Finite Group Databasebeta

← #7660387

Subgroups — #7660387

Order 512.

4165 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52283C213yesmaximal
2#42774C213yesmaximal, complemented
3#42773C213yesmaximal
4#42562C213yesmaximal
5#42553C213yesmaximal, complemented
6#42461C213yesmaximal
7#42455C213yesmaximal
8#40189C213yesmaximal, complemented
9#40155C213yesmaximal
10#40143C213yesmaximal, complemented
11#40024C213yesmaximal, complemented
12#39788C213yesmaximal
13#39635C213yesmaximal, complemented
14#37413C213yesmaximal, complemented
15#37344C213yesmaximal, complemented
16#37328C213yesmaximal
17Q8×#126C211yesmaximal, characteristic
18Q8×#125C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36466C211yesmaximal, characteristic, complemented
21#36448C211yesmaximal, characteristic
22#36447C211yesmaximal, characteristic, complemented
23#35971C211yesmaximal, characteristic, complemented
24#35920C211yesmaximal, characteristic
25#35883C211yesmaximal, characteristic
26#35868C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic
28#35786C211yesmaximal, characteristic
29#34337C211yesmaximal, characteristic, complemented
30#34337C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2863C2213yes—
37#2863C2213yes—
38#2859C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2839C2216yes—
42#2836C2216yes—
43#2802C2216yes—
44#2802C2213yes—
45#2802C2216yes—
46#2802C2216yes—
47#2798C2213yes—
48#2794C2213yes—
49#2789C2213yes—
50#2783C2213yes—
51#2776C2216yes—
52#2776C2216yes—
53#2776C2213yes—
54#2772C2216yes—
55#2772C2213yes—
56#2769C2216yes—
57#2766C2216yes—
58#2766C2216yes—
59#2766C2213yes—
60#2766C2216yes—
61#2762C2216yes—
62#2762C2216yes—
63#2758C2216yes—
64#2758C2213yes—
65#2755C2216yes—
66#2754C2213yes—
67#2725C2211yescharacteristic
68#2725C2213yes—
69#2725C2216yes—
70#2725C2216yes—
71#2721C2213yes—
72#2719C2216yes—
73#2719C2216yes—
74#2719C2213yes—
75#2719C2216yes—
76#2716C2213yes—
77#2713C2213yes—
78#2664C2216yes—
79#2655C2216yes—
80#2655C2216yes—
81#2647C2216yes—
82#2647C2213yes—
83#2647C2213yes—
84#2645C2213yes—
85#2645C2213yes—
86#2637C2216yes—
87#2634C2216yes—
88#2629C2213yes—
89#2629C2213yes—
90#2584C2213yes—
91#2584C2213yes—
92#2582C2213yes—
93#2582C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2565C2213yes—
101#2565C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2551C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2533C2216yes—
111#2528C2216yes—
112#2514C2213yes—
113#2514C2213yes—
114#2514C2213yes—
115#2514C2213yes—
116#2511C2213yes—
117#2511C2213yes—
118#2511C2213yes—
119#2511C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2497C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2496C2213yes—
149#2496C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2495C2213yes—
153#2495C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2469C2216yes—
157#2462C2216yes—
158#2453C2213yes—
159#2453C2213yes—
160#2453C2216yes—
161#2453C2216yes—
162#2451C2213yes—
163#2451C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2439C2213yes—
167#2439C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2401C2213yes—
171#2401C2213yes—
172#2396C2213yes—
173#2396C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2365C2213yes—
179#2365C2213yes—
180#2356C2213yes—
181#2355C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2213yes—
199Q8×C4⋊C4C2213yes—
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2347C2213yes—
205#2346C2213yes—
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2336C2216yes—
213#2330C2213yes—
214#2330C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2327C2216yes—
218#2320C2213yes—
219#2314C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×C4⋊Q8C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×#125C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2295C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2311yescharacteristic
245C2×#126C2313yes—
246C2×#126C2316yes—
247C2×#125C2311yescharacteristic
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257#519—28no—
258C2×C4×Q8C2313yes—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2316yes—
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C2×#117C2313yes—
279C2×#117C2313yes—
280#401C2313yes—
281#401C2316yes—
282#401C2313yes—
283#401C2316yes—
284#400C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2313yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2313yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2313yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2311yescharacteristic
315#400C2313yes—
316#400C2313yes—
317#399C2313yes—
318#399C2313yes—
319#398C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2316yes—
348#397C2313yes—
349#397C2313yes—
350#397C2316yes—
351#397C2311yescharacteristic
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#396C2316yes—
356#396C2316yes—
357#396C2313yes—
358#396C2313yes—
359#396C2316yes—
360#396C2313yes—
361#396C2311yescharacteristic
362#396C2311yescharacteristic
363#396C2311yescharacteristic
364#395C2316yes—
365#395C2316yes—
366#395C2313yes—
367#395C2313yes—
368#393C2313yes—
369#393C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2316yes—
381#391C2316yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#389C2311yescharacteristic
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2311yescharacteristic
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2316yes—
402#389C2316yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2316yes—
426#389C2316yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2316yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2316yes—
458#389C2311yescharacteristic
459#389C2311yescharacteristic
460#388C2311yescharacteristic
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2316yes—
468#388C2313yes—
469#388C2313yes—
470#388C2316yes—
471#388C2311yescharacteristic
