Finite Group Databasebeta

← #8429347

Subgroups — #8429347

Order 512.

4641 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59659C212yesmaximal, complemented
3#59451C212yesmaximal, complemented
4#59259C212yesmaximal, complemented
5#53763C218yesmaximal, complemented
6#53082C214yesmaximal, complemented
7#53016C214yesmaximal, complemented
8#52974C214yesmaximal, complemented
9#42924C214yesmaximal, complemented
10#42868C214yesmaximal, complemented
11#42804C214yesmaximal, complemented
12#39617C212yesmaximal, complemented
13#39497C212yesmaximal, complemented
14#39489C212yesmaximal, complemented
15#39377C212yesmaximal, complemented
16#39351C212yesmaximal, complemented
17#39147C212yesmaximal, complemented
18#37637C212yesmaximal, complemented
19#37627C212yesmaximal, complemented
20#37624C212yesmaximal, complemented
21#36593C211yesmaximal, characteristic, complemented
22Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
23#36187C211yesmaximal, characteristic
24#34954C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34941C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#557C2212yes—
29C2×#555C2212yes—
30C2×#554C2212yes—
31C2×#542C2214yes—
32#2868C2212yes—
33#2868C2212yes—
34#2868C2211yescharacteristic
35#2856C2212yes—
36#2841C2218yes—
37#2838C2218yes—
38#2837C2218yes—
39#2837C2218yes—
40#2831C2218yes—
41#2820C2218yes—
42#2814C2218yes—
43#2790C2218yes—
44#2787C2218yes—
45#2773C2218yes—
46#2768C2218yes—
47#2757C2218yes—
48#2732C2214yes—
49#2731C2218yes—
50#2729C2218yes—
51#2723C2218yes—
52#2718C2218yes—
53#2701C2218yes—
54#2694C2218yes—
55#2690C2218yes—
56#2677C2218yes—
57#2677C2218yes—
58#2674C2218yes—
59#2674C2218yes—
60#2674C2218yes—
61#2672C2218yes—
62#2666C2218yes—
63#2664C2218yes—
64#2660C2214yes—
65#2651C2218yes—
66#2647C2214yes—
67#2644C2214yes—
68#2637C2218yes—
69#2629C2214yes—
70#2629C2214yes—
71#2628C2214yes—
72#2625C2214yes—
73#2624C2214yes—
74#2620C2214yes—
75#2596C2218yes—
76#2593C2214yes—
77#2585C2218yes—
78#2582C2211yescharacteristic
79#2574C2214yes—
80#2573C2214yes—
81#2571C2211yescharacteristic
82#2571C2211yescharacteristic
83#2570C2214yes—
84#2568C2211yescharacteristic
85#2567C2212yes—
86#2567C2214yes—
87#2567C2211yescharacteristic
88#2566C2214yes—
89#2565C2214yes—
90#2563C2212yes—
91#2563C2211yescharacteristic
92#2552C2211yescharacteristic
93#2552C2214yes—
94#2552C2212yes—
95#2552C2214yes—
96#2552C2212yes—
97#2552C2212yes—
98#2551C2214yes—
99#2551C2214yes—
100#2551C2212yes—
101#2551C2212yes—
102#2550C2214yes—
103#2548C2211yescharacteristic
104#2548C2211yescharacteristic
105#2547C2211yescharacteristic
106#2546C2214yes—
107#2546C2212yes—
108#2545C2218yes—
109#2542C2212yes—
110#2542C2214yes—
111#2538C2212yes—
112#2538C2211yescharacteristic
113#2538C2214yes—
114#2538C2211yescharacteristic
115#2537C2212yes—
116#2537C2212yes—
117#2514C2212yes—
118#2513C2214yes—
119#2513C2212yes—
120#2513C2212yes—
121#2512C2214yes—
122#2508C2214yes—
123#2508C2212yes—
124#2507C2214yes—
125#2501C2214yes—
126#2500C2214yes—
127#2499C2214yes—
128#2497C2212yes—
129#2497C2214yes—
130#2496C2214yes—
131#2494C2212yes—
132#2491C2214yes—
133#2491C2214yes—
134#2491C2214yes—
135#2491C2214yes—
136#2490C2214yes—
137#2489C2214yes—
138#2454C2212yes—
139#2454C2214yes—
140#2452C2214yes—
141#2448C2212yes—
142#2448C2214yes—
143#2448C2212yes—
144#2447C2212yes—
145#2441C2214yes—
146#2441C2214yes—
147#2440C2214yes—
148#2440C2214yes—
149#2439C2214yes—
150#2439C2214yes—
151#2426C2214yes—
152#2426C2214yes—
153#2423C2214yes—
154#2423C2214yes—
155#2423C2212yes—
156#2423C2214yes—
157#2422C2214yes—
158#2422C2214yes—
159#2422C2214yes—
160#2421C2212yes—
161#2417C2214yes—
162#2401C2214yes—
163#2396C2214yes—
164#2395C2214yes—
165#2366C2212yes—
166#2362C2214yes—
167#2362C2214yes—
168#2355C2214yes—
169#2354C2212yes—
170#2354C2212yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174Q8×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176#2326C2214yes—
177#2317C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#127C2211yescharacteristic
183C4×#125C2212yes—
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2293C2212yes—
191#2293C2212yes—
192#2293C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199Q82—48no—
200#557—48no—
201#555—48no—
202#554—48no—
203#542—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2318yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×#127C2311yescharacteristic
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2318yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2312yes—
226C2×#124C2318yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×#117C2314yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2312yes—
266#401C2314yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2314yes—
275#399C2318yes—
276#399C2318yes—
277#399C2314yes—
278#399C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2314yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2314yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2314yes—
332#394C2314yes—
333#393C2314yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2318yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#390C2312yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2312yes—
360#390C2312yes—
361#390C2318yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#389C2314yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2318yes—
388#389C2318yes—
389#389C2312yes—
390#389C2312yes—
391#389C2318yes—
392#389C2318yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#386C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2314yes—
