Finite Group Databasebeta

← #8095210

Subgroups — #8095210

Order 512.

4312 conjugacy classes of subgroups.

The subgroup lattice has 1477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53145C212yesmaximal, complemented
2#53143C212yesmaximal, complemented
3#53137C211yesmaximal, characteristic, complemented
4#53032C211yesmaximal, characteristic, complemented
5#52993C211yesmaximal, characteristic, complemented
6#52991C211yesmaximal, characteristic, complemented
7#52947C214yesmaximal, complemented
8#52944C212yesmaximal, complemented
9#52942C212yesmaximal, complemented
10#52929C212yesmaximal, complemented
11#52926C212yesmaximal, complemented
12#52921C214yesmaximal, complemented
13#45759C212yesmaximal, complemented
14#45747C212yesmaximal, complemented
15#45736C214yesmaximal, complemented
16#45700C212yesmaximal, complemented
17#45691C212yesmaximal, complemented
18#45679C214yesmaximal, complemented
19#45677C212yesmaximal, complemented
20#45617C212yesmaximal, complemented
21#45504C212yesmaximal, complemented
22#45497C212yesmaximal, complemented
23#35647C212yesmaximal, complemented
24#35635C212yesmaximal, complemented
25#35613C212yesmaximal, complemented
26#35315C212yesmaximal, complemented
27#35244C212yesmaximal, complemented
28#35244C212yesmaximal, complemented
29#34971C211yesmaximal, characteristic, complemented
30#34952C211yesmaximal, characteristic, complemented
31#34876C211yesmaximal, characteristic
32C2×#541C2212yes—
33C2×#529C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2212yes—
38#2855C2212yes—
39#2855C2212yes—
40#2852C2214yes—
41#2852C2214yes—
42#2851C2212yes—
43#2851C2214yes—
44#2851C2214yes—
45#2844C2214yes—
46#2841C2214yes—
47#2841C2212yes—
48#2841C2214yes—
49#2841C2212yes—
50#2839C2214yes—
51#2839C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2838C2214yes—
56#2838C2214yes—
57#2836C2214yes—
58#2835C2212yes—
59#2835C2212yes—
60#2835C2212yes—
61#2834C2212yes—
62#2833C2214yes—
63#2833C2214yes—
64#2831C2214yes—
65#2827C2214yes—
66#2827C2214yes—
67#2826C2212yes—
68#2824C2212yes—
69#2807C2212yes—
70#2805C2214yes—
71#2802C2214yes—
72#2802C2214yes—
73#2796C2214yes—
74#2792C2214yes—
75#2792C2214yes—
76#2790C2214yes—
77#2788C2214yes—
78#2784C2214yes—
79#2782C2214yes—
80#2780C2214yes—
81#2780C2214yes—
82#2779C2214yes—
83#2778C2214yes—
84#2776C2214yes—
85#2774C2214yes—
86#2772C2214yes—
87#2771C2212yes—
88#2768C2214yes—
89#2766C2214yes—
90#2763C2212yes—
91#2763C2212yes—
92#2760C2212yes—
93#2750C2214yes—
94#2747C2214yes—
95#2747C2214yes—
96#2746C2214yes—
97#2744C2214yes—
98#2744C2214yes—
99#2743C2214yes—
100#2742C2214yes—
101#2742C2212yes—
102#2742C2214yes—
103#2740C2214yes—
104#2739C2214yes—
105#2737C2214yes—
106#2722C2212yes—
107#2708C2214yes—
108#2701C2214yes—
109#2695C2214yes—
110#2693C2214yes—
111#2693C2212yes—
112#2691C2214yes—
113#2647C2212yes—
114#2645C2212yes—
115#2645C2212yes—
116#2642C2212yes—
117#2637C2214yes—
118#2637C2214yes—
119#2634C2214yes—
120#2634C2214yes—
121#2611C2211yescharacteristic
122#2611C2211yescharacteristic
123#2610C2211yescharacteristic
124#2610C2211yescharacteristic
125#2604C2212yes—
126#2603C2212yes—
127#2599C2212yes—
128#2599C2212yes—
129#2590C2214yes—
130#2587C2214yes—
131#2584C2212yes—
132#2582C2212yes—
133#2581C2212yes—
134#2581C2212yes—
135#2580C2212yes—
136#2579C2212yes—
137#2579C2212yes—
138#2578C2214yes—
139#2577C2214yes—
140#2576C2214yes—
141#2575C2214yes—
142#2573C2214yes—
143#2568C2212yes—
144#2564C2211yescharacteristic
145#2564C2211yescharacteristic
146#2562C2212yes—
147#2559C2214yes—
148#2558C2214yes—
149#2556C2214yes—
150#2553C2214yes—
151#2553C2214yes—
152#2543C2211yescharacteristic
153#2543C2211yescharacteristic
154#2542C2212yes—
155#2538C2212yes—
156#2536C2212yes—
157#2533C2214yes—
158#2533C2214yes—
159#2530C2214yes—
160#2528C2214yes—
161#2528C2214yes—
162#2528C2214yes—
