Finite Group Databasebeta

← #8750678

Subgroups — #8750678

Order 512.

4285 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59935C212yesmaximal, complemented
2#59933C211yesmaximal, characteristic, complemented
3#58758C214yesmaximal, complemented
4#58753C212yesmaximal, complemented
5#57122C214yesmaximal, complemented
6#56117C214yesmaximal, complemented
7#55724C214yesmaximal, complemented
8#53081C212yesmaximal, complemented
9#53007C212yesmaximal, complemented
10#52958C211yesmaximal, characteristic, complemented
11#52608C214yesmaximal, complemented
12#47819C212yesmaximal, complemented
13#45300C212yesmaximal, complemented
14#45232C212yesmaximal, complemented
15#45201C212yesmaximal, complemented
16#45115C211yesmaximal, characteristic, complemented
17#45113C212yesmaximal, complemented
18#42920C212yesmaximal, complemented
19#42911C211yesmaximal, characteristic, complemented
20#42851C212yesmaximal, complemented
21#42775C212yesmaximal, complemented
22#42756C212yesmaximal, complemented
23#42405C212yesmaximal, complemented
24#42061C214yesmaximal, complemented
25#39761C212yesmaximal, complemented
26#39744C211yesmaximal, characteristic, complemented
27#36694C211yesmaximal, characteristic
28#35759C211yesmaximal, characteristic, complemented
29#35758C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#552C2212yes—
33C2×#536C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2868C2211yescharacteristic
36#2844C2211yescharacteristic
37#2841C2214yes—
38#2838C2214yes—
39#2837C2214yes—
40#2837C2214yes—
41#2835C2212yes—
42#2832C2211yescharacteristic
43#2832C2212yes—
44#2832C2211yescharacteristic
45#2832C2212yes—
46#2832C2212yes—
47#2832C2214yes—
48#2831C2214yes—
49#2831C2214yes—
50#2831C2214yes—
51#2828C2212yes—
52#2828C2212yes—
53#2828C2212yes—
54#2823C2214yes—
55#2821C2212yes—
56#2819C2212yes—
57#2819C2211yescharacteristic
58#2811C2212yes—
59#2809C2214yes—
60#2805C2214yes—
61#2799C2214yes—
62#2799C2212yes—
63#2799C2212yes—
64#2798C2214yes—
65#2798C2214yes—
66#2797C2214yes—
67#2794C2214yes—
68#2793C2214yes—
69#2793C2214yes—
70#2793C2214yes—
71#2792C2214yes—
72#2787C2214yes—
73#2784C2214yes—
74#2781C2214yes—
75#2779C2214yes—
76#2774C2214yes—
77#2759C2214yes—
78#2758C2214yes—
79#2754C2214yes—
80#2754C2214yes—
81#2752C2214yes—
82#2751C2214yes—
83#2748C2212yes—
84#2747C2214yes—
85#2740C2214yes—
86#2730C2214yes—
87#2725C2214yes—
88#2721C2214yes—
89#2721C2214yes—
90#2719C2214yes—
91#2718C2214yes—
92#2718C2214yes—
93#2716C2214yes—
94#2716C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2715C2214yes—
98#2715C2214yes—
99#2713C2214yes—
100#2712C2212yes—
101#2712C2214yes—
102#2710C2214yes—
103#2707C2214yes—
104#2707C2214yes—
105#2705C2214yes—
106#2705C2214yes—
107#2702C2214yes—
108#2702C2214yes—
109#2698C2214yes—
110#2693C2214yes—
111#2693C2212yes—
112#2666C2214yes—
113#2663C2214yes—
114#2662C2214yes—
115#2662C2212yes—
116#2658C2212yes—
117#2655C2214yes—
118#2653C2214yes—
119#2651C2214yes—
120#2649C2214yes—
121#2647C2214yes—
122#2645C2212yes—
123#2640C2214yes—
124#2636C2212yes—
125#2632C2212yes—
126#2630C2214yes—
127#2616C2211yescharacteristic
128#2616C2212yes—
129#2616C2211yescharacteristic
130#2612C2212yes—
131#2612C2214yes—
132#2607C2214yes—
133#2604C2212yes—
134#2602C2214yes—
135#2589C2214yes—
136#2589C2214yes—
137#2588C2214yes—
138#2586C2214yes—
139#2582C2212yes—
140#2582C2212yes—
141#2581C2212yes—
142#2575C2214yes—
143#2574C2214yes—
144#2574C2214yes—
145#2572C2212yes—
146#2568C2212yes—
147#2567C2212yes—
148#2567C2212yes—
149#2557C2214yes—
150#2557C2214yes—
151#2553C2214yes—
152#2547C2211yescharacteristic
153#2547C2212yes—
154#2546C2211yescharacteristic
155#2546C2212yes—
156#2545C2212yes—
157#2542C2212yes—
158#2538C2212yes—
159#2538C2212yes—
160#2527C2214yes—
161#2523C2212yes—
162#2523C2214yes—
163#2522C2214yes—
164#2521C2214yes—
165#2516C2214yes—
166#2512C2214yes—
167#2511C2214yes—
168#2511C2214yes—
169#2503C2211yescharacteristic
170#2499C2212yes—
171#2499C2212yes—
172#2497C2212yes—
173#2497C2214yes—
174#2497C2214yes—
175#2496C2212yes—
176#2496C2212yes—
177#2496C2212yes—
178#2496C2214yes—
179#2495C2212yes—
180#2492C2212yes—
181#2492C2214yes—
182#2492C2212yes—
183#2492C2212yes—
184#2492C2212yes—
185#2492C2212yes—
