Finite Group Databasebeta

← #7694412

Subgroups — #7694412

Order 512.

4778 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59711C213yesmaximal, complemented
2#59428C213yesmaximal, complemented
3#59244C213yesmaximal, complemented
4#52233C213yesmaximal, complemented
5#45370C213yesmaximal, complemented
6#45341C213yesmaximal, complemented
7#45329C213yesmaximal, complemented
8#45295C213yesmaximal, complemented
9#45286C213yesmaximal, complemented
10#45165C213yesmaximal, complemented
11#39800C213yesmaximal, complemented
12#39294C213yesmaximal, complemented
13#39152C213yesmaximal, complemented
14#38980C213yesmaximal, complemented
15#38236C213yesmaximal, complemented
16#37960C213yesmaximal, complemented
17#36467C211yesmaximal, characteristic
18#36448C211yesmaximal, characteristic, complemented
19#36435C211yesmaximal, characteristic, complemented
20#35948C211yesmaximal, characteristic
21#35937C211yesmaximal, characteristic, complemented
22#35920C211yesmaximal, characteristic, complemented
23#35898C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34337C211yesmaximal, characteristic, complemented
28#34335C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic
30#34263C211yesmaximal, characteristic, complemented
31#34196C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2216yes—
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2863C2213yes—
40#2861C2213yes—
41#2851C2213yes—
42#2810C2216yes—
43#2798C2216yes—
44#2789C2213yes—
45#2789C2216yes—
46#2788C2211yescharacteristic
47#2788C2216yes—
48#2787C2213yes—
49#2787C2216yes—
50#2786C2213yes—
51#2783C2213yes—
52#2783C2216yes—
53#2783C2216yes—
54#2777C2213yes—
55#2776C2216yes—
56#2775C2213yes—
57#2775C2216yes—
58#2767C2213yes—
59#2762C2213yes—
60#2759C2213yes—
61#2758C2213yes—
62#2745C2213yes—
63#2745C2216yes—
64#2740C2213yes—
65#2716C2216yes—
66#2715C2213yes—
67#2715C2216yes—
68#2700C2213yes—
69#2689C2213yes—
70#2689C2216yes—
71#2660C2213yes—
72#2645C2213yes—
73#2644C2213yes—
74#2644C2213yes—
75#2640C2213yes—
76#2629C2213yes—
77#2599C2216yes—
78#2594C2216yes—
79#2594C2216yes—
80#2592C2213yes—
81#2592C2213yes—
82#2588C2216yes—
83#2584C2213yes—
84#2581C2216yes—
85#2581C2213yes—
86#2577C2216yes—
87#2573C2216yes—
88#2566C2213yes—
89#2565C2213yes—
90#2562C2213yes—
91#2551C2213yes—
92#2551C2213yes—
93#2550C2213yes—
94#2550C2213yes—
95#2547C2213yes—
96#2546C2213yes—
97#2538C2213yes—
98#2523C2216yes—
99#2514C2213yes—
100#2514C2213yes—
101#2513C2213yes—
102#2513C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2512C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2511C2213yes—
110#2511C2213yes—
111#2497C2213yes—
112#2497C2213yes—
113#2496C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2496C2213yes—
117#2496C2213yes—
118#2496C2213yes—
119#2495C2213yes—
120#2494C2213yes—
121#2494C2213yes—
122#2494C2213yes—
123#2492C2213yes—
124#2492C2213yes—
125#2492C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2491C2213yes—
129#2490C2213yes—
130#2489C2213yes—
131#2485C2216yes—
132#2478C2216yes—
133#2478C2216yes—
134#2474C2216yes—
135#2469C2216yes—
136#2469C2216yes—
137#2469C2216yes—
138#2466C2216yes—
139#2465C2216yes—
140#2454C2213yes—
141#2453C2213yes—
142#2452C2213yes—
143#2451C2213yes—
144#2447C2216yes—
145#2446C2216yes—
146#2442C2213yes—
147#2442C2213yes—
148#2440C2213yes—
149#2440C2213yes—
150#2439C2216yes—
151#2421C2216yes—
152#2401C2213yes—
153#2401C2213yes—
154#2401C2213yes—
155#2399C2213yes—
156#2398C2213yes—
157#2396C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2369C2213yes—
163#2367C2213yes—
164#2365C2213yes—
165#2365C2213yes—
166#2365C2213yes—
167#2365C2213yes—
168#2361C2213yes—
169#2360C2213yes—
170#2357C2213yes—
171#2355C2213yes—
172#2355C2213yes—
173#2355C2213yes—
174#2354C2213yes—
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179Q8×C4⋊C4C2213yes—
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189D4×C4⋊C4C2213yes—
190#2345C2213yes—
191#2344C2213yes—
192#2344C2213yes—
193#2344C2213yes—
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2331C2213yes—
205#2331C2213yes—
206#2330C2213yes—
207#2330C2213yes—
208#2330C2213yes—
209#2330C2213yes—
210#2326C2213yes—
211#2323C2213yes—
212#2320C2213yes—
213#2320C2213yes—
214#2319C2213yes—
215#2314C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×C4⋊Q8C2213yes—
219C4×#126C2213yes—
220C4×#124C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×#121C2213yes—
223#2298C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2293C2213yes—
228#2290C2213yes—
229#2285C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241#557—28no—
242#557—28no—
243#556—424no—
244#548—28no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2316yes—
