Finite Group Databasebeta

← #8757428

Subgroups — #8757428

Order 512.

3636 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58495C214yesmaximal, complemented
2#58477C214yesmaximal, complemented
3#58477C214yesmaximal, complemented
4#55768C214yesmaximal
5#54220C214yesmaximal
6#53734C214yesmaximal, complemented
7#51007C214yesmaximal
8#50201C214yesmaximal
9#49138C214yesmaximal
10#47340C214yesmaximal, complemented
11#46924C214yesmaximal, complemented
12#46680C214yesmaximal
13#46242C212yesmaximal, complemented
14#46242C212yesmaximal, complemented
15#46234C212yesmaximal
16#46160C212yesmaximal, complemented
17#46160C212yesmaximal, complemented
18#46144C211yesmaximal, characteristic
19#46144C211yesmaximal, characteristic
20#35339C211yesmaximal, characteristic
21#35142C212yesmaximal
22#2864C2212yes—
23#2864C2212yes—
24#2864C2212yes—
25#2859C2212yes—
26#2851C2212yes—
27#2851C2212yes—
28#2845C2211yescharacteristic
29#2845C2211yescharacteristic
30#2845C2212yes—
31#2839C2214yes—
32#2839C2214yes—
33#2839C2214yes—
34#2839C2214yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2822C2211yescharacteristic
39#2822C2211yescharacteristic
40#2822C2212yes—
41#2810C2214yes—
42#2802C2214yes—
43#2802C2214yes—
44#2802C2214yes—
45#2802C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2794C2214yes—
56#2794C2214yes—
57#2794C2214yes—
58#2794C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2791C2214yes—
71#2791C2214yes—
72#2791C2214yes—
73#2791C2214yes—
74#2791C2214yes—
75#2791C2214yes—
76#2790C2214yes—
77#2787C2214yes—
78#2787C2214yes—
79#2776C2214yes—
80#2776C2214yes—
81#2776C2214yes—
82#2776C2214yes—
83#2776C2214yes—
84#2776C2214yes—
85#2770C2214yes—
86#2770C2214yes—
87#2769C2214yes—
88#2769C2214yes—
89#2767C2214yes—
90#2767C2214yes—
91#2767C2214yes—
92#2767C2214yes—
93#2767C2214yes—
94#2766C2214yes—
95#2766C2214yes—
96#2766C2214yes—
97#2747C2214yes—
98#2747C2214yes—
99#2726C2214yes—
100#2722C2214yes—
101#2722C2214yes—
102#2722C2214yes—
103#2722C2214yes—
104#2722C2214yes—
105#2719C2214yes—
106#2719C2214yes—
107#2719C2214yes—
108#2719C2214yes—
109#2655C2214yes—
110#2655C2214yes—
111#2655C2214yes—
112#2655C2214yes—
113#2652C2214yes—
114#2652C2214yes—
115#2652C2214yes—
116#2647C2212yes—
117#2647C2212yes—
118#2647C2214yes—
119#2606C2214yes—
120#2606C2214yes—
121#2590C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2590C2214yes—
125#2590C2214yes—
126#2590C2214yes—
127#2590C2214yes—
128#2590C2214yes—
129#2590C2214yes—
130#2590C2214yes—
131#2590C2214yes—
132#2585C2214yes—
133#2585C2214yes—
134#2585C2214yes—
135#2585C2214yes—
136#2585C2214yes—
137#2585C2214yes—
138#2585C2214yes—
139#2577C2214yes—
140#2570C2214yes—
141#2570C2214yes—
142#2570C2214yes—
143#2569C2214yes—
144#2569C2214yes—
145#2569C2214yes—
146#2569C2214yes—
147#2552C2214yes—
148#2533C2214yes—
149#2533C2214yes—
150#2533C2214yes—
151#2533C2214yes—
152#2533C2214yes—
153#2530C2214yes—
154#2528C2214yes—
155#2528C2214yes—
156#2528C2214yes—
157#2528C2214yes—
158#2528C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2524C2214yes—
162#2524C2214yes—
163#2509C2212yes—
164#2508C2212yes—
165#2507C2214yes—
166#2507C2214yes—
167#2507C2212yes—
168#2507C2214yes—
169#2507C2214yes—
170#2506C2214yes—
171#2506C2212yes—
172#2505C2214yes—
173#2505C2214yes—
174#2497C2212yes—
175#2496C2214yes—
176#2496C2212yes—
177#2496C2214yes—
178#2495C2212yes—
179#2494C2212yes—
180#2478C2214yes—
181#2478C2214yes—
182#2478C2214yes—
183#2475C2214yes—
184#2473C2214yes—
185#2473C2214yes—
186#2383C2214yes—
187#2382C2212yes—
188#2382C2212yes—
189#2382C2212yes—
190#2382C2212yes—
191#2373C2214yes—
192#2336C2214yes—
193#2336C2214yes—
194#2334C2214yes—
195#2330C2214yes—
196#2317C2212yes—
197#2316C2212yes—
198C4×#125C2212yes—
199C4×#125C2212yes—
200#2285C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C4×#117C2211yescharacteristic
203C2×#126C2314yes—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2314yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#117C2311yescharacteristic
212C2×#117C2312yes—
