Finite Group Databasebeta

← #8701660

Subgroups — #8701660

Order 512.

4387 conjugacy classes of subgroups.

The subgroup lattice has 1443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C212yesmaximal, complemented
2#59857C212yesmaximal, complemented
3#59293C212yesmaximal, complemented
4#59234C212yesmaximal, complemented
5#58945C212yesmaximal, complemented
6#57943C214yesmaximal, complemented
7#56179C214yesmaximal, complemented
8#53595C212yesmaximal, complemented
9#52297C211yesmaximal, characteristic
10#51949C214yesmaximal, complemented
11#50564C214yesmaximal, complemented
12#50310C214yesmaximal, complemented
13#46342C211yesmaximal, characteristic, complemented
14#46001C212yesmaximal, complemented
15#45351C211yesmaximal, characteristic, complemented
16#45330C211yesmaximal, characteristic, complemented
17#45237C212yesmaximal, complemented
18#44971C212yesmaximal, complemented
19#42920C212yesmaximal, complemented
20#42918C211yesmaximal, characteristic, complemented
21#42911C211yesmaximal, characteristic, complemented
22#42714C212yesmaximal, complemented
23#39959C212yesmaximal, complemented
24#39659C212yesmaximal, complemented
25#39606C212yesmaximal, complemented
26#37261C212yesmaximal, complemented
27#37051C214yesmaximal, complemented
28#36594C211yesmaximal, characteristic, complemented
29#36491C212yesmaximal, complemented
30C2×#556C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#552C2212yes—
33C2×#544C2211yescharacteristic
34C2×#536C2211yescharacteristic
35#2868C2211yescharacteristic
36#2866C2214yes—
37#2863C2212yes—
38#2858C2212yes—
39#2857C2212yes—
40#2843C2214yes—
41#2837C2214yes—
42#2831C2214yes—
43#2830C2212yes—
44#2821C2212yes—
45#2821C2212yes—
46#2805C2214yes—
47#2803C2212yes—
48#2803C2214yes—
49#2799C2212yes—
50#2797C2214yes—
51#2795C2211yescharacteristic
52#2793C2214yes—
53#2792C2212yes—
54#2792C2211yescharacteristic
55#2791C2214yes—
56#2788C2214yes—
57#2788C2214yes—
58#2784C2211yescharacteristic
59#2784C2214yes—
60#2779C2214yes—
61#2777C2214yes—
62#2777C2214yes—
63#2775C2214yes—
64#2775C2214yes—
65#2770C2214yes—
66#2768C2214yes—
67#2768C2214yes—
68#2764C2212yes—
69#2757C2214yes—
70#2757C2214yes—
71#2756C2212yes—
72#2754C2214yes—
73#2748C2214yes—
74#2748C2214yes—
75#2738C2214yes—
76#2737C2214yes—
77#2737C2212yes—
78#2734C2214yes—
79#2730C2214yes—
80#2729C2214yes—
81#2728C2212yes—
82#2725C2214yes—
83#2723C2214yes—
84#2722C2214yes—
85#2722C2212yes—
86#2720C2214yes—
87#2718C2214yes—
88#2716C2214yes—
89#2715C2214yes—
90#2714C2212yes—
91#2713C2214yes—
92#2711C2214yes—
93#2710C2214yes—
94#2710C2214yes—
95#2709C2212yes—
96#2707C2214yes—
97#2706C2214yes—
98#2705C2212yes—
99#2702C2214yes—
100#2699C2211yescharacteristic
101#2695C2214yes—
102#2694C2214yes—
103#2690C2214yes—
104#2689C2214yes—
105#2677C2214yes—
106#2674C2214yes—
107#2674C2214yes—
108#2673C2212yes—
109#2672C2214yes—
110#2665C2214yes—
111#2664C2214yes—
112#2664C2212yes—
113#2662C2214yes—
114#2662C2212yes—
115#2651C2214yes—
116#2651C2214yes—
117#2651C2214yes—
118#2634C2212yes—
119#2632C2212yes—
120#2629C2214yes—
121#2625C2211yescharacteristic
122#2616C2211yescharacteristic
123#2601C2214yes—
124#2600C2212yes—
125#2597C2214yes—
126#2596C2214yes—
127#2596C2214yes—
128#2595C2214yes—
129#2593C2214yes—
130#2590C2214yes—
131#2587C2214yes—
132#2586C2212yes—
133#2586C2212yes—
134#2586C2214yes—
135#2586C2214yes—
136#2584C2214yes—
137#2567C2212yes—
138#2567C2212yes—
139#2554C2214yes—
140#2552C2212yes—
141#2551C2212yes—
142#2550C2214yes—
143#2550C2214yes—
144#2547C2211yescharacteristic
145#2547C2211yescharacteristic
146#2547C2212yes—
147#2546C2212yes—
148#2545C2212yes—
149#2545C2212yes—
150#2542C2212yes—
151#2538C2212yes—
152#2538C2212yes—
153#2538C2212yes—
154#2525C2214yes—
155#2525C2214yes—
156#2525C2214yes—
157#2524C2214yes—
158#2524C2214yes—
159#2524C2214yes—
160#2521C2214yes—
161#2519C2214yes—
162#2519C2214yes—
163#2517C2212yes—
164#2513C2214yes—
165#2512C2214yes—
166#2512C2214yes—
167#2511C2212yes—
168#2507C2214yes—
169#2507C2214yes—
170#2507C2212yes—
171#2506C2212yes—
172#2502C2211yescharacteristic
173#2502C2212yes—
174#2497C2212yes—
175#2497C2212yes—
176#2496C2212yes—
177#2495C2214yes—
178#2492C2212yes—
179#2492C2212yes—
180#2492C2212yes—
181#2491C2214yes—
182#2489C2212yes—
183#2486C2211yescharacteristic
