Finite Group Databasebeta

← #7658672

Subgroups — #7658672

Order 512.

4037 conjugacy classes of subgroups.

The subgroup lattice has 1177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42782C213yesmaximal, complemented
2#42780C213yesmaximal
3#42774C213yesmaximal, complemented
4#42773C213yesmaximal
5#42765C213yesmaximal, complemented
6#42764C213yesmaximal
7#42716C213yesmaximal
8#42710C213yesmaximal, complemented
9#42527C213yesmaximal, complemented
10#42511C213yesmaximal, complemented
11#42470C213yesmaximal
12#42461C213yesmaximal
13#37638C213yesmaximal, complemented
14#37597C213yesmaximal
15#37580C213yesmaximal, complemented
16#36700C213yesmaximal
17#35971C211yesmaximal, characteristic, complemented
18#35971C211yesmaximal, characteristic, complemented
19#35957C211yesmaximal, characteristic, complemented
20#35920C211yesmaximal, characteristic
21#35883C211yesmaximal, characteristic
22#35883C211yesmaximal, characteristic
23#35883C211yesmaximal, characteristic
24#35868C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35845C211yesmaximal, characteristic
28#35786C211yesmaximal, characteristic
29#34337C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2839C2213yes—
36#2839C2213yes—
37#2839C2213yes—
38#2839C2213yes—
39#2836C2213yes—
40#2836C2211yescharacteristic
41#2836C2213yes—
42#2836C2213yes—
43#2833C2213yes—
44#2833C2216yes—
45#2833C2213yes—
46#2833C2213yes—
47#2833C2213yes—
48#2831C2213yes—
49#2831C2213yes—
50#2831C2213yes—
51#2831C2213yes—
52#2802C2216yes—
53#2794C2216yes—
54#2776C2216yes—
55#2776C2216yes—
56#2772C2216yes—
57#2769C2216yes—
58#2766C2216yes—
59#2766C2216yes—
60#2758C2216yes—
61#2758C2216yes—
62#2755C2216yes—
63#2754C2216yes—
64#2725C2216yes—
65#2721C2216yes—
66#2719C2216yes—
67#2719C2216yes—
68#2666C2216yes—
69#2664C2216yes—
70#2660C2213yes—
71#2655C2216yes—
72#2655C2216yes—
73#2655C2216yes—
74#2655C2216yes—
75#2655C2216yes—
76#2654C2216yes—
77#2647C2213yes—
78#2647C2216yes—
79#2647C2213yes—
80#2647C2213yes—
81#2647C2213yes—
82#2647C2213yes—
83#2645C2213yes—
84#2645C2216yes—
85#2645C2213yes—
86#2645C2213yes—
87#2645C2213yes—
88#2634C2216yes—
89#2634C2216yes—
90#2629C2213yes—
91#2628C2213yes—
92#2584C2213yes—
93#2582C2213yes—
94#2581C2213yes—
95#2571C2213yes—
96#2571C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2567C2213yes—
103#2567C2213yes—
104#2565C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2552C2213yes—
108#2552C2213yes—
109#2552C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2533C2216yes—
113#2528C2216yes—
114#2514C2216yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2514C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2511C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2509C2213yes—
132#2508C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2507C2213yes—
140#2507C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2216yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2506C2213yes—
148#2497C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2496C2213yes—
152#2496C2213yes—
153#2496C2213yes—
154#2495C2213yes—
155#2495C2213yes—
156#2495C2213yes—
157#2494C2213yes—
158#2494C2213yes—
159#2494C2213yes—
160#2469C2216yes—
161#2462C2216yes—
162#2453C2213yes—
163#2453C2213yes—
164#2453C2213yes—
165#2451C2213yes—
166#2441C2213yes—
167#2441C2213yes—
168#2441C2213yes—
169#2439C2213yes—
170#2402C2213yes—
171#2402C2213yes—
172#2402C2213yes—
173#2402C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2401C2213yes—
179#2399C2213yes—
180#2396C2213yes—
181#2396C2213yes—
182#2370C2213yes—
183#2370C2213yes—
184#2370C2213yes—
185#2370C2213yes—
186#2369C2213yes—
187#2365C2213yes—
188#2356C2213yes—
189#2355C2213yes—
190#2355C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2213yes—
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212#2347C2213yes—
213#2346C2213yes—
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220#2331C2213yes—
221#2330C2213yes—
222#2330C2213yes—
223#2330C2213yes—
224#2320C2213yes—
225#2314C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2295C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2316yes—
244C2×#125C2313yes—
245C2×#125C2313yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2316yes—
249C2×#125C2316yes—
250C2×#125C2316yes—
251#519—28no—
252C2×C4×Q8C2313yes—
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2313yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
269C2×C4×Q8C2316yes—
270C2×C4×Q8C2311yescharacteristic
