Finite Group Databasebeta

← #8107650

Subgroups — #8107650

Order 512.

4430 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#52994C212yesmaximal, complemented
3#52950C214yesmaximal, complemented
4#52913C214yesmaximal, complemented
5#45428C211yesmaximal, characteristic, complemented
6#45427C211yesmaximal, characteristic, complemented
7#45395C211yesmaximal, characteristic, complemented
8#45362C211yesmaximal, characteristic, complemented
9#44859C214yesmaximal, complemented
10#43286C214yesmaximal, complemented
11#42819C212yesmaximal, complemented
12#42698C212yesmaximal, complemented
13#42525C212yesmaximal, complemented
14#42495C212yesmaximal, complemented
15#42371C214yesmaximal, complemented
16#42335C214yesmaximal, complemented
17#41533C214yesmaximal, complemented
18#40836C214yesmaximal, complemented
19#36200C212yesmaximal, complemented
20#36199C212yesmaximal, complemented
21#36117C212yesmaximal
22#36116C212yesmaximal, complemented
23#35315C211yesmaximal, characteristic, complemented
24#35271C211yesmaximal, characteristic
25#35247C212yesmaximal, complemented
26#35111C212yesmaximal, complemented
27C2×#2399C211yesmaximal, characteristic, complemented
28C2×#529C2212yes—
29C2×#529C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2855C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2851C2211yescharacteristic
41#2851C2211yescharacteristic
42#2843C2214yes—
43#2841C2214yes—
44#2841C2214yes—
45#2838C2214yes—
46#2838C2214yes—
47#2838C2214yes—
48#2838C2214yes—
49#2838C2214yes—
50#2836C2214yes—
51#2836C2214yes—
52#2835C2214yes—
53#2830C2214yes—
54#2805C2214yes—
55#2802C2214yes—
56#2792C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2792C2214yes—
60#2791C2214yes—
61#2791C2214yes—
62#2790C2214yes—
63#2787C2214yes—
64#2784C2214yes—
65#2780C2214yes—
66#2773C2214yes—
67#2770C2214yes—
68#2768C2214yes—
69#2765C2214yes—
70#2761C2214yes—
71#2757C2214yes—
72#2747C2214yes—
73#2745C2214yes—
74#2742C2214yes—
75#2742C2214yes—
76#2738C2214yes—
77#2738C2214yes—
78#2737C2214yes—
79#2737C2214yes—
80#2737C2214yes—
81#2725C2214yes—
82#2723C2214yes—
83#2720C2214yes—
84#2690C2214yes—
85#2689C2214yes—
86#2667C2214yes—
87#2666C2214yes—
88#2654C2214yes—
89#2651C2214yes—
90#2650C2214yes—
91#2647C2214yes—
92#2647C2211yescharacteristic
93#2647C2211yescharacteristic
94#2645C2212yes—
95#2644C2212yes—
96#2642C2211yescharacteristic
97#2641C2211yescharacteristic
98#2638C2214yes—
99#2637C2214yes—
100#2637C2214yes—
101#2627C2214yes—
102#2623C2214yes—
103#2614C2214yes—
104#2606C2214yes—
105#2604C2214yes—
106#2604C2214yes—
107#2599C2214yes—
108#2599C2214yes—
109#2592C2212yes—
110#2592C2212yes—
111#2592C2212yes—
112#2592C2212yes—
113#2588C2214yes—
114#2585C2214yes—
115#2584C2212yes—
116#2584C2212yes—
117#2584C2212yes—
118#2584C2212yes—
119#2582C2212yes—
120#2582C2212yes—
121#2581C2212yes—
122#2581C2212yes—
123#2580C2212yes—
124#2580C2212yes—
125#2579C2214yes—
126#2570C2212yes—
127#2570C2212yes—
128#2566C2212yes—
129#2565C2212yes—
130#2552C2212yes—
131#2552C2212yes—
132#2548C2212yes—
133#2547C2212yes—
134#2538C2212yes—
135#2538C2212yes—
136#2533C2214yes—
137#2531C2214yes—
138#2531C2214yes—
139#2531C2214yes—
140#2529C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2525C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2515C2214yes—
149#2514C2212yes—
150#2513C2212yes—
151#2512C2212yes—
152#2512C2214yes—
153#2511C2212yes—
154#2509C2212yes—
155#2508C2212yes—
156#2507C2212yes—
157#2507C2214yes—
158#2507C2214yes—
159#2506C2212yes—
160#2505C2214yes—
161#2501C2214yes—
162#2496C2214yes—
163#2493C2214yes—
164#2493C2214yes—
