Finite Group Databasebeta

← #7688379

Subgroups — #7688379

Order 512.

4491 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59639C212yesmaximal
3#59505C214yesmaximal, complemented
4#59443C214yesmaximal, complemented
5#59427C212yesmaximal
6#59081C212yesmaximal, complemented
7#45342C214yesmaximal, complemented
8#43758C218yesmaximal, complemented
9#40023C214yesmaximal
10#39225C214yesmaximal, complemented
11#39149C212yesmaximal, complemented
12#38984C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36590C212yesmaximal
15#36560C211yesmaximal, characteristic, complemented
16#36535C212yesmaximal, complemented
17#36508C212yesmaximal
18#36314C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic
20#35901C214yesmaximal, complemented
21#34951C212yesmaximal, complemented
22#34945C211yesmaximal, characteristic
23#34328C212yesmaximal, complemented
24#34231C212yesmaximal, complemented
25C4×Q82C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic
27C2×Q82C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×#533C2212yes—
31#2868C2211yescharacteristic
32#2864C2214yes—
33#2862C2212yes—
34#2861C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2809C2214yes—
38#2798C2218yes—
39#2793C2218yes—
40#2783C2218yes—
41#2776C2218yes—
42#2776C2218yes—
43#2772C2218yes—
44#2767C2218yes—
45#2762C2218yes—
46#2739C2218yes—
47#2729C2218yes—
48#2650C2218yes—
49#2645C2214yes—
50#2596C2218yes—
51#2594C2218yes—
52#2592C2214yes—
53#2590C2218yes—
54#2588C2218yes—
55#2585C2218yes—
56#2582C2212yes—
57#2581C2214yes—
58#2573C2214yes—
59#2571C2212yes—
60#2571C2211yescharacteristic
61#2571C2212yes—
62#2570C2218yes—
63#2570C2214yes—
64#2570C2214yes—
65#2568C2214yes—
66#2568C2214yes—
67#2568C2212yes—
68#2568C2211yescharacteristic
69#2568C2212yes—
70#2565C2214yes—
71#2565C2214yes—
72#2552C2212yes—
73#2550C2214yes—
74#2547C2211yescharacteristic
75#2546C2212yes—
76#2546C2212yes—
77#2546C2212yes—
78#2546C2212yes—
79#2545C2214yes—
80#2542C2212yes—
81#2538C2212yes—
82#2538C2211yescharacteristic
83#2533C2218yes—
84#2533C2218yes—
85#2532C2218yes—
86#2530C2218yes—
87#2529C2218yes—
88#2525C2218yes—
89#2519C2218yes—
90#2519C2218yes—
91#2514C2212yes—
92#2514C2218yes—
93#2514C2214yes—
94#2513C2214yes—
95#2511C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2509C2214yes—
99#2508C2214yes—
100#2508C2214yes—
101#2506C2214yes—
102#2506C2214yes—
103#2499C2214yes—
104#2497C2214yes—
105#2495C2214yes—
106#2494C2212yes—
107#2494C2214yes—
108#2492C2214yes—
109#2453C2214yes—
110#2451C2214yes—
111#2447C2212yes—
112#2446C2214yes—
113#2446C2218yes—
114#2446C2214yes—
115#2441C2214yes—
116#2439C2214yes—
117#2429C2214yes—
118#2429C2214yes—
119#2429C2214yes—
120#2423C2214yes—
121#2421C2214yes—
122#2421C2212yes—
123#2421C2214yes—
124#2402C2218yes—
125#2401C2214yes—
126#2373C2214yes—
127#2371C2218yes—
128#2370C2214yes—
129#2369C2212yes—
130#2369C2212yes—
131#2369C2211yescharacteristic
132#2369C2214yes—
133#2369C2212yes—
134#2367C2212yes—
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2365C2212yes—
141#2362C2212yes—
142#2362C2214yes—
143#2362C2214yes—
144#2362C2214yes—
145#2362C2214yes—
146#2356C2214yes—
147#2356C2214yes—
148#2356C2212yes—
149#2356C2218yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2355C2212yes—
153#2355C2214yes—
154#2355C2212yes—
155#2355C2212yes—
156#2354C2212yes—
157#2354C2211yescharacteristic
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2211yescharacteristic
162Q8×C4⋊C4C2211yescharacteristic
163#2347C2214yes—
164#2347C2212yes—
165#2346C2214yes—
166#2336C2218yes—
167#2332C2218yes—
168#2327C2214yes—
169#2320C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2214yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#125C2214yes—
180C4×#125C2214yes—
181C4×#125C2214yes—
182C4×#126C2214yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187#2295C2212yes—
188#2295C2214yes—
189#2295C2214yes—
190#2283C2212yes—
191#2276C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199Q82—28no—
200#557—216no—
201#556—28no—
202#533—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C22×C42C2312yes—
253#401C2318yes—
254#401C2314yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#397C2314yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#396C2314yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#393C2318yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2312yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2318yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2318yes—
320#390C2312yes—
321#390C2314yes—
322#390C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2312yes—
330#389C2314yes—
331#389C2318yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2312yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#385C2314yes—
416#385C2314yes—
417#384C2311yescharacteristic
418#384C2314yes—
419#384C2312yes—
420#384C2314yes—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#383C2314yes—
429#383C2314yes—
430#383C2318yes—
431#383C2318yes—
432#382C2312yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2314yes—