186#2489C2212yes—
187#2487C2211yescharacteristic
188#2486C2212yes—
189#2485C2212yes—
190#2485C2214yes—
191#2475C2214yes—
192#2471C2214yes—
193#2469C2214yes—
194#2467C2214yes—
195#2466C2214yes—
196#2462C2214yes—
197#2460C2214yes—
198#2459C2214yes—
199#2458C2214yes—
200#2453C2214yes—
201#2442C2212yes—
202#2441C2212yes—
203#2441C2212yes—
204#2440C2212yes—
205#2439C2212yes—
206#2439C2214yes—
207#2439C2212yes—
208#2439C2214yes—
209#2434C2211yescharacteristic
210#2429C2212yes—
211#2429C2212yes—
212#2429C2212yes—
213#2423C2212yes—
214#2423C2212yes—
215#2423C2212yes—
216#2421C2212yes—
217#2417C2212yes—
218#2417C2212yes—
219#2417C2212yes—
220#2415C2212yes—
221#2415C2212yes—
222#2409C2211yescharacteristic
223#2409C2212yes—
224#2398C2212yes—
225#2398C2212yes—
226#2398C2212yes—
227#2398C2212yes—
228#2395C2214yes—
229#2388C2212yes—
230#2388C2212yes—
231#2388C2211yescharacteristic
232#2388C2211yescharacteristic
233#2372C2212yes—
234#2372C2214yes—
235#2362C2212yes—
236#2362C2212yes—
237#2360C2212yes—
238#2360C2212yes—
239#2360C2212yes—
240#2355C2212yes—
241#2354C2212yes—
242#2352C2212yes—
243#2352C2212yes—
244#2347C2211yescharacteristic
245#2346C2211yescharacteristic
246#2345C2212yes—
247#2345C2212yes—
248Q8×C22⋊C4C2212yes—
249#2331C2212yes—
250#2331C2214yes—
251#2330C2212yes—
252#2327C2212yes—
253#2327C2212yes—
254#2311C2212yes—
255C4×#124C2211yescharacteristic
256C4×#124C2212yes—
257#2295C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#557—44no—
263#556—44no—
264#552—48no—
265#536—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2312yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2311yescharacteristic
300C2×C22⋊Q8C2311yescharacteristic
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303#520—44no—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2312yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2312yes—
421#395C2312yes—
422#395C2311yescharacteristic
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2311yescharacteristic
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2312yes—
434#394C2311yescharacteristic
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2311yescharacteristic
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#394C2314yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2312yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#393C2312yes—
461#393C2312yes—
462#393C2312yes—
463#393C2312yes—
464#393C2312yes—
465#393C2312yes—
466#393C2311yescharacteristic
467#393C2312yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2312yes—
472#393C2314yes—
473#393C2311yescharacteristic
474#393C2312yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#392C2312yes—
480#392C2312yes—
481#392C2312yes—
482#392C2312yes—
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2311yescharacteristic
487#392C2311yescharacteristic
488#392C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2311yescharacteristic
504#391C2314yes—
505#391C2314yes—
506#391C2312yes—
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2314yes—
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#390C2314yes—
520#390C2311yescharacteristic
521#390C2312yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
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#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2312yes—
633#386C2314yes—
634#386C2312yes—
635#386C2314yes—
636#386C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#384C2314yes—
647#384C2314yes—
648#384C2312yes—
649#384C2312yes—
650#384C2312yes—
651#384C2314yes—
652#383C2312yes—
653#383C2314yes—
654#382C2311yescharacteristic
655#382C2312yes—
656#382C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#381C2314yes—
662#381C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2311yescharacteristic
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716C43C2311yescharacteristic
717C2×#41—42no—
718C2×#41—44no—
719C2×#41—42no—
720C2×#41—44no—
721C22×Q8—42no—
722C22×Q8—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C4⋊Q8—28no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—82no—
758C4⋊Q8—82no—
759#126—44no—
760#126—44no—
761#126—48no—
762#126—84no—
763#126—84no—
764#126—84no—
765#125—28no—
766#125—48no—
767#125—48no—
768#124—28no—
769#124—24no—