271C2×#117C2313yes—
272C2×#117C2313yes—
273#401C2313yes—
274#401C2313yes—
275#401C2313yes—
276#401C2313yes—
277#401C2316yes—
278#401C2316yes—
279#401C2316yes—
280#400C2313yes—
281#400C2313yes—
282#400C2313yes—
283#400C2316yes—
284#400C2316yes—
285#400C2313yes—
286#400C2313yes—
287#400C2313yes—
288#400C2313yes—
289#400C2313yes—
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2311yescharacteristic
297#400C2313yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2311yescharacteristic
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#399C2311yescharacteristic
332#399C2313yes—
333#399C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2311yescharacteristic
349#398C2311yescharacteristic
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2316yes—
359#398C2316yes—
360#398C2311yescharacteristic
361#398C2311yescharacteristic
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#398C2316yes—
373#398C2316yes—
374#397C2311yescharacteristic
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2311yescharacteristic
383#397C2311yescharacteristic
384#397C2313yes—
385#397C2313yes—
386#396C2311yescharacteristic
387#396C2311yescharacteristic
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2316yes—
395#395C2313yes—
396#395C2313yes—
397#395C2316yes—
398#395C2316yes—
399#395C2313yes—
400#395C2313yes—
401#395C2313yes—
402#395C2313yes—
403#393C2313yes—
404#393C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2316yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2316yes—
421#391C2316yes—
422#391C2313yes—
423#391C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2316yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2311yescharacteristic
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2316yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2316yes—
467#389C2316yes—
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2316yes—
480#389C2316yes—
481#389C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2311yescharacteristic
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2316yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2316yes—
537#384C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#383C2316yes—
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#382C2316yes—
558#382C2316yes—
559#382C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
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⋊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×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
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—
631#126—86no—
632#125—212no—
633#125—212no—
634#125—212no—
635#125—212no—
636#125—86no—
637#125—86no—
638#125—86no—
639C4×Q8—24no—
640C4×Q8—24no—
641C4×Q8—24no—
642C4×Q8—24no—
643C4×Q8—24no—
644C4×Q8—24no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—212no—
653C4×Q8—212no—
654C4×Q8—212no—
655C4×Q8—212no—
656C4×Q8—86no—
657C4×Q8#4118yes—
658#117—212no—
659#117—212no—
660C2×C4⋊C4C2413yes—
661C2×C4⋊C4C2413yes—
662C2×C4⋊C4C2413yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2413yes—
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
682C2×C4⋊C4C2416yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2416yes—
685C2×C4⋊C4C2416yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2416yes—
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⋊C4C2416yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2416yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2411yescharacteristic
742C2×C22⋊C4C2411yescharacteristic
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C42C2416yes—
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×C42C2413yes—
764C2×C42C2416yes—
765C2×C42C2416yes—
766C2×C42C2416yes—
767C2×C42C2411yescharacteristic
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2416yes—
771C2×C42C2416yes—
772C2×C42C2413yes—
773#95C2411yescharacteristic
774#95C2411yescharacteristic
775#95C2411yescharacteristic
776#95C2411yescharacteristic
777#95C2411yescharacteristic
778#95C2413yes—
779#95C2413yes—
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#95C2413yes—
795#95C2416yes—
796#95C2416yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2416yes—
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2416yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2416yes—
834#95C2416yes—
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#95C2416yes—
852#95C2416yes—
853#95C2416yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861C24C2511yescharacteristic
