Finite Group Databasebeta

← #8429500

Subgroups — #8429500

Order 512.

5001 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59817C212yesmaximal, complemented
3#59647C212yesmaximal
4#59127C212yesmaximal, complemented
5#53451C218yesmaximal, complemented
6#53136C214yesmaximal, complemented
7#53118C214yesmaximal, complemented
8#53001C214yesmaximal, complemented
9#42807C214yesmaximal, complemented
10#42561C214yesmaximal, complemented
11#42551C214yesmaximal, complemented
12#39633C212yesmaximal, complemented
13#39625C212yesmaximal, complemented
14#39167C212yesmaximal, complemented
15#39156C212yesmaximal, complemented
16#38954C212yesmaximal, complemented
17#38911C212yesmaximal, complemented
18#37629C212yesmaximal, complemented
19#37628C212yesmaximal, complemented
20#37615C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22Q8×#127C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34951C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34934C211yesmaximal, characteristic
27C2×#556C2212yes—
28C2×D4×Q8C2212yes—
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2214yes—
32C2×D4×Q8C2212yes—
33C22×C4⋊Q8C2212yes—
34C2×#529C2212yes—
35#2868C2211yescharacteristic
36#2868C2212yes—
37#2862C2212yes—
38#2857C2212yes—
39#2838C2218yes—
40#2838C2218yes—
41#2836C2218yes—
42#2830C2218yes—
43#2827C2218yes—
44#2821C2218yes—
45#2817C2218yes—
46#2797C2218yes—
47#2796C2218yes—
48#2792C2218yes—
49#2790C2218yes—
50#2777C2218yes—
51#2740C2218yes—
52#2734C2218yes—
53#2729C2218yes—
54#2729C2218yes—
55#2728C2218yes—
56#2727C2214yes—
57#2723C2218yes—
58#2723C2218yes—
59#2698C2218yes—
60#2698C2218yes—
61#2689C2218yes—
62#2687C2218yes—
63#2683C2218yes—
64#2677C2218yes—
65#2660C2214yes—
66#2654C2218yes—
67#2647C2214yes—
68#2644C2214yes—
69#2644C2214yes—
70#2640C2214yes—
71#2640C2214yes—
72#2638C2218yes—
73#2638C2218yes—
74#2625C2214yes—
75#2623C2218yes—
76#2621C2214yes—
77#2621C2214yes—
78#2600C2218yes—
79#2585C2214yes—
80#2582C2211yescharacteristic
81#2582C2212yes—
82#2573C2214yes—
83#2571C2212yes—
84#2571C2211yescharacteristic
85#2570C2214yes—
86#2568C2211yescharacteristic
87#2568C2211yescharacteristic
88#2568C2212yes—
89#2567C2214yes—
90#2554C2214yes—
91#2552C2211yescharacteristic
92#2552C2211yescharacteristic
93#2551C2212yes—
94#2551C2212yes—
95#2551C2214yes—
96#2551C2214yes—
97#2550C2214yes—
98#2548C2211yescharacteristic
99#2548C2212yes—
100#2547C2211yescharacteristic
101#2546C2212yes—
102#2546C2211yescharacteristic
103#2544C2214yes—
104#2542C2214yes—
105#2542C2214yes—
106#2542C2212yes—
107#2542C2212yes—
108#2542C2214yes—
109#2542C2212yes—
110#2542C2212yes—
111#2541C2211yescharacteristic
112#2538C2211yescharacteristic
113#2538C2211yescharacteristic
114#2538C2214yes—
115#2538C2212yes—
116#2514C2212yes—
117#2513C2214yes—
118#2512C2214yes—
119#2512C2212yes—
120#2511C2214yes—
121#2511C2212yes—
122#2509C2212yes—
123#2507C2214yes—
124#2504C2214yes—
125#2502C2214yes—
126#2499C2214yes—
127#2497C2214yes—
128#2494C2212yes—
129#2492C2214yes—
130#2490C2212yes—
131#2490C2214yes—
132#2453C2212yes—
133#2452C2214yes—
134#2452C2214yes—
135#2452C2218yes—
136#2452C2214yes—
137#2451C2214yes—
138#2451C2214yes—
139#2449C2218yes—
140#2448C2214yes—
141#2447C2214yes—
142#2447C2214yes—
143#2447C2212yes—
144#2447C2214yes—
145#2446C2212yes—
146#2446C2214yes—
147#2445C2212yes—
148#2440C2214yes—
149#2440C2214yes—
150#2440C2214yes—
151#2434C2214yes—
152#2434C2214yes—
153#2429C2214yes—
154#2426C2212yes—
155#2421C2212yes—
156#2421C2214yes—
157#2420C2214yes—
158#2415C2214yes—
159#2415C2214yes—
160#2415C2214yes—
161#2409C2214yes—
162#2409C2214yes—
163#2409C2214yes—
164#2409C2214yes—
165#2402C2214yes—
166#2401C2214yes—
167#2392C2214yes—
168#2366C2214yes—
169#2365C2212yes—
170#2361C2214yes—
171#2355C2212yes—
172#2355C2212yes—
173#2354C2212yes—
