Finite Group Databasebeta

← #8429488

Subgroups — #8429488

Order 512.

5093 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59654C212yesmaximal, complemented
3#59305C212yesmaximal, complemented
4#59125C212yesmaximal, complemented
5#53436C218yesmaximal, complemented
6#53039C214yesmaximal, complemented
7#53011C214yesmaximal, complemented
8#52992C214yesmaximal, complemented
9#42926C214yesmaximal, complemented
10#42576C214yesmaximal, complemented
11#42514C214yesmaximal, complemented
12#39618C212yesmaximal, complemented
13#39148C212yesmaximal, complemented
14#38955C212yesmaximal, complemented
15#38941C212yesmaximal, complemented
16#38930C212yesmaximal, complemented
17#38908C212yesmaximal, complemented
18#37628C212yesmaximal, complemented
19#37623C212yesmaximal, complemented
20#37615C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36179C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34943C211yesmaximal, characteristic, complemented
26#34934C211yesmaximal, characteristic, complemented
27C2×#554C2212yes—
28C2×D4×Q8C2212yes—
29C2×#548C2214yes—
30C2×#547C2212yes—
31C2×#547C2212yes—
32C2×#547C2212yes—
33C22×C4⋊Q8C2212yes—
34C2×#529C2212yes—
35#2868C2211yescharacteristic
36#2862C2212yes—
37#2857C2212yes—
38#2856C2212yes—
39#2843C2218yes—
40#2841C2218yes—
41#2838C2218yes—
42#2836C2218yes—
43#2827C2218yes—
44#2821C2218yes—
45#2814C2218yes—
46#2790C2218yes—
47#2749C2218yes—
48#2746C2218yes—
49#2743C2218yes—
50#2738C2218yes—
51#2737C2218yes—
52#2732C2214yes—
53#2717C2218yes—
54#2708C2218yes—
55#2695C2218yes—
56#2693C2218yes—
57#2692C2218yes—
58#2692C2218yes—
59#2688C2218yes—
60#2687C2218yes—
61#2687C2218yes—
62#2686C2218yes—
63#2681C2218yes—
64#2674C2218yes—
65#2660C2214yes—
66#2660C2214yes—
67#2654C2218yes—
68#2647C2214yes—
69#2647C2214yes—
70#2644C2214yes—
71#2640C2214yes—
72#2630C2218yes—
73#2627C2218yes—
74#2625C2214yes—
75#2623C2218yes—
76#2621C2214yes—
77#2621C2214yes—
78#2582C2212yes—
79#2579C2218yes—
80#2573C2214yes—
81#2572C2214yes—
82#2571C2211yescharacteristic
83#2571C2211yescharacteristic
84#2571C2212yes—
85#2570C2214yes—
86#2568C2211yescharacteristic
87#2568C2212yes—
88#2566C2214yes—
89#2563C2214yes—
90#2563C2211yescharacteristic
91#2563C2211yescharacteristic
92#2554C2214yes—
93#2552C2211yescharacteristic
94#2552C2212yes—
95#2551C2212yes—
96#2551C2212yes—
97#2548C2211yescharacteristic
98#2547C2211yescharacteristic
99#2546C2212yes—
100#2542C2212yes—
101#2542C2212yes—
102#2542C2212yes—
103#2542C2212yes—
104#2541C2211yescharacteristic
105#2538C2214yes—
106#2538C2212yes—
107#2538C2211yescharacteristic
108#2538C2211yescharacteristic
109#2537C2211yescharacteristic
110#2536C2214yes—
111#2535C2214yes—
112#2514C2212yes—
113#2513C2214yes—
114#2512C2212yes—
115#2511C2214yes—
116#2507C2214yes—
117#2504C2214yes—
118#2503C2214yes—
119#2502C2214yes—
120#2501C2214yes—
121#2501C2214yes—
122#2501C2214yes—
123#2497C2214yes—
124#2495C2212yes—
125#2495C2212yes—
126#2494C2212yes—
127#2491C2214yes—
128#2491C2214yes—
129#2490C2212yes—
130#2461C2218yes—
131#2454C2214yes—
132#2447C2212yes—
133#2446C2214yes—
134#2445C2212yes—
135#2443C2218yes—
136#2442C2214yes—
137#2442C2214yes—
138#2442C2214yes—
139#2440C2214yes—
140#2440C2214yes—
141#2440C2214yes—
142#2440C2214yes—
143#2434C2214yes—
144#2432C2214yes—
145#2429C2214yes—
146#2428C2214yes—
147#2427C2214yes—
148#2426C2212yes—
149#2421C2212yes—
150#2421C2214yes—
151#2420C2214yes—
152#2420C2214yes—
153#2420C2214yes—
154#2420C2212yes—
155#2420C2212yes—
156#2417C2214yes—
157#2417C2214yes—
158#2417C2214yes—
159#2417C2214yes—
160#2416C2214yes—
161#2409C2214yes—
162#2409C2214yes—
163#2409C2214yes—
164#2407C2214yes—
165#2401C2214yes—
166#2398C2214yes—
167#2392C2214yes—
168#2366C2212yes—
169#2365C2212yes—
170#2361C2214yes—
171#2355C2212yes—
172#2355C2212yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2214yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177#2328C2214yes—
178#2319C2214yes—
179#2311C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192C2×#384C2212yes—
193#2283C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200C23×Q8C2314yes—
201#554—48no—
202D4×Q8—48no—
203#548—416no—
204#547—48no—
205#547—48no—
206#547—48no—
207C2×C4⋊Q8—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×#127C2312yes—
218C2×#127C2311yescharacteristic
219#529—48no—
220C2×#126C2314yes—
221C2×#125C2314yes—
222C2×#125C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280#401C2314yes—
281#400C2314yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2314yes—
290#400C2318yes—
291#400C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2318yes—
313#397C2318yes—
314#397C2314yes—
315#397C2318yes—
316#397C2318yes—
317#397C2314yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2314yes—
326#396C2314yes—
327#396C2318yes—
328#396C2318yes—
329#396C2314yes—
330#395C2318yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#394C2314yes—
336#394C2318yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2318yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#393C2318yes—
345#393C2314yes—
346#393C2314yes—
347#393C2318yes—
348#393C2318yes—
349#392C2318yes—
350#392C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2314yes—
367#390C2312yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2314yes—
374#390C2312yes—
