Finite Group Databasebeta

← #7653365

Subgroups — #7653365

Order 512.

4237 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42703C213yesmaximal, complemented
2#42670C213yesmaximal
3#42511C213yesmaximal, complemented
4#42461C213yesmaximal
5#40227C213yesmaximal
6#40155C213yesmaximal
7#40143C213yesmaximal, complemented
8#40107C213yesmaximal, complemented
9#39653C213yesmaximal, complemented
10#39534C213yesmaximal
11#39526C213yesmaximal, complemented
12#39225C213yesmaximal
13#37592C213yesmaximal
14Q8×#126C211yesmaximal, characteristic
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic
19#36448C211yesmaximal, characteristic
20#36448C211yesmaximal, characteristic
21#36447C211yesmaximal, characteristic, complemented
22#35971C211yesmaximal, characteristic, complemented
23#35937C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic
25#35711C211yesmaximal, characteristic
26#35187C213yesmaximal, complemented
27#35115C213yesmaximal, complemented
28#34973C213yesmaximal
29#34262C211yesmaximal, characteristic
30C4×Q82C211yesmaximal, characteristic, complemented
31C4×#557C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2864C2213yes—
38#2863C2213yes—
39#2863C2213yes—
40#2863C2213yes—
41#2863C2213yes—
42#2859C2213yes—
43#2839C2216yes—
44#2836C2216yes—
45#2802C2216yes—
46#2798C2216yes—
47#2789C2216yes—
48#2776C2216yes—
49#2772C2216yes—
50#2766C2216yes—
51#2762C2216yes—
52#2762C2216yes—
53#2758C2216yes—
54#2758C2216yes—
55#2755C2216yes—
56#2755C2216yes—
57#2725C2216yes—
58#2719C2216yes—
59#2716C2216yes—
60#2713C2216yes—
61#2666C2216yes—
62#2660C2213yes—
63#2655C2216yes—
64#2655C2216yes—
65#2655C2216yes—
66#2650C2216yes—
67#2647C2213yes—
68#2637C2216yes—
69#2634C2216yes—
70#2634C2216yes—
71#2629C2213yes—
72#2628C2213yes—
73#2584C2213yes—
74#2582C2213yes—
75#2581C2213yes—
76#2571C2213yes—
77#2571C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2570C2213yes—
84#2570C2213yes—
85#2568C2213yes—
86#2565C2213yes—
87#2552C2213yes—
88#2551C2213yes—
89#2551C2213yes—
90#2550C2213yes—
91#2550C2213yes—
92#2546C2213yes—
93#2533C2216yes—
94#2528C2216yes—
95#2524C2216yes—
96#2524C2213yes—
97#2524C2213yes—
98#2524C2213yes—
99#2524C2213yes—
100#2519C2213yes—
101#2519C2213yes—
102#2519C2213yes—
103#2519C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2216yes—
107#2514C2213yes—
108#2514C2213yes—
109#2514C2213yes—
110#2514C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2511C2213yes—
115#2511C2213yes—
116#2511C2213yes—
117#2509C2213yes—
118#2509C2213yes—
119#2509C2213yes—
120#2509C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2508C2213yes—
125#2508C2213yes—
126#2508C2213yes—
127#2508C2213yes—
128#2507C2213yes—
129#2507C2213yes—
130#2507C2213yes—
131#2507C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2506C2213yes—
135#2506C2213yes—
136#2506C2213yes—
137#2497C2213yes—
138#2497C2213yes—
139#2497C2213yes—
140#2496C2213yes—
141#2496C2213yes—
142#2496C2213yes—
143#2495C2213yes—
144#2495C2213yes—
145#2495C2213yes—
146#2494C2213yes—
147#2494C2213yes—
148#2494C2213yes—
149#2469C2213yes—
150#2469C2211yescharacteristic
151#2469C2213yes—
152#2469C2213yes—
153#2462C2213yes—
154#2462C2213yes—
155#2462C2213yes—
156#2462C2213yes—
157#2453C2213yes—
158#2451C2213yes—
159#2451C2213yes—
160#2451C2213yes—
161#2446C2216yes—
162#2441C2213yes—
163#2439C2213yes—
164#2439C2213yes—
165#2439C2213yes—
166#2402C2213yes—
167#2399C2213yes—
168#2396C2213yes—
169#2396C2213yes—
170#2370C2213yes—
171#2370C2213yes—
172#2369C2213yes—
173#2369C2213yes—
174#2369C2213yes—
175#2365C2213yes—
176#2356C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190Q8×C4⋊C4C2213yes—
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2347C2213yes—
201#2346C2213yes—
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2336C2216yes—
209#2336C2216yes—
210#2327C2216yes—
211#2320C2213yes—
212#2320C2216yes—
213#2314C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2276C2211yescharacteristic
