Finite Group Databasebeta

← #7986732

Subgroups — #7986732

Order 512.

4615 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59639C212yesmaximal, complemented
3#59234C212yesmaximal, complemented
4#59081C212yesmaximal, complemented
5#51382C218yesmaximal, complemented
6#46117C214yesmaximal, complemented
7#45348C214yesmaximal, complemented
8#45065C214yesmaximal, complemented
9#42549C214yesmaximal, complemented
10#42457C214yesmaximal, complemented
11#40179C214yesmaximal, complemented
12#39727C212yesmaximal, complemented
13#39609C212yesmaximal, complemented
14#39505C212yesmaximal
15#39125C212yesmaximal, complemented
16#36563C212yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36480C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35201C212yesmaximal, complemented
22#35184C212yesmaximal, complemented
23#34932C211yesmaximal, characteristic
24#34929C211yesmaximal, characteristic, complemented
25#34374C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×Q82C2212yes—
28C2×#556C2211yescharacteristic
29C2×#533C2212yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2868C2212yes—
34#2863C2214yes—
35#2861C2214yes—
36#2859C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2838C2218yes—
40#2810C2214yes—
41#2801C2218yes—
42#2798C2218yes—
43#2795C2218yes—
44#2777C2218yes—
45#2776C2218yes—
46#2775C2218yes—
47#2774C2218yes—
48#2759C2218yes—
49#2758C2218yes—
50#2742C2218yes—
51#2731C2218yes—
52#2729C2218yes—
53#2725C2218yes—
54#2716C2218yes—
55#2702C2218yes—
56#2674C2218yes—
57#2663C2218yes—
58#2654C2218yes—
59#2632C2218yes—
60#2628C2214yes—
61#2620C2214yes—
62#2605C2218yes—
63#2604C2218yes—
64#2596C2218yes—
65#2592C2214yes—
66#2582C2214yes—
67#2571C2212yes—
68#2568C2212yes—
69#2568C2212yes—
70#2568C2212yes—
71#2567C2214yes—
72#2567C2212yes—
73#2567C2214yes—
74#2563C2212yes—
75#2556C2214yes—
76#2553C2214yes—
77#2552C2212yes—
78#2552C2211yescharacteristic
79#2551C2214yes—
80#2551C2212yes—
81#2551C2212yes—
82#2551C2211yescharacteristic
83#2551C2214yes—
84#2550C2214yes—
85#2550C2214yes—
86#2547C2214yes—
87#2547C2211yescharacteristic
88#2546C2211yescharacteristic
89#2542C2212yes—
90#2542C2211yescharacteristic
91#2542C2211yescharacteristic
92#2538C2212yes—
93#2538C2212yes—
94#2538C2211yescharacteristic
95#2537C2211yescharacteristic
96#2536C2214yes—
97#2525C2218yes—
98#2525C2218yes—
99#2514C2214yes—
100#2514C2214yes—
101#2514C2214yes—
102#2513C2214yes—
103#2511C2214yes—
104#2509C2214yes—
105#2507C2218yes—
106#2506C2212yes—
107#2500C2214yes—
108#2499C2214yes—
109#2497C2214yes—
110#2497C2214yes—
111#2496C2212yes—
112#2495C2214yes—
113#2492C2214yes—
114#2492C2214yes—
115#2492C2212yes—
116#2492C2214yes—
117#2492C2214yes—
118#2491C2214yes—
119#2491C2214yes—
120#2489C2212yes—
121#2474C2218yes—
122#2465C2218yes—
123#2453C2214yes—
124#2452C2212yes—
125#2451C2218yes—
126#2451C2214yes—
127#2448C2214yes—
128#2446C2218yes—
129#2441C2214yes—
130#2439C2214yes—
131#2439C2214yes—
132#2439C2214yes—
133#2429C2212yes—
134#2429C2214yes—
135#2429C2214yes—
136#2427C2212yes—
137#2423C2214yes—
138#2423C2214yes—
139#2422C2212yes—
140#2421C2214yes—
141#2415C2214yes—
142#2415C2214yes—
143#2396C2214yes—
144#2395C2214yes—
145#2382C2218yes—
146#2373C2214yes—
147#2369C2214yes—
148#2369C2212yes—
149#2367C2212yes—
150#2365C2212yes—
151#2365C2214yes—
152#2365C2214yes—
153#2365C2211yescharacteristic
154#2362C2212yes—
155#2362C2214yes—
156#2356C2212yes—
157#2355C2214yes—
158#2355C2211yescharacteristic
159#2355C2212yes—
160#2355C2212yes—
161#2355C2212yes—
162#2355C2212yes—
163#2354C2212yes—
164#2354C2212yes—
165#2354C2211yescharacteristic
166Q8×C4⋊C4C2212yes—
167Q8×C4⋊C4C2212yes—
168Q8×C4⋊C4C2212yes—
169Q8×C4⋊C4C2214yes—
170#2347C2214yes—
171#2347C2212yes—
172#2323C2214yes—
173#2323C2214yes—
174#2323C2214yes—
175#2323C2214yes—
176#2323C2218yes—
177#2314C2214yes—
178#2314C2214yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2214yes—
185C4×#126C2214yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199Q82—48no—
200#556—28no—
201#533—216no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217#529—48no—
218C2×#126C2314yes—
219C2×#126C2314yes—
220C2×#125C2314yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2318yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×#117C2314yes—
262C2×#117C2312yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269#401C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#399C2318yes—
281#399C2314yes—
282#399C2314yes—
283#399C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#397C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2314yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#396C2314yes—
302#396C2318yes—
303#396C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2314yes—
310#394C2318yes—
311#394C2318yes—
312#394C2314yes—
313#394C2314yes—
314#394C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2318yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2318yes—
335#391C2314yes—
336#391C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2318yes—
341#391C2318yes—
342#391C2312yes—
343#390C2314yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#389C2312yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2318yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2318yes—
