Finite Group Databasebeta

← #7687637

Subgroups — #7687637

Order 512.

4908 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59715C213yesmaximal, complemented
2#59712C213yesmaximal, complemented
3#59711C213yesmaximal, complemented
4#59428C213yesmaximal, complemented
5#59250C213yesmaximal, complemented
6#45065C213yesmaximal, complemented
7#45032C213yesmaximal, complemented
8#44984C213yesmaximal, complemented
9#44979C213yesmaximal, complemented
10#39801C213yesmaximal, complemented
11#39293C213yesmaximal, complemented
12#38241C213yesmaximal, complemented
13#37963C213yesmaximal, complemented
14Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
15#36473C213yesmaximal, complemented
16#36467C211yesmaximal, characteristic
17#36458C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic, complemented
20#36371C213yesmaximal, complemented
21#35948C211yesmaximal, characteristic
22#35937C211yesmaximal, characteristic, complemented
23#35920C211yesmaximal, characteristic, complemented
24#35748C211yesmaximal, characteristic, complemented
25#34867C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34335C211yesmaximal, characteristic, complemented
28#34294C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic, complemented
30C4×Q82C211yesmaximal, characteristic, complemented
31#34128C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2216yes—
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2863C2213yes—
40#2861C2213yes—
41#2860C2213yes—
42#2860C2213yes—
43#2857C2213yes—
44#2805C2216yes—
45#2788C2216yes—
46#2787C2216yes—
47#2777C2216yes—
48#2777C2216yes—
49#2776C2216yes—
50#2759C2216yes—
51#2759C2216yes—
52#2758C2216yes—
53#2716C2216yes—
54#2700C2216yes—
55#2689C2216yes—
56#2689C2216yes—
57#2689C2216yes—
58#2660C2213yes—
59#2645C2213yes—
60#2640C2213yes—
61#2628C2213yes—
62#2605C2213yes—
63#2605C2216yes—
64#2604C2216yes—
65#2604C2213yes—
66#2604C2216yes—
67#2601C2213yes—
68#2599C2213yes—
69#2599C2216yes—
70#2594C2213yes—
71#2592C2213yes—
72#2592C2213yes—
73#2588C2213yes—
74#2584C2213yes—
75#2582C2213yes—
76#2581C2216yes—
77#2580C2213yes—
78#2577C2213yes—
79#2567C2213yes—
80#2562C2213yes—
81#2560C2213yes—
82#2551C2213yes—
83#2551C2213yes—
84#2550C2213yes—
85#2550C2213yes—
86#2547C2213yes—
87#2546C2213yes—
88#2542C2213yes—
89#2532C2216yes—
90#2532C2213yes—
91#2528C2213yes—
92#2527C2216yes—
93#2525C2216yes—
94#2524C2213yes—
95#2521C2213yes—
96#2521C2216yes—
97#2514C2213yes—
98#2514C2213yes—
99#2513C2213yes—
100#2513C2213yes—
101#2512C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2511C2213yes—
106#2511C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2496C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2496C2213yes—
117#2495C2213yes—
118#2495C2213yes—
119#2495C2213yes—
120#2494C2213yes—
121#2492C2213yes—
122#2492C2213yes—
123#2492C2216yes—
124#2492C2213yes—
125#2491C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2490C2213yes—
129#2489C2213yes—
130#2478C2216yes—
131#2478C2213yes—
132#2474C2213yes—
133#2469C2213yes—
134#2469C2216yes—
135#2466C2216yes—
136#2465C2216yes—
137#2465C2211yescharacteristic
138#2465C2216yes—
139#2452C2213yes—
140#2452C2213yes—
141#2451C2213yes—
142#2451C2213yes—
143#2447C2216yes—
144#2446C2216yes—
145#2440C2213yes—
146#2440C2213yes—
147#2440C2213yes—
148#2440C2213yes—
149#2415C2216yes—
150#2401C2213yes—
151#2399C2213yes—
152#2398C2213yes—
153#2396C2213yes—
154#2373C2216yes—
155#2370C2213yes—
156#2370C2213yes—
157#2369C2213yes—
158#2369C2213yes—
159#2369C2213yes—
160#2369C2213yes—
161#2367C2213yes—
162#2365C2213yes—
163#2365C2213yes—
164#2365C2213yes—
165#2362C2216yes—
166#2361C2213yes—
167#2360C2213yes—
168#2357C2213yes—
169#2356C2213yes—
170#2356C2213yes—
171#2355C2213yes—
172#2354C2213yes—
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2213yes—
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2213yes—
187D4×C4⋊C4C2213yes—
188#2345C2213yes—
189#2344C2213yes—
190#2344C2213yes—
191#2344C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202#2331C2213yes—
203#2331C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2326C2213yes—
207#2323C2213yes—
208#2319C2213yes—
209#2314C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×C4⋊Q8C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×#126C2213yes—
218C4×#124C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×#121C2213yes—
221#2298C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2293C2213yes—
227#2290C2213yes—
228#2283C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×Q8C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241Q82—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⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2316yes—
253C2×#126C2313yes—
254C2×#126C2313yes—
255C2×#126C2313yes—
256C2×#126C2316yes—
257C2×#126C2316yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2316yes—
269C2×#121C2313yes—
270#520—28no—
