Finite Group Databasebeta

← #8094665

Subgroups — #8094665

Order 512.

4305 conjugacy classes of subgroups.

The subgroup lattice has 1475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53024C212yesmaximal, complemented
2#53017C211yesmaximal, characteristic, complemented
3#53008C211yesmaximal, characteristic, complemented
4#53007C211yesmaximal, characteristic, complemented
5#53006C212yesmaximal, complemented
6#53005C211yesmaximal, characteristic, complemented
7#52954C212yesmaximal, complemented
8#52951C212yesmaximal, complemented
9#52939C214yesmaximal, complemented
10#52910C212yesmaximal, complemented
11#52896C212yesmaximal, complemented
12#52871C214yesmaximal, complemented
13#46311C212yesmaximal, complemented
14#46235C212yesmaximal, complemented
15#45841C214yesmaximal, complemented
16#45704C212yesmaximal, complemented
17#45700C212yesmaximal, complemented
18#45636C214yesmaximal, complemented
19#45634C212yesmaximal, complemented
20#45618C212yesmaximal, complemented
21#45504C212yesmaximal, complemented
22#45497C212yesmaximal, complemented
23#35657C212yesmaximal, complemented
24#35645C212yesmaximal, complemented
25#35637C212yesmaximal, complemented
26#35309C212yesmaximal, complemented
27#35244C212yesmaximal, complemented
28#35231C212yesmaximal, complemented
29#34971C211yesmaximal, characteristic, complemented
30#34947C211yesmaximal, characteristic, complemented
31#34909C211yesmaximal, characteristic
32C2×#541C2212yes—
33C2×#533C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2212yes—
38#2855C2212yes—
39#2855C2212yes—
40#2852C2214yes—
41#2852C2214yes—
42#2851C2214yes—
43#2851C2212yes—
44#2851C2214yes—
45#2845C2214yes—
46#2844C2212yes—
47#2843C2214yes—
48#2843C2212yes—
49#2841C2212yes—
50#2841C2212yes—
51#2841C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2838C2214yes—
56#2837C2214yes—
57#2837C2214yes—
58#2837C2214yes—
59#2836C2214yes—
60#2835C2214yes—
61#2834C2212yes—
62#2832C2214yes—
63#2831C2214yes—
64#2827C2214yes—
65#2826C2214yes—
66#2824C2212yes—
67#2823C2212yes—
68#2822C2212yes—
69#2807C2212yes—
70#2805C2214yes—
71#2802C2214yes—
72#2795C2214yes—
73#2794C2214yes—
74#2792C2212yes—
75#2792C2212yes—
76#2792C2214yes—
77#2790C2214yes—
78#2785C2212yes—
79#2784C2214yes—
80#2781C2214yes—
81#2780C2214yes—
82#2780C2214yes—
83#2772C2214yes—
84#2769C2212yes—
85#2768C2214yes—
86#2768C2214yes—
87#2764C2212yes—
88#2763C2212yes—
89#2762C2214yes—
90#2758C2214yes—
91#2757C2214yes—
92#2756C2214yes—
93#2756C2214yes—
94#2755C2214yes—
95#2753C2214yes—
96#2752C2212yes—
97#2750C2214yes—
98#2747C2214yes—
99#2747C2214yes—
100#2747C2214yes—
101#2745C2214yes—
102#2744C2214yes—
103#2744C2214yes—
104#2743C2214yes—
105#2742C2214yes—
106#2742C2214yes—
107#2739C2214yes—
108#2708C2214yes—
109#2707C2214yes—
110#2705C2214yes—
111#2704C2214yes—
112#2698C2214yes—
113#2655C2214yes—
114#2654C2214yes—
115#2637C2214yes—
116#2634C2214yes—
117#2629C2212yes—
118#2621C2212yes—
119#2616C2212yes—
120#2616C2212yes—
121#2611C2214yes—
122#2604C2214yes—
123#2601C2214yes—
124#2600C2212yes—
125#2600C2212yes—
126#2599C2211yescharacteristic
127#2599C2211yescharacteristic
128#2599C2212yes—
129#2599C2212yes—
130#2598C2211yescharacteristic
131#2598C2211yescharacteristic
132#2597C2214yes—
133#2587C2214yes—
134#2581C2212yes—
135#2581C2211yescharacteristic
136#2580C2211yescharacteristic
137#2575C2214yes—
138#2573C2214yes—
139#2571C2212yes—
140#2568C2211yescharacteristic
141#2567C2211yescharacteristic
142#2566C2212yes—
143#2565C2212yes—
144#2565C2214yes—
145#2565C2212yes—
146#2564C2212yes—
147#2564C2212yes—
148#2563C2211yescharacteristic
149#2562C2212yes—
150#2560C2214yes—
151#2556C2214yes—
152#2550C2212yes—
153#2546C2212yes—
154#2542C2212yes—
155#2542C2211yescharacteristic
156#2538C2212yes—
157#2536C2212yes—
158#2536C2212yes—
159#2536C2211yescharacteristic