163#2524C2214yes—
164#2521C2214yes—
165#2519C2214yes—
166#2515C2214yes—
167#2514C2212yes—
168#2511C2212yes—
169#2509C2212yes—
170#2508C2214yes—
171#2507C2212yes—
172#2506C2214yes—
173#2505C2214yes—
174#2505C2214yes—
175#2502C2212yes—
176#2499C2212yes—
177#2498C2212yes—
178#2497C2212yes—
179#2496C2212yes—
180#2496C2214yes—
181#2495C2214yes—
182#2493C2214yes—
183#2493C2214yes—
184#2489C2212yes—
185#2489C2212yes—
186#2487C2211yescharacteristic
187#2487C2211yescharacteristic
188#2486C2212yes—
189#2486C2211yescharacteristic
190#2486C2211yescharacteristic
191#2485C2212yes—
192#2484C2212yes—
193#2481C2214yes—
194#2481C2214yes—
195#2478C2214yes—
196#2473C2214yes—
197#2473C2214yes—
198#2470C2214yes—
199#2469C2214yes—
200#2469C2214yes—
201#2462C2214yes—
202#2462C2214yes—
203#2453C2212yes—
204#2453C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2442C2212yes—
208#2442C2212yes—
209#2442C2212yes—
210#2441C2212yes—
211#2434C2212yes—
212#2434C2212yes—
213#2430C2212yes—
214#2429C2212yes—
215#2429C2212yes—
216#2421C2212yes—
217#2421C2212yes—
218#2417C2212yes—
219#2417C2212yes—
220#2417C2212yes—
221#2417C2212yes—
222#2417C2212yes—
223#2415C2212yes—
224#2415C2212yes—
225#2415C2212yes—
226#2409C2211yescharacteristic
227#2409C2212yes—
228#2409C2211yescharacteristic
229#2409C2211yescharacteristic
230#2409C2212yes—
231#2409C2211yescharacteristic
232#2406C2212yes—
233#2399C2211yescharacteristic
234#2399C2212yes—
235#2398C2211yescharacteristic
236#2398C2211yescharacteristic
237#2398C2212yes—
238#2397C2211yescharacteristic
239#2396C2212yes—
240#2396C2212yes—
241#2383C2214yes—
242#2377C2214yes—
243#2376C2214yes—
244#2376C2214yes—
245#2330C2212yes—
246#2327C2212yes—
247#2323C2212yes—
248#2323C2212yes—
249#2320C2212yes—
250#2320C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256C4×#123C2212yes—
257C4×#121C2212yes—
258C4×#121C2212yes—
259#2297C2212yes—
260#2296C2212yes—
261#2290C2212yes—
262#2290C2212yes—
263#2285C2211yescharacteristic
264#2283C2211yescharacteristic
265#2274C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#541—48no—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273#529—44no—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2311yescharacteristic
283C2×#124C2311yescharacteristic
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×#123C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
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×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C4×#41—44no—
301C2×C4×Q8—44no—
302C2×C4×Q8—44no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
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×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2312yes—
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341#401C2314yes—
342#401C2314yes—
343#401C2314yes—
344#400C2314yes—
345#400C2311yescharacteristic
346#400C2311yescharacteristic
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#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2312yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#399C2311yescharacteristic
384#399C2311yescharacteristic
385#399C2312yes—
386#399C2314yes—
387#399C2312yes—
388#399C2312yes—
389#399C2314yes—
390#399C2314yes—
391#398C2314yes—
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#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2311yescharacteristic
412#398C2312yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2311yescharacteristic
421#397C2314yes—
422#397C2314yes—
423#397C2312yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2312yes—
433#397C2311yescharacteristic
434#397C2311yescharacteristic
435#397C2314yes—
436#397C2312yes—
437#397C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#395C2311yescharacteristic
450#395C2311yescharacteristic
451#395C2314yes—
452#395C2312yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2312yes—