184#2485C2212yes—
185#2485C2212yes—
186#2479C2214yes—
187#2475C2214yes—
188#2475C2214yes—
189#2474C2214yes—
190#2474C2214yes—
191#2474C2214yes—
192#2470C2214yes—
193#2461C2214yes—
194#2461C2214yes—
195#2454C2214yes—
196#2453C2212yes—
197#2451C2212yes—
198#2446C2212yes—
199#2441C2212yes—
200#2441C2212yes—
201#2440C2212yes—
202#2440C2212yes—
203#2434C2211yescharacteristic
204#2429C2212yes—
205#2429C2212yes—
206#2423C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2417C2212yes—
210#2417C2212yes—
211#2415C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2415C2212yes—
216#2415C2214yes—
217#2415C2212yes—
218#2409C2211yescharacteristic
219#2409C2212yes—
220#2395C2211yescharacteristic
221#2392C2212yes—
222#2388C2211yescharacteristic
223#2388C2212yes—
224#2383C2214yes—
225#2376C2212yes—
226#2370C2214yes—
227#2370C2214yes—
228#2370C2212yes—
229#2369C2214yes—
230#2365C2212yes—
231#2362C2212yes—
232#2362C2212yes—
233#2355C2212yes—
234#2354C2212yes—
235#2354C2212yes—
236#2354C2212yes—
237D4×C4⋊C4C2212yes—
238#2347C2212yes—
239#2347C2212yes—
240#2347C2211yescharacteristic
241#2347C2211yescharacteristic
242Q8×C22⋊C4C2212yes—
243#2335C2214yes—
244#2324C2214yes—
245#2323C2214yes—
246#2323C2212yes—
247#2311C2212yes—
248C4×C4⋊Q8C2212yes—
249C4×#127C2211yescharacteristic
250C4×#125C2214yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256#2296C2212yes—
257#2285C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#556—44no—
262#556—44no—
263#552—48no—
264#544—44no—
265#536—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2311yescharacteristic
330C2×#117C2314yes—
331C2×#117C2312yes—
332C2×#117C2314yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C42C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2311yescharacteristic
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2311yescharacteristic
357#399C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2311yescharacteristic
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2311yescharacteristic
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#395C2312yes—
420#395C2314yes—
421#395C2312yes—
422#395C2311yescharacteristic
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#394C2314yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2314yes—
443#394C2311yescharacteristic
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2314yes—
452#393C2311yescharacteristic
453#393C2312yes—
454#393C2314yes—
455#393C2314yes—
456#393C2312yes—
457#393C2314yes—
458#393C2314yes—
459#392C2311yescharacteristic
460#392C2312yes—
461#392C2312yes—
462#392C2312yes—
463#392C2312yes—
464#392C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#390C2311yescharacteristic
484#390C2311yescharacteristic
485#390C2312yes—
486#390C2312yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2312yes—
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#388C2312yes—
579#388C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
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#387C2312yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2312yes—
623#386C2312yes—
624#386C2312yes—
625#386C2312yes—
626#386C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#384C2311yescharacteristic
642#384C2312yes—
643#384C2312yes—
644#384C2314yes—
645#384C2314yes—
646#384C2312yes—
647#384C2312yes—
648#384C2312yes—
649#383C2312yes—
650#383C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2314yes—
656#382C2314yes—
657#382C2314yes—
658#381C2312yes—
659#381C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2311yescharacteristic
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C43C2311yescharacteristic
716C43C2312yes—
717C2×#41—42no—
718C2×#41—44no—
719C22×Q8—42no—
720C22×Q8—44no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—48no—
754C4⋊Q8—82no—
755#127—42no—
756#126—28no—
757#126—48no—
758#126—44no—
759#126—44no—
760#126—48no—
761#126—84no—
762#125—28no—
763#125—216no—
764#125—44no—
765#125—48no—
766#125—84no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—82no—
771#124—82no—
772#124—84no—
773#123—28no—
774#123—48no—
775#123—48no—
776#123—44no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—42no—
787C22⋊Q8—42no—
788C22⋊Q8—84no—
789#121—28no—
790#121—44no—
791C4×Q8—24no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—42no—
803C4×D4—42no—