251C2×#126C2313yes—
252C2×#126C2316yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2316yes—
265C2×#121C2313yes—
266#520—28no—
267C2×C4×Q8—28no—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2316yes—
285C2×C4×Q8C2316yes—
286C2×C4×Q8C2316yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2316yes—
293C2×#117C2313yes—
294C2×#117C2316yes—
295C2×#117C2316yes—
296C22×C4⋊C4C2313yes—
297C22×C4⋊C4C2313yes—
298C22×C42C2313yes—
299#401C2313yes—
300#401C2316yes—
301#401C2313yes—
302#401C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2311yescharacteristic
315#400C2311yescharacteristic
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#399C2313yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2311yescharacteristic
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#397C2313yes—
334#397C2313yes—
335#397C2316yes—
336#397C2316yes—
337#397C2316yes—
338#397C2316yes—
339#397C2313yes—
340#397C2313yes—
341#397C2316yes—
342#397C2316yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2316yes—
351#396C2313yes—
352#396C2316yes—
353#396C2316yes—
354#396C2316yes—
355#396C2316yes—
356#396C2313yes—
357#396C2311yescharacteristic
358#396C2313yes—
359#396C2313yes—
360#395C2313yes—
361#395C2316yes—
362#395C2313yes—
363#395C2316yes—
364#395C2313yes—
365#395C2311yescharacteristic
366#395C2313yes—
367#395C2316yes—
368#394C2316yes—
369#394C2313yes—
370#394C2313yes—
371#393C2313yes—
372#393C2316yes—
373#393C2316yes—
374#393C2316yes—
375#393C2313yes—
376#393C2311yescharacteristic
377#391C2313yes—
378#391C2313yes—
379#391C2316yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2316yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2313yes—
392#391C2316yes—
393#391C2316yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2311yescharacteristic
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2316yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2311yescharacteristic
450#389C2311yescharacteristic
451#388C2311yescharacteristic
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2313yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2313yes—
465#388C2313yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2313yes—
471#388C2316yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2311yescharacteristic
476#388C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2316yes—
482#387C2313yes—
483#387C2316yes—
484#387C2313yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2311yescharacteristic
520#386C2313yes—
521#386C2313yes—
522#385C2316yes—
523#385C2316yes—
524#385C2316yes—
525#385C2316yes—
526#385C2313yes—
527#385C2316yes—
528#385C2313yes—
529#385C2311yescharacteristic
530#385C2311yescharacteristic
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#383C2313yes—
540#383C2313yes—
541#383C2313yes—
542#383C2316yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2316yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#381C2316yes—
552#381C2313yes—
553#381C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2316yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2311yescharacteristic
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
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×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2313yes—
621#376C2313yes—
622#376C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2416yes—
636C22×Q8C2411yescharacteristic
637C22×D4C2413yes—
638C22×D4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2416yes—
643C23×C4C2411yescharacteristic
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—212no—
648C4⋊Q8—212no—
649C4⋊Q8—412no—
650#126—212no—
651#126—412no—
652#126—412no—
653#126—412no—
654#125—212no—
655#125—212no—
656#125—212no—
657#125—212no—
658#124—212no—
659#124—212no—
660#124—412no—
661C22⋊Q8—212no—
662C22⋊Q8—212no—
663C22⋊Q8—412no—
664#121—212no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—212no—
680C4×Q8—212no—
681C4×Q8—412no—
682C4×Q8—412no—
683C4×Q8—412no—
684C4×Q8#4118yes—
685C4×Q8#4118yes—
686C4×D4—212no—
687C4×D4—212no—
688C4×D4—212no—
689C4×D4—412no—
690#117—212no—
691#117—412no—
692#117—412no—
693C2×C4⋊C4—212no—
694C2×C4⋊C4—212no—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2416yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2416yes—
767C2×C22⋊C4C2416yes—
768C2×C22⋊C4C2416yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C42—212no—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2416yes—
802C2×C42C2416yes—
803C2×C42C2416yes—
804C2×C42C2416yes—
805C2×C42C2416yes—
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2416yes—
847#95C2416yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2413yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2416yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2513yes—