174Q8×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177#2330C2214yes—
178#2326C2214yes—
179#2310C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2212yes—
184C4×#127C2212yes—
185C4×#127C2211yescharacteristic
186C4×#127C2212yes—
187C4×#125C2212yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200C23×Q8C2314yes—
201#556—48no—
202D4×Q8—48no—
203D4×Q8—48no—
204D4×Q8—48no—
205D4×Q8—48no—
206D4×Q8—416no—
207C2×C4⋊Q8—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2318yes—
222C2×#127C2311yescharacteristic
223C2×#127C2312yes—
224#529—48no—
225C2×#126C2314yes—
226C2×#126C2318yes—
227C2×#125C2312yes—
228C2×#125C2312yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#124C2314yes—
232C2×#123C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2318yes—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C42C2312yes—
277#401C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2318yes—
313#397C2314yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#396C2318yes—
323#396C2318yes—
324#396C2314yes—
325#396C2318yes—
326#396C2318yes—
327#396C2314yes—
328#396C2314yes—
329#395C2318yes—
330#395C2318yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#395C2318yes—
336#395C2318yes—
337#394C2314yes—
338#394C2318yes—
339#394C2314yes—
340#394C2318yes—
341#394C2318yes—
342#394C2314yes—
343#393C2318yes—
344#393C2318yes—
345#393C2318yes—
346#393C2318yes—
347#392C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2318yes—
357#391C2318yes—
358#391C2312yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#391C2314yes—
368#391C2312yes—
369#390C2314yes—
370#390C2312yes—
371#390C2312yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2312yes—
376#390C2314yes—
377#390C2312yes—
378#390C2312yes—
379#390C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2318yes—
384#390C2312yes—
385#390C2312yes—
386#390C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2312yes—
397#389C2318yes—
398#389C2318yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2318yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2318yes—
411#389C2312yes—
412#389C2312yes—
413#389C2318yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2314yes—
428#388C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2318yes—
432#387C2318yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2318yes—
439#387C2318yes—
440#387C2314yes—
441#387C2314yes—
442#387C2318yes—
443#387C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2314yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#384C2312yes—
459#384C2312yes—
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2312yes—
464#384C2314yes—
465#384C2312yes—
466#384C2312yes—
467#384C2314yes—
468#384C2312yes—
469#384C2314yes—
470#384C2314yes—
471#383C2314yes—
472#382C2312yes—
473#382C2314yes—
474#382C2312yes—
475#382C2314yes—
476#382C2314yes—
477#382C2312yes—
478#382C2312yes—
479#381C2318yes—
480#381C2318yes—
481#381C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2311yescharacteristic
515C4×C4⋊C4C2311yescharacteristic
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523#376C2314yes—
524C43C2312yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C22×Q8—216no—
528C22×Q8—48no—
529C22×Q8—48no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2418yes—
539C22×Q8C2418yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2414yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2418yes—
551C23×C4C2418yes—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—44no—
564C4⋊Q8—48no—
565C4⋊Q8—416no—
566#127—28no—
567#127—24no—
568#126—48no—
569#126—416no—
570#125—28no—
571#125—44no—
572#124—28no—
573#124—44no—
574#124—48no—
575#123—48no—
576C22⋊Q8—28no—
577C22⋊Q8—416no—
578C22⋊Q8—416no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—44no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—416no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590#121—28no—
