Finite Group Databasebeta

← #7654178

Subgroups — #7654178

Order 512.

4295 conjugacy classes of subgroups.

The subgroup lattice has 1205 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42687C213yesmaximal, complemented
2#42657C213yesmaximal, complemented
3#42530C213yesmaximal, complemented
4#42469C213yesmaximal, complemented
5#40202C213yesmaximal, complemented
6#40130C213yesmaximal, complemented
7#40059C213yesmaximal, complemented
8#40051C213yesmaximal, complemented
9#39780C213yesmaximal, complemented
10#39250C213yesmaximal, complemented
11#39032C213yesmaximal, complemented
12#39027C213yesmaximal, complemented
13#37597C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic
15#36585C211yesmaximal, characteristic
16#36584C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36475C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic
21#36458C211yesmaximal, characteristic
22#36040C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic
26#35185C213yesmaximal, complemented
27#35116C213yesmaximal, complemented
28#34973C213yesmaximal, complemented
29#34263C211yesmaximal, characteristic
30C4×#557C211yesmaximal, characteristic, complemented
31C4×#557C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2864C2213yes—
38#2860C2213yes—
39#2860C2213yes—
40#2860C2213yes—
41#2860C2213yes—
42#2859C2213yes—
43#2833C2216yes—
44#2831C2216yes—
45#2798C2216yes—
46#2794C2216yes—
47#2789C2216yes—
48#2783C2216yes—
49#2776C2216yes—
50#2772C2216yes—
51#2766C2216yes—
52#2747C2216yes—
53#2747C2216yes—
54#2744C2216yes—
55#2744C2216yes—
56#2739C2216yes—
57#2722C2216yes—
58#2721C2216yes—
59#2690C2216yes—
60#2689C2216yes—
61#2664C2216yes—
62#2660C2213yes—
63#2655C2216yes—
64#2655C2216yes—
65#2654C2216yes—
66#2654C2216yes—
67#2650C2216yes—
68#2650C2216yes—
69#2647C2213yes—
70#2637C2216yes—
71#2629C2213yes—
72#2628C2213yes—
73#2584C2213yes—
74#2580C2213yes—
75#2571C2213yes—
76#2571C2213yes—
77#2571C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2570C2213yes—
84#2570C2213yes—
85#2567C2213yes—
86#2566C2213yes—
87#2563C2213yes—
88#2552C2213yes—
89#2552C2213yes—
90#2550C2213yes—
91#2550C2213yes—
92#2538C2213yes—
93#2524C2213yes—
94#2524C2213yes—
95#2524C2211yescharacteristic
96#2524C2213yes—
97#2519C2213yes—
98#2519C2213yes—
99#2519C2213yes—
100#2519C2213yes—
101#2513C2213yes—
102#2513C2213yes—
103#2513C2213yes—
104#2513C2213yes—
105#2513C2213yes—
106#2513C2213yes—
107#2513C2213yes—
108#2513C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2512C2213yes—
112#2512C2213yes—
113#2509C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2509C2213yes—
118#2509C2213yes—
119#2509C2213yes—
120#2509C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2508C2213yes—
125#2508C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2507C2213yes—
129#2507C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2497C2213yes—
134#2497C2213yes—
135#2496C2213yes—
136#2496C2213yes—
137#2496C2216yes—
138#2495C2213yes—
139#2495C2213yes—
140#2494C2213yes—
141#2494C2213yes—
142#2494C2213yes—
143#2494C2213yes—
144#2494C2213yes—
145#2494C2213yes—
146#2478C2216yes—
147#2475C2216yes—
148#2469C2213yes—
149#2469C2216yes—
150#2469C2213yes—
151#2469C2213yes—
152#2469C2213yes—
153#2462C2213yes—
154#2462C2213yes—
155#2462C2213yes—
156#2462C2213yes—
157#2454C2213yes—
158#2454C2213yes—
159#2454C2213yes—
160#2452C2213yes—
161#2442C2213yes—
162#2442C2213yes—
163#2442C2213yes—
164#2440C2213yes—
165#2421C2216yes—
166#2402C2213yes—
167#2399C2213yes—
168#2396C2213yes—
169#2396C2213yes—
170#2370C2213yes—
171#2370C2213yes—
172#2370C2213yes—
173#2370C2213yes—
174#2365C2213yes—
175#2365C2213yes—
176#2357C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2354C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2345C2213yes—
201#2344C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2334C2216yes—
209#2334C2216yes—
210#2323C2216yes—
211#2319C2213yes—
212#2314C2216yes—
213#2314C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2293C2213yes—
230#2276C2211yescharacteristic
231C42×Q8C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2213yes—
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2313yes—
247C2×#126C2316yes—
248C2×#126C2316yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×C22⋊Q8C2316yes—
258#520—28no—