457#395C2312yes—
458#395C2312yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2311yescharacteristic
469#394C2314yes—
470#394C2312yes—
471#394C2311yescharacteristic
472#394C2314yes—
473#393C2311yescharacteristic
474#393C2311yescharacteristic
475#393C2312yes—
476#393C2314yes—
477#393C2312yes—
478#393C2312yes—
479#393C2312yes—
480#393C2314yes—
481#393C2312yes—
482#392C2311yescharacteristic
483#392C2311yescharacteristic
484#392C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#388C2314yes—
538#388C2314yes—
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#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#387C2312yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
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#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2312yes—
622#386C2312yes—
623#386C2312yes—
624#386C2312yes—
625#386C2314yes—
626#386C2314yes—
627#386C2312yes—
628#386C2312yes—
629#386C2314yes—
630#386C2312yes—
631#386C2312yes—
632#385C2312yes—
633#385C2312yes—
634#385C2312yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2312yes—
646#385C2312yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2312yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#384C2312yes—
662#384C2312yes—
663#384C2314yes—
664#383C2314yes—
665#383C2314yes—
666#383C2314yes—
667#383C2312yes—
668#382C2314yes—
669#382C2314yes—
670#382C2314yes—
671#382C2314yes—
672#382C2312yes—
673#382C2312yes—
674#382C2312yes—
675#382C2314yes—
676#381C2312yes—
677#381C2314yes—
678#381C2312yes—
679#381C2314yes—
680#381C2314yes—
681#381C2312yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2314yes—
690#380C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2314yes—
694#380C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2314yes—
698#380C2314yes—
699#380C2311yescharacteristic
700#380C2311yescharacteristic
701#380C2312yes—
702#380C2312yes—
703#380C2311yescharacteristic
704#380C2311yescharacteristic
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729#376C2312yes—
730#376C2312yes—
731#376C2311yescharacteristic
732#376C2311yescharacteristic
733#376C2311yescharacteristic
734#376C2311yescharacteristic
735#376C2312yes—
736C2×#95C2311yescharacteristic
737C2×#95C2311yescharacteristic
738C2×#95C2312yes—
739C2×#41—24no—
740C2×#41—42no—
741C2×#41—42no—
742C22×Q8—42no—
743C22×Q8—42no—
744C22×Q8—44no—
745C22×Q8—44no—
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C22×D4C2411yescharacteristic
759C23×C4C2412yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2412yes—
776C4⋊Q8—44no—
777C4⋊Q8—44no—
778#126—44no—
779#126—48no—
780#126—48no—
781#126—48no—
782#125—44no—
783#125—42no—
784#125—48no—
785#125—48no—
786#125—44no—
787#124—42no—
788#123—28no—
789#123—48no—
790#123—44no—
791#123—44no—
792C22⋊Q8—42no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800C22⋊Q8—44no—
801#121—28no—
802#121—42no—
803#121—44no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—42no—
809C4×Q8—42no—
810C4×Q8—42no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×Q8—44no—
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—42no—
824C4×D4—44no—
825#117—28no—
826#117—42no—
827#117—42no—
828#117—42no—
829#117—44no—
830#117—44no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—42no—
833C2×C4⋊C4—42no—
834C2×C4⋊C4—44no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2411yescharacteristic
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
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×C42C2411yescharacteristic
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2411yescharacteristic
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
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—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—22no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—24no—
1059C2×Q8—42no—
