Finite Group Databasebeta

← #8172749

Subgroups — #8172749

Order 512.

4172 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59298C212yesmaximal, complemented
2#59114C212yesmaximal, complemented
3#58749C212yesmaximal
4#58589C212yesmaximal, complemented
5#55674C214yesmaximal, complemented
6#55613C212yesmaximal
7#55610C212yesmaximal, complemented
8#55192C214yesmaximal, complemented
9#53124C212yesmaximal, complemented
10#53081C211yesmaximal, characteristic, complemented
11#53033C211yesmaximal, characteristic, complemented
12#52947C214yesmaximal, complemented
13#45435C211yesmaximal, characteristic, complemented
14#45384C211yesmaximal, characteristic, complemented
15#45190C212yesmaximal, complemented
16#42821C212yesmaximal, complemented
17#42722C212yesmaximal, complemented
18#42713C212yesmaximal, complemented
19#42488C212yesmaximal, complemented
20#42376C212yesmaximal, complemented
21#42344C212yesmaximal, complemented
22#40155C214yesmaximal, complemented
23#39867C212yesmaximal, complemented
24#38072C212yesmaximal, complemented
25#38051C212yesmaximal
26#37602C212yesmaximal, complemented
27#37266C212yesmaximal, complemented
28#36451C212yesmaximal, complemented
29#35248C211yesmaximal, characteristic, complemented
30#34953C211yesmaximal, characteristic, complemented
31#34602C211yesmaximal, characteristic
32C2×#556C2212yes—
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2864C2214yes—
38#2855C2212yes—
39#2855C2212yes—
40#2844C2212yes—
41#2844C2214yes—
42#2843C2212yes—
43#2841C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2838C2214yes—
47#2838C2214yes—
48#2833C2214yes—
49#2833C2214yes—
50#2832C2212yes—
51#2831C2214yes—
52#2823C2212yes—
53#2821C2214yes—
54#2809C2212yes—
55#2805C2214yes—
56#2802C2214yes—
57#2799C2212yes—
58#2794C2212yes—
59#2794C2212yes—
60#2792C2214yes—
61#2792C2214yes—
62#2789C2212yes—
63#2788C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2773C2214yes—
70#2772C2214yes—
71#2772C2214yes—
72#2772C2214yes—
73#2771C2214yes—
74#2769C2212yes—
75#2767C2214yes—
76#2767C2214yes—
77#2765C2214yes—
78#2765C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2744C2214yes—
84#2743C2214yes—
85#2742C2214yes—
86#2742C2214yes—
87#2741C2214yes—
88#2739C2214yes—
89#2738C2214yes—
90#2734C2212yes—
91#2734C2212yes—
92#2734C2214yes—
93#2734C2214yes—
94#2718C2214yes—
95#2717C2214yes—
96#2716C2214yes—
97#2716C2214yes—
98#2700C2214yes—
99#2698C2214yes—
100#2698C2214yes—
101#2689C2214yes—
102#2689C2214yes—
103#2686C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2667C2214yes—
107#2666C2214yes—
108#2666C2214yes—
109#2655C2214yes—
110#2654C2214yes—
111#2650C2214yes—
112#2649C2214yes—
113#2647C2212yes—
114#2645C2212yes—
115#2637C2212yes—
116#2637C2212yes—
117#2637C2214yes—
118#2634C2211yescharacteristic
119#2634C2211yescharacteristic
120#2634C2212yes—
121#2634C2212yes—
122#2632C2211yescharacteristic
123#2632C2211yescharacteristic
124#2628C2214yes—
125#2628C2212yes—
126#2627C2211yescharacteristic
127#2627C2211yescharacteristic
128#2625C2212yes—
129#2623C2212yes—
130#2618C2211yescharacteristic
131#2618C2211yescharacteristic
132#2614C2212yes—
133#2609C2212yes—
134#2604C2214yes—
135#2588C2214yes—
136#2586C2212yes—
137#2586C2212yes—
138#2584C2212yes—
139#2584C2212yes—
140#2583C2212yes—
141#2583C2212yes—
142#2581C2212yes—
143#2581C2212yes—
144#2581C2212yes—
145#2581C2214yes—
146#2576C2214yes—
147#2575C2214yes—
148#2575C2214yes—
149#2574C2214yes—
150#2573C2214yes—
151#2572C2212yes—
152#2571C2212yes—
153#2570C2214yes—
154#2568C2211yescharacteristic
