Finite Group Databasebeta

← #8095178

Subgroups — #8095178

Order 512.

4594 conjugacy classes of subgroups.

The subgroup lattice has 1542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53056C212yesmaximal, complemented
2#53044C212yesmaximal, complemented
3#53009C211yesmaximal, characteristic, complemented
4#53005C211yesmaximal, characteristic, complemented
5#52960C211yesmaximal, characteristic, complemented
6#52957C211yesmaximal, characteristic, complemented
7#52934C214yesmaximal, complemented
8#52919C212yesmaximal, complemented
9#52916C212yesmaximal, complemented
10#52408C212yesmaximal, complemented
11#52406C212yesmaximal, complemented
12#52403C214yesmaximal, complemented
13#46322C212yesmaximal, complemented
14#46241C212yesmaximal, complemented
15#45916C214yesmaximal, complemented
16#45758C212yesmaximal, complemented
17#45747C212yesmaximal, complemented
18#45738C214yesmaximal, complemented
19#45689C212yesmaximal, complemented
20#45676C212yesmaximal, complemented
21#45663C212yesmaximal, complemented
22#45499C212yesmaximal, complemented
23#35607C212yesmaximal, complemented
24#35551C212yesmaximal, complemented
25#35548C212yesmaximal, complemented
26#35258C212yesmaximal, complemented
27#35243C212yesmaximal, complemented
28#35163C212yesmaximal, complemented
29#34977C211yesmaximal, characteristic, complemented
30#34952C211yesmaximal, characteristic, complemented
31#34909C211yesmaximal, characteristic, complemented
32C2×#542C2212yes—
33C2×#532C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2866C2214yes—
38#2864C2214yes—
39#2857C2212yes—
40#2855C2212yes—
41#2854C2212yes—
42#2852C2214yes—
43#2850C2212yes—
44#2850C2214yes—
45#2844C2212yes—
46#2844C2212yes—
47#2841C2214yes—
48#2837C2214yes—
49#2837C2214yes—
50#2835C2212yes—
51#2832C2214yes—
52#2830C2214yes—
53#2830C2214yes—
54#2830C2212yes—
55#2829C2214yes—
56#2829C2214yes—
57#2828C2214yes—
58#2828C2212yes—
59#2827C2214yes—
60#2826C2212yes—
61#2824C2212yes—
62#2824C2214yes—
63#2824C2212yes—
64#2824C2214yes—
65#2821C2214yes—
66#2820C2214yes—
67#2813C2214yes—
68#2813C2214yes—
69#2805C2214yes—
70#2803C2214yes—
71#2799C2214yes—
72#2797C2214yes—
73#2796C2214yes—
74#2791C2214yes—
75#2788C2214yes—
76#2788C2214yes—
77#2785C2212yes—
78#2784C2212yes—
79#2784C2212yes—
80#2779C2214yes—
81#2772C2214yes—
82#2769C2212yes—
83#2763C2212yes—
84#2761C2214yes—
85#2753C2214yes—
86#2742C2214yes—
87#2742C2214yes—
88#2741C2214yes—
89#2737C2214yes—
90#2737C2214yes—
91#2730C2214yes—
92#2730C2214yes—
93#2729C2214yes—
94#2723C2214yes—
95#2720C2214yes—
96#2714C2214yes—
97#2713C2214yes—
98#2710C2214yes—
99#2709C2214yes—
100#2708C2214yes—
101#2706C2214yes—
102#2705C2214yes—
103#2701C2214yes—
104#2694C2214yes—
105#2693C2212yes—
106#2688C2214yes—
107#2681C2214yes—
108#2677C2212yes—
109#2675C2212yes—
110#2673C2214yes—
111#2672C2214yes—
112#2671C2214yes—
113#2652C2214yes—
114#2649C2214yes—
115#2637C2214yes—
116#2632C2214yes—
117#2628C2212yes—
118#2620C2212yes—
119#2616C2212yes—
120#2615C2212yes—
121#2610C2212yes—
122#2610C2212yes—
123#2602C2214yes—
124#2600C2212yes—
125#2600C2212yes—
126#2599C2211yescharacteristic
127#2599C2211yescharacteristic
128#2598C2211yescharacteristic
129#2598C2211yescharacteristic
130#2582C2212yes—
131#2581C2211yescharacteristic
132#2581C2212yes—
133#2580C2211yescharacteristic
134#2580C2212yes—
135#2579C2212yes—
136#2579C2212yes—
137#2578C2214yes—
138#2577C2214yes—
139#2567C2211yescharacteristic
140#2566C2212yes—
141#2564C2214yes—
142#2563C2211yescharacteristic