1060C2×Q8—42no—
1061C2×Q8—41no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8—42no—
1067C2×Q8—416no—
1068C2×Q8—416no—
1069C2×D4—22no—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—41no—
1077C2×D4—41no—
1078C2×D4—41no—
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—22no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—22no—
1109C22×C4—22no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2514yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2514yes—
1147C22×C4C2514yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2514yes—
1151C22×C4C2514yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—41no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—41no—
1195C4⋊C4—42no—
1196C4⋊C4—41no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
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—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—28no—
1273C42—28no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—42no—
1278C42—42no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42H(5,𝔽2)14yes—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—21no—
1295C23—21no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23C2×2−1+412yes—
1307C23C2×2−1+412yes—
1308C23#58512yes—
1309C23C2611yescharacteristic
1310Q8—44no—
1311Q8—48no—
1312Q8—48no—
1313Q8—48no—
1314Q8—48no—
1315Q8—82no—
1316D4—44no—
1317D4—44no—
1318D4—44no—
1319D4—84no—
1320D4—84no—
1321D4—84no—
1322D4—82no—
1323C2×C4—28no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—21no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—48no—
1396C2×C4—48no—
1397C2×C4—44no—
1398C2×C4—48no—
1399C2×C4—44no—
1400C2×C4—44no—
1401C2×C4—82no—
1402C2×C4—82no—
1403C2×C4—84no—
1404C2×C4—84no—
1405C2×C4—84no—
1406C2×C4—84no—
1407C2×C4—164no—
1408C2×C4C2×H(5,𝔽2)12yes—
1409C2×C4C2×H(5,𝔽2)12yes—
1410C2×C4C2×H(5,𝔽2)12yes—
1411C2×C4C2×2−1+412yes—
1412C2×C4#58514yes—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—24no—
1417C22—24no—
1418C22—24no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22C22×H(5,𝔽2)11yescharacteristic
1436C22C22×2−1+411yescharacteristic
1437C22C2×#58511yescharacteristic
1438C22C2×#58512yes—
1439C222−1+612yes—
1440C4—22no—
1441C4—22no—
1442C4—22no—
1443C4—41no—
1444C4—41no—
1445C4—44no—
1446C4—42no—
1447C4—41no—
1448C4—41no—
1449C4—44no—
1450C4—41no—
1451C4—42no—
1452C4—41no—
1453C4—42no—
1454C4—41no—
1455C4—41no—
1456C4—44no—
1457C4—44no—
1458C4—44no—
1459C4—42no—
1460C4—42no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4—44no—
1465C4—44no—
1466C4#352914yes—
1467C2—42no—
1468C2—42no—
1469C2—42no—
1470C2—82no—
1471C2C2×#352911yescharacteristic
1472C2#6281911yescharacteristic
1473C2#6288611yescharacteristic
1474C2#6295012yes—
1475C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34876C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53145C2semidirect
2. #53143C2semidirect
3. #53137C2semidirect
4. #53032C2semidirect
5. #52993C2semidirect
6. #52991C2semidirect
7. #52947C2semidirect
8. #52944C2semidirect
9. #52942C2semidirect
10. #52929C2semidirect
11. #52926C2semidirect
12. #52921C2semidirect
13. #45759C2semidirect
14. #45747C2semidirect
15. #45736C2semidirect
16. #45700C2semidirect
17. #45691C2semidirect
18. #45679C2semidirect
19. #45677C2semidirect
20. #45617C2semidirect
21. #45504C2semidirect
22. #45497C2semidirect
23. #35647C2semidirect
24. #35635C2semidirect
25. #35613C2semidirect
26. #35315C2semidirect
27. #35244C2semidirect
28. #35244C2semidirect
29. #34971C2semidirect
30. #34952C2semidirect

Maximal subgroups

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

subgroupindex
#531452
#531432
#531372
#530322
#529932
#529912
#529472
#529442
#529422
#529292
#529262
#529212
#457592
#457472
#457362
#457002
#456912
#456792
#456772
#456172
#455042
#454972
#356472
#356352
#356132
#353152
#352442
#349712
#349522
#348762