160#2535C2211yescharacteristic
161#2533C2214yes—
162#2533C2214yes—
163#2533C2214yes—
164#2530C2214yes—
165#2529C2214yes—
166#2526C2214yes—
167#2525C2214yes—
168#2524C2214yes—
169#2524C2214yes—
170#2524C2214yes—
171#2522C2214yes—
172#2519C2214yes—
173#2519C2214yes—
174#2515C2214yes—
175#2514C2212yes—
176#2511C2212yes—
177#2510C2214yes—
178#2509C2212yes—
179#2508C2214yes—
180#2506C2212yes—
181#2506C2214yes—
182#2505C2214yes—
183#2502C2212yes—
184#2497C2212yes—
185#2496C2212yes—
186#2495C2212yes—
187#2495C2212yes—
188#2492C2212yes—
189#2489C2212yes—
190#2489C2212yes—
191#2489C2212yes—
192#2487C2212yes—
193#2486C2211yescharacteristic
194#2486C2211yescharacteristic
195#2485C2212yes—
196#2484C2212yes—
197#2481C2214yes—
198#2473C2214yes—
199#2469C2214yes—
200#2468C2214yes—
201#2468C2214yes—
202#2466C2214yes—
203#2466C2214yes—
204#2462C2214yes—
205#2462C2214yes—
206#2462C2214yes—
207#2460C2214yes—
208#2460C2214yes—
209#2453C2212yes—
210#2453C2212yes—
211#2446C2212yes—
212#2446C2212yes—
213#2442C2212yes—
214#2442C2212yes—
215#2434C2212yes—
216#2429C2212yes—
217#2429C2212yes—
218#2429C2212yes—
219#2429C2212yes—
220#2423C2212yes—
221#2421C2212yes—
222#2421C2212yes—
223#2421C2212yes—
224#2417C2212yes—
225#2417C2212yes—
226#2417C2212yes—
227#2417C2212yes—
228#2409C2211yescharacteristic
229#2409C2212yes—
230#2409C2211yescharacteristic
231#2407C2212yes—
232#2406C2212yes—
233#2399C2212yes—
234#2398C2212yes—
235#2396C2212yes—
236#2396C2212yes—
237#2395C2211yescharacteristic
238#2395C2211yescharacteristic
239#2388C2211yescharacteristic
240#2388C2211yescharacteristic
241#2383C2214yes—
242#2382C2214yes—
243#2377C2214yes—
244#2376C2214yes—
245#2330C2212yes—
246#2327C2212yes—
247#2323C2212yes—
248#2323C2212yes—
249#2320C2212yes—
250#2314C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×#123C2212yes—
257C4×#123C2212yes—
258C4×#121C2212yes—
259#2297C2212yes—
260#2290C2212yes—
261#2290C2212yes—
262#2285C2212yes—
263#2283C2211yescharacteristic
264#2283C2211yescharacteristic
265#2276C2212yes—
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#541—48no—
271#533—44no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2312yes—
299C4×#41—44no—
300C4×#41—44no—
301C2×C4×Q8—44no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×#117C2312yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2312yes—
331C2×#117C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2312yes—
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341#401C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2311yescharacteristic
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#399C2312yes—
375#399C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2311yescharacteristic
379#399C2311yescharacteristic
380#399C2314yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2311yescharacteristic
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2311yescharacteristic
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2312yes—
423#397C2311yescharacteristic
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2311yescharacteristic
431#397C2312yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#395C2312yes—
446#395C2312yes—
447#395C2314yes—
448#395C2314yes—
449#395C2311yescharacteristic
450#395C2311yescharacteristic
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2312yes—
455#395C2314yes—
456#395C2312yes—
457#395C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2311yescharacteristic
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2312yes—
467#394C2312yes—
468#394C2314yes—
469#394C2311yescharacteristic
470#394C2312yes—
471#394C2314yes—
472#394C2312yes—
473#393C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2312yes—
477#393C2314yes—
478#393C2311yescharacteristic
479#393C2311yescharacteristic
480#393C2312yes—
481#392C2311yescharacteristic
482#392C2312yes—