770#124—44no—
771#124—44no—
772#124—84no—
773#124—82no—
774#123—48no—
775#123—48no—
776#123—84no—
777C22⋊Q8—28no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—42no—
785C22⋊Q8—42no—
786C22⋊Q8—84no—
787C4×Q8—24no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—42no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—42no—
802C4×D4—48no—
803#117—24no—
804#117—24no—
805#117—44no—
806#117—44no—
807#117—48no—
808C2×C4⋊C4—28no—
809C2×C4⋊C4—44no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2411yescharacteristic
942#95C2411yescharacteristic
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2411yescharacteristic
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2411yescharacteristic
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2512yes—
1014C24C2511yescharacteristic
1015C24C2511yescharacteristic
1016C24C2512yes—
1017#41—416no—
1018#41—88no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—42no—
1038C2×Q8—41no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—88no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C22×C4—24no—
1072C22×C4—22no—
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—28no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—41no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4H(5,𝔽2)14yes—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—41no—
1203C22⋊C4—41no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C42—24no—
1226C42—24no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—42no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—41no—
1246C422−1+414yes—
1247C23—22no—
1248C23—21no—
1249C23—21no—
1250C23—22no—
1251C23—21no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—21no—
1264C23—21no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23C2611yescharacteristic
1272Q8—44no—
1273Q8—44no—
1274Q8—48no—
1275Q8—82no—
1276Q8—84no—
1277Q8—84no—
1278Q8—84no—
1279Q8—84no—
1280Q8—82no—
1281Q8—164no—
1282D4—44no—
1283D4—48no—
1284D4—82no—
1285D4—84no—
1286D4—84no—
1287D4—84no—
1288D4—84no—
1289D4—84no—
1290D4—82no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—44no—
1356C2×C4—48no—
1357C2×C4—44no—
1358C2×C4—48no—
1359C2×C4—88no—
1360C2×C4—84no—
1361C2×C4—162no—
1362C2×C4—164no—
1363C2×C4C2×H(5,𝔽2)14yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×2−1+414yes—
1366C2×C4C2×2−1+412yes—
1367C2×C4#58514yes—
1368C22—41no—
1369C22—41no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—41no—
1374C22—42no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—41no—
1383C22—41no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22C22×H(5,𝔽2)11yescharacteristic
1393C22C22×2−1+411yescharacteristic
1394C22C2×#58512yes—
1395C22H(7,𝔽2)11yescharacteristic
1396C222−1+612yes—
1397C4—24no—
1398C4—22no—
1399C4—24no—
1400C4—41no—
1401C4—42no—
1402C4—42no—
1403C4—41no—
1404C4—44no—
1405C4—42no—
1406C4—41no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—44no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4#354014yes—
1422C2—81no—
1423C2—82no—
1424C2—81no—
1425C2—82no—
1426C2C2×#354011yescharacteristic
1427C2#6291711yescharacteristic
1428C2#6293212yes—
1429C2#6306311yescharacteristic
1430C2#6306512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36694C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59935C2semidirect
2. #59933C2semidirect
3. #58758C2semidirect
4. #58753C2semidirect
5. #57122C2semidirect
6. #56117C2semidirect
7. #55724C2semidirect
8. #53081C2semidirect
9. #53007C2semidirect
10. #52958C2semidirect
11. #52608C2semidirect
12. #47819C2semidirect
13. #45300C2semidirect
14. #45232C2semidirect
15. #45201C2semidirect
16. #45115C2semidirect
17. #45113C2semidirect
18. #42920C2semidirect
19. #42911C2semidirect
20. #42851C2semidirect
21. #42775C2semidirect
22. #42756C2semidirect
23. #42405C2semidirect
24. #42061C2semidirect
25. #39761C2semidirect
26. #39744C2semidirect
28. #35759C2semidirect
29. #35758C2semidirect

Maximal subgroups

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

subgroupindex
#599352
#599332
#587582
#587532
#571222
#561172
#557242
#530812
#530072
#529582
#526082
#478192
#453002
#452322
#452012
#451152
#451132
#429202
#429112
#428512
#427752
#427562
#424052
#420612
#397612
#397442
#366942
#357592
#357582