143#2562C2212yes—
144#2559C2214yes—
145#2558C2214yes—
146#2555C2214yes—
147#2553C2214yes—
148#2552C2212yes—
149#2551C2212yes—
150#2548C2211yescharacteristic
151#2544C2212yes—
152#2541C2211yescharacteristic
153#2540C2212yes—
154#2538C2212yes—
155#2537C2212yes—
156#2537C2212yes—
157#2536C2211yescharacteristic
158#2535C2211yescharacteristic
159#2533C2214yes—
160#2529C2214yes—
161#2521C2214yes—
162#2518C2214yes—
163#2518C2214yes—
164#2517C2214yes—
165#2517C2214yes—
166#2515C2214yes—
167#2511C2212yes—
168#2511C2212yes—
169#2508C2212yes—
170#2507C2212yes—
171#2505C2214yes—
172#2505C2214yes—
173#2500C2212yes—
174#2499C2212yes—
175#2497C2212yes—
176#2497C2212yes—
177#2496C2212yes—
178#2495C2212yes—
179#2495C2214yes—
180#2492C2212yes—
181#2491C2212yes—
182#2491C2214yes—
183#2489C2212yes—
184#2489C2212yes—
185#2487C2211yescharacteristic
186#2487C2211yescharacteristic
187#2485C2212yes—
188#2485C2212yes—
189#2476C2214yes—
190#2470C2214yes—
191#2469C2214yes—
192#2467C2214yes—
193#2466C2214yes—
194#2465C2214yes—
195#2465C2214yes—
196#2463C2214yes—
197#2461C2214yes—
198#2460C2214yes—
199#2459C2214yes—
200#2458C2214yes—
201#2457C2214yes—
202#2455C2214yes—
203#2454C2212yes—
204#2451C2212yes—
205#2449C2214yes—
206#2448C2212yes—
207#2447C2212yes—
208#2443C2214yes—
209#2441C2212yes—
210#2440C2212yes—
211#2436C2212yes—
212#2432C2214yes—
213#2431C2212yes—
214#2430C2214yes—
215#2428C2212yes—
216#2427C2212yes—
217#2427C2212yes—
218#2426C2212yes—
219#2425C2214yes—
220#2423C2212yes—
221#2422C2212yes—
222#2422C2212yes—
223#2422C2212yes—
224#2419C2214yes—
225#2416C2212yes—
226#2415C2212yes—
227#2414C2212yes—
228#2414C2212yes—
229#2409C2212yes—
230#2409C2211yescharacteristic
231#2409C2211yescharacteristic
232#2407C2212yes—
233#2396C2212yes—
234#2396C2212yes—
235#2395C2211yescharacteristic
236#2395C2211yescharacteristic
237#2388C2211yescharacteristic
238#2388C2211yescharacteristic
239#2388C2212yes—
240#2388C2212yes—
241#2379C2214yes—
242#2378C2214yes—
243#2377C2214yes—
244#2376C2214yes—
245#2330C2212yes—
246#2326C2212yes—
247#2324C2212yes—
248#2323C2212yes—
249#2320C2212yes—
250#2314C2212yes—
251C4×#127C2212yes—
252C4×#124C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×#121C2212yes—
257C4×#121C2212yes—
258C4×#121C2212yes—
259#2297C2212yes—
260#2296C2212yes—
261#2290C2212yes—
262#2290C2212yes—
263#2285C2211yescharacteristic
264#2283C2211yescharacteristic
265#2275C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C22×#41C2312yes—
270C23×Q8C2311yescharacteristic
271#542—48no—
272#532—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C4×#41—44no—
313C4×#41—44no—
314C2×C4×Q8—44no—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×#117C2312yes—
342C2×#117C2311yescharacteristic
343C2×#117C2311yescharacteristic
344C2×#117C2311yescharacteristic
345C2×#117C2311yescharacteristic
346C2×#117C2312yes—
347C2×#117C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2311yescharacteristic
350C22×C42C2311yescharacteristic
351C22×C42C2311yescharacteristic
352C22×C42C2311yescharacteristic
353C22×C42C2312yes—
354C22×C42C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2311yescharacteristic
371#400C2311yescharacteristic
372#400C2312yes—
373#399C2314yes—
374#399C2311yescharacteristic
375#399C2314yes—
376#399C2312yes—
377#399C2314yes—
378#399C2311yescharacteristic
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#399C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2311yescharacteristic
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2311yescharacteristic