483#392C2311yescharacteristic
484#392C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2314yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
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#387C2312yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2312yes—
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2312yes—
627#386C2312yes—
628#386C2312yes—
629#386C2312yes—
630#386C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2312yes—
651#385C2314yes—
652#385C2312yes—
653#385C2314yes—
654#385C2312yes—
655#384C2312yes—
656#384C2312yes—
657#384C2314yes—
658#384C2312yes—
659#384C2312yes—
660#383C2314yes—
661#383C2314yes—
662#383C2314yes—
663#383C2314yes—
664#383C2311yescharacteristic
665#383C2311yescharacteristic
666#383C2312yes—
667#382C2312yes—
668#382C2312yes—
669#382C2314yes—
670#382C2312yes—
671#382C2312yes—
672#382C2314yes—
673#382C2314yes—
674#382C2311yescharacteristic
675#382C2311yescharacteristic
676#382C2312yes—
677#382C2314yes—
678#382C2314yes—
679#381C2312yes—
680#381C2312yes—
681#381C2314yes—
682#381C2314yes—
683#381C2312yes—
684#381C2312yes—
685#380C2311yescharacteristic
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2314yes—
696#380C2314yes—
697#380C2314yes—
698#380C2314yes—
699#380C2314yes—
700#380C2314yes—
701#380C2312yes—
702#380C2312yes—
703#380C2311yescharacteristic
704#380C2312yes—
705#380C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2314yes—
719C4×C4⋊C4C2314yes—
720C4×C4⋊C4C2314yes—
721C4×C4⋊C4C2314yes—
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2312yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2311yescharacteristic
728C4×C22⋊C4C2311yescharacteristic
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2314yes—
735#376C2312yes—
736#376C2314yes—
737#376C2312yes—
738C2×#95C2312yes—
739C2×#41—24no—
740C2×#41—42no—
741C2×#41—42no—
742C2×#41—44no—
743C2×#41—42no—
744C22×Q8—42no—
745C22×Q8—44no—
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2412yes—
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C4⋊Q8—42no—
775C4⋊Q8—44no—
776C4⋊Q8—42no—
777C4⋊Q8—44no—
778#126—48no—
779#126—48no—
780#126—48no—
781#125—48no—
782#125—44no—
783#125—44no—
784#125—44no—
785#125—48no—
786#125—48no—
787#123—28no—
788#123—44no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800#121—28no—
801C4×Q8—28no—
802C4×Q8—28no—
803C4×Q8—44no—
804C4×Q8—42no—
805C4×Q8—42no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—42no—
809C4×Q8—42no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×D4—42no—
814C4×D4—42no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—42no—
819C4×D4—42no—
820C4×D4—42no—
821C4×D4—42no—
822C4×D4—42no—
823C4×D4—44no—
824C4×D4—44no—
825#117—28no—
826#117—42no—
827#117—42no—
828#117—42no—
829#117—42no—
830#117—44no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—42no—
833C2×C4⋊C4—44no—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C42—24no—
942C2×C42—24no—
943C2×C42—24no—
944C2×C42—44no—
945C2×C42—44no—
946C2×C42—44no—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2411yescharacteristic
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2411yescharacteristic
994#95C2412yes—
995#95C2411yescharacteristic
996#95C2414yes—
997#95C2414yes—
998#95C2411yescharacteristic
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2512yes—
1048C24C2511yescharacteristic
1049C24C2511yescharacteristic
1050C24C2511yescharacteristic
1051#41—416no—
1052#41—416no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—24no—
1059C2×Q8—22no—
1060C2×Q8—24no—
1061C2×Q8—42no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—44no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—44no—
1068C2×Q8—416no—
1069C2×D4—22no—
1070C2×D4—22no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—22no—
1074C2×D4—41no—
1075C2×D4—41no—
1076C2×D4—41no—
1077C2×D4—41no—
1078C2×D4—42no—