437#382C2318yes—
438#382C2318yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#381C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2318yes—
516#376C2314yes—
517#376C2318yes—
518C43C2314yes—
519C43C2314yes—
520C43C2311yescharacteristic
521C43C2312yes—
522C43C2312yes—
523C22×Q8C2414yes—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—216no—
535C4⋊Q8—216no—
536C4⋊Q8—28no—
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544C4⋊Q8#4118yes—
545#126—216no—
546#125—216no—
547#125—232no—
548#125—216no—
549#124—28no—
550#124—44no—
551C22⋊Q8—216no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554C22⋊Q8—216no—
555C22⋊Q8—48no—
556C4×Q8—216no—
557C4×Q8—24no—
558C4×Q8—28no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—28no—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—216no—
565C4×Q8—28no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—28no—
570C4×Q8—44no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—44no—
574C4×Q8—44no—
575C4×Q8—42no—
576C4×Q8#4118yes—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—42no—
580#117—216no—
581#117—28no—
582#117—44no—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C42—28no—
656C2×C42C2418yes—
657C2×C42C2414yes—
658C2×C42C2411yescharacteristic
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2418yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2418yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#95C2414yes—
694#95C2414yes—
695#95C2412yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2414yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2412yes—
726#95C2414yes—
727#95C2412yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24C2512yes—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—28no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—28no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—44no—
763C2×Q8—44no—
764C2×Q8C2×#4114yes—
765C2×Q8C2×#4118yes—
766C2×Q82−1+414yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2518yes—
794C22×C4C2511yescharacteristic
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—22no—
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—216no—
823C4⋊C4—28no—
824C4⋊C4—24no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—42no—
848C4⋊C4—44no—
849C4⋊C4—42no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4C2×#4114yes—
860C4⋊C4C2×#4118yes—
861C4⋊C4C2×#4118yes—
862C4⋊C4C2×#4118yes—
863C22⋊C4—216no—
864C22⋊C4—28no—
865C22⋊C4—24no—
866C22⋊C4—28no—
867C22⋊C4—24no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—42no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—216no—
880C42—28no—
881C42—216no—
882C42—28no—
883C42—24no—
884C42—24no—
885C42—28no—
886C42—28no—
887C42—24no—
888C42—24no—
889C42—22no—
890C42—24no—
891C42—28no—
892C42—22no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—28no—
897C42—22no—
898C42—42no—
899C42—44no—
900C42—44no—
901C42—41no—
902C42—42no—
903C42—48no—
904C42—44no—
905C42—42no—
906C42—44no—
907C42—48no—
908C42—44no—
909C42C2×#4114yes—
910C42C2×#4114yes—
911C42C2×#4118yes—
912C422−1+414yes—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23C2611yescharacteristic
921Q8—28no—
922Q8—28no—
923Q8—48no—
924Q8—416no—
925Q8—48no—
926Q8—48no—
927Q8—88no—
928D4—44no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—24no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4C22×#4114yes—
992C2×C4C22×#4118yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4114yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4#58512yes—
1006C2×C4#58512yes—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22C23×#4111yescharacteristic
1015C22C23×#4111yescharacteristic
1016C22C22×2−1+411yescharacteristic
1017C22C22×2−1+411yescharacteristic
1018C22C2×#58511yescharacteristic
1019C22C2×#58511yescharacteristic
1020C222−1+611yescharacteristic
1021C4—22no—
1022C4—28no—
1023C4—24no—
1024C4—22no—
1025C4—24no—
1026C4—22no—
1027C4—24no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—44no—
1032C4—42no—
1033C4—42no—
1034C4—41no—
1035C4—44no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—48no—
1043C4#348014yes—
1044C4#351814yes—
1045C4#352314yes—
1046C2—82no—
1047C2C2×#348011yescharacteristic
1048C2C2×#352311yescharacteristic
1049C2C2×#351811yescharacteristic
1050C2#6295611yescharacteristic
1051C2#6299111yescharacteristic
1052C2#6300111yescharacteristic
1053C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59869C2semidirect
3. #59505C2semidirect
4. #59443C2semidirect
6. #59081C2semidirect
7. #45342C2semidirect
8. #43758C2semidirect
10. #39225C2semidirect
11. #39149C2semidirect
12. #38984C2semidirect
13. #36598C2semidirect
15. #36560C2semidirect
16. #36535C2semidirect
18. #36314C2semidirect
20. #35901C2semidirect
21. #34951C2semidirect
23. #34328C2semidirect
24. #34231C2semidirect
25. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#598692
#596392
#595052
#594432
#594272
#590812
#453422
#437582
#400232
#392252
#391492
#389842
#365982
#365902
#365602
#365352
#365082
#363142
#361342
#359012
#349512
#349452
#343282
#342312
C4×Q822
C4×#5562