213C2×#117C2311yescharacteristic
214C22×C4⋊C4C2312yes—
215C22×C42C2311yescharacteristic
216#401C2314yes—
217#401C2314yes—
218#401C2314yes—
219#400C2314yes—
220#400C2314yes—
221#400C2314yes—
222#400C2314yes—
223#400C2314yes—
224#400C2314yes—
225#400C2314yes—
226#400C2314yes—
227#400C2314yes—
228#400C2314yes—
229#400C2314yes—
230#400C2314yes—
231#400C2314yes—
232#400C2314yes—
233#400C2314yes—
234#400C2314yes—
235#400C2314yes—
236#400C2314yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#396C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#384C2314yes—
517#384C2314yes—
518#384C2314yes—
519#384C2312yes—
520#384C2312yes—
521#384C2311yescharacteristic
522#384C2311yescharacteristic
523#384C2314yes—
524#384C2314yes—
525#383C2314yes—
526#383C2314yes—
527#383C2314yes—
528#383C2314yes—
529#383C2314yes—
530#382C2312yes—
531#382C2312yes—
532#382C2311yescharacteristic
533#382C2311yescharacteristic
534#382C2312yes—
535#382C2314yes—
536#382C2314yes—
537#382C2314yes—
538#382C2314yes—
539#382C2312yes—
540#382C2312yes—
541#382C2312yes—
542#382C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2312yes—
546#380C2312yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2312yes—
551#380C2312yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2312yes—
557C4×C4⋊C4C2312yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2312yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2312yes—
562C4×C4⋊C4C2312yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C22⋊C4C2312yes—
572C4×C22⋊C4C2312yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575#376C2314yes—
576#376C2314yes—
577#376C2312yes—
578C2×#95C2314yes—
579C43C2312yes—
580C23×C4C2411yescharacteristic
581C23×C4C2412yes—
582C23×C4C2414yes—
583#126—48no—
584#126—48no—
585#126—48no—
586#125—28no—
587#125—28no—
588#125—48no—
589#125—48no—
590#125—48no—
591#117—42no—
592#117—44no—
593#117—42no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2411yescharacteristic
670C2×C22⋊C4C2411yescharacteristic
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C42—24no—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2411yescharacteristic
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774C24C2511yescharacteristic
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—24no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C22⋊C4—24no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C42—24no—
883C42—22no—
884C42—42no—
885C42—42no—
886C42—42no—
887C42—42no—
888C42—44no—
889C42—44no—
890C42—44no—
891C42—44no—
892C42—44no—
893C42—44no—
894C42—44no—
895C42—42no—
896C42—42no—
897C42—44no—
898C42—44no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—44no—
903C422−1+414yes—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23#58512yes—
909C23C2611yescharacteristic
910C2×C4—28no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—84no—
969C2×C4—164no—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+414yes—
972C2×C4#58512yes—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—42no—
977C22—42no—
978C22C22×2−1+411yescharacteristic
979C22C2×#58511yescharacteristic
980C22C2×#58511yescharacteristic
981C222−1+612yes—
982C222−1+612yes—
983C4—22no—
984C4—22no—
985C4—24no—
986C4—42no—
987C4—44no—
988C4—42no—
989C4—44no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—44no—
995C4—44no—
996C4—42no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—42no—
1003C2—42no—
1004C2#6282511yescharacteristic
1005C2#6288912yes—
1006C2#6306212yes—
1007C2#6306811yescharacteristic
1008C2#6306811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58495C2semidirect
2. #58477C2semidirect
3. #58477C2semidirect
6. #53734C2semidirect
10. #47340C2semidirect
11. #46924C2semidirect
13. #46242C2semidirect
14. #46242C2semidirect
16. #46160C2semidirect
17. #46160C2semidirect

Maximal subgroups

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

subgroupindex
#584952
#584772
#557682
#542202
#537342
#510072
#502012
#491382
#473402
#469242
#466802
#462422
#462342
#461602
#461442
#353392
#351422