Finite Group Databasebeta

← #8429318

Subgroups — #8429318

Order 512.

5057 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59646C212yesmaximal, complemented
3#59042C212yesmaximal, complemented
4#59036C212yesmaximal, complemented
5#54859C218yesmaximal, complemented
6#53108C214yesmaximal, complemented
7#53082C214yesmaximal, complemented
8#53045C214yesmaximal, complemented
9#42786C214yesmaximal, complemented
10#42624C214yesmaximal, complemented
11#42457C214yesmaximal, complemented
12#39625C212yesmaximal, complemented
13#39505C212yesmaximal, complemented
14#39481C212yesmaximal, complemented
15#39343C212yesmaximal, complemented
16#39343C212yesmaximal, complemented
17#39156C212yesmaximal, complemented
18#37640C212yesmaximal, complemented
19#37634C212yesmaximal, complemented
20#37625C212yesmaximal, complemented
21Q8×#127C211yesmaximal, characteristic, complemented
22#36134C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34941C211yesmaximal, characteristic, complemented
26#34925C211yesmaximal, characteristic
27C2×D4×Q8C2212yes—
28C2×D4×Q8C2212yes—
29C2×D4×Q8C2212yes—
30C2×#536C2214yes—
31C2×#533C2212yes—
32C2×#533C2212yes—
33C2×#532C2212yes—
34C2×#532C2212yes—
35#2868C2211yescharacteristic
36#2868C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2838C2218yes—
40#2837C2218yes—
41#2829C2218yes—
42#2829C2218yes—
43#2820C2218yes—
44#2816C2218yes—
45#2814C2218yes—
46#2808C2214yes—
47#2803C2218yes—
48#2801C2218yes—
49#2795C2218yes—
50#2792C2218yes—
51#2777C2218yes—
52#2773C2218yes—
53#2741C2218yes—
54#2740C2218yes—
55#2734C2218yes—
56#2731C2218yes—
57#2730C2218yes—
58#2729C2218yes—
59#2692C2218yes—
60#2690C2218yes—
61#2674C2218yes—
62#2674C2218yes—
63#2672C2218yes—
64#2672C2218yes—
65#2663C2218yes—
66#2660C2214yes—
67#2644C2214yes—
68#2641C2214yes—
69#2632C2218yes—
70#2630C2218yes—
71#2624C2218yes—
72#2624C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2616C2214yes—
76#2616C2214yes—
77#2616C2214yes—
78#2602C2218yes—
79#2592C2214yes—
80#2574C2214yes—
81#2573C2214yes—
82#2571C2211yescharacteristic
83#2568C2211yescharacteristic
84#2567C2214yes—
85#2567C2211yescharacteristic
86#2563C2211yescharacteristic
87#2563C2212yes—
88#2555C2214yes—
89#2552C2212yes—
90#2552C2212yes—
91#2552C2211yescharacteristic
92#2551C2214yes—
93#2551C2211yescharacteristic
94#2551C2214yes—
95#2550C2214yes—
96#2548C2214yes—
97#2548C2212yes—
98#2547C2211yescharacteristic
99#2547C2212yes—
100#2542C2212yes—
101#2542C2212yes—
102#2542C2212yes—
103#2542C2212yes—
104#2542C2212yes—
105#2542C2214yes—
106#2542C2214yes—
107#2542C2214yes—
108#2541C2211yescharacteristic
109#2541C2211yescharacteristic
110#2538C2214yes—
111#2538C2214yes—
112#2538C2212yes—
113#2538C2212yes—
114#2538C2211yescharacteristic
115#2538C2211yescharacteristic
116#2537C2211yescharacteristic
117#2536C2214yes—
118#2536C2214yes—
119#2514C2212yes—
120#2513C2214yes—
121#2513C2214yes—
122#2508C2212yes—
123#2507C2214yes—
124#2500C2214yes—
125#2500C2214yes—
126#2499C2214yes—
127#2497C2212yes—
128#2497C2214yes—
129#2494C2212yes—
130#2492C2214yes—
131#2491C2214yes—
132#2491C2214yes—
133#2491C2212yes—
134#2491C2212yes—
135#2490C2214yes—
136#2485C2214yes—
137#2477C2218yes—
138#2465C2218yes—
139#2454C2214yes—
140#2454C2212yes—
141#2451C2214yes—
142#2447C2212yes—
143#2445C2214yes—
144#2445C2214yes—
145#2441C2214yes—
146#2441C2214yes—
147#2439C2214yes—
148#2429C2214yes—
149#2429C2214yes—
150#2428C2212yes—
151#2428C2212yes—
152#2427C2214yes—
153#2423C2212yes—
154#2423C2214yes—
155#2423C2214yes—
156#2423C2214yes—
157#2422C2214yes—
158#2422C2214yes—
159#2421C2212yes—
160#2421C2214yes—
161#2415C2214yes—
162#2415C2214yes—
163#2409C2214yes—
164#2409C2214yes—
165#2401C2214yes—
166#2396C2214yes—
167#2388C2214yes—
168#2367C2214yes—
169#2365C2212yes—
170#2365C2212yes—
171#2363C2214yes—
172#2355C2212yes—
173#2354C2212yes—
174#2354C2212yes—
175#2354C2212yes—
176#2354C2212yes—
177Q8×C4⋊C4C2212yes—
178Q8×C4⋊C4C2212yes—
179Q8×C22⋊C4C2214yes—
180#2330C2214yes—
