Finite Group Databasebeta

← #7661764

Subgroups — #7661764

Order 512.

4108 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52251C213yesmaximal
2#42782C213yesmaximal, complemented
3#42753C213yesmaximal
4#42744C213yesmaximal, complemented
5#42728C213yesmaximal
6#42703C213yesmaximal, complemented
7#42689C213yesmaximal, complemented
8#40096C213yesmaximal
9#40082C213yesmaximal, complemented
10#40082C213yesmaximal, complemented
11#39907C213yesmaximal
12#39250C213yesmaximal
13#39157C213yesmaximal
14#37404C213yesmaximal, complemented
15#37344C213yesmaximal, complemented
16#37295C213yesmaximal
17#36584C211yesmaximal, characteristic, complemented
18#36577C211yesmaximal, characteristic
19#36475C211yesmaximal, characteristic, complemented
20#36448C211yesmaximal, characteristic
21#36448C211yesmaximal, characteristic
22#36435C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35971C211yesmaximal, characteristic, complemented
25#35957C211yesmaximal, characteristic, complemented
26#35920C211yesmaximal, characteristic
27#35883C211yesmaximal, characteristic
28#35868C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34192C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2864C2213yes—
36#2863C2213yes—
37#2863C2213yes—
38#2859C2213yes—
39#2857C2213yes—
40#2851C2213yes—
41#2839C2216yes—
42#2833C2216yes—
43#2802C2216yes—
44#2794C2216yes—
45#2794C2216yes—
46#2789C2216yes—
47#2776C2213yes—
48#2776C2216yes—
49#2776C2216yes—
50#2769C2213yes—
51#2769C2216yes—
52#2769C2216yes—
53#2766C2213yes—
54#2762C2213yes—
55#2762C2213yes—
56#2762C2216yes—
57#2762C2216yes—
58#2762C2216yes—
59#2758C2213yes—
60#2758C2216yes—
61#2758C2216yes—
62#2755C2213yes—
63#2755C2216yes—
64#2747C2216yes—
65#2747C2213yes—
66#2744C2211yescharacteristic
67#2739C2213yes—
68#2722C2213yes—
69#2722C2216yes—
70#2719C2216yes—
71#2719C2213yes—
72#2719C2216yes—
73#2704C2213yes—
74#2698C2213yes—
75#2690C2213yes—
76#2689C2213yes—
77#2689C2216yes—
78#2666C2216yes—
79#2660C2213yes—
80#2655C2216yes—
81#2655C2216yes—
82#2655C2216yes—
83#2652C2216yes—
84#2647C2213yes—
85#2647C2213yes—
86#2647C2213yes—
87#2645C2213yes—
88#2645C2213yes—
89#2645C2216yes—
90#2584C2213yes—
91#2582C2213yes—
92#2581C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2571C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2568C2213yes—
103#2567C2213yes—
104#2565C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2552C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2533C2216yes—
111#2533C2216yes—
112#2524C2216yes—
113#2524C2216yes—
114#2514C2213yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2509C2213yes—
132#2509C2213yes—
133#2509C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2508C2213yes—
138#2508C2213yes—
139#2507C2213yes—
140#2507C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2497C2213yes—
147#2496C2213yes—
148#2496C2213yes—
149#2496C2213yes—
150#2496C2216yes—
151#2496C2213yes—
152#2496C2213yes—
153#2495C2213yes—
154#2495C2213yes—
155#2495C2213yes—
156#2494C2213yes—
157#2494C2213yes—
158#2494C2213yes—
159#2489C2216yes—
160#2453C2213yes—
161#2453C2213yes—
162#2453C2213yes—
163#2451C2213yes—
164#2442C2213yes—
165#2442C2213yes—
166#2442C2213yes—
167#2440C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2369C2213yes—
179#2369C2213yes—
180#2356C2213yes—
181#2356C2213yes—
182#2355C2213yes—
183#2355C2213yes—
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2345C2213yes—
205#2345C2213yes—
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2334C2216yes—
213#2331C2213yes—
214#2331C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2330C2216yes—
218#2320C2213yes—
219#2320C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2283C2213yes—
231#2283C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#126C2313yes—
245C2×#126C2316yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×C22⋊Q8C2313yes—
254C2×C22⋊Q8C2313yes—
255C2×C4×Q8—28no—
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2313yes—
258C2×C4×Q8C2313yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2311yescharacteristic
274C22×C4⋊C4C2313yes—
275C22×C42C2313yes—
276#401C2316yes—
277#401C2316yes—
278#401C2316yes—
279#401C2313yes—
280#401C2313yes—
281#400C2316yes—
282#400C2316yes—
283#400C2313yes—
284#400C2316yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2313yes—