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2311yescharacteristic
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2311yescharacteristic
414#397C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2311yescharacteristic
438#395C2311yescharacteristic
439#395C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2311yescharacteristic
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2312yes—
469#394C2312yes—
470#394C2311yescharacteristic
471#394C2312yes—
472#394C2312yes—
473#393C2312yes—
474#393C2312yes—
475#393C2314yes—
476#393C2314yes—
477#393C2312yes—
478#393C2311yescharacteristic
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2311yescharacteristic
486#392C2311yescharacteristic
487#392C2312yes—
488#392C2312yes—
489#392C2314yes—
490#392C2312yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2311yescharacteristic
497#392C2312yes—
498#392C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2312yes—
519#390C2314yes—
520#390C2314yes—
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2314yes—
525#390C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
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#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#387C2312yes—
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#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2312yes—
629#386C2312yes—
630#386C2312yes—
631#386C2312yes—
632#386C2314yes—
633#386C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2312yes—
639#386C2314yes—
640#386C2312yes—
641#386C2312yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2312yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2312yes—
655#385C2312yes—
656#385C2314yes—
657#385C2312yes—
658#385C2312yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2312yes—
663#385C2312yes—
664#385C2312yes—
665#385C2314yes—
666#385C2314yes—
667#384C2312yes—
668#384C2312yes—
669#384C2312yes—
670#384C2312yes—
671#384C2312yes—
672#383C2314yes—
673#383C2314yes—
674#383C2311yescharacteristic
675#383C2311yescharacteristic
676#382C2312yes—
677#382C2314yes—
678#382C2312yes—
679#382C2314yes—
680#382C2312yes—
681#382C2311yescharacteristic
682#382C2311yescharacteristic
683#382C2314yes—
684#382C2314yes—
685#381C2314yes—
686#381C2312yes—
687#381C2314yes—
688#380C2311yescharacteristic
689#380C2312yes—
690#380C2312yes—
691#380C2312yes—
692#380C2312yes—
693#380C2314yes—
694#380C2314yes—
695#380C2312yes—
696#380C2314yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#380C2311yescharacteristic
705#380C2314yes—
706#380C2312yes—
707#380C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2311yescharacteristic
726C4×C22⋊C4C2311yescharacteristic
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2312yes—
735#376C2312yes—
736#376C2312yes—
737C2×#95C2314yes—
738C43C2312yes—
739C2×#41—24no—
740C2×#41—42no—
741C2×#41—42no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—42no—
745C2×#41—84no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2411yescharacteristic
756C22×D4C2411yescharacteristic
757C22×D4C2411yescharacteristic
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2414yes—
768C22×D4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2411yescharacteristic
773C23×C4C2412yes—
774C23×C4C2411yescharacteristic
775C23×C4C2411yescharacteristic
776C23×C4C2411yescharacteristic
777C23×C4C2411yescharacteristic
778C23×C4C2414yes—
779C23×C4C2412yes—
780C23×C4C2411yescharacteristic
781C23×C4C2412yes—
782C23×C4C2412yes—
783C23×C4C2412yes—
