Finite Group Databasebeta

← #7661959

Subgroups — #7661959

Order 512.

4095 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52283C213yesmaximal
2#42765C213yesmaximal, complemented
3#42764C213yesmaximal
4#42738C213yesmaximal
5#42733C213yesmaximal, complemented
6#42663C213yesmaximal
7#42657C213yesmaximal
8#40107C213yesmaximal, complemented
9#40082C213yesmaximal, complemented
10#40075C213yesmaximal
11#40024C213yesmaximal, complemented
12#39762C213yesmaximal, complemented
13#39225C213yesmaximal
14#37413C213yesmaximal, complemented
15#37344C213yesmaximal, complemented
16#37328C213yesmaximal
17#36584C211yesmaximal, characteristic, complemented
18#36475C211yesmaximal, characteristic, complemented
19#36466C211yesmaximal, characteristic, complemented
20#36448C211yesmaximal, characteristic
21#36448C211yesmaximal, characteristic
22#36447C211yesmaximal, characteristic, complemented
23#35971C211yesmaximal, characteristic, complemented
24#35883C211yesmaximal, characteristic
25#35883C211yesmaximal, characteristic
26#35868C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic
28#35786C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2863C2213yes—
37#2863C2213yes—
38#2859C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2833C2216yes—
42#2831C2216yes—
43#2802C2216yes—
44#2802C2213yes—
45#2798C2213yes—
46#2794C2213yes—
47#2789C2213yes—
48#2783C2211yescharacteristic
49#2783C2216yes—
50#2776C2216yes—
51#2776C2216yes—
52#2776C2213yes—
53#2776C2216yes—
54#2776C2216yes—
55#2772C2216yes—
56#2772C2213yes—
57#2769C2216yes—
58#2766C2216yes—
59#2766C2216yes—
60#2766C2213yes—
61#2766C2216yes—
62#2762C2216yes—
63#2762C2216yes—
64#2758C2216yes—
65#2758C2213yes—
66#2755C2216yes—
67#2754C2213yes—
68#2725C2213yes—
69#2725C2213yes—
70#2725C2216yes—
71#2721C2213yes—
72#2719C2213yes—
73#2719C2216yes—
74#2719C2216yes—
75#2719C2216yes—
76#2716C2213yes—
77#2713C2213yes—
78#2666C2216yes—
79#2655C2216yes—
80#2655C2216yes—
81#2654C2216yes—
82#2650C2216yes—
83#2647C2213yes—
84#2647C2213yes—
85#2645C2213yes—
86#2645C2213yes—
87#2642C2216yes—
88#2629C2213yes—
89#2629C2213yes—
90#2584C2213yes—
91#2584C2213yes—
92#2582C2213yes—
93#2582C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2571C2213yes—
97#2571C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2565C2213yes—
103#2565C2213yes—
104#2552C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2551C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2533C2216yes—
111#2528C2216yes—
112#2524C2216yes—
113#2519C2216yes—
114#2514C2216yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2216yes—
118#2514C2213yes—
119#2514C2213yes—
120#2514C2213yes—
121#2514C2213yes—
122#2514C2213yes—
123#2514C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2511C2213yes—
127#2511C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2509C2213yes—
132#2509C2213yes—
133#2509C2213yes—
134#2509C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2508C2213yes—
138#2508C2213yes—
139#2508C2213yes—
140#2507C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2506C2213yes—
148#2497C2213yes—
149#2497C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2495C2213yes—
153#2495C2213yes—
154#2495C2213yes—
155#2495C2213yes—
156#2494C2213yes—
157#2494C2213yes—
158#2494C2213yes—
159#2494C2213yes—
160#2453C2213yes—
161#2453C2213yes—
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#2369C2213yes—
179#2369C2213yes—
180#2356C2213yes—
181#2355C2213yes—
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
195Q8×C4⋊C4C2211yescharacteristic
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#2347C2213yes—
205#2346C2213yes—
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2336C2216yes—
213#2331C2213yes—
214#2331C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2330C2216yes—
218#2320C2213yes—
219#2314C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
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×#126C2313yes—
245C2×#126C2313yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2316yes—
254C2×#125C2316yes—
255#519—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
274C2×#117C2313yes—
275C2×#117C2313yes—
276#401C2316yes—
277#401C2316yes—
278#401C2316yes—
279#401C2316yes—
280#401C2313yes—
281#401C2313yes—
282#400C2313yes—
283#400C2316yes—
284#400C2316yes—
285#400C2316yes—
286#400C2313yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2313yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2313yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2311yescharacteristic
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2316yes—
317#399C2313yes—
318#399C2313yes—
319#398C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2313yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2311yescharacteristic
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#397C2313yes—
345#397C2316yes—
346#397C2316yes—
347#397C2313yes—
348#397C2313yes—
349#397C2311yescharacteristic
350#397C2311yescharacteristic
351#397C2313yes—
352#396C2313yes—
353#396C2316yes—
354#396C2313yes—
355#396C2313yes—
356#396C2316yes—
357#396C2311yescharacteristic
358#396C2311yescharacteristic
359#396C2313yes—
360#395C2316yes—
361#395C2313yes—
362#395C2316yes—
363#395C2313yes—
364#393C2313yes—
365#393C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2313yes—
374#391C2313yes—
375#391C2316yes—
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#389C2311yescharacteristic
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2311yescharacteristic
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2316yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2316yes—
440#389C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#388C2311yescharacteristic
455#388C2311yescharacteristic
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2316yes—
462#388C2313yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2311yescharacteristic
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2311yescharacteristic
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2316yes—
479#387C2316yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
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#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2316yes—
521#387C2311yescharacteristic
522#387C2311yescharacteristic
523#387C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#383C2313yes—
535#383C2313yes—
536#383C2316yes—
537#383C2316yes—
538#383C2316yes—
539#383C2316yes—
540#383C2316yes—