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×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×#117C2313yes—
282C2×#117C2316yes—
283C22×C4⋊C4C2313yes—
284#401C2316yes—
285#401C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2313yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2311yescharacteristic
303#400C2313yes—
304#400C2311yescharacteristic
305#400C2313yes—
306#400C2313yes—
307#399C2313yes—
308#399C2316yes—
309#399C2313yes—
310#398C2313yes—
311#398C2316yes—
312#398C2316yes—
313#398C2316yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2313yes—
318#398C2313yes—
319#398C2313yes—
320#398C2316yes—
321#398C2316yes—
322#398C2311yescharacteristic
323#398C2313yes—
324#398C2313yes—
325#398C2316yes—
326#398C2311yescharacteristic
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#397C2316yes—
333#397C2316yes—
334#397C2316yes—
335#397C2316yes—
336#397C2316yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#396C2313yes—
343#396C2316yes—
344#396C2316yes—
345#396C2316yes—
346#396C2316yes—
347#396C2313yes—
348#396C2313yes—
349#396C2313yes—
350#395C2313yes—
351#395C2316yes—
352#395C2313yes—
353#395C2313yes—
354#395C2313yes—
355#395C2313yes—
356#395C2313yes—
357#393C2313yes—
358#393C2316yes—
359#393C2313yes—
360#391C2316yes—
361#391C2316yes—
362#391C2316yes—
363#390C2313yes—
364#390C2313yes—
365#390C2313yes—
366#390C2313yes—
367#390C2313yes—
368#390C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2313yes—
372#390C2313yes—
373#390C2313yes—
374#390C2313yes—
375#389C2313yes—
376#389C2313yes—
377#389C2313yes—
378#389C2313yes—
379#389C2313yes—
380#389C2313yes—
381#389C2313yes—
382#389C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2316yes—
396#389C2316yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#388C2313yes—
431#388C2313yes—
432#388C2313yes—
433#388C2313yes—
434#388C2313yes—
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2313yes—
448#388C2316yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#387C2311yescharacteristic
459#387C2311yescharacteristic
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2311yescharacteristic
471#387C2311yescharacteristic
472#387C2311yescharacteristic
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2311yescharacteristic
510#385C2316yes—
511#385C2316yes—
512#385C2316yes—
513#385C2316yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2316yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#383C2311yescharacteristic
523#383C2311yescharacteristic
524#383C2313yes—
525#383C2313yes—
526#382C2311yescharacteristic
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2316yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#381C2316yes—
546#380C2316yes—
547#380C2316yes—
548#380C2313yes—
549#380C2313yes—
550#380C2316yes—
551#380C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
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⋊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⋊C4C2311yescharacteristic
607C4×C4⋊C4C2311yescharacteristic
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615#376C2313yes—
616C43C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×D4C2413yes—
628C23×C4C2413yes—
629C23×C4C2416yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632#126—412no—
633#126—412no—
634#126—46no—
635#126—46no—
636#126—46no—
637#126—46no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—46no—
643#125—46no—
644#125—46no—
645#125—46no—
646C22⋊Q8—412no—
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—24no—
659C4×Q8—24no—
660C4×Q8—212no—
661C4×Q8—212no—
662C4×Q8—46no—
663C4×Q8—46no—
664C4×Q8—46no—
665C4×Q8—46no—
666C4×Q8#4118yes—
667C4×D4—212no—
668C4×D4—212no—
669#117—212no—
670#117—412no—
671C2×C4⋊C4—212no—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2416yes—
750C2×C22⋊C4C2416yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2416yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2416yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2411yescharacteristic
781C2×C42C2413yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2416yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798#95C2411yescharacteristic
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2411yescharacteristic
803#95C2411yescharacteristic
804#95C2411yescharacteristic