271C2×C4×Q8—28no—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2316yes—
290C2×C4×Q8C2316yes—
291C2×C4×Q8C2316yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2316yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2316yes—
303C22×C4⋊C4C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C42C2313yes—
306#401C2313yes—
307#401C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2316yes—
311#400C2316yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#399C2316yes—
323#399C2313yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#397C2313yes—
334#397C2313yes—
335#397C2313yes—
336#397C2316yes—
337#397C2316yes—
338#397C2313yes—
339#397C2313yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#396C2313yes—
346#396C2311yescharacteristic
347#396C2313yes—
348#396C2316yes—
349#396C2316yes—
350#395C2316yes—
351#395C2316yes—
352#395C2316yes—
353#395C2313yes—
354#395C2313yes—
355#395C2316yes—
356#395C2311yescharacteristic
357#395C2313yes—
358#395C2316yes—
359#395C2311yescharacteristic
360#394C2313yes—
361#394C2316yes—
362#394C2313yes—
363#393C2313yes—
364#393C2313yes—
365#393C2316yes—
366#393C2311yescharacteristic
367#393C2316yes—
368#393C2316yes—
369#393C2316yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2316yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2316yes—
380#391C2316yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2316yes—
386#391C2316yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2316yes—
393#391C2313yes—
394#391C2311yescharacteristic
395#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2316yes—
419#389C2316yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
433#389C2316yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2311yescharacteristic
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#388C2311yescharacteristic
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2313yes—
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2313yes—
460#388C2316yes—
461#388C2316yes—
462#388C2313yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2316yes—
468#388C2313yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2313yes—
474#388C2316yes—
475#388C2311yescharacteristic
476#388C2313yes—
477#387C2311yescharacteristic
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2313yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2311yescharacteristic
516#386C2313yes—
517#386C2313yes—
518#385C2311yescharacteristic
519#385C2316yes—
520#385C2316yes—
521#385C2316yes—
522#385C2316yes—
523#385C2313yes—
524#385C2313yes—
525#385C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#383C2313yes—
535#383C2313yes—
536#383C2313yes—
537#383C2316yes—
538#383C2316yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#381C2316yes—
545#381C2316yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
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⋊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⋊C4C2316yes—
578C4×C4⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2311yescharacteristic
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2316yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8C2411yescharacteristic
632C22×Q8C2413yes—
633C22×Q8C2411yescharacteristic
634C22×Q8C2413yes—
635C22×Q8C2416yes—
636C22×Q8C2416yes—
637C22×Q8C2411yescharacteristic
638C22×D4C2413yes—
639C22×D4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2416yes—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—212no—
648C4⋊Q8—212no—
649C4⋊Q8—212no—
650C4⋊Q8—212no—
651C4⋊Q8—212no—
652C4⋊Q8—412no—
653#126—212no—
654#126—212no—
655#126—46no—
656#126—412no—
657#126—412no—
658#126—412no—
659#125—212no—
660#125—212no—
661#124—212no—
662#124—212no—
663#124—412no—
664C22⋊Q8—212no—
665C22⋊Q8—24no—
666C22⋊Q8—412no—
667C22⋊Q8—412no—
668C22⋊Q8—412no—
669#121—212no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—212no—
682C4×Q8—24no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—212no—
686C4×Q8—212no—
687C4×Q8—412no—
688C4×Q8—412no—
689C4×Q8—46no—
690C4×Q8—412no—
691C4×Q8#4118yes—
692C4×Q8#4118yes—
693C4×D4—212no—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—412no—
697#117—212no—
698#117—212no—
699#117—46no—
700#117—412no—
701C2×C4⋊C4—212no—
702C2×C4⋊C4—212no—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2416yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C42—212no—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2416yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2416yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2411yescharacteristic
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2416yes—
833#95C2413yes—
834#95C2413yes—
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#95C2416yes—
849#95C2416yes—
850#95C2416yes—
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2416yes—
871#95C2413yes—
872#95C2413yes—
873#95C2416yes—
874#95C2416yes—
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896C24C2513yes—