165#2486C2214yes—
166#2486C2214yes—
167#2484C2214yes—
168#2481C2214yes—
169#2479C2214yes—
170#2479C2214yes—
171#2478C2214yes—
172#2478C2214yes—
173#2473C2214yes—
174#2468C2214yes—
175#2454C2212yes—
176#2454C2212yes—
177#2453C2212yes—
178#2453C2212yes—
179#2449C2214yes—
180#2448C2212yes—
181#2448C2212yes—
182#2447C2212yes—
183#2447C2212yes—
184#2444C2214yes—
185#2442C2214yes—
186#2425C2214yes—
187#2425C2214yes—
188#2425C2214yes—
189#2419C2214yes—
190#2419C2214yes—
191#2419C2214yes—
192#2413C2214yes—
193#2413C2214yes—
194#2413C2214yes—
195#2409C2214yes—
196#2399C2211yescharacteristic
197#2399C2212yes—
198#2399C2211yescharacteristic
199#2399C2212yes—
200#2399C2212yes—
201#2399C2211yescharacteristic
202#2399C2212yes—
203#2399C2211yescharacteristic
204#2399C2212yes—
205#2399C2212yes—
206C2×#398C2212yes—
207C2×#398C2212yes—
208C2×#395C2212yes—
209C2×#395C2212yes—
210#2373C2214yes—
211#2371C2214yes—
212#2370C2212yes—
213#2370C2212yes—
214#2366C2212yes—
215#2365C2212yes—
216#2361C2214yes—
217#2359C2214yes—
218#2357C2212yes—
219#2356C2212yes—
220#2354C2214yes—
221Q8×C4⋊C4C2212yes—
222D4×C4⋊C4C2214yes—
223D4×C4⋊C4C2212yes—
224#2344C2214yes—
225#2343C2214yes—
226#2330C2211yescharacteristic
227#2330C2211yescharacteristic
228#2328C2211yescharacteristic
229#2327C2211yescharacteristic
230#2323C2214yes—
231#2323C2214yes—
232#2322C2214yes—
233#2322C2214yes—
234#2320C2212yes—
235#2319C2212yes—
236C4×C22⋊Q8C2212yes—
237C4×#121C2212yes—
238#2285C2212yes—
239#2283C2212yes—
240C2×C4×C4⋊C4C2212yes—
241C2×C4×C4⋊C4C2212yes—
242C2×#376C2211yescharacteristic
243C23×Q8C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247#529—48no—
248#529—48no—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2311yescharacteristic
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×C4×Q8—44no—
270C2×C4×Q8—44no—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2312yes—
309C22×C42C2312yes—
310#401C2314yes—
311#401C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#384C2312yes—
595#384C2312yes—
596#384C2311yescharacteristic
597#384C2311yescharacteristic
598#384C2314yes—
599#384C2314yes—
600#384C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#382C2312yes—
606#382C2312yes—
607#382C2311yescharacteristic
608#382C2311yescharacteristic
609#382C2314yes—
610#382C2314yes—
611#382C2314yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2311yescharacteristic
667#376C2314yes—
668#376C2314yes—
669#376C2311yescharacteristic
670#376C2312yes—
671#376C2312yes—
672C2×#95C2312yes—
673C2×#95C2312yes—
674C2×#95C2312yes—
675C2×#95C2312yes—
676C2×#95C2312yes—
677C2×#95C2312yes—
678C22×Q8—42no—
679C22×Q8—42no—
680C22×Q8—44no—
681C22×Q8—44no—
682C22×Q8C2412yes—
683C22×Q8C2411yescharacteristic
684C22×Q8C2412yes—
685C22×Q8C2411yescharacteristic
686C22×Q8C2412yes—
687C22×Q8C2411yescharacteristic
688C22×Q8C2411yescharacteristic
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C4⋊Q8—24no—
705#127—24no—
706#126—48no—
707#126—48no—
708#126—48no—
709#125—24no—
710#125—24no—
711#125—44no—
712#125—44no—
713#125—48no—
714#124—44no—
715#124—44no—
716#123—48no—
717#123—48no—
718#123—48no—
719#123—48no—
720#123—48no—
721C22⋊Q8—28no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724#121—28no—
725#121—48no—
726C4×Q8—28no—
727C4×Q8—42no—
728C4×Q8—42no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×Q8—42no—
732C4×Q8—42no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8—42no—
736C4×Q8—42no—
737C4×Q8—42no—
738C4×Q8—42no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×D4—28no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—48no—