862C2×Q8—26no—
863C2×Q8—26no—
864C2×Q8—26no—
865C2×Q8—26no—
866C2×Q8—26no—
867C2×Q8—43no—
868C2×Q8—43no—
869C2×Q8—43no—
870C2×Q8—43no—
871C2×Q8—416no—
872C2×Q8C2×#4114yes—
873C2×Q82−1+414yes—
874C2×Q82−1+414yes—
875C22×C4—26no—
876C22×C4—26no—
877C22×C4—26no—
878C22×C4C2513yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2513yes—
887C22×C4C2513yes—
888C22×C4C2513yes—
889C22×C4C2513yes—
890C22×C4C2513yes—
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2511yescharacteristic
907C22×C4C2513yes—
908C4⋊C4—26no—
909C4⋊C4—26no—
910C4⋊C4—26no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—26no—
914C4⋊C4—26no—
915C4⋊C4—26no—
916C4⋊C4—26no—
917C4⋊C4—26no—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—212no—
922C4⋊C4—212no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—43no—
932C4⋊C4—43no—
933C4⋊C4—46no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—43no—
939C4⋊C4—43no—
940C4⋊C4—43no—
941C4⋊C4—43no—
942C4⋊C4—43no—
943C4⋊C4—43no—
944C4⋊C4—43no—
945C4⋊C4—43no—
946C4⋊C4—43no—
947C4⋊C4—43no—
948C4⋊C4—43no—
949C4⋊C4—46no—
950C4⋊C4—43no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—46no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—43no—
963C4⋊C4—46no—
964C4⋊C4—41no—
965C4⋊C4—43no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—46no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—46no—
974C4⋊C4—43no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—46no—
981C4⋊C4—46no—
982C4⋊C4C2×#41112yes—
983C22⋊C4—26no—
984C22⋊C4—22no—
985C22⋊C4—41no—
986C22⋊C4—43no—
987C22⋊C4—43no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—43no—
993C22⋊C4—41no—
994C22⋊C4—43no—
995C22⋊C4—43no—
996C22⋊C4—43no—
997C42—26no—
998C42—212no—
999C42—26no—
1000C42—26no—
1001C42—26no—
1002C42—26no—
1003C42—26no—
1004C42—26no—
1005C42—26no—
1006C42—26no—
1007C42—26no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—43no—
1012C42—46no—
1013C42—43no—
1014C42—41no—
1015C42—46no—
1016C42—43no—
1017C42—46no—
1018C42—46no—
1019C42—46no—
1020C42C2×#41112yes—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23C2611yescharacteristic
1029Q8—412no—
1030Q8—412no—
1031Q8—86no—
1032Q8#541116yes—
1033C2×C4—21no—
1034C2×C4—23no—
1035C2×C4—23no—
1036C2×C4—21no—
1037C2×C4—23no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—23no—
1045C2×C4—23no—
1046C2×C4—23no—
1047C2×C4—23no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—23no—
1057C2×C4—23no—
1058C2×C4—23no—
1059C2×C4—23no—
1060C2×C4—23no—
1061C2×C4—23no—
1062C2×C4—23no—
1063C2×C4—23no—
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—23no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—23no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—23no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—23no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—412no—
1119C2×C4C22×#4116yes—
1120C2×C4C22×#4112yes—
1121C2×C4C22×#4116yes—
1122C2×C4C2×2−1+416yes—
1123C2×C4C2×2−1+416yes—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22C23×#4111yescharacteristic
1132C22C22×2−1+411yescharacteristic
1133C22C22×2−1+411yescharacteristic
1134C22H(7,𝔽2)11yescharacteristic
1135C222−1+611yescharacteristic
1136C222−1+611yescharacteristic
1137C222−1+611yescharacteristic
1138C4—22no—
1139C4—26no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—43no—
1147C4—43no—
1148C4—41no—
1149C4—41no—
1150C4—43no—
1151C4—43no—
1152C4—43no—
1153C4—43no—
1154C4—43no—
1155C4—43no—
1156C4—43no—
1157C4—41no—
1158C4—43no—
1159C4—43no—
1160C4—43no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—43no—
1165C4—41no—
1166C4—43no—
1167C4C2×#541112yes—
1168C2—81no—
1169C2C22×#54111yescharacteristic
1170C2#6285111yescharacteristic
1171C2#6286111yescharacteristic
1172C2#6305711yescharacteristic
1173C2#6305711yescharacteristic
1174C2#6306111yescharacteristic
1175C2#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
1. #42782C2semidirect
3. #42774C2semidirect
5. #42765C2semidirect
8. #42710C2semidirect
9. #42527C2semidirect
10. #42511C2semidirect
13. #37638C2semidirect
15. #37580C2semidirect
17. #35971C2semidirect
18. #35971C2semidirect
19. #35957C2semidirect
24. #35868C2semidirect
25. #35868C2semidirect
26. #35868C2semidirect
29. #34337C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#427822
#427802
#427742
#427732
#427652
#427642
#427162
#427102
#425272
#425112
#424702
#424612
#376382
#375972
#375802
#367002
#359712
#359572
#359202
#358832
#358682
#358452
#357862
#343372
#343362
#342622