1079C2×D4—41no—
1080C2×D4—42no—
1081C2×D4—41no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—42no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D42−1+414yes—
1089C22×C4—22no—
1090C22×C4—22no—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—24no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—24no—
1101C22×C4—22no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2514yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2514yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C42—22no—
1262C42—22no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—24no—
1271C42—28no—
1272C42—28no—
1273C42—24no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—44no—
1278C42—42no—
1279C42—42no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42H(5,𝔽2)14yes—
1287C23—21no—
1288C23—21no—
1289C23—22no—
1290C23—22no—
1291C23—21no—
1292C23—21no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—21no—
1297C23—21no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—21no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23C2×2−1+412yes—
1308C23C2×2−1+412yes—
1309C23C2611yescharacteristic
1310Q8—44no—
1311Q8—48no—
1312Q8—44no—
1313Q8—48no—
1314Q8—48no—
1315Q8—84no—
1316D4—44no—
1317D4—44no—
1318D4—44no—
1319D4—44no—
1320D4—48no—
1321D4—84no—
1322D4—84no—
1323C2×C4—28no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—48no—
1395C2×C4—44no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—48no—
1399C2×C4—84no—
1400C2×C4—82no—
1401C2×C4—82no—
1402C2×C4—84no—
1403C2×C4—84no—
1404C2×C4—88no—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×H(5,𝔽2)12yes—
1407C2×C4C2×H(5,𝔽2)12yes—
1408C2×C4C2×2−1+412yes—
1409C2×C4#58512yes—
1410C2×C4#58514yes—
1411C22—22no—
1412C22—22no—
1413C22—24no—
1414C22—24no—
1415C22—41no—
1416C22—41no—
1417C22—42no—
1418C22—42no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—42no—
1423C22—41no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—41no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22C22×H(5,𝔽2)11yescharacteristic
1434C22C22×2−1+411yescharacteristic
1435C22C2×#58511yescharacteristic
1436C22C2×#58512yes—
1437C222−1+612yes—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—41no—
1443C4—42no—
1444C4—44no—
1445C4—41no—
1446C4—42no—
1447C4—41no—
1448C4—41no—
1449C4—44no—
1450C4—42no—
1451C4—42no—
1452C4—44no—
1453C4—44no—
1454C4—44no—
1455C4—41no—
1456C4—41no—
1457C4—42no—
1458C4—41no—
1459C4—44no—
1460C4—44no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4#352914yes—
1465C2—42no—
1466C2—42no—
1467C2—81no—
1468C2—82no—
1469C2C2×#352911yescharacteristic
1470C2#6281911yescharacteristic
1471C2#6288611yescharacteristic
1472C2#6293912yes—
1473C2#6295012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34909C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53024C2semidirect
2. #53017C2semidirect
3. #53008C2semidirect
4. #53007C2semidirect
5. #53006C2semidirect
6. #53005C2semidirect
7. #52954C2semidirect
8. #52951C2semidirect
9. #52939C2semidirect
10. #52910C2semidirect
11. #52896C2semidirect
12. #52871C2semidirect
13. #46311C2semidirect
14. #46235C2semidirect
15. #45841C2semidirect
16. #45704C2semidirect
17. #45700C2semidirect
18. #45636C2semidirect
19. #45634C2semidirect
20. #45618C2semidirect
21. #45504C2semidirect
22. #45497C2semidirect
23. #35657C2semidirect
24. #35645C2semidirect
25. #35637C2semidirect
26. #35309C2semidirect
27. #35244C2semidirect
28. #35231C2semidirect
29. #34971C2semidirect
30. #34947C2semidirect

Maximal subgroups

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

subgroupindex
#530242
#530172
#530082
#530072
#530062
#530052
#529542
#529512
#529392
#529102
#528962
#528712
#463112
#462352
#458412
#457042
#457002
#456362
#456342
#456182
#455042
#454972
#356572
#356452
#356372
#353092
#352442
#352312
#349712
#349472
#349092