Finite Group Databasebeta

← #9062268

Subgroups — #9062268

Order 512.

4582 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60049C212yesmaximal, complemented
2#60047C211yesmaximal, characteristic
3#60046C211yesmaximal, characteristic
4#58592C212yesmaximal, complemented
5#55136C214yesmaximal, complemented
6#53726C212yesmaximal, complemented
7#51326C212yesmaximal
8#49568C214yesmaximal, complemented
9#47660C212yesmaximal, complemented
10#47642C214yesmaximal, complemented
11#47640C214yesmaximal, complemented
12#46426C212yesmaximal
13#45435C212yesmaximal, complemented
14#45272C214yesmaximal, complemented
15#45044C214yesmaximal, complemented
16#44861C212yesmaximal, complemented
17#44741C214yesmaximal, complemented
18#44369C214yesmaximal, complemented
19#44323C214yesmaximal, complemented
20#35872C214yesmaximal, complemented
21#35749C212yesmaximal, complemented
22#35667C211yesmaximal, characteristic
23#35576C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#557C2212yes—
26C2×#544C2212yes—
27C2×#544C2212yes—
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic
32#2839C2214yes—
33#2838C2214yes—
34#2833C2212yes—
35#2817C2212yes—
36#2810C2212yes—
37#2809C2211yescharacteristic
38#2805C2214yes—
39#2805C2212yes—
40#2799C2212yes—
41#2793C2214yes—
42#2792C2214yes—
43#2792C2214yes—
44#2790C2214yes—
45#2777C2214yes—
46#2774C2214yes—
47#2774C2214yes—
48#2773C2214yes—
49#2772C2214yes—
50#2766C2214yes—
51#2762C2214yes—
52#2755C2214yes—
53#2734C2212yes—
54#2734C2214yes—
55#2734C2211yescharacteristic
56#2729C2214yes—
57#2729C2214yes—
58#2727C2212yes—
59#2726C2214yes—
60#2726C2212yes—
61#2726C2214yes—
62#2726C2212yes—
63#2726C2212yes—
64#2725C2214yes—
65#2725C2214yes—
66#2724C2212yes—
67#2724C2211yescharacteristic
68#2720C2214yes—
69#2720C2214yes—
70#2719C2214yes—
71#2718C2214yes—
72#2717C2212yes—
73#2716C2214yes—
74#2713C2214yes—
75#2713C2214yes—
76#2713C2214yes—
77#2713C2214yes—
78#2713C2214yes—
79#2704C2214yes—
80#2698C2214yes—
81#2689C2214yes—
82#2689C2214yes—
83#2683C2211yescharacteristic
84#2680C2214yes—
85#2677C2214yes—
86#2677C2214yes—
87#2674C2214yes—
88#2674C2214yes—
89#2674C2214yes—
90#2663C2214yes—
91#2655C2214yes—
92#2650C2214yes—
93#2634C2212yes—
94#2634C2212yes—
95#2621C2212yes—
96#2612C2214yes—
97#2611C2212yes—
98#2611C2212yes—
99#2599C2212yes—
100#2599C2212yes—
101#2596C2214yes—
102#2594C2214yes—
103#2593C2212yes—
104#2586C2214yes—
105#2586C2212yes—
106#2586C2212yes—
107#2585C2214yes—
108#2585C2214yes—
109#2585C2214yes—
110#2585C2214yes—
111#2583C2214yes—
112#2583C2214yes—
113#2583C2212yes—
114#2581C2212yes—
115#2575C2214yes—
116#2574C2214yes—
117#2573C2214yes—
118#2567C2214yes—
119#2558C2214yes—
120#2556C2214yes—
121#2556C2214yes—
122#2556C2214yes—
123#2556C2214yes—
124#2556C2214yes—
125#2552C2214yes—
126#2551C2214yes—
127#2551C2214yes—
128#2551C2214yes—
129#2551C2214yes—
130#2551C2214yes—
131#2551C2214yes—
132#2551C2214yes—
133#2550C2214yes—
134#2550C2214yes—
135#2550C2214yes—
136#2550C2214yes—
137#2550C2214yes—
138#2546C2212yes—
139#2546C2212yes—
140#2546C2212yes—
141#2546C2214yes—
142#2545C2212yes—
143#2545C2212yes—
144#2529C2214yes—
145#2529C2214yes—
146#2527C2214yes—
147#2521C2214yes—
148#2519C2214yes—
149#2519C2214yes—
150#2519C2214yes—
151#2509C2214yes—
152#2508C2214yes—
153#2507C2214yes—
154#2506C2214yes—
155#2479C2214yes—
156#2478C2214yes—
157#2478C2214yes—
158#2478C2214yes—
159#2477C2214yes—
160#2475C2214yes—
161#2475C2214yes—
162#2475C2214yes—
163#2475C2214yes—
164#2474C2214yes—
165#2474C2214yes—
166#2470C2214yes—
167#2470C2214yes—
168#2462C2214yes—
169#2462C2214yes—
170#2462C2214yes—