897C24C2511yescharacteristic
898#41—416no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—212no—
905C2×Q8—212no—
906C2×Q8—26no—
907C2×Q8—22no—
908C2×Q8—22no—
909C2×Q8—26no—
910C2×Q8—22no—
911C2×Q8—41no—
912C2×Q8—43no—
913C2×Q8—46no—
914C2×Q8—46no—
915C2×Q8—46no—
916C2×Q8—46no—
917C2×Q8—416no—
918C2×Q8C2×#4114yes—
919C2×Q8C2×#4114yes—
920C2×Q82−1+414yes—
921C2×D4—26no—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—43no—
927C22×C4—26no—
928C22×C4—22no—
929C22×C4—26no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—22no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—212no—
938C22×C4—43no—
939C22×C4—41no—
940C22×C4—46no—
941C22×C4—46no—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2513yes—
963C22×C4C2513yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2513yes—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—212no—
975C4⋊C4—22no—
976C4⋊C4—26no—
977C4⋊C4—22no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
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—212no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—22no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—46no—
1016C4⋊C4—46no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—46no—
1027C4⋊C4C2×#41112yes—
1028C4⋊C4C2×#41112yes—
1029C4⋊C42−1+414yes—
1030C22⋊C4—26no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—22no—
1037C22⋊C4—26no—
1038C22⋊C4—212no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—26no—
1044C22⋊C4—26no—
1045C22⋊C4—26no—
1046C22⋊C4—22no—
1047C22⋊C4—26no—
1048C22⋊C4—46no—
1049C22⋊C4—41no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—43no—
1053C22⋊C4—46no—
1054C22⋊C4—46no—
1055C22⋊C4—46no—
1056C22⋊C4—46no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4H(5,𝔽2)14yes—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—22no—
1075C42—22no—
1076C42—22no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—41no—
1083C42—43no—
1084C42—43no—
1085C42—43no—
1086C42—43no—
1087C42—46no—
1088C42—46no—
1089C42—43no—
1090C42—43no—
1091C42—46no—
1092C42C2×#41112yes—
1093C42C2×#41112yes—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—23no—
1101C23—23no—
1102C23—23no—
1103C23—23no—
1104C23—23no—
1105C23—23no—
1106C23—23no—
1107C23C2×H(5,𝔽2)12yes—
1108C23C2611yescharacteristic
1109Q8—28no—
1110Q8—412no—
1111Q8—44no—
1112Q8—412no—
1113Q8—812no—
1114Q8—812no—
1115Q8#556116yescomplemented
1116D4—412no—
1117D4—412no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—44no—
1193C2×C4—412no—
1194C2×C4—412no—
1195C2×C4—412no—
1196C2×C4—812no—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4112yes—
1200C2×C4C22×#4116yes—
1201C2×C4C22×#4116yes—
1202C2×C4C22×#4116yes—
1203C2×C4C2×H(5,𝔽2)12yes—
1204C2×C4C2×H(5,𝔽2)12yes—
1205C2×C4C2×2−1+412yes—
1206C2×C4C2×2−1+412yes—
1207C2×C4C2×2−1+412yes—
1208C2×C4C2×2−1+416yes—
1209C2×C4#58512yes—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—43no—
1218C22—43no—
1219C22—43no—
1220C22—43no—
1221C22—43no—
1222C22—43no—
1223C22—43no—
1224C22C23×#4111yescharacteristic
1225C22C23×#4111yescharacteristic
1226C22C22×H(5,𝔽2)11yescharacteristic
1227C22C22×2−1+411yescharacteristic
1228C22C22×2−1+411yescharacteristic
1229C22C2×#58511yescharacteristic
1230C222−1+611yescharacteristic
1231C4—26no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—26no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—41no—
1245C4—41no—
1246C4—43no—
1247C4—43no—
1248C4—41no—
1249C4—43no—
1250C4—43no—
1251C4—43no—
1252C4—43no—
1253C4—43no—
1254C4—41no—
1255C4—41no—
1256C4—43no—
1257C4—41no—
1258C4—43no—
1259C4C2×#556112yes—
1260C2—42no—
1261C2—83no—
1262C2C22×#55611yescharacteristic
1263C2#6278811yescharacteristic
1264C2#6280011yescharacteristic
1265C2#6295311yescharacteristic
1266C2#6298511yescharacteristic
1267C2#6299811yescharacteristic
1268C2#6303711yescharacteristic
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. #59715C2semidirect
2. #59712C2semidirect
3. #59711C2semidirect
4. #59428C2semidirect
5. #59250C2semidirect
6. #45065C2semidirect
7. #45032C2semidirect
8. #44984C2semidirect
9. #44979C2semidirect
10. #39801C2semidirect
11. #39293C2semidirect
12. #38241C2semidirect
13. #37963C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. #36473C2semidirect
17. #36458C2semidirect
18. #36458C2semidirect
19. #36448C2semidirect
20. #36371C2semidirect
22. #35937C2semidirect
23. #35920C2semidirect
24. #35748C2semidirect
25. #34867C2semidirect
26. #34337C2semidirect
27. #34335C2semidirect
29. #34263C2semidirect
30. C4×Q82C2semidirect
31. #34128C2semidirect
1115. Q8#556semidirect

Maximal subgroups

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

subgroupindex
#597152
#597122
#597112
#594282
#592502
#450652
#450322
#449842
#449792
#398012
#392932
#382412
#379632
Q8×C22⋊Q82
#364732
#364672
#364582
#364482
#363712
#359482
#359372
#359202
#357482
#348672
#343372
#343352
#342942
#342632
C4×Q822
#341282