Finite Group Databasebeta

← #7987059

Subgroups — #7987059

Order 512.

4729 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59659C212yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59245C212yesmaximal, complemented
5#50316C218yesmaximal, complemented
6#46062C214yesmaximal, complemented
7#45290C214yesmaximal, complemented
8#45040C214yesmaximal, complemented
9#42874C214yesmaximal, complemented
10#42754C214yesmaximal, complemented
11#39761C212yesmaximal, complemented
12#39505C212yesmaximal, complemented
13#39249C214yesmaximal, complemented
14#38958C212yesmaximal, complemented
15#38941C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×#124C212yesmaximal, complemented
19#36460C212yesmaximal, complemented
20#36187C211yesmaximal, characteristic
21#35192C212yesmaximal, complemented
22#35185C212yesmaximal, complemented
23#34954C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34487C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#556C2211yescharacteristic
29C2×#555C2212yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2212yes—
32#2868C2212yes—
33#2868C2211yescharacteristic
34#2864C2214yes—
35#2862C2212yes—
36#2862C2214yes—
37#2860C2214yes—
38#2856C2212yes—
39#2832C2218yes—
40#2808C2218yes—
41#2798C2218yes—
42#2795C2218yes—
43#2793C2218yes—
44#2788C2218yes—
45#2759C2218yes—
46#2745C2218yes—
47#2737C2218yes—
48#2731C2218yes—
49#2731C2218yes—
50#2716C2218yes—
51#2715C2218yes—
52#2702C2218yes—
53#2700C2218yes—
54#2700C2218yes—
55#2686C2218yes—
56#2683C2214yes—
57#2665C2218yes—
58#2650C2218yes—
59#2649C2218yes—
60#2640C2214yes—
61#2620C2214yes—
62#2605C2218yes—
63#2593C2214yes—
64#2588C2218yes—
65#2582C2212yes—
66#2582C2211yescharacteristic
67#2573C2218yes—
68#2573C2214yes—
69#2571C2212yes—
70#2571C2211yescharacteristic
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2568C2212yes—
74#2568C2214yes—
75#2568C2211yescharacteristic
76#2567C2212yes—
77#2567C2214yes—
78#2563C2214yes—
79#2563C2212yes—
80#2560C2218yes—
81#2559C2218yes—
82#2551C2214yes—
83#2551C2212yes—
84#2551C2212yes—
85#2551C2214yes—
86#2551C2212yes—
87#2548C2211yescharacteristic
88#2548C2211yescharacteristic
89#2547C2211yescharacteristic
90#2545C2218yes—
91#2538C2211yescharacteristic
92#2538C2212yes—
93#2538C2212yes—
94#2537C2212yes—
95#2537C2212yes—
96#2526C2218yes—
97#2514C2212yes—
98#2513C2214yes—
99#2513C2212yes—
100#2513C2212yes—
101#2512C2214yes—
102#2511C2214yes—
103#2511C2214yes—
104#2509C2214yes—
105#2500C2214yes—
106#2500C2214yes—
107#2499C2214yes—
108#2497C2214yes—
109#2496C2214yes—
110#2494C2212yes—
111#2492C2214yes—
112#2492C2218yes—
113#2492C2214yes—
114#2492C2214yes—
115#2492C2218yes—
116#2491C2214yes—
117#2491C2214yes—
118#2491C2214yes—
119#2491C2214yes—
120#2491C2214yes—
121#2469C2218yes—
122#2452C2214yes—
123#2452C2214yes—
124#2448C2212yes—
125#2448C2212yes—
126#2447C2212yes—
127#2446C2214yes—
128#2439C2214yes—
129#2439C2214yes—
130#2439C2214yes—
131#2439C2214yes—
132#2439C2214yes—
133#2439C2214yes—
134#2436C2214yes—
135#2427C2214yes—
136#2426C2214yes—
137#2426C2214yes—
138#2421C2214yes—
139#2421C2212yes—
140#2420C2214yes—
141#2420C2214yes—
142#2409C2214yes—
143#2401C2214yes—
144#2395C2214yes—
145#2378C2218yes—
146#2373C2214yes—
147#2369C2214yes—
148#2367C2212yes—
149#2366C2212yes—
150#2365C2211yescharacteristic
151#2365C2212yes—
152#2363C2214yes—
153#2362C2212yes—
154#2362C2214yes—
155#2362C2214yes—
156#2357C2214yes—
157#2356C2212yes—
158#2355C2212yes—
159#2355C2212yes—
160#2355C2211yescharacteristic
161#2354C2211yescharacteristic
162#2354C2212yes—
163#2354C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166#2347C2212yes—
167Q8×C22⋊C4C2214yes—
168Q8×C22⋊C4C2214yes—
169#2332C2218yes—
170#2331C2214yes—
171#2331C2214yes—
172#2323C2214yes—
173#2319C2214yes—
174#2314C2214yes—
175#2310C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#127C2211yescharacteristic
181C4×#126C2214yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2214yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2293C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C23×Q8C2314yes—
200Q82—48no—
201#556—28no—
202#555—48no—
203D4×Q8—216no—
204D4×Q8—48no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2318yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126C2314yes—
219C2×#126C2318yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C2×#117C2314yes—
262C22×C42C2312yes—
263#401C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#399C2314yes—
275#398C2318yes—
276#398C2314yes—
277#397C2318yes—
278#397C2314yes—
279#397C2314yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2318yes—
287#396C2314yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2314yes—
303#394C2314yes—
304#394C2318yes—
305#394C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#391C2318yes—
315#391C2314yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2318yes—
332#391C2314yes—
333#391C2312yes—
334#391C2318yes—
335#391C2318yes—
336#391C2318yes—
337#391C2318yes—
338#391C2314yes—
339#391C2312yes—
340#390C2318yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#383C2314yes—
445#383C2314yes—
446#382C2312yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#382C2312yes—
451#382C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#381C2318yes—
457#381C2318yes—
458#381C2314yes—
459#380C2314yes—
460#380C2318yes—
461#380C2314yes—
462#380C2318yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2314yes—
520C43C2314yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C43C2312yes—