155#2568C2211yescharacteristic
156#2567C2211yescharacteristic
157#2567C2212yes—
158#2567C2211yescharacteristic
159#2553C2214yes—
160#2551C2212yes—
161#2551C2214yes—
162#2551C2212yes—
163#2550C2212yes—
164#2546C2211yescharacteristic
165#2546C2211yescharacteristic
166#2546C2211yescharacteristic
167#2546C2211yescharacteristic
168#2533C2214yes—
169#2533C2214yes—
170#2530C2214yes—
171#2528C2214yes—
172#2528C2214yes—
173#2528C2214yes—
174#2524C2214yes—
175#2521C2214yes—
176#2519C2214yes—
177#2515C2214yes—
178#2514C2212yes—
179#2511C2212yes—
180#2509C2212yes—
181#2509C2212yes—
182#2508C2212yes—
183#2508C2214yes—
184#2508C2212yes—
185#2508C2214yes—
186#2507C2212yes—
187#2507C2214yes—
188#2503C2212yes—
189#2502C2212yes—
190#2499C2212yes—
191#2497C2212yes—
192#2497C2214yes—
193#2496C2212yes—
194#2496C2214yes—
195#2494C2214yes—
196#2494C2212yes—
197#2492C2212yes—
198#2489C2212yes—
199#2489C2212yes—
200#2485C2212yes—
201#2485C2212yes—
202#2484C2212yes—
203#2484C2212yes—
204#2478C2214yes—
205#2474C2214yes—
206#2470C2214yes—
207#2469C2214yes—
208#2469C2214yes—
209#2462C2214yes—
210#2462C2214yes—
211#2453C2212yes—
212#2453C2212yes—
213#2451C2212yes—
214#2451C2212yes—
215#2446C2212yes—
216#2442C2212yes—
217#2441C2212yes—
218#2441C2212yes—
219#2439C2214yes—
220#2439C2214yes—
221#2439C2212yes—
222#2439C2212yes—
223#2434C2212yes—
224#2434C2212yes—
225#2429C2212yes—
226#2423C2212yes—
227#2417C2212yes—
228#2415C2212yes—
229#2399C2211yescharacteristic
230#2399C2211yescharacteristic
231#2399C2212yes—
232#2399C2212yes—
233#2398C2211yescharacteristic
234#2398C2211yescharacteristic
235#2396C2212yes—
236#2396C2212yes—
237#2370C2212yes—
238#2370C2212yes—
239#2365C2214yes—
240#2362C2212yes—
241#2362C2212yes—
242#2360C2212yes—
243#2355C2212yes—
244#2352C2212yes—
245#2351C2212yes—
246#2346C2214yes—
247#2346C2212yes—
248#2345C2212yes—
249#2344C2212yes—
250#2330C2212yes—
251#2327C2212yes—
252#2327C2214yes—
253#2327C2212yes—
254#2323C2212yes—
255#2320C2212yes—
256#2316C2212yes—
257C4×C4⋊Q8C2212yes—
258C4×C4⋊Q8C2212yes—
259C4×#126C2214yes—
260C4×#123C2212yes—
261C4×#123C2212yes—
262#2296C2212yes—
263#2296C2212yes—
264#2283C2211yescharacteristic
265#2283C2211yescharacteristic
266C4×#117C2211yescharacteristic
267C23×Q8C2311yescharacteristic
268#556—48no—
269#533—44no—
270#533—44no—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282#529—44no—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2312yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2311yescharacteristic
290C2×#125C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2314yes—
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×#123C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2311yescharacteristic
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×#121C2311yescharacteristic
304C2×C4×Q8—44no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336#401C2314yes—
337#401C2314yes—
338#401C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
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#400C2312yes—
373#400C2311yescharacteristic
374#400C2311yescharacteristic
375#400C2311yescharacteristic
376#400C2311yescharacteristic
377#400C2314yes—
378#400C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2314yes—
383#399C2312yes—
384#399C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2314yes—
394#398C2312yes—
395#398C2312yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2312yes—
411#398C2314yes—
412#398C2314yes—
413#398C2311yescharacteristic
414#398C2311yescharacteristic
415#398C2311yescharacteristic