804C4×D4—84no—
805#117—24no—
806#117—24no—
807#117—28no—
808#117—42no—
809#117—48no—
810#117—44no—
811#117—44no—
812#117—84no—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C42—44no—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2411yescharacteristic
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2411yescharacteristic
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
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—
1021C24C2511yescharacteristic
1022C24C2512yes—
1023C24C2511yescharacteristic
1024#41—88no—
1025C2×Q8—22no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—88no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—41no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
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—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—28no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
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—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4H(5,𝔽2)14yes—
1183C4⋊C42−1+418yes—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
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—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—41no—
1213C22⋊C4—41no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C42—28no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—22no—
1240C42—24no—
1241C42—28no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—22no—
1247C42—42no—
1248C42—42no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42—41no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—21no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—21no—
1278C23—22no—
1279C23—22no—
1280C23—21no—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23C2611yescharacteristic
1285Q8—44no—
1286Q8—48no—
1287Q8—84no—
1288Q8—84no—
1289Q8—84no—
1290Q8—82no—
1291Q8—164no—
1292D4—48no—
1293D4—84no—
1294D4—84no—
1295D4—84no—
1296D4—82no—
1297D4—82no—
1298D4—84no—
1299D4—84no—
1300D4—82no—
1301C2×C4—21no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—48no—
1364C2×C4—44no—
1365C2×C4—48no—
1366C2×C4—44no—
1367C2×C4—48no—
1368C2×C4—84no—
1369C2×C4—88no—
1370C2×C4—84no—
1371C2×C4—162no—
1372C2×C4C2×H(5,𝔽2)14yes—
1373C2×C4C2×H(5,𝔽2)12yes—
1374C2×C4C2×2−1+414yes—
1375C2×C4C2×2−1+414yes—
1376C2×C4C2×2−1+414yes—
1377C2×C4#58512yes—
1378C2×C4#58514yes—
1379C22—41no—
1380C22—42no—
1381C22—42no—
1382C22—41no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—41no—
1391C22—42no—
1392C22—41no—
1393C22—42no—
1394C22—41no—
1395C22—42no—
1396C22—41no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22C22×H(5,𝔽2)11yescharacteristic
1404C22C22×2−1+412yes—
1405C22C2×#58512yes—
1406C22C2×#58511yescharacteristic
1407C22H(7,𝔽2)11yescharacteristic
1408C4—24no—
1409C4—24no—
1410C4—24no—
1411C4—22no—
1412C4—24no—
1413C4—42no—
1414C4—41no—
1415C4—42no—
1416C4—41no—
1417C4—44no—
1418C4—42no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—41no—
1423C4—44no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4—44no—
1431C4—42no—
1432C4#355114yes—
1433C2—81no—
1434C2—82no—
1435C2—82no—
1436C2—81no—
1437C2C2×#355111yescharacteristic
1438C2#6289911yescharacteristic
1439C2#6292612yes—
1440C2#6302512yes—
1441C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52297C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59925C2semidirect
2. #59857C2semidirect
3. #59293C2semidirect
4. #59234C2semidirect
5. #58945C2semidirect
6. #57943C2semidirect
7. #56179C2semidirect
8. #53595C2semidirect
10. #51949C2semidirect
11. #50564C2semidirect
12. #50310C2semidirect
13. #46342C2semidirect
14. #46001C2semidirect
15. #45351C2semidirect
16. #45330C2semidirect
17. #45237C2semidirect
18. #44971C2semidirect
19. #42920C2semidirect
20. #42918C2semidirect
21. #42911C2semidirect
22. #42714C2semidirect
23. #39959C2semidirect
24. #39659C2semidirect
25. #39606C2semidirect
26. #37261C2semidirect
27. #37051C2semidirect
28. #36594C2semidirect
29. #36491C2semidirect

Maximal subgroups

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

subgroupindex
#599252
#598572
#592932
#592342
#589452
#579432
#561792
#535952
#522972
#519492
#505642
#503102
#463422
#460012
#453512
#453302
#452372
#449712
#429202
#429182
#429112
#427142
#399592
#396592
#396062
#372612
#370512
#365942
#364912