289#400C2313yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2313yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2313yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2313yes—
304#400C2313yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2313yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2316yes—
313#400C2313yes—
314#400C2313yes—
315#400C2311yescharacteristic
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2316yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2311yescharacteristic
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#396C2313yes—
359#396C2311yescharacteristic
360#395C2313yes—
361#395C2316yes—
362#395C2313yes—
363#395C2316yes—
364#395C2313yes—
365#395C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2316yes—
369#391C2313yes—
370#391C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2316yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2316yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2316yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#388C2311yescharacteristic
449#388C2311yescharacteristic
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2316yes—
455#387C2313yes—
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2311yescharacteristic
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2316yes—
467#387C2316yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2313yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2311yescharacteristic
510#387C2311yescharacteristic
511#385C2313yes—
512#385C2316yes—
513#385C2313yes—
514#385C2313yes—
515#385C2311yescharacteristic
516#384C2313yes—
517#384C2316yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#383C2313yes—
526#383C2313yes—
527#383C2316yes—
528#383C2316yes—
529#383C2316yes—
530#383C2313yes—
531#383C2313yes—
532#383C2316yes—
533#382C2311yescharacteristic
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2316yes—
545#382C2313yes—
546#382C2313yes—
547#382C2316yes—
548#382C2313yes—
549#382C2316yes—
550#382C2313yes—
551#382C2313yes—
552#381C2313yes—
553#381C2311yescharacteristic
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2316yes—
563#380C2313yes—
564#380C2311yescharacteristic
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2316yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2316yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C23×C4C2413yes—
629C23×C4C2411yescharacteristic
630C23×C4C2413yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633#126—46no—
634#126—46no—
635#126—412no—
636#125—212no—
637#125—212no—
638#125—212no—
639#125—212no—
640#125—46no—
641#125—46no—
642#125—412no—
643C22⋊Q8—46no—
644C22⋊Q8—46no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8—212no—
661C4×Q8—212no—
662C4×Q8#4118yes—
663C2×C4⋊C4—212no—
664C2×C4⋊C4C2413yes—
665C2×C4⋊C4C2416yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2416yes—
690C2×C4⋊C4C2416yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2416yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C22⋊C4C2411yescharacteristic
736C2×C22⋊C4C2413yes—
737C2×C22⋊C4C2413yes—
738C2×C22⋊C4C2413yes—
739C2×C22⋊C4C2411yescharacteristic
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2411yescharacteristic
747C2×C42—212no—
748C2×C42C2413yes—
749C2×C42C2413yes—
750C2×C42C2413yes—
751C2×C42C2413yes—
752C2×C42C2413yes—
753C2×C42C2413yes—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2411yescharacteristic
764C2×C42C2413yes—
765C2×C42C2416yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2416yes—
769C2×C42C2411yescharacteristic
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2416yes—
774C2×C42C2416yes—
775C2×C42C2413yes—
776#95C2411yescharacteristic
777#95C2411yescharacteristic
778#95C2411yescharacteristic
779#95C2411yescharacteristic
780#95C2413yes—
781#95C2413yes—
782#95C2413yes—
783#95C2413yes—
784#95C2413yes—
785#95C2413yes—
786#95C2413yes—
787#95C2413yes—
788#95C2413yes—
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
794#95C2416yes—
795#95C2416yes—
796#95C2416yes—
797#95C2416yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2413yes—
815#95C2413yes—
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2413yes—
825#95C2416yes—
826#95C2416yes—
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2416yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2416yes—
842#95C2416yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864C24C2511yescharacteristic