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2316yes—
528#387C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#383C2313yes—
544#383C2313yes—
545#383C2316yes—
546#383C2316yes—
547#383C2316yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2316yes—
559#382C2316yes—
560#382C2316yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
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⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2316yes—
616#376C2313yes—
617#376C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C23×C4C2413yes—
629C4⋊Q8—212no—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632#126—24no—
633#126—46no—
634#126—86no—
635#125—212no—
636#125—212no—
637#125—24no—
638#125—212no—
639#125—212no—
640#125—412no—
641#125—46no—
642#125—46no—
643#125—86no—
644#125—86no—
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—86no—
663C4×Q8—86no—
664C4×Q8#4118yes—
665#117—212no—
666#117—212no—
667C2×C4⋊C4C2413yes—
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2416yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2411yescharacteristic
757C2×C22⋊C4C2413yes—
758C2×C42C2416yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2416yes—
779C2×C42C2416yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2411yescharacteristic
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788#95C2411yescharacteristic
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2416yes—
803#95C2416yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2411yescharacteristic
816#95C2416yes—
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2416yes—
826#95C2416yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2416yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868C24C2511yescharacteristic
869C2×Q8—26no—
870C2×Q8—26no—
871C2×Q8—26no—
872C2×Q8—26no—
873C2×Q8—26no—
874C2×Q8—26no—
875C2×Q8—26no—
876C2×Q8—43no—
877C2×Q8—43no—
878C2×Q8—416no—
879C2×Q8C2×#4114yes—
880C2×Q82−1+414yes—
881C2×Q82−1+414yes—
882C22×C4—26no—
883C22×C4—26no—
884C22×C4—26no—
885C22×C4C2513yes—
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2513yes—
892C22×C4C2511yescharacteristic
893C22×C4C2513yes—
894C22×C4C2513yes—
895C22×C4C2513yes—
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2511yescharacteristic
900C22×C4C2513yes—
901C22×C4C2511yescharacteristic
902C22×C4C2511yescharacteristic
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C4⋊C4—26no—
916C4⋊C4—26no—
917C4⋊C4—26no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—26no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—212no—
929C4⋊C4—212no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—41no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—43no—
959C4⋊C4—46no—
960C4⋊C4—43no—
961C4⋊C4—46no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—46no—
969C4⋊C4—46no—
970C4⋊C4—43no—
971C4⋊C4—46no—
972C4⋊C4—46no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—46no—
986C4⋊C4—46no—
987C4⋊C4—46no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4C2×#41112yes—
991C4⋊C42−1+414yes—
992C22⋊C4—26no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—41no—
999C22⋊C4—43no—
1000C22⋊C4—41no—
1001C22⋊C4—43no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C42—26no—
1007C42—212no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—22no—
1021C42—22no—
1022C42—26no—
1023C42—26no—
1024C42—41no—
1025C42—43no—
1026C42—43no—
1027C42—46no—
1028C42—43no—
1029C42—43no—
1030C42—46no—
1031C42—46no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42C2×#41112yes—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23C2611yescharacteristic
1044Q8—412no—
1045Q8—412no—
1046Q8—412no—
1047Q8#541116yes—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—23no—
1054C2×C4—21no—
1055C2×C4—23no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—23no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—23no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—412no—
1130C2×C4C22×#4116yes—
1131C2×C4C22×#4112yes—
1132C2×C4C22×#4116yes—
1133C2×C4C2×2−1+412yes—
1134C2×C4C2×2−1+412yes—
1135C2×C4C2×2−1+412yes—
1136C2×C4C2×2−1+416yes—
1137C2×C4C2×2−1+416yes—
1138C2×C4#58512yes—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22C23×#4111yescharacteristic
1147C22C22×2−1+411yescharacteristic
1148C22C22×2−1+411yescharacteristic
1149C22C22×2−1+411yescharacteristic
1150C22C2×#58511yescharacteristic
1151C22H(7,𝔽2)11yescharacteristic
1152C222−1+611yescharacteristic
1153C4—26no—
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—41no—
1160C4—43no—
1161C4—43no—
1162C4—43no—
1163C4—41no—
1164C4—41no—
1165C4—43no—
1166C4—43no—
1167C4—41no—
1168C4—41no—
1169C4—43no—
1170C4—41no—
1171C4—43no—
1172C4—43no—
1173C4—43no—
1174C4—43no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—43no—
1179C4—43no—
1180C4—43no—
1181C4—43no—
1182C4C2×#541112yes—
1183C2—81no—
1184C2C22×#54111yescharacteristic
1185C2#6294711yescharacteristic
1186C2#6295211yescharacteristic
1187C2#6300011yescharacteristic
1188C2#6300711yescharacteristic
1189C2#6303811yescharacteristic
1190C2#6306111yescharacteristic
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. #42774C2semidirect
5. #42553C2semidirect
8. #40189C2semidirect
10. #40143C2semidirect
11. #40024C2semidirect
13. #39635C2semidirect
14. #37413C2semidirect
15. #37344C2semidirect
18. Q8×#125C2semidirect
19. #36475C2semidirect
20. #36466C2semidirect
22. #36447C2semidirect
23. #35971C2semidirect
26. #35868C2semidirect
29. #34337C2semidirect
30. #34337C2semidirect

Maximal subgroups

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

subgroupindex
#522832
#427742
#427732
#425622
#425532
#424612
#424552
#401892
#401552
#401432
#400242
#397882
#396352
#374132
#373442
#373282
Q8×#1262
Q8×#1252
#364752
#364662
#364482
#364472
#359712
#359202
#358832
#358682
#357862
#343372
#342622