Finite Group Databasebeta

← #8429491

Subgroups — #8429491

Order 512.

4735 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59827C212yesmaximal, complemented
3#59641C212yesmaximal
4#59136C212yesmaximal, complemented
5#55526C218yesmaximal, complemented
6#53114C214yesmaximal, complemented
7#53097C214yesmaximal, complemented
8#52999C214yesmaximal, complemented
9#42596C214yesmaximal, complemented
10#42506C214yesmaximal, complemented
11#42481C214yesmaximal, complemented
12#39626C212yesmaximal, complemented
13#39158C212yesmaximal, complemented
14#38977C212yesmaximal, complemented
15#38975C212yesmaximal, complemented
16#38964C212yesmaximal, complemented
17#38921C212yesmaximal, complemented
18#37632C212yesmaximal, complemented
19#37631C212yesmaximal, complemented
20#37629C212yesmaximal, complemented
21#36563C211yesmaximal, characteristic, complemented
22#36559C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34950C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34934C211yesmaximal, characteristic
27C2×#559C2214yes—
28C2×#554C2212yes—
29C2×D4×Q8C2212yes—
30C22×C4⋊Q8C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2859C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2838C2218yes—
37#2836C2218yes—
38#2834C2218yes—
39#2831C2218yes—
40#2830C2218yes—
41#2821C2218yes—
42#2814C2218yes—
43#2808C2214yes—
44#2806C2218yes—
45#2792C2218yes—
46#2765C2218yes—
47#2765C2218yes—
48#2763C2218yes—
49#2761C2218yes—
50#2759C2218yes—
51#2739C2218yes—
52#2729C2218yes—
53#2724C2218yes—
54#2720C2218yes—
55#2710C2218yes—
56#2707C2218yes—
57#2700C2218yes—
58#2700C2218yes—
59#2698C2218yes—
60#2680C2218yes—
61#2680C2218yes—
62#2660C2214yes—
63#2650C2218yes—
64#2645C2214yes—
65#2644C2214yes—
66#2644C2214yes—
67#2640C2214yes—
68#2640C2214yes—
69#2638C2218yes—
70#2638C2218yes—
71#2628C2214yes—
72#2628C2214yes—
73#2625C2214yes—
74#2614C2218yes—
75#2592C2214yes—
76#2586C2214yes—
77#2582C2211yescharacteristic
78#2582C2212yes—
79#2582C2214yes—
80#2580C2214yes—
81#2573C2214yes—
82#2571C2211yescharacteristic
83#2568C2211yescharacteristic
84#2567C2211yescharacteristic
85#2567C2212yes—
86#2567C2211yescharacteristic
87#2567C2214yes—
88#2566C2214yes—
89#2563C2212yes—
90#2563C2212yes—
91#2554C2214yes—
92#2552C2212yes—
93#2552C2214yes—
94#2552C2211yescharacteristic
95#2551C2212yes—
96#2551C2212yes—
97#2551C2211yescharacteristic
98#2550C2214yes—
99#2550C2214yes—
100#2548C2211yescharacteristic
101#2548C2212yes—
102#2547C2214yes—
103#2547C2211yescharacteristic
104#2547C2212yes—
105#2546C2212yes—
106#2541C2211yescharacteristic
107#2538C2211yescharacteristic
108#2538C2212yes—
109#2538C2211yescharacteristic
110#2538C2212yes—
111#2514C2212yes—
112#2513C2214yes—
113#2512C2212yes—
114#2508C2214yes—
115#2507C2212yes—
116#2507C2212yes—
117#2507C2214yes—
118#2507C2214yes—
119#2503C2214yes—
120#2501C2214yes—
121#2494C2214yes—
122#2494C2212yes—
123#2494C2214yes—
124#2492C2214yes—
125#2491C2214yes—
126#2490C2212yes—
127#2489C2214yes—
128#2486C2214yes—
129#2486C2214yes—
130#2486C2214yes—
131#2485C2214yes—
132#2485C2214yes—
133#2455C2218yes—
134#2452C2214yes—
135#2452C2214yes—
136#2452C2214yes—
137#2452C2214yes—
138#2451C2212yes—
139#2451C2212yes—
140#2451C2214yes—
141#2451C2214yes—
142#2448C2214yes—
143#2447C2214yes—
144#2447C2214yes—
145#2447C2218yes—
146#2447C2214yes—
147#2447C2212yes—
148#2445C2214yes—
149#2445C2212yes—
150#2442C2214yes—
151#2440C2214yes—
152#2440C2214yes—
153#2440C2214yes—
154#2439C2214yes—
155#2434C2214yes—
156#2426C2212yes—
157#2422C2214yes—
158#2421C2212yes—
159#2417C2214yes—
160#2415C2214yes—
161#2409C2218yes—
162#2401C2214yes—
163#2399C2214yes—
164#2392C2214yes—
165#2369C2212yes—
166#2361C2214yes—
167#2355C2212yes—
168#2355C2212yes—
169#2354C2212yes—
170#2354C2212yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2214yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177#2331C2214yes—
178#2319C2214yes—
179#2317C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2212yes—
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#127C2212yes—
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—
200#559—416no—
201#554—48no—
202D4×Q8—48no—
203C2×C4⋊Q8—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×#127C2311yescharacteristic
216C2×#127C2312yes—
217#529—48no—
218C2×#126C2314yes—
219C2×#125C2314yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C42C2312yes—
268#401C2314yes—
269#401C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#399C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2314yes—
292#398C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2314yes—
315#396C2314yes—
316#395C2314yes—
317#395C2318yes—
318#395C2314yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2314yes—
323#395C2318yes—
324#395C2318yes—
325#395C2314yes—
326#394C2314yes—
327#394C2318yes—
328#394C2314yes—
329#394C2318yes—
330#394C2314yes—
331#394C2318yes—
332#393C2318yes—
333#393C2318yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#392C2314yes—
339#391C2314yes—
340#391C2312yes—
341#391C2314yes—
342#391C2314yes—
343#391C2312yes—
344#391C2314yes—
345#391C2318yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2318yes—
352#391C2312yes—
353#391C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2314yes—
357#391C2318yes—
358#391C2318yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#390C2312yes—
366#390C2314yes—
367#390C2314yes—
368#390C2312yes—
369#390C2314yes—
370#390C2312yes—
371#390C2312yes—
372#390C2314yes—
373#390C2314yes—
374#390C2312yes—
375#390C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2318yes—
401#389C2314yes—