416#398C2311yescharacteristic
417#398C2312yes—
418#398C2312yes—
419#398C2312yes—
420#398C2314yes—
421#398C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2312yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2312yes—
440#396C2314yes—
441#396C2312yes—
442#396C2314yes—
443#396C2312yes—
444#396C2312yes—
445#396C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2312yes—
449#395C2312yes—
450#395C2312yes—
451#395C2312yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2311yescharacteristic
465#395C2311yescharacteristic
466#395C2314yes—
467#395C2312yes—
468#395C2312yes—
469#395C2312yes—
470#395C2312yes—
471#395C2311yescharacteristic
472#395C2311yescharacteristic
473#394C2311yescharacteristic
474#394C2314yes—
475#394C2314yes—
476#394C2311yescharacteristic
477#394C2311yescharacteristic
478#394C2311yescharacteristic
479#394C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2312yes—
485#393C2314yes—
486#393C2312yes—
487#393C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2314yes—
506#391C2312yes—
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
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#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2314yes—
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#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#386C2314yes—
641#386C2312yes—
642#386C2314yes—
643#386C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2314yes—
657#384C2312yes—
658#384C2312yes—
659#383C2314yes—
660#383C2314yes—
661#383C2311yescharacteristic
662#383C2311yescharacteristic
663#383C2312yes—
664#382C2312yes—
665#382C2312yes—
666#382C2314yes—
667#382C2314yes—
668#382C2312yes—
669#382C2312yes—
670#382C2314yes—
671#382C2314yes—
672#382C2314yes—
673#382C2314yes—
674#382C2314yes—
675#382C2314yes—
676#382C2314yes—
677#382C2312yes—
678#382C2312yes—
679#381C2314yes—
680#381C2312yes—
681#381C2312yes—
682#381C2314yes—
683#381C2314yes—
684#381C2312yes—
685#381C2312yes—
686#380C2314yes—
687#380C2314yes—
688#380C2312yes—
689#380C2314yes—
690#380C2312yes—
691#380C2312yes—
692#380C2312yes—
693#380C2314yes—
694#380C2312yes—
695#380C2311yescharacteristic
696#380C2311yescharacteristic
697#380C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735#376C2314yes—
736#376C2311yescharacteristic
737#376C2312yes—
738C43C2312yes—
739C22×Q8—42no—
740C22×Q8—42no—
741C22×Q8—42no—
742C22×Q8C2412yes—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2411yescharacteristic
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2414yes—
762C23×C4C2411yescharacteristic
763C4⋊Q8—42no—
764C4⋊Q8—42no—
765C4⋊Q8—42no—
766C4⋊Q8—44no—
767C4⋊Q8—44no—
768C4⋊Q8—44no—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771C4⋊Q8—48no—
772C4⋊Q8—48no—
773C4⋊Q8—44no—
774#126—48no—
775#126—44no—
776#126—48no—
777#126—48no—
778#125—28no—
779#125—42no—
780#125—44no—
781#125—44no—
782#124—42no—
783#124—48no—
784#123—44no—
785#123—44no—
786#123—44no—
787C22⋊Q8—28no—
788C22⋊Q8—28no—
789C22⋊Q8—42no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794#121—42no—
795C4×Q8—28no—
796C4×Q8—42no—
797C4×Q8—42no—
798C4×Q8—42no—
799C4×Q8—42no—
800C4×Q8—42no—
801C4×Q8—42no—
802C4×Q8—42no—
803C4×Q8—42no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—48no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×D4—28no—
812C4×D4—42no—
813#117—28no—
814#117—28no—
815#117—44no—
816#117—48no—
817#117—44no—
818#117—44no—
819C2×C4⋊C4—28no—
820C2×C4⋊C4—42no—
821C2×C4⋊C4—42no—
822C2×C4⋊C4—42no—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C42—24no—