171#2453C2214yes—
172#2451C2214yes—
173#2446C2214yes—
174#2441C2214yes—
175#2440C2214yes—
176#2434C2214yes—
177#2434C2214yes—
178#2432C2212yes—
179#2429C2214yes—
180#2429C2214yes—
181#2429C2214yes—
182#2413C2214yes—
183#2413C2214yes—
184#2406C2212yes—
185#2402C2214yes—
186#2399C2212yes—
187#2399C2212yes—
188#2396C2212yes—
189#2396C2214yes—
190#2374C2212yes—
191#2374C2212yes—
192#2373C2214yes—
193#2373C2214yes—
194#2370C2214yes—
195#2370C2214yes—
196#2370C2214yes—
197#2370C2214yes—
198#2370C2214yes—
199#2369C2212yes—
200#2365C2214yes—
201#2362C2214yes—
202#2362C2214yes—
203#2360C2214yes—
204#2356C2212yes—
205#2334C2214yes—
206#2332C2212yes—
207#2331C2214yes—
208#2330C2214yes—
209#2330C2214yes—
210#2323C2214yes—
211#2317C2212yes—
212#2317C2212yes—
213#2310C2211yescharacteristic
214#2297C2211yescharacteristic
215#2296C2211yescharacteristic
216#2296C2212yes—
217#2296C2212yes—
218#2274C2212yes—
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#563—48no—
223#557—48no—
224#544—48no—
225#544—48no—
226#536—44no—
227#536—44no—
228C2×C4⋊Q8—44no—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#125C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#123C2312yes—
261C2×#123C2312yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274#519—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C42C2311yescharacteristic
297#401C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#398C2314yes—
323#398C2312yes—
324#398C2314yes—
325#398C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2312yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2312yes—
384#395C2312yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#393C2312yes—
404#393C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2311yescharacteristic
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2311yescharacteristic
421#391C2312yes—
422#391C2314yes—
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
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#386C2312yes—
554#386C2312yes—
555#386C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#384C2314yes—
572#384C2314yes—
573#384C2314yes—
574#384C2314yes—
575#383C2312yes—
576#383C2312yes—
577#382C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#381C2312yes—
583#381C2314yes—
584#380C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2312yes—
620#376C2314yes—
621#376C2312yes—
622C2×#41—42no—
623C2×#41—42no—
624C2×#41—42no—
625C22×Q8—24no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2414yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2414yes—
639C22×Q8C2412yes—
640C22×D4C2412yes—
641C22×D4C2411yescharacteristic
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C4⋊Q8—44no—
651C4⋊Q8—48no—
652C4⋊Q8—44no—
653C4⋊Q8—48no—
654C4⋊Q8—44no—
655C4⋊Q8—44no—
656C4⋊Q8—48no—
657C4⋊Q8—48no—
658C4⋊Q8—44no—
659C4⋊Q8—44no—
660C4⋊Q8—48no—
661C4⋊Q8—48no—
662C4⋊Q8—48no—
663C4⋊Q8—48no—
664C4⋊Q8—48no—
665#126—216no—
666#126—48no—
667#126—48no—
668#125—216no—
669#125—216no—
670#125—216no—
671#125—44no—
672#125—44no—
673#125—48no—
674#125—48no—
675#125—48no—
676#125—48no—
677#125—48no—
678#124—44no—
679#124—44no—
680#124—44no—
681#123—28no—
682#123—48no—
683#123—44no—
684#123—44no—
685#123—44no—
686C22⋊Q8—216no—
687C22⋊Q8—28no—
688C22⋊Q8—216no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—44no—
694C22⋊Q8—44no—
695C4×Q8—28no—
696C4×Q8—44no—
697C4×Q8—44no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×Q8—48no—
702C4×Q8—44no—
703#117—24no—
704#117—28no—
705#117—28no—
706#117—42no—
707#117—44no—
708#117—44no—
709#117—48no—
710#117—42no—
711#117—44no—