451#384C2314yes—
452#384C2314yes—
453#384C2312yes—
454#384C2314yes—
455#384C2314yes—
456#384C2312yes—
457#384C2312yes—
458#383C2314yes—
459#382C2312yes—
460#382C2314yes—
461#382C2318yes—
462#382C2312yes—
463#382C2312yes—
464#382C2312yes—
465#382C2312yes—
466#382C2312yes—
467#382C2314yes—
468#381C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2312yes—
480#380C2318yes—
481#380C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×D4C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2418yes—
535C23×C4C2414yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2418yes—
540C4⋊Q8—24no—
541C4⋊Q8—28no—
542C4⋊Q8—24no—
543C4⋊Q8—48no—
544C4⋊Q8—44no—
545C4⋊Q8—48no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—416no—
549C4⋊Q8—82no—
550C4⋊Q8—84no—
551C4⋊Q8—84no—
552#127—24no—
553#126—416no—
554#125—44no—
555#125—48no—
556#125—48no—
557#125—416no—
558#124—28no—
559#124—28no—
560#124—416no—
561#124—44no—
562#124—416no—
563#123—416no—
564#123—88no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—416no—
568C22⋊Q8—416no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571C22⋊Q8—88no—
572#121—48no—
573#121—48no—
574#121—48no—
575#121—84no—
576C4×Q8—216no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—44no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×D4—28no—
589C4×D4—24no—
590C4×D4—28no—
591C4×D4—24no—
592C4×D4—42no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4—44no—
596#117—48no—
597#117—48no—
598#117—48no—
599#117—48no—
600C2×C4⋊C4—48no—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C42—28no—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2411yescharacteristic
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2418yes—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2418yes—
709C2×C42C2418yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758C24C2512yes—
759C24C2514yes—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—28no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—42no—
770C2×Q8—44no—
771C2×Q8—42no—
772C2×Q8—44no—
773C2×Q8—48no—
774C2×Q8—48no—
775C2×Q8—48no—
776C2×Q8H(5,𝔽2)14yes—
777C2×Q82−1+414yes—
778C2×D4—24no—
779C2×D4—22no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—22no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C22×C4—28no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2518yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—216no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—42no—
890C22⋊C4—28no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—24no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—42no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C42—24no—
920C42—28no—
921C42—28no—
922C42—24no—
923C42—22no—
924C42—24no—
925C42—216no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—22no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—22no—
938C42—48no—
939C42—48no—
940C42—41no—
941C42—42no—
942C42—42no—
943C42H(5,𝔽2)14yes—
944C422−1+414yes—
945C422−1+414yes—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—22no—
960C23C2611yescharacteristic
961Q8—28no—
962Q8—28no—
963Q8—48no—
964Q8—84no—
965Q8—88no—
966Q8—168no—
967D4—48no—
968D4—48no—
969D4—44no—
970D4—84no—
971D4—168no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—24no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—416no—
1033C2×C4—84no—
1034C2×C4—168no—
1035C2×C4C2×H(5,𝔽2)14yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×H(5,𝔽2)12yes—
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2×2−1+414yes—
1042C2×C4C2×2−1+412yes—
1043C2×C4C2×2−1+412yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4C2×2−1+412yes—
1048C2×C4#58512yes—
1049C22—42no—
1050C22—44no—
1051C22—44no—
1052C22—42no—
1053C22—42no—
1054C22—44no—
1055C22—42no—
1056C22—44no—
1057C22—44no—
1058C22—42no—
1059C22—42no—
1060C22—44no—
1061C22—42no—
1062C22—44no—
1063C22C22×H(5,𝔽2)11yescharacteristic
1064C22C22×H(5,𝔽2)11yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C22×2−1+411yescharacteristic
1067C22C22×2−1+411yescharacteristic
1068C22C2×#58511yescharacteristic
1069C22H(7,𝔽2)11yescharacteristic
1070C4—24no—
1071C4—24no—
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—42no—
1076C4—44no—
1077C4—44no—
1078C4—42no—
1079C4—44no—
1080C4—42no—
1081C4—42no—
1082C4—41no—
1083C4—44no—
1084C4—44no—
1085C4—48no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4#354414yes—
1092C4#355214yes—
1093C4#355414yes—
1094C2—82no—
1095C2—84no—
1096C2C2×#355211yescharacteristic
1097C2C2×#355411yescharacteristic
1098C2C2×#354411yescharacteristic
1099C2#6291611yescharacteristic
1100C2#6292911yescharacteristic
1101C2#6294311yescharacteristic
1102C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36187C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59659C2semidirect
3. #59451C2semidirect
4. #59259C2semidirect
5. #53763C2semidirect
6. #53082C2semidirect
7. #53016C2semidirect
8. #52974C2semidirect
9. #42924C2semidirect
10. #42868C2semidirect
11. #42804C2semidirect
12. #39617C2semidirect
13. #39497C2semidirect
14. #39489C2semidirect
15. #39377C2semidirect
16. #39351C2semidirect
17. #39147C2semidirect
18. #37637C2semidirect
19. #37627C2semidirect
20. #37624C2semidirect
21. #36593C2semidirect
22. Q8×C4⋊Q8C2semidirect
24. #34954C2semidirect
25. #34945C2semidirect
26. #34941C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#596592
#594512
#592592
#537632
#530822
#530162
#529742
#429242
#428682
#428042
#396172
#394972
#394892
#393772
#393512
#391472
#376372
#376272
#376242
#365932
Q8×C4⋊Q82
#361872
#349542
#349452
#349412