541#382C2311yescharacteristic
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2316yes—
554#382C2313yes—
555#382C2313yes—
556#382C2316yes—
557#382C2316yes—
558#382C2316yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
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⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2316yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2316yes—
586C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
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—46no—
632#126—46no—
633#126—46no—
634#125—212no—
635#125—212no—
636#125—212no—
637#125—212no—
638#125—46no—
639#125—412no—
640#125—46no—
641#125—412no—
642#125—46no—
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—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—212no—
657C4×Q8—212no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8#4118yes—
661#117—212no—
662#117—212no—
663C2×C4⋊C4C2413yes—
664C2×C4⋊C4C2413yes—
665C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2416yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2416yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2416yes—
711C2×C4⋊C4C2416yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
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⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C22⋊C4C2413yes—
737C2×C22⋊C4C2411yescharacteristic
738C2×C22⋊C4C2411yescharacteristic
739C2×C22⋊C4C2411yescharacteristic
740C2×C22⋊C4C2413yes—
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C42C2416yes—
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×C42C2411yescharacteristic
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2416yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2416yes—
778C2×C42C2416yes—
779C2×C42C2413yes—
780#95C2411yescharacteristic
781#95C2411yescharacteristic
782#95C2411yescharacteristic
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#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2411yescharacteristic
808#95C2413yes—
809#95C2413yes—
810#95C2416yes—
811#95C2411yescharacteristic
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2411yescharacteristic
822#95C2416yes—
823#95C2416yes—
824#95C2411yescharacteristic
825#95C2416yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2416yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2416yes—
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—26no—
879C22×C4—26no—
880C22×C4—26no—
881C22×C4C2513yes—
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2513yes—
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2513yes—
890C22×C4C2511yescharacteristic
891C22×C4C2513yes—
892C22×C4C2513yes—
893C22×C4C2513yes—
894C22×C4C2511yescharacteristic
895C22×C4C2513yes—
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C4⋊C4—26no—
912C4⋊C4—26no—
913C4⋊C4—26no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—26no—
917C4⋊C4—26no—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—212no—
925C4⋊C4—212no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—22no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—43no—
948C4⋊C4—43no—
949C4⋊C4—41no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—43no—
953C4⋊C4—43no—
954C4⋊C4—43no—
955C4⋊C4—41no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—46no—
960C4⋊C4—46no—
961C4⋊C4—41no—
962C4⋊C4—46no—
963C4⋊C4—46no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—46no—
971C4⋊C4—46no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4C2×#41112yes—
984C22⋊C4—26no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—43no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—43no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—43no—
995C22⋊C4—43no—
996C22⋊C4—43no—
997C22⋊C4—43no—
998C42—26no—
999C42—212no—
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—22no—
1013C42—26no—
1014C42—43no—
1015C42—46no—
1016C42—43no—
1017C42—41no—
1018C42—43no—
1019C42—43no—
1020C42—46no—
1021C42—41no—
1022C42—43no—
1023C42—46no—
1024C42—43no—
1025C42—43no—
1026C42—43no—
1027C42C2×#41112yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23C2611yescharacteristic
1036Q8—412no—
1037Q8—86no—
1038Q8—86no—
1039Q8#541116yes—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—23no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—23no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—23no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—23no—
1057C2×C4—23no—
1058C2×C4—23no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
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—23no—
1081C2×C4—21no—
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—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—23no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—412no—
1124C2×C4C22×#4116yes—
1125C2×C4C22×#4112yes—
1126C2×C4C22×#4116yes—
1127C2×C4C2×2−1+416yes—
1128C2×C4C2×2−1+416yes—
1129C2×C4#58512yes—
1130C2×C4#58512yes—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22C23×#4111yescharacteristic
1139C22C22×2−1+411yescharacteristic
1140C22C22×2−1+411yescharacteristic
1141C22C2×#58511yescharacteristic
1142C22C2×#58511yescharacteristic
1143C222−1+611yescharacteristic
1144C222−1+611yescharacteristic
1145C4—22no—
1146C4—26no—
1147C4—22no—
1148C4—22no—
1149C4—43no—
1150C4—41no—
1151C4—41no—
1152C4—43no—
1153C4—43no—
1154C4—41no—
1155C4—43no—
1156C4—43no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—43no—
1161C4—43no—
1162C4—43no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—43no—
1167C4—43no—
1168C4—41no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—43no—
1174C4C2×#541112yes—
1175C2—81no—
1176C2C22×#54111yescharacteristic
1177C2#6294911yescharacteristic
1178C2#6294911yescharacteristic
1179C2#6300711yescharacteristic
1180C2#6300911yescharacteristic
1181C2#6303411yescharacteristic
1182C2#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. #42765C2semidirect
5. #42733C2semidirect
8. #40107C2semidirect
9. #40082C2semidirect
11. #40024C2semidirect
12. #39762C2semidirect
14. #37413C2semidirect
15. #37344C2semidirect
17. #36584C2semidirect
18. #36475C2semidirect
19. #36466C2semidirect
22. #36447C2semidirect
23. #35971C2semidirect
26. #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
#522832
#427652
#427642
#427382
#427332
#426632
#426572
#401072
#400822
#400752
#400242
#397622
#392252
#374132
#373442
#373282
#365842
#364752
#364662
#364482
#364472
#359712
#358832
#358682
#357862
#343362
#342622