383#389C2312yes—
384#389C2312yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#386C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#384C2314yes—
435#384C2311yescharacteristic
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#383C2314yes—
449#383C2318yes—
450#383C2318yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2314yes—
462#380C2312yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C43C2314yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2414yes—
530C22×Q8C2418yes—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2414yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C4⋊Q8—28no—
541C4⋊Q8—28no—
542C4⋊Q8—28no—
543C4⋊Q8—24no—
544C4⋊Q8—24no—
545C4⋊Q8—28no—
546C4⋊Q8—24no—
547C4⋊Q8—44no—
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—416no—
552C4⋊Q8—82no—
553C4⋊Q8—84no—
554#126—216no—
555#126—48no—
556#125—216no—
557#125—44no—
558#125—48no—
559#124—28no—
560#124—44no—
561#124—88no—
562#123—48no—
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—28no—
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—48no—
570C22⋊Q8—44no—
571C22⋊Q8—48no—
572C22⋊Q8—48no—
573C22⋊Q8—84no—
574#121—44no—
575#121—44no—
576C4×Q8—24no—
577C4×Q8—216no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—44no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—88no—
589C4×Q8#4118yes—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—42no—
596C4×D4—48no—
597#117—28no—
598#117—28no—
599#117—216no—
600#117—48no—
601#117—48no—
602#117—84no—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C42—28no—
686C2×C42—28no—
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C24C2512yes—
763C2×Q8—28no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—48no—
781C2×Q8—48no—
782C2×Q8—48no—
783C2×Q8C2×#4114yes—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4C2511yescharacteristic
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—22no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—42no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—44no—
889C4⋊C4C2×#4114yes—
890C4⋊C4C2×#4118yes—
891C4⋊C42−1+414yes—
892C4⋊C42−1+414yes—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—24no—
899C22⋊C4—28no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—42no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—28no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—28no—
926C42—24no—
927C42—28no—
928C42—22no—
929C42—24no—
930C42—22no—
931C42—28no—
932C42—24no—
933C42—22no—
934C42—24no—
935C42—48no—
936C42—48no—
937C42—44no—
938C42—48no—
939C42—44no—
940C42—48no—
941C42—42no—
942C42—41no—
943C42C2×#4114yes—
944C42C2×#4118yes—
945C42H(5,𝔽2)14yes—
946C422−1+414yes—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23C2611yescharacteristic
962Q8—28no—
963Q8—416no—
964Q8—48no—
965Q8—48no—
966Q8—48no—
967Q8—88no—
968Q8—168no—
969D4—44no—
970D4—44no—
971D4—88no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—28no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—48no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—84no—
1034C2×C4C22×#4114yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4114yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×2−1+414yes—
1043C2×C4C2×2−1+412yes—
1044C2×C4C2×2−1+414yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4C2×2−1+412yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4#58512yes—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22C23×#4111yescharacteristic
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C22×2−1+411yescharacteristic
1067C22C22×2−1+411yescharacteristic
1068C22C22×2−1+411yescharacteristic
1069C22C2×#58511yescharacteristic
1070C22H(7,𝔽2)11yescharacteristic
1071C4—22no—
1072C4—24no—
1073C4—24no—
1074C4—24no—
1075C4—24no—
1076C4—22no—
1077C4—22no—
1078C4—44no—
1079C4—42no—
1080C4—44no—
1081C4—41no—
1082C4—42no—
1083C4—44no—
1084C4—42no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4—42no—
1089C4—44no—
1090C4—48no—
1091C4—42no—
1092C4#351114yes—
1093C4#351814yes—
1094C4#355014yes—
1095C2—82no—
1096C2—82no—
1097C2C2×#355011yescharacteristic
1098C2C2×#351811yescharacteristic
1099C2C2×#351111yescharacteristic
1100C2#6294311yescharacteristic
1101C2#6295511yescharacteristic
1102C2#6300011yescharacteristic
1103C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59639C2semidirect
3. #59234C2semidirect
4. #59081C2semidirect
5. #51382C2semidirect
6. #46117C2semidirect
7. #45348C2semidirect
8. #45065C2semidirect
9. #42549C2semidirect
10. #42457C2semidirect
11. #40179C2semidirect
12. #39727C2semidirect
13. #39609C2semidirect
15. #39125C2semidirect
16. #36563C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. #36480C2semidirect
19. #36194C2semidirect
20. #36134C2semidirect
21. #35201C2semidirect
22. #35184C2semidirect
24. #34929C2semidirect
25. #34374C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598752
#596392
#592342
#590812
#513822
#461172
#453482
#450652
#425492
#424572
#401792
#397272
#396092
#395052
#391252
#365632
Q8×C4⋊Q82
#364802
#361942
#361342
#352012
#351842
#349322
#349292
#343742
C4×#5562