidirect
22. #42123C2semidirect
23. #40212C2semidirect
24. #40083C2semidirect
25. #39744C2semidirect
26. #39654C2semidirect
27. #39633C2semidirect
28. #36089C2semidirect
29. #35686C2semidirect

Maximal subgroups

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

subgroupindex
#599512
#599462
#596562
#596422
#594342
#564812
#545612
#543172
#539002
#530452
#529582
#523072
#475432
#469692
#453642
#453302
#452372
#440682
#429112
#424462
#423822
#421232
#402122
#400832
#397442
#396542
#396332
#360892
#356862