784C23×C4C2414yes—
785C23×C4C2414yes—
786C4⋊Q8—42no—
787C4⋊Q8—44no—
788C4⋊Q8—84no—
789#127—42no—
790#127—44no—
791#126—48no—
792#126—84no—
793#125—44no—
794#125—84no—
795#124—28no—
796#124—44no—
797#124—48no—
798#124—44no—
799#124—44no—
800#124—84no—
801#123—48no—
802#123—48no—
803#123—84no—
804#123—84no—
805#123—84no—
806C22⋊Q8—28no—
807C22⋊Q8—48no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812C22⋊Q8—84no—
813C22⋊Q8—84no—
814#121—44no—
815#121—48no—
816#121—44no—
817#121—44no—
818#121—44no—
819#121—44no—
820#121—44no—
821#121—44no—
822#121—84no—
823#121—84no—
824#121—84no—
825C4×Q8—28no—
826C4×Q8—44no—
827C4×Q8—42no—
828C4×Q8—42no—
829C4×Q8—44no—
830C4×Q8—42no—
831C4×Q8—42no—
832C4×Q8—44no—
833C4×D4—28no—
834C4×D4—42no—
835C4×D4—42no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—42no—
841C4×D4—42no—
842C4×D4—42no—
843C4×D4—42no—
844C4×D4—42no—
845C4×D4—42no—
846C4×D4—44no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—84no—
850C4×D4—84no—
851#117—28no—
852#117—42no—
853#117—42no—
854#117—42no—
855#117—42no—
856#117—44no—
857#117—44no—
858C2×C4⋊C4—42no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2411yescharacteristic
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2411yescharacteristic
928C2×C22⋊C4C2411yescharacteristic
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C42—24no—
972C2×C42—24no—
973C2×C42—24no—
974C2×C42—44no—
975C2×C42—44no—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2414yes—
997C2×C42C2414yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2411yescharacteristic
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2411yescharacteristic
1020#95C2412yes—
1021#95C2411yescharacteristic
1022#95C2411yescharacteristic
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062C24C2512yes—
1063C24C2514yes—
1064C24C2511yescharacteristic
1065C24C2511yescharacteristic
1066C24C2511yescharacteristic
1067#41—416no—
1068#41—416no—
1069#41—816no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—42no—
1074C2×Q8—41no—
1075C2×Q8—41no—
1076C2×Q8—44no—
1077C2×Q8—41no—
1078C2×Q8—42no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—416no—
1085C2×Q82−1+414yes—
1086C2×D4—22no—
1087C2×D4—22no—
1088C2×D4—24no—
1089C2×D4—28no—
1090C2×D4—24no—
1091C2×D4—22no—
1092C2×D4—22no—
1093C2×D4—22no—
1094C2×D4—24no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—41no—
1098C2×D4—41no—
1099C2×D4—41no—
1100C2×D4—41no—
1101C2×D4—42no—
1102C2×D4—41no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—42no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C22×C4—22no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—24no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—28no—
1149C22×C4—24no—
1150C22×C4—42no—
1151C22×C4—44no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—42no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—42no—
1163C22×C4—44no—
1164C22×C4—42no—
1165C22×C4—42no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C22×C4C2514yes—
1181C22×C4C2514yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2514yes—
1186C22×C4C2514yes—
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2512yes—
1190C22×C4C2514yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C4⋊C4—24no—
1199C4⋊C4—28no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—44no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—24no—
1319C42—28no—
1320C42—24no—
1321C42—24no—
1322C42—24no—
1323C42—42no—
1324C42—42no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—42no—