926C2×C42—24no—
927C2×C42—24no—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
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—
1040C24C2512yes—
1041C24C2511yescharacteristic
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—24no—
1050C2×Q8—24no—
1051C2×Q8—41no—
1052C2×Q8—41no—
1053C2×Q8—41no—
1054C2×Q8—41no—
1055C2×Q8—41no—
1056C2×Q8—41no—
1057C2×Q8—41no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—44no—
1067C2×Q8—44no—
1068C2×Q8—42no—
1069C2×Q8—44no—
1070C2×Q8—416no—
1071C2×D4—24no—
1072C2×D4—41no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—28no—
1089C22×C4—42no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4H(5,𝔽2)14yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2514yes—
1122C22×C4C2514yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2514yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—41no—
1178C4⋊C4—41no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C42−1+418yes—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—22no—
1234C42—22no—
1235C42—22no—
1236C42—22no—
1237C42—22no—
1238C42—22no—
1239C42—22no—
1240C42—22no—
1241C42—22no—
1242C42—28no—
1243C42—24no—
1244C42—28no—
1245C42—24no—
1246C42—28no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—42no—
1257C42—44no—
1258C42—42no—
1259C42—44no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23C2×H(5,𝔽2)12yes—
1272C23C2611yescharacteristic
1273Q8—44no—
1274Q8—44no—
1275Q8—44no—
1276Q8—44no—
1277Q8—48no—
1278Q8—84no—
1279Q8—84no—
1280Q8—88no—
1281Q8—82no—
1282Q8—84no—
1283D4—84no—
1284D4—82no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—28no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—48no—
1364C2×C4—88no—
1365C2×C4—82no—
1366C2×C4—82no—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×2−1+418yes—
1370C2×C4C2×2−1+414yes—
1371C2×C4#58512yes—
1372C2×C4#58512yes—
1373C22—22no—
1374C22—22no—
1375C22—22no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22C22×H(5,𝔽2)11yescharacteristic
1386C22C22×2−1+412yes—
1387C22C2×#58511yescharacteristic
1388C22C2×#58511yescharacteristic
1389C222−1+612yes—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—28no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—42no—
1399C4—44no—
1400C4—44no—
1401C4—42no—
1402C4—44no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—42no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4#354414yes—
1419C2—42no—
1420C2—82no—
1421C2#6272911yescharacteristic
1422C2C2×#354411yescharacteristic
1423C2#6288611yescharacteristic
1424C2#6295012yes—
1425C2#6295312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59298C2semidirect
2. #59114C2semidirect
4. #58589C2semidirect
5. #55674C2semidirect
7. #55610C2semidirect
8. #55192C2semidirect
9. #53124C2semidirect
10. #53081C2semidirect
11. #53033C2semidirect
12. #52947C2semidirect
13. #45435C2semidirect
14. #45384C2semidirect
15. #45190C2semidirect
16. #42821C2semidirect
17. #42722C2semidirect
18. #42713C2semidirect
19. #42488C2semidirect
20. #42376C2semidirect
21. #42344C2semidirect
22. #40155C2semidirect
23. #39867C2semidirect
24. #38072C2semidirect
26. #37602C2semidirect
27. #37266C2semidirect
28. #36451C2semidirect
29. #35248C2semidirect
30. #34953C2semidirect

Maximal subgroups

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

subgroupindex
#592982
#591142
#587492
#585892
#556742
#556132
#556102
#551922
#531242
#530812
#530332
#529472
#454352
#453842
#451902
#428212
#427222
#427132
#424882
#423762
#423442
#401552
#398672
#380722
#380512
#376022
#372662
#364512
#352482
#349532
#346022