524C22×Q8—216no—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2414yes—
532C22×Q8C2418yes—
533C22×Q8C2418yes—
534C22×D4C2411yescharacteristic
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2418yes—
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2412yes—
544C4⋊Q8—216no—
545C4⋊Q8—24no—
546C4⋊Q8—28no—
547C4⋊Q8—44no—
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—48no—
552C4⋊Q8—416no—
553C4⋊Q8—82no—
554C4⋊Q8—84no—
555C4⋊Q8#4118yes—
556#127—24no—
557#126—216no—
558#126—88no—
559#124—28no—
560#124—28no—
561#124—44no—
562#124—44no—
563#124—416no—
564#124—88no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—232no—
568C22⋊Q8—28no—
569C22⋊Q8—416no—
570C22⋊Q8—48no—
571#121—48no—
572#121—48no—
573#121—48no—
574#121—84no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—28no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—44no—
584C4×Q8—42no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—84no—
588C4×D4—216no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—42no—
594C4×D4—48no—
595C4×D4—44no—
596#117—28no—
597#117—48no—
598#117—44no—
599#117—48no—
600#117—48no—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C42—28no—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2411yescharacteristic
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2418yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#95C2412yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2414yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757C24C2512yes—
758C24C2514yes—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—216no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—44no—
772C2×Q8—48no—
773C2×Q8—44no—
774C2×Q8—48no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—48no—
778C2×Q8—832no—
779C2×Q8C2×#4118yes—
780C2×Q82−1+414yes—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—24no—
805C22×C4—216no—
806C22×C4—24no—
807C22×C4—48no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—48no—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2518yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—216no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—28no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—42no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—42no—
881C4⋊C4—44no—
882C4⋊C4C2×#4118yes—
883C4⋊C4C2×#4118yes—
884C22⋊C4—28no—
885C22⋊C4—216no—
886C22⋊C4—28no—
887C22⋊C4—24no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—24no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—42no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C42—28no—
914C42—28no—
915C42—24no—
916C42—28no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—22no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—22no—
929C42—22no—
930C42—24no—
931C42—44no—
932C42—48no—
933C42—42no—
934C42—44no—
935C42—48no—
936C42—42no—
937C42—48no—
938C42—44no—
939C42—41no—
940C42—42no—
941C42C2×#4114yes—
942C42H(5,𝔽2)14yes—
943C422−1+414yes—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23C2611yescharacteristic
959Q8—216no—
960Q8—28no—
961Q8—48no—
962Q8—44no—
963Q8—88no—
964Q8—816no—
965Q8—168no—
966D4—44no—
967D4—48no—
968D4—48no—
969D4—84no—
970D4—168no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—28no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—28no—
1029C2×C4—416no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—84no—
1033C2×C4—816no—
1034C2×C4C22×#4118yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×2−1+412yes—
1042C2×C4C2×2−1+414yes—
1043C2×C4C2×2−1+412yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4#58512yes—
1047C2×C4#58512yes—
1048C22—42no—
1049C22—44no—
1050C22—42no—
1051C22—44no—
1052C22—44no—
1053C22—42no—
1054C22—42no—
1055C22—44no—
1056C22—42no—
1057C22—44no—
1058C22—42no—
1059C22—44no—
1060C22—42no—
1061C22—44no—
1062C22C23×#4111yescharacteristic
1063C22C22×H(5,𝔽2)11yescharacteristic
1064C22C22×2−1+411yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C2×#58511yescharacteristic
1067C22C2×#58511yescharacteristic
1068C22H(7,𝔽2)11yescharacteristic
1069C4—22no—
1070C4—24no—
1071C4—28no—
1072C4—22no—
1073C4—22no—
1074C4—42no—
1075C4—44no—
1076C4—42no—
1077C4—44no—
1078C4—44no—
1079C4—42no—
1080C4—41no—
1081C4—42no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—48no—
1088C4—44no—
1089C4—42no—
1090C4#351414yes—
1091C4#351814yes—
1092C4#355214yes—
1093C2—82no—
1094C2—84no—
1095C2C2×#355211yescharacteristic
1096C2C2×#351411yescharacteristic
1097C2C2×#351811yescharacteristic
1098C2#6292911yescharacteristic
1099C2#6296111yescharacteristic
1100C2#6299911yescharacteristic
1101C2#6303411yescharacteristic
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. #59817C2semidirect
2. #59659C2semidirect
3. #59421C2semidirect
4. #59245C2semidirect
5. #50316C2semidirect
6. #46062C2semidirect
7. #45290C2semidirect
8. #45040C2semidirect
9. #42874C2semidirect
10. #42754C2semidirect
11. #39761C2semidirect
12. #39505C2semidirect
13. #39249C2semidirect
14. #38958C2semidirect
15. #38941C2semidirect
16. #36598C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×#124C2semidirect
19. #36460C2semidirect
21. #35192C2semidirect
22. #35185C2semidirect
23. #34954C2semidirect
24. #34945C2semidirect
25. #34487C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596592
#594212
#592452
#503162
#460622
#452902
#450402
#428742
#427542
#397612
#395052
#392492
#389582
#389412
#365982
Q8×C4⋊Q82
Q8×#1242
#364602
#361872
#351922
#351852
#349542
#349452
#344872
C4×#5562