231C42×Q8C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239Q82—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2316yes—
246C2×#126C2311yescharacteristic
247C2×#126C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
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×Q8C2311yescharacteristic
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2311yescharacteristic
281C2×#117C2313yes—
282C2×#117C2313yes—
283#401C2316yes—
284#401C2316yes—
285#401C2316yes—
286#400C2313yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2313yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2311yescharacteristic
310#400C2313yes—
311#400C2313yes—
312#399C2313yes—
313#399C2313yes—
314#398C2313yes—
315#398C2316yes—
316#398C2313yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#396C2313yes—
342#396C2316yes—
343#396C2316yes—
344#396C2311yescharacteristic
345#396C2313yes—
346#396C2313yes—
347#395C2313yes—
348#395C2313yes—
349#395C2316yes—
350#395C2316yes—
351#395C2316yes—
352#395C2313yes—
353#395C2311yescharacteristic
354#395C2313yes—
355#395C2313yes—
356#393C2316yes—
357#393C2311yescharacteristic
358#393C2313yes—
359#391C2316yes—
360#391C2316yes—
361#391C2316yes—
362#391C2316yes—
363#391C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2316yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2316yes—
372#391C2313yes—
373#391C2313yes—
374#391C2316yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#389C2311yescharacteristic
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#389C2316yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2316yes—
400#389C2316yes—
401#389C2313yes—
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#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#388C2311yescharacteristic
437#388C2311yescharacteristic
438#388C2311yescharacteristic
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#388C2311yescharacteristic
453#387C2313yes—
454#387C2313yes—
455#387C2313yes—
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2311yescharacteristic
466#387C2311yescharacteristic
467#387C2311yescharacteristic
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2316yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
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#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#383C2313yes—
525#383C2313yes—
526#383C2313yes—
527#383C2313yes—
528#383C2316yes—
529#383C2316yes—
530#383C2316yes—
531#383C2316yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2316yes—
547#382C2313yes—
548#382C2316yes—
549#382C2316yes—
550#380C2313yes—
551#380C2313yes—
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⋊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⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2316yes—
615#376C2313yes—
616C43C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—412no—
635#126—24no—
636#126—46no—
637#126—46no—
638#126—46no—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—46no—
643#125—412no—
644#125—46no—
645#125—46no—
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—24no—
659C4×Q8—212no—
660C4×Q8—24no—
661C4×Q8—212no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—412no—
665C4×Q8—46no—
666C4×Q8—46no—
667C4×Q8—46no—
668C4×Q8#4118yes—
669#117—212no—
670#117—212no—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2416yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2411yescharacteristic
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C42C2416yes—
758C2×C42C2413yes—
759C2×C42C2411yescharacteristic
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2411yescharacteristic
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2416yes—
792C2×C42C2413yes—
793#95C2411yescharacteristic
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2416yes—
800#95C2416yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2416yes—
821#95C2413yes—
822#95C2413yes—
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2416yes—
834#95C2413yes—
835#95C2416yes—
836#95C2416yes—
837#95C2416yes—