591#121—44no—
592C4×Q8—24no—
593C4×Q8—24no—
594C4×Q8—24no—
595C4×Q8—24no—
596C4×Q8—24no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—24no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—24no—
605C4×D4—28no—
606C4×D4—24no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—44no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—416no—
615#117—48no—
616#117—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C42—28no—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2418yes—
722C2×C42C2418yes—
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24C2514yes—
774C24C2512yes—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—24no—
785C2×Q8—216no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8—48no—
793C2×Q8—48no—
794C2×Q8—48no—
795C2×Q8—832no—
796C2×Q8—832no—
797C2×Q8H(5,𝔽2)14yes—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—28no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D42−1+414yes—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—216no—
828C22×C4—42no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2518yes—
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C42−1+414yes—
915C22⋊C4—24no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—48no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—22no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—22no—
952C42—22no—
953C42—24no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—41no—
960C42—42no—
961C42—42no—
962C42—48no—
963C42—48no—
964C42H(5,𝔽2)14yes—
965C42H(5,𝔽2)14yes—
966C422−1+414yes—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23C2×2−1+414yes—
981C23C2611yescharacteristic
982Q8—28no—
983Q8—48no—
984Q8—416no—
985Q8—44no—
986Q8—48no—
987Q8—816no—
988Q8—816no—
989D4—28no—
990D4—416no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—88no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—48no—
1054C2×C4—416no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—816no—
1058C2×C4—816no—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)14yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×2−1+414yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+412yes—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22C22×H(5,𝔽2)11yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×2−1+411yescharacteristic
1091C22C22×2−1+411yescharacteristic
1092C22C22×2−1+411yescharacteristic
1093C222−1+611yescharacteristic
1094C4—24no—
1095C4—24no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—44no—
1100C4—42no—
1101C4—44no—
1102C4—48no—
1103C4—44no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—42no—
1109C4—44no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—42no—
1115C4#354314yes—
1116C4#355014yes—
1117C4#355214yes—
1118C2—44no—
1119C2—84no—
1120C2C2×#354311yescharacteristic
1121C2C2×#355211yescharacteristic
1122C2C2×#355011yescharacteristic
1123C2#6291311yescharacteristic
1124C2#6294211yescharacteristic
1125C2#6294611yescharacteristic
1126C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59817C2semidirect
4. #59127C2semidirect
5. #53451C2semidirect
6. #53136C2semidirect
7. #53118C2semidirect
8. #53001C2semidirect
9. #42807C2semidirect
10. #42561C2semidirect
11. #42551C2semidirect
12. #39633C2semidirect
13. #39625C2semidirect
14. #39167C2semidirect
15. #39156C2semidirect
16. #38954C2semidirect
17. #38911C2semidirect
18. #37629C2semidirect
19. #37628C2semidirect
20. #37615C2semidirect
21. #36598C2semidirect
22. Q8×#127C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34951C2semidirect
25. #34945C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#598172
#596472
#591272
#534512
#531362
#531182
#530012
#428072
#425612
#425512
#396332
#396252
#391672
#391562
#389542
#389112
#376292
#376282
#376152
#365982
Q8×#1272
D4×C4⋊Q82
#349512
#349452
#349342