181#2314C2214yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#127C2211yescharacteristic
185C4×#127C2212yes—
186C4×#125C2212yes—
187C4×#124C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200C23×Q8C2314yes—
201D4×Q8—48no—
202D4×Q8—48no—
203D4×Q8—48no—
204#536—416no—
205#533—48no—
206#533—48no—
207#532—48no—
208#532—48no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2318yes—
220C2×#127C2311yescharacteristic
221C2×#127C2312yes—
222C2×#127C2312yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#125C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#124C2318yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2318yes—
247C2×#121C2312yes—
248C2×#121C2314yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2311yescharacteristic
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284#401C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2318yes—
289#400C2314yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#399C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2314yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2314yes—
319#396C2314yes—
320#396C2318yes—
321#396C2318yes—
322#396C2314yes—
323#395C2318yes—
324#395C2318yes—
325#395C2314yes—
326#395C2318yes—
327#395C2314yes—
328#395C2318yes—
329#395C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2314yes—
344#394C2318yes—
345#394C2314yes—
346#394C2314yes—
347#393C2314yes—
348#393C2318yes—
349#393C2314yes—
350#393C2318yes—
351#393C2318yes—
352#392C2314yes—
353#392C2314yes—
354#392C2314yes—
355#391C2312yes—
356#391C2312yes—
357#391C2312yes—
358#391C2314yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2312yes—
363#391C2318yes—
364#391C2318yes—
365#391C2314yes—
366#391C2314yes—
367#390C2314yes—
368#390C2312yes—
369#390C2314yes—
370#390C2314yes—
371#390C2312yes—
372#390C2312yes—
373#390C2314yes—
374#390C2312yes—
375#390C2318yes—
376#390C2314yes—
377#390C2318yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#390C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2318yes—
392#389C2318yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2318yes—
397#389C2318yes—
398#389C2312yes—
399#389C2314yes—
400#389C2318yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2318yes—
417#388C2314yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2318yes—
438#387C2314yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2314yes—
446#386C2314yes—
447#385C2314yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#384C2312yes—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2314yes—
456#384C2314yes—
457#384C2312yes—
458#384C2314yes—
459#384C2312yes—
460#384C2314yes—
461#384C2312yes—
462#384C2312yes—
463#384C2314yes—
464#384C2312yes—
465#383C2314yes—
466#382C2312yes—
467#382C2314yes—
468#382C2314yes—
469#382C2312yes—
470#382C2312yes—
471#382C2312yes—
472#381C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2314yes—
480#380C2318yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2314yes—
524#376C2314yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—48no—
528C2×#41—48no—
529C2×#41—48no—
530C22×Q8—216no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×Q8C2414yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2418yes—
556C23×C4C2412yes—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566C4⋊Q8—48no—
567C4⋊Q8—416no—
568#127—24no—
569#127—44no—
570#127—44no—
571#125—28no—
572#125—48no—
573#125—48no—
574#124—48no—
575#124—48no—
576#124—44no—
577#124—48no—
578#124—416no—
579#123—416no—
580#123—416no—
581C22⋊Q8—28no—
582C22⋊Q8—28no—
583C22⋊Q8—416no—
584C22⋊Q8—416no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592C22⋊Q8—48no—
593C22⋊Q8—48no—
594C22⋊Q8—416no—
595#121—28no—
596#121—48no—
597#121—48no—
598#121—44no—
599#121—44no—
600#121—44no—
601#121—44no—
602#121—44no—
603C4×Q8—24no—
604C4×Q8—24no—
605C4×Q8—24no—
606C4×Q8—28no—
607C4×Q8—44no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—48no—
611C4×Q8—48no—
612C4×D4—24no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—28no—