865C2×Q8—26no—
866C2×Q8—26no—
867C2×Q8—26no—
868C2×Q8—26no—
869C2×Q8—26no—
870C2×Q8—43no—
871C2×Q8—43no—
872C2×Q8—43no—
873C2×Q8—43no—
874C2×Q8—416no—
875C2×Q8C2×#4114yes—
876C2×Q82−1+414yes—
877C2×Q82−1+414yes—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—26no—
881C22×C4—26no—
882C22×C4—26no—
883C22×C4—26no—
884C22×C4—41no—
885C22×C4—43no—
886C22×C4—43no—
887C22×C4C2513yes—
888C22×C4C2511yescharacteristic
889C22×C4C2513yes—
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2513yes—
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C4⋊C4—26no—
918C4⋊C4—212no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—212no—
930C4⋊C4—212no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—22no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—43no—
947C4⋊C4—41no—
948C4⋊C4—43no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—43no—
952C4⋊C4—43no—
953C4⋊C4—43no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—43no—
960C4⋊C4—46no—
961C4⋊C4—46no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—46no—
976C4⋊C4—46no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—46no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—46no—
983C4⋊C4—43no—
984C4⋊C4—46no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4C2×#41112yes—
988C22⋊C4—26no—
989C22⋊C4—26no—
990C22⋊C4—22no—
991C22⋊C4—26no—
992C22⋊C4—22no—
993C22⋊C4—26no—
994C22⋊C4—22no—
995C22⋊C4—41no—
996C22⋊C4—43no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—43no—
1000C42—26no—
1001C42—26no—
1002C42—26no—
1003C42—26no—
1004C42—26no—
1005C42—26no—
1006C42—26no—
1007C42—26no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—22no—
1016C42—43no—
1017C42—46no—
1018C42—43no—
1019C42—43no—
1020C42—46no—
1021C42—41no—
1022C42—46no—
1023C42—43no—
1024C42—43no—
1025C42—46no—
1026C42—43no—
1027C42C2×#41112yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23#58512yes—
1035C23C2611yescharacteristic
1036Q8—412no—
1037Q8—86no—
1038Q8—86no—
1039Q8#541116yes—
1040C2×C4—21no—
1041C2×C4—23no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—23no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—23no—
1052C2×C4—23no—
1053C2×C4—23no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—23no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—23no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—23no—
1073C2×C4—23no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—23no—
1079C2×C4—21no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—23no—
1093C2×C4—21no—
1094C2×C4—23no—
1095C2×C4—21no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—44no—
1125C2×C4—412no—
1126C2×C4—86no—
1127C2×C4C22×#4112yes—
1128C2×C4C22×#4116yes—
1129C2×C4C22×#4116yes—
1130C2×C4C2×2−1+416yes—
1131C2×C4C2×2−1+416yes—
1132C2×C4#58512yes—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22C23×#4111yescharacteristic
1141C22C22×2−1+411yescharacteristic
1142C22C22×2−1+411yescharacteristic
1143C22C2×#58511yescharacteristic
1144C22C2×#58511yescharacteristic
1145C222−1+611yescharacteristic
1146C222−1+611yescharacteristic
1147C4—22no—
1148C4—26no—
1149C4—22no—
1150C4—41no—
1151C4—43no—
1152C4—41no—
1153C4—43no—
1154C4—43no—
1155C4—41no—
1156C4—41no—
1157C4—43no—
1158C4—43no—
1159C4—41no—
1160C4—41no—
1161C4—43no—
1162C4—43no—
1163C4—43no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—43no—
1168C4—43no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4—41no—
1173C4—41no—
1174C4—43no—
1175C4—43no—
1176C4C2×#541112yes—
1177C2—42no—
1178C2C22×#54111yescharacteristic
1179C2#6294911yescharacteristic
1180C2#6294911yescharacteristic
1181C2#6300511yescharacteristic
1182C2#6300911yescharacteristic
1183C2#6303311yescharacteristic
1184C2#6305711yescharacteristic
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
2. #42782C2semidirect
4. #42744C2semidirect
6. #42703C2semidirect
7. #42689C2semidirect
9. #40082C2semidirect
10. #40082C2semidirect
14. #37404C2semidirect
15. #37344C2semidirect
17. #36584C2semidirect
19. #36475C2semidirect
23. #35971C2semidirect
24. #35971C2semidirect
25. #35957C2semidirect
28. #35868C2semidirect
29. #34336C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#522512
#427822
#427532
#427442
#427282
#427032
#426892
#400962
#400822
#399072
#392502
#391572
#374042
#373442
#372952
#365842
#365772
#364752
#364482
#364352
#359712
#359572
#359202
#358832
#358682
#343362
#341922