402#389C2318yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2318yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#388C2314yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2318yes—
425#388C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#386C2318yes—
439#386C2314yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#384C2312yes—
451#384C2312yes—
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2312yes—
459#384C2318yes—
460#384C2314yes—
461#384C2312yes—
462#383C2314yes—
463#382C2314yes—
464#382C2314yes—
465#382C2312yes—
466#382C2312yes—
467#382C2312yes—
468#382C2318yes—
469#382C2314yes—
470#381C2314yes—
471#381C2318yes—
472#381C2318yes—
473#381C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8—48no—
525C22×Q8—48no—
526C22×Q8—84no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2418yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2418yes—
546C4⋊Q8—28no—
547C4⋊Q8—24no—
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—48no—
551C4⋊Q8—48no—
552C4⋊Q8—44no—
553C4⋊Q8—48no—
554C4⋊Q8—44no—
555C4⋊Q8—48no—
556C4⋊Q8—82no—
557#127—28no—
558#127—24no—
559#126—48no—
560#125—44no—
561#125—48no—
562#125—84no—
563#124—28no—
564#124—44no—
565#124—48no—
566#124—416no—
567#123—416no—
568#123—48no—
569#123—416no—
570#123—88no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—416no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—48no—
577C22⋊Q8—88no—
578#121—28no—
579#121—44no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—24no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×Q8—42no—
589C4×Q8—48no—
590C4×D4—24no—
591C4×D4—216no—
592C4×D4—28no—
593C4×D4—24no—
594C4×D4—28no—
595C4×D4—24no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—44no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—416no—
602C4×D4—84no—
603#117—48no—
604#117—48no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C42—28no—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2418yes—
710C2×C42C2412yes—
711C2×C42C2418yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
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#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24C2514yes—
763C24C2512yes—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—22no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—48no—
781C2×Q8—48no—
782C2×Q8—48no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—832no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—28no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—42no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4H(5,𝔽2)14yes—
804C22×C4—24no—
805C22×C4—216no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—42no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2518yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C4⋊C4—22no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C42−1+414yes—
903C22⋊C4—24no—
904C22⋊C4—216no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—24no—
909C22⋊C4—28no—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—22no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—28no—
943C42—24no—
944C42—22no—
945C42—24no—
946C42—48no—
947C42—48no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—41no—
952C42H(5,𝔽2)14yes—
953C422−1+414yes—
954C422−1+414yes—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23C2×H(5,𝔽2)14yes—
969C23C2611yescharacteristic
970Q8—48no—
971Q8—48no—
972Q8—44no—
973Q8—44no—
974Q8—88no—
975Q8—88no—
976Q8—816no—
977D4—28no—
978D4—416no—
979D4—48no—
980D4—48no—
981D4—48no—
982D4—88no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—28no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—416no—
1046C2×C4—816no—
1047C2×C4—168no—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×2−1+414yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4C2×2−1+412yes—
1059C2×C4C2×2−1+412yes—
1060C2×C4#58512yes—
1061C22—24no—
1062C22—24no—
1063C22—24no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×H(5,𝔽2)11yescharacteristic
1077C22C22×2−1+411yescharacteristic
1078C22C22×2−1+411yescharacteristic
1079C22C22×2−1+411yescharacteristic
1080C22C2×#58511yescharacteristic
1081C22H(7,𝔽2)11yescharacteristic
1082C4—24no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—42no—
1087C4—44no—
1088C4—42no—
1089C4—44no—
1090C4—41no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—44no—
1097C4—48no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—42no—
1103C4#354414yes—
1104C4#355014yes—
1105C4#355414yes—
1106C2—44no—
1107C2—84no—
1108C2C2×#355411yescharacteristic
1109C2C2×#354411yescharacteristic
1110C2C2×#355011yescharacteristic
1111C2#6291211yescharacteristic
1112C2#6292611yescharacteristic
1113C2#6294311yescharacteristic
1114C2#6301311yescharacteristic
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. #59863C2semidirect
2. #59827C2semidirect
4. #59136C2semidirect
5. #55526C2semidirect
6. #53114C2semidirect
7. #53097C2semidirect
8. #52999C2semidirect
9. #42596C2semidirect
10. #42506C2semidirect
11. #42481C2semidirect
12. #39626C2semidirect
13. #39158C2semidirect
14. #38977C2semidirect
15. #38975C2semidirect
16. #38964C2semidirect
17. #38921C2semidirect
18. #37632C2semidirect
19. #37631C2semidirect
20. #37629C2semidirect
21. #36563C2semidirect
22. #36559C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34950C2semidirect
25. #34945C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#598272
#596412
#591362
#555262
#531142
#530972
#529992
#425962
#425062
#424812
#396262
#391582
#389772
#389752
#389642
#389212
#376322
#376312
#376292
#365632
#365592
D4×C4⋊Q82
#349502
#349452
#349342