748#117—48no—
749#117—48no—
750#117—48no—
751C2×C4⋊C4—48no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—44no—
754C2×C4⋊C4—44no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—42no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C42—24no—
857C2×C42—28no—
858C2×C42—28no—
859C2×C42—24no—
860C2×C42—24no—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958C24C2514yes—
959C24C2511yescharacteristic
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—41no—
966C2×Q8—42no—
967C2×Q8—41no—
968C2×Q8—42no—
969C2×Q8—41no—
970C2×Q8—41no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—416no—
978C2×Q8—416no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—28no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—44no—
987C2×D4—44no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—28no—
1007C22×C4—28no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4H(5,𝔽2)14yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—41no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—42no—
1087C4⋊C4—41no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—22no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—24no—
1155C42—24no—
1156C42—24no—
1157C42—22no—
1158C42—22no—
1159C42—28no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C422−1+414yes—
1169C422−1+414yes—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23C2×H(5,𝔽2)12yes—
1181C23#58514yes—
1182C23C2611yescharacteristic
1183Q8—44no—
1184Q8—48no—
1185Q8—44no—
1186Q8—48no—
1187Q8—44no—
1188Q8—44no—
1189Q8—48no—
1190D4—416no—
1191D4—48no—
1192D4—88no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—28no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—48no—
1259C2×C4—48no—
1260C2×C4—48no—
1261C2×C4—44no—
1262C2×C4—48no—
1263C2×C4—44no—
1264C2×C4—48no—
1265C2×C4—88no—
1266C2×C4—88no—
1267C2×C4—84no—
1268C2×C4—88no—
1269C2×C4C2×H(5,𝔽2)12yes—
1270C2×C4C2×H(5,𝔽2)12yes—
1271C2×C4C2×2−1+414yes—
1272C2×C4C2×2−1+414yes—
1273C2×C4C2×2−1+412yes—
1274C2×C4C2×2−1+412yes—
1275C2×C4#58514yes—
1276C22—22no—
1277C22—22no—
1278C22—24no—
1279C22—24no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22#353914yes—
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C22×2−1+411yescharacteristic
1290C22C22×2−1+411yescharacteristic
1291C22C2×#58512yes—
1292C22C2×#58512yes—
1293C4—24no—
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—44no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—44no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4#354414yes—
1318C2—24no—
1319C2—84no—
1320C2C2×#353911yescharacteristic
1321C2#6272911yescharacteristic
1322C2C2×#354411yescharacteristic
1323C2#6283112yes—
1324C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53153C2semidirect
2. #52994C2semidirect
3. #52950C2semidirect
4. #52913C2semidirect
5. #45428C2semidirect
6. #45427C2semidirect
7. #45395C2semidirect
8. #45362C2semidirect
9. #44859C2semidirect
10. #43286C2semidirect
11. #42819C2semidirect
12. #42698C2semidirect
13. #42525C2semidirect
14. #42495C2semidirect
15. #42371C2semidirect
16. #42335C2semidirect
17. #41533C2semidirect
18. #40836C2semidirect
19. #36200C2semidirect
20. #36199C2semidirect
22. #36116C2semidirect
23. #35315C2semidirect
25. #35247C2semidirect
26. #35111C2semidirect
27. C2×#2399C2semidirect

Maximal subgroups

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

subgroupindex
#531532
#529942
#529502
#529132
#454282
#454272
#453952
#453622
#448592
#432862
#428192
#426982
#425252
#424952
#423712
#423352
#415332
#408362
#362002
#361992
#361172
#361162
#353152
#352712
#352472
#351112
C2×#23992