375#390C2312yes—
376#390C2314yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#388C2314yes—
411#388C2318yes—
412#388C2314yes—
413#388C2318yes—
414#388C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2314yes—
454#384C2312yes—
455#384C2314yes—
456#383C2314yes—
457#383C2314yes—
458#383C2314yes—
459#382C2312yes—
460#382C2314yes—
461#382C2312yes—
462#382C2314yes—
463#382C2312yes—
464#382C2314yes—
465#382C2312yes—
466#382C2312yes—
467#382C2312yes—
468#382C2312yes—
469#381C2314yes—
470#381C2314yes—
471#381C2314yes—
472#381C2318yes—
473#381C2318yes—
474#380C2318yes—
475#380C2318yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2318yes—
481#380C2318yes—
482#380C2318yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2314yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2314yes—
523#376C2314yes—
524#376C2314yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C2×#41—216no—
528C2×#41—48no—
529C2×#41—48no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2414yes—
546C22×D4C2418yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2418yes—
555C23×C4C2418yes—
556C23×C4C2418yes—
557C4⋊Q8—24no—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—24no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566#127—28no—
567#127—24no—
568#126—48no—
569#125—44no—
570#125—48no—
571#124—28no—
572#124—44no—
573#124—416no—
574#123—416no—
575#123—416no—
576#123—48no—
577#123—416no—
578C22⋊Q8—416no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589#121—28no—
590#121—28no—
591#121—416no—
592#121—44no—
593#121—44no—
594#121—48no—
595#121—48no—
596#121—48no—
597C4×Q8—24no—
598C4×Q8—28no—
599C4×Q8—24no—
600C4×Q8—44no—
601C4×Q8—42no—
602C4×Q8—48no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—28no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—28no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—416no—
619#117—48no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4—48no—
624C2×C4⋊C4—48no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C42—28no—
711C2×C42—28no—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2418yes—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24C2514yes—
777C24C2512yes—
778C24C2512yes—
779#41—832no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—42no—
791C2×Q8—48no—
792C2×Q8—48no—
793C2×Q8—48no—
794C2×Q8—42no—
795C2×Q8—832no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—216no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—22no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—44no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4H(5,𝔽2)14yes—
822C2×D42−1+414yes—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—216no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2518yes—
869C22×C4C2514yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—42no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—42no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—24no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—28no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—22no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—22no—
975C42—41no—
976C42—42no—
977C42—48no—
978C42—42no—
979C42H(5,𝔽2)14yes—
980C42H(5,𝔽2)14yes—
981C422−1+414yes—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23C2×H(5,𝔽2)14yes—
1002C23C2×2−1+414yes—
1003C23C2611yescharacteristic
1004Q8—48no—
1005Q8—416no—
1006Q8—44no—
1007Q8—84no—
1008Q8—816no—
1009D4—28no—
1010D4—28no—
1011D4—416no—
1012D4—48no—
1013D4—48no—
1014D4—84no—
1015D4—88no—
1016D4—88no—
1017D4—816no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—416no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—816no—
1083C2×C4—816no—
1084C2×C4—168no—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4#58512yes—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C222−1+611yescharacteristic
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—44no—
1129C4—42no—
1130C4—48no—
1131C4—44no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—41no—
1137C4—44no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4#354314yes—
1146C4#354714yes—
1147C4#355214yes—
1148C2—44no—
1149C2—44no—
1150C2—84no—
1151C2C2×#354311yescharacteristic
1152C2C2×#355211yescharacteristic
1153C2C2×#354711yescharacteristic
1154C2#6291511yescharacteristic
1155C2#6293111yescharacteristic
1156C2#6294211yescharacteristic
1157C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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. #59654C2semidirect
3. #59305C2semidirect
4. #59125C2semidirect
5. #53436C2semidirect
6. #53039C2semidirect
7. #53011C2semidirect
8. #52992C2semidirect
9. #42926C2semidirect
10. #42576C2semidirect
11. #42514C2semidirect
12. #39618C2semidirect
13. #39148C2semidirect
14. #38955C2semidirect
15. #38941C2semidirect
16. #38930C2semidirect
17. #38908C2semidirect
18. #37628C2semidirect
19. #37623C2semidirect
20. #37615C2semidirect
21. #36598C2semidirect
22. #36179C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34945C2semidirect
25. #34943C2semidirect
26. #34934C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#596542
#593052
#591252
#534362
#530392
#530112
#529922
#429262
#425762
#425142
#396182
#391482
#389552
#389412
#389302
#389082
#376282
#376232
#376152
#365982
#361792
D4×C4⋊Q82
#349452
#349432
#349342