838#95C2416yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871C24C2511yescharacteristic
872C2×Q8—22no—
873C2×Q8—26no—
874C2×Q8—26no—
875C2×Q8—212no—
876C2×Q8—22no—
877C2×Q8—26no—
878C2×Q8—26no—
879C2×Q8—22no—
880C2×Q8—26no—
881C2×Q8—43no—
882C2×Q8—46no—
883C2×Q8—46no—
884C2×Q8—416no—
885C2×Q8C2×#4114yes—
886C2×Q82−1+414yes—
887C2×Q82−1+414yes—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4C2513yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2513yes—
896C22×C4C2513yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2513yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2513yes—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—22no—
925C4⋊C4—26no—
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—212no—
935C4⋊C4—22no—
936C4⋊C4—22no—
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—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—26no—
959C4⋊C4—22no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—46no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—46no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—46no—
973C4⋊C4—46no—
974C4⋊C4—43no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—46no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4C2×#41112yes—
992C4⋊C42−1+414yes—
993C22⋊C4—26no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—43no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C42—26no—
1008C42—212no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—22no—
1014C42—22no—
1015C42—22no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—22no—
1026C42—22no—
1027C42—26no—
1028C42—26no—
1029C42—26no—
1030C42—26no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—43no—
1039C42—43no—
1040C42—43no—
1041C42—46no—
1042C42C2×#41112yes—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23C2611yescharacteristic
1051Q8—28no—
1052Q8—412no—
1053Q8—412no—
1054Q8—812no—
1055Q8#541116yes—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
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—23no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
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—21no—
1129C2×C4—23no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—412no—
1136C2×C4C22×#4116yes—
1137C2×C4C22×#4112yes—
1138C2×C4C22×#4116yes—
1139C2×C4C2×2−1+412yes—
1140C2×C4C2×2−1+412yes—
1141C2×C4C2×2−1+412yes—
1142C2×C4C2×2−1+416yes—
1143C2×C4C2×2−1+416yes—
1144C2×C4#58512yes—
1145C2×C4#58512yes—
1146C2×C4#58512yes—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22C23×#4111yescharacteristic
1155C22C22×2−1+411yescharacteristic
1156C22C22×2−1+411yescharacteristic
1157C22C22×2−1+411yescharacteristic
1158C22C2×#58511yescharacteristic
1159C22C2×#58511yescharacteristic
1160C22C2×#58511yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—22no—
1167C4—26no—
1168C4—22no—
1169C4—41no—
1170C4—43no—
1171C4—41no—
1172C4—41no—
1173C4—43no—
1174C4—43no—
1175C4—43no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—41no—
1180C4—41no—
1181C4—43no—
1182C4—43no—
1183C4—41no—
1184C4—43no—
1185C4—41no—
1186C4—43no—
1187C4—43no—
1188C4—43no—
1189C4—43no—
1190C4C2×#541112yes—
1191C2—81no—
1192C2C22×#54111yescharacteristic
1193C2#6278811yescharacteristic
1194C2#6281011yescharacteristic
1195C2#6303211yescharacteristic
1196C2#6303411yescharacteristic
1197C2#6303411yescharacteristic
1198C2#6303811yescharacteristic
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. #42703C2semidirect
3. #42511C2semidirect
7. #40143C2semidirect
8. #40107C2semidirect
9. #39653C2semidirect
11. #39526C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
17. #36475C2semidirect
21. #36447C2semidirect
22. #35971C2semidirect
23. #35937C2semidirect
26. #35187C2semidirect
27. #35115C2semidirect
30. C4×Q82C2semidirect
31. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#427032
#426702
#425112
#424612
#402272
#401552
#401432
#401072
#396532
#395342
#395262
#392252
#375922
Q8×#1262
#364752
#364482
#364472
#359712
#359372
#357862
#357112
#351872
#351152
#349732
#342622
C4×Q822
C4×#5572