712#117—44no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C42—42no—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2412yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893C24C2512yes—
894C24C2511yescharacteristic
895#41—88no—
896C2×Q8—24no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—28no—
900C2×Q8—24no—
901C2×Q8—28no—
902C2×Q8—24no—
903C2×Q8—24no—
904C2×Q8—22no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—41no—
913C2×Q8—41no—
914C2×Q8—44no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—44no—
918C2×Q8—44no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—44no—
922C2×Q8—416no—
923C2×Q8—88no—
924C2×D4—24no—
925C2×D4—22no—
926C2×D4—42no—
927C2×D4—41no—
928C2×D4—41no—
929C2×D4—42no—
930C22×C4—24no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—24no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—42no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4H(5,𝔽2)14yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4H(5,𝔽2)14yes—
1043C4⋊C42−1+418yes—
1044C4⋊C42−1+418yes—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—42no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—42no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C42—24no—
1067C42—24no—
1068C42—24no—
1069C42—24no—
1070C42—28no—
1071C42—28no—
1072C42—28no—
1073C42—28no—
1074C42—28no—
1075C42—28no—
1076C42—41no—
1077C42—41no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—42no—
1088C42—44no—
1089C42—42no—
1090C42—44no—
1091C42—44no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—21no—
1096C23—22no—
1097C23—22no—
1098C23—24no—
1099C23—24no—
1100C23—22no—
1101C23C2×H(5,𝔽2)12yes—
1102C23C2611yescharacteristic
1103Q8—48no—
1104Q8—48no—
1105Q8—48no—
1106Q8—88no—
1107Q8—84no—
1108Q8—84no—
1109Q8—82no—
1110Q8—162no—
1111Q8—164no—
1112D4—82no—
1113D4—84no—
1114C2×C4—216no—
1115C2×C4—28no—
1116C2×C4—21no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—44no—
1170C2×C4—84no—
1171C2×C4—84no—
1172C2×C4—162no—
1173C2×C4C2×H(5,𝔽2)14yes—
1174C2×C4C2×H(5,𝔽2)12yes—
1175C2×C4C2×H(5,𝔽2)14yes—
1176C2×C4C2×2−1+418yes—
1177C2×C4C2×2−1+418yes—
1178C2×C4C2×2−1+414yes—
1179C2×C4C2×2−1+414yes—
1180C2×C4#58512yes—
1181C22—22no—
1182C22—24no—
1183C22—41no—
1184C22—42no—
1185C22—41no—
1186C22—42no—
1187C22—44no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22C22×H(5,𝔽2)11yescharacteristic
1192C22C22×H(5,𝔽2)11yescharacteristic
1193C22C22×2−1+412yes—
1194C22C22×2−1+412yes—
1195C22C2×#58511yescharacteristic
1196C4—28no—
1197C4—28no—
1198C4—24no—
1199C4—22no—
1200C4—22no—
1201C4—24no—
1202C4—24no—
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—44no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—42no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C2—42no—
1218C2—82no—
1219C2#6281811yescharacteristic
1220C2#6283312yes—
1221C2#6301611yescharacteristic
1222C2#6303212yes—
1223C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60049C2semidirect
4. #58592C2semidirect
5. #55136C2semidirect
6. #53726C2semidirect
8. #49568C2semidirect
9. #47660C2semidirect
10. #47642C2semidirect
11. #47640C2semidirect
13. #45435C2semidirect
14. #45272C2semidirect
15. #45044C2semidirect
16. #44861C2semidirect
17. #44741C2semidirect
18. #44369C2semidirect
19. #44323C2semidirect
20. #35872C2semidirect
21. #35749C2semidirect
23. #35576C2semidirect

Maximal subgroups

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

subgroupindex
#600492
#600472
#600462
#585922
#551362
#537262
#513262
#495682
#476602
#476422
#476402
#464262
#454352
#452722
#450442
#448612
#447412
#443692
#443232
#358722
#357492
#356672
#355762