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2411yescharacteristic
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2416yes—
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2416yes—
821#95C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2416yes—
839#95C2416yes—
840#95C2416yes—
841#95C2416yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872C24C2513yes—
873#41—416no—
874C2×Q8—26no—
875C2×Q8—26no—
876C2×Q8—26no—
877C2×Q8—43no—
878C2×Q8—43no—
879C2×Q8—43no—
880C2×Q8C2×#4114yes—
881C2×Q82−1+414yes—
882C2×Q82−1+414yes—
883C2×D4—26no—
884C2×D4—26no—
885C2×D4—26no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—212no—
890C22×C4—46no—
891C22×C4—46no—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2511yescharacteristic
899C22×C4C2511yescharacteristic
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—212no—
936C4⋊C4—212no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—26no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—46no—
961C4⋊C4—43no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—46no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—46no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4C2×#41112yes—
993C22⋊C4—26no—
994C22⋊C4—26no—
995C22⋊C4—26no—
996C22⋊C4—26no—
997C22⋊C4—26no—
998C22⋊C4—26no—
999C22⋊C4—46no—
1000C22⋊C4—46no—
1001C22⋊C4—46no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—46no—
1007C22⋊C4—46no—
1008C22⋊C4—46no—
1009C22⋊C4—43no—
1010C22⋊C4—43no—
1011C22⋊C4—43no—
1012C22⋊C4—43no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—22no—
1028C42—22no—
1029C42—26no—
1030C42—22no—
1031C42—26no—
1032C42—22no—
1033C42—22no—
1034C42—46no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—43no—
1039C42—43no—
1040C42—43no—
1041C42—43no—
1042C42—43no—
1043C42—43no—
1044C42—43no—
1045C42—43no—
1046C42—43no—
1047C42C2×#41112yes—
1048C23—23no—
1049C23—23no—
1050C23—23no—
1051C23—23no—
1052C23—23no—
1053C23—23no—
1054C23—23no—
1055C23C2611yescharacteristic
1056Q8—412no—
1057Q8—412no—
1058Q8#541116yes—
1059D4—412no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—23no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—23no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—412no—
1142C2×C4—812no—
1143C2×C4C22×#4112yes—
1144C2×C4C22×#4116yes—
1145C2×C4C22×#4116yes—
1146C2×C4C2×2−1+416yes—
1147C2×C4C2×2−1+416yes—
1148C2×C4#58512yes—
1149C2×C4#58512yes—
1150C2×C4#58512yes—
1151C2×C4#58512yes—
1152C22—43no—
1153C22—43no—
1154C22—43no—
1155C22—43no—
1156C22—43no—
1157C22—43no—
1158C22—43no—
1159C22C23×#4111yescharacteristic
1160C22C22×2−1+411yescharacteristic
1161C22C22×2−1+411yescharacteristic
1162C22C2×#58511yescharacteristic
1163C22C2×#58511yescharacteristic
1164C22C2×#58511yescharacteristic
1165C22C2×#58511yescharacteristic
1166C4—22no—
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—26no—
1171C4—22no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—43no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—43no—
1180C4—43no—
1181C4—41no—
1182C4—41no—
1183C4—43no—
1184C4—43no—
1185C4—41no—
1186C4—41no—
1187C4—43no—
1188C4—43no—
1189C4—43no—
1190C4—41no—
1191C4—41no—
1192C4—43no—
1193C4—43no—
1194C4—41no—
1195C4C2×#541112yes—
1196C2—83no—
1197C2C22×#54111yescharacteristic
1198C2#6279311yescharacteristic
1199C2#6281011yescharacteristic
1200C2#6303311yescharacteristic
1201C2#6303311yescharacteristic
1202C2#6303311yescharacteristic
1203C2#6303411yescharacteristic
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. #42687C2semidirect
2. #42657C2semidirect
3. #42530C2semidirect
4. #42469C2semidirect
5. #40202C2semidirect
6. #40130C2semidirect
7. #40059C2semidirect
8. #40051C2semidirect
9. #39780C2semidirect
10. #39250C2semidirect
11. #39032C2semidirect
12. #39027C2semidirect
13. #37597C2semidirect
16. #36584C2semidirect
17. #36475C2semidirect
18. #36475C2semidirect
19. #36475C2semidirect
23. #35971C2semidirect
24. #35957C2semidirect
26. #35185C2semidirect
27. #35116C2semidirect
28. #34973C2semidirect
30. C4×#557C2semidirect
31. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#426872
#426572
#425302
#424692
#402022
#401302
#400592
#400512
#397802
#392502
#390322
#390272
#375972
#365852
#365842
#364752
#364582
#360402
#359712
#359572
#358162
#351852
#351162
#349732
#342632
C4×#5572