890C24C2511yescharacteristic
891#41—416no—
892C2×Q8—22no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—212no—
898C2×Q8—26no—
899C2×Q8—26no—
900C2×Q8—26no—
901C2×Q8—41no—
902C2×Q8—41no—
903C2×Q8—43no—
904C2×Q8—43no—
905C2×Q8—46no—
906C2×Q8—46no—
907C2×Q8—416no—
908C2×Q8C2×#4114yes—
909C2×Q8C2×#4114yes—
910C2×Q82−1+414yes—
911C2×D4—26no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4—26no—
916C2×D4—43no—
917C22×C4—26no—
918C22×C4—22no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—212no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—43no—
930C22×C4—46no—
931C22×C4—46no—
932C22×C4C2513yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—212no—
965C4⋊C4—22no—
966C4⋊C4—26no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—212no—
983C4⋊C4—212no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—41no—
994C4⋊C4—43no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—43no—
999C4⋊C4—41no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—41no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—46no—
1016C4⋊C4—46no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4C2×#41112yes—
1020C4⋊C4C2×#41112yes—
1021C22⋊C4—26no—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—22no—
1028C22⋊C4—26no—
1029C22⋊C4—212no—
1030C22⋊C4—26no—
1031C22⋊C4—26no—
1032C22⋊C4—41no—
1033C22⋊C4—43no—
1034C22⋊C4—41no—
1035C22⋊C4—43no—
1036C22⋊C4—46no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—43no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—46no—
1048C22⋊C4—46no—
1049C22⋊C4—46no—
1050C22⋊C4H(5,𝔽2)14yes—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—43no—
1067C42—41no—
1068C42—41no—
1069C42—43no—
1070C42—43no—
1071C42—43no—
1072C42—46no—
1073C42—46no—
1074C42—46no—
1075C42—46no—
1076C42—46no—
1077C42C2×#41112yes—
1078C42C2×#41112yes—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—23no—
1086C23—23no—
1087C23—23no—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2611yescharacteristic
1094Q8—412no—
1095Q8—412no—
1096Q8—44no—
1097Q8—412no—
1098Q8—812no—
1099Q8#556116yescomplemented
1100D4—412no—
1101D4—412no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
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—21no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—412no—
1181C2×C4—44no—
1182C2×C4—412no—
1183C2×C4—412no—
1184C2×C4—812no—
1185C2×C4C22×#4112yes—
1186C2×C4C22×#4116yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C22×#4116yes—
1190C2×C4C22×#4116yes—
1191C2×C4C2×H(5,𝔽2)12yes—
1192C2×C4C2×H(5,𝔽2)12yes—
1193C2×C4C2×2−1+416yes—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—43no—
1202C22—43no—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22C23×#4111yescharacteristic
1209C22C23×#4111yescharacteristic
1210C22C22×H(5,𝔽2)11yescharacteristic
1211C22C22×2−1+411yescharacteristic
1212C222−1+611yescharacteristic
1213C222−1+611yescharacteristic
1214C222−1+611yescharacteristic
1215C4—26no—
1216C4—26no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—43no—
1222C4—43no—
1223C4—43no—
1224C4—43no—
1225C4—43no—
1226C4—43no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—43no—
1234C4—43no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—43no—
1239C4—43no—
1240C4—43no—
1241C4—41no—
1242C4—43no—
1243C4C2×#556112yes—
1244C2—42no—
1245C2—83no—
1246C2C22×#55611yescharacteristic
1247C2#6285011yescharacteristic
1248C2#6285011yescharacteristic
1249C2#6294611yescharacteristic
1250C2#6298511yescharacteristic
1251C2#6298511yescharacteristic
1252C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59711C2semidirect
2. #59428C2semidirect
3. #59244C2semidirect
4. #52233C2semidirect
5. #45370C2semidirect
6. #45341C2semidirect
7. #45329C2semidirect
8. #45295C2semidirect
9. #45286C2semidirect
10. #45165C2semidirect
11. #39800C2semidirect
12. #39294C2semidirect
13. #39152C2semidirect
14. #38980C2semidirect
15. #38236C2semidirect
16. #37960C2semidirect
18. #36448C2semidirect
19. #36435C2semidirect
21. #35937C2semidirect
22. #35920C2semidirect
23. #35898C2semidirect
24. #35898C2semidirect
25. #35816C2semidirect
26. #34337C2semidirect
27. #34337C2semidirect
28. #34335C2semidirect
30. #34263C2semidirect
31. #34196C2semidirect
1099. Q8#556semidirect

Maximal subgroups

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

subgroupindex
#597112
#594282
#592442
#522332
#453702
#453412
#453292
#452952
#452862
#451652
#398002
#392942
#391522
#389802
#382362
#379602
#364672
#364482
#364352
#359482
#359372
#359202
#358982
#358162
#343372
#343352
#342942
#342632
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