1332C42H(5,𝔽2)14yes—
1333C23—21no—
1334C23—21no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—24no—
1339C23—21no—
1340C23—21no—
1341C23—22no—
1342C23—24no—
1343C23—21no—
1344C23—21no—
1345C23—22no—
1346C23—24no—
1347C23—24no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—21no—
1352C23—22no—
1353C23—24no—
1354C23—21no—
1355C23—22no—
1356C23—22no—
1357C23—22no—
1358C23—24no—
1359C23—22no—
1360C23—24no—
1361C23#58512yes—
1362C23C2611yescharacteristic
1363Q8—44no—
1364Q8—48no—
1365Q8—44no—
1366Q8—48no—
1367Q8—84no—
1368Q8—164no—
1369D4—44no—
1370D4—44no—
1371D4—44no—
1372D4—44no—
1373D4—48no—
1374D4—48no—
1375D4—84no—
1376D4—84no—
1377D4—88no—
1378D4—84no—
1379D4—88no—
1380D4—84no—
1381D4—88no—
1382D4—164no—
1383D4—164no—
1384C2×C4—28no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—24no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—44no—
1449C2×C4—44no—
1450C2×C4—44no—
1451C2×C4—48no—
1452C2×C4—44no—
1453C2×C4—44no—
1454C2×C4—44no—
1455C2×C4—48no—
1456C2×C4—84no—
1457C2×C4—82no—
1458C2×C4—82no—
1459C2×C4—88no—
1460C2×C4—84no—
1461C2×C4—84no—
1462C2×C4—164no—
1463C2×C4—164no—
1464C2×C4C2×H(5,𝔽2)12yes—
1465C2×C4C2×H(5,𝔽2)12yes—
1466C2×C4C2×H(5,𝔽2)12yes—
1467C2×C4C2×2−1+412yes—
1468C2×C4C2×2−1+412yes—
1469C2×C4C2×2−1+412yes—
1470C2×C4#58514yes—
1471C22—22no—
1472C22—24no—
1473C22—41no—
1474C22—41no—
1475C22—42no—
1476C22—41no—
1477C22—41no—
1478C22—42no—
1479C22—44no—
1480C22—41no—
1481C22—44no—
1482C22—42no—
1483C22—41no—
1484C22—42no—
1485C22—41no—
1486C22—41no—
1487C22—44no—
1488C22—42no—
1489C22—42no—
1490C22—44no—
1491C22—44no—
1492C22—42no—
1493C22—42no—
1494C22—44no—
1495C22—44no—
1496C22—42no—
1497C22—42no—
1498C22—42no—
1499C22—42no—
1500C22C22×H(5,𝔽2)11yescharacteristic
1501C22C22×2−1+411yescharacteristic
1502C22C2×#58511yescharacteristic
1503C22C2×#58512yes—
1504C22H(7,𝔽2)12yes—
1505C4—22no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—22no—
1510C4—42no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—44no—
1515C4—44no—
1516C4—42no—
1517C4—41no—
1518C4—41no—
1519C4—42no—
1520C4—41no—
1521C4—44no—
1522C4—44no—
1523C4—42no—
1524C4—42no—
1525C4—44no—
1526C4—42no—
1527C4—42no—
1528C4—44no—
1529C4—44no—
1530C4#352914yes—
1531C2—42no—
1532C2—81no—
1533C2—81no—
1534C2—82no—
1535C2—84no—
1536C2C2×#352911yescharacteristic
1537C2#6281911yescharacteristic
1538C2#6287411yescharacteristic
1539C2#6295212yes—
1540C2#6297012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53056C2semidirect
2. #53044C2semidirect
3. #53009C2semidirect
4. #53005C2semidirect
5. #52960C2semidirect
6. #52957C2semidirect
7. #52934C2semidirect
8. #52919C2semidirect
9. #52916C2semidirect
10. #52408C2semidirect
11. #52406C2semidirect
12. #52403C2semidirect
13. #46322C2semidirect
14. #46241C2semidirect
15. #45916C2semidirect
16. #45758C2semidirect
17. #45747C2semidirect
18. #45738C2semidirect
19. #45689C2semidirect
20. #45676C2semidirect
21. #45663C2semidirect
22. #45499C2semidirect
23. #35607C2semidirect
24. #35551C2semidirect
25. #35548C2semidirect
26. #35258C2semidirect
27. #35243C2semidirect
28. #35163C2semidirect
29. #34977C2semidirect
30. #34952C2semidirect
31. #34909C2semidirect

Maximal subgroups

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

subgroupindex
#530562
#530442
#530092
#530052
#529602
#529572
#529342
#529192
#529162
#524082
#524062
#524032
#463222
#462412
#459162
#457582
#457472
#457382
#456892
#456762
#456632
#454992
#356072
#355512
#355482
#352582
#352432
#351632
#349772
#349522
#349092