616C4×D4—28no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—42no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—44no—
625C4×D4—48no—
626#117—48no—
627#117—48no—
628#117—48no—
629#117—48no—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C42—28no—
717C2×C42—28no—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2418yes—
737C2×C42C2411yescharacteristic
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780C24C2512yes—
781C24C2512yes—
782C24C2514yes—
783#41—832no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—28no—
791C2×Q8—216no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—832no—
802C2×Q8H(5,𝔽2)14yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—22no—
816C2×D4—24no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—216no—
852C22×C4—42no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2518yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—42no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C42−1+414yes—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—42no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—22no—
974C42—24no—
975C42—24no—
976C42—22no—
977C42—28no—
978C42—24no—
979C42—24no—
980C42—28no—
981C42—22no—
982C42—41no—
983C42—42no—
984C42—48no—
985C42—48no—
986C42—48no—
987C42H(5,𝔽2)14yes—
988C42H(5,𝔽2)14yes—
989C422−1+414yes—
990C23—22no—
991C23—22no—
992C23—24no—
993C23—24no—
994C23—22no—
995C23—22no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23C2611yescharacteristic
1012Q8—28no—
1013Q8—48no—
1014Q8—416no—
1015Q8—48no—
1016Q8—816no—
1017Q8—88no—
1018D4—48no—
1019D4—48no—
1020D4—44no—
1021D4—48no—
1022D4—44no—
1023D4—88no—
1024D4—88no—
1025D4—88no—
1026D4—88no—
1027D4—88no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—21no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—48no—
1084C2×C4—416no—
1085C2×C4—48no—
1086C2×C4—48no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—84no—
1090C2×C4—816no—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)14yes—
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2×2−1+414yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4C2×2−1+412yes—
1103C2×C4C2×2−1+412yes—
1104C2×C4#58512yes—
1105C22—44no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—42no—
1111C22—42no—
1112C22—44no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—44no—
1117C22—44no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×H(5,𝔽2)11yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C22C22×2−1+411yescharacteristic
1131C22C2×#58511yescharacteristic
1132C222−1+611yescharacteristic
1133C4—24no—
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—44no—
1141C4—48no—
1142C4—42no—
1143C4—44no—
1144C4—42no—
1145C4—41no—
1146C4—42no—
1147C4—44no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—44no—
1152C4—42no—
1153C4#354314yes—
1154C4#354714yes—
1155C4#355014yes—
1156C2—84no—
1157C2—82no—
1158C2—82no—
1159C2C2×#354311yescharacteristic
1160C2C2×#354711yescharacteristic
1161C2C2×#355011yescharacteristic
1162C2#6291311yescharacteristic
1163C2#6292511yescharacteristic
1164C2#6294211yescharacteristic
1165C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34925C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59646C2semidirect
3. #59042C2semidirect
4. #59036C2semidirect
5. #54859C2semidirect
6. #53108C2semidirect
7. #53082C2semidirect
8. #53045C2semidirect
9. #42786C2semidirect
10. #42624C2semidirect
11. #42457C2semidirect
12. #39625C2semidirect
13. #39505C2semidirect
14. #39481C2semidirect
15. #39343C2semidirect
16. #39343C2semidirect
17. #39156C2semidirect
18. #37640C2semidirect
19. #37634C2semidirect
20. #37625C2semidirect
21. Q8×#127C2semidirect
22. #36134C2semidirect
23. #36134C2semidirect
24. #34945C2semidirect
25. #34941C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#596462
#590422
#590362
#548592
#531082
#530822
#530452
#427862
#426242
#424572
#396252
#395052
#394812
#393432
#391562
#376402
#376342
#376252
Q8×#1272
#361342
#349452
#349412
#349252