Finite Group Databasebeta

← #7688625

Subgroups — #7688625

Order 512.

4509 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#59870C211yesmaximal, characteristic, complemented
2#59511C214yesmaximal, complemented
3#59443C212yesmaximal, complemented
4#59437C212yesmaximal
5#59330C214yesmaximal, complemented
6#59256C212yesmaximal, complemented
7#45221C214yesmaximal
8#43752C218yesmaximal, complemented
9#40028C214yesmaximal, complemented
10#39769C212yesmaximal, complemented
11#39250C214yesmaximal, complemented
12#39173C212yesmaximal
13#36599C212yesmaximal, complemented
14#36598C211yesmaximal, characteristic, complemented
15#36593C211yesmaximal, characteristic, complemented
16#36556C212yesmaximal, complemented
17#36314C212yesmaximal, complemented
18#36188C212yesmaximal
19#36188C211yesmaximal, characteristic
20#35870C214yesmaximal, complemented
21#34951C211yesmaximal, characteristic, complemented
22#34948C212yesmaximal, complemented
23#34328C212yesmaximal, complemented
24#34324C212yesmaximal
25C4×#554C211yesmaximal, characteristic
26C4×#556C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#556C2212yes—
29C2×#556C2211yescharacteristic
30C2×#554C2211yescharacteristic
31#2868C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2862C2212yes—
35#2857C2214yes—
36#2857C2212yes—
37#2805C2214yes—
38#2794C2218yes—
39#2794C2218yes—
40#2787C2218yes—
41#2776C2218yes—
42#2770C2218yes—
43#2770C2218yes—
44#2747C2218yes—
45#2747C2218yes—
46#2690C2218yes—
47#2690C2218yes—
48#2655C2218yes—
49#2642C2214yes—
50#2590C2218yes—
51#2588C2218yes—
52#2585C2218yes—
53#2585C2214yes—
54#2582C2212yes—
55#2582C2211yescharacteristic
56#2581C2214yes—
57#2577C2218yes—
58#2571C2212yes—
59#2571C2212yes—
60#2570C2214yes—
61#2570C2214yes—
62#2570C2214yes—
63#2570C2214yes—
64#2569C2218yes—
65#2569C2218yes—
66#2568C2212yes—
67#2568C2212yes—
68#2568C2212yes—
69#2568C2211yescharacteristic
70#2567C2212yes—
71#2565C2214yes—
72#2552C2212yes—
73#2552C2214yes—
74#2552C2211yescharacteristic
75#2552C2212yes—
76#2552C2214yes—
77#2547C2212yes—
78#2547C2214yes—
79#2547C2214yes—
80#2547C2212yes—
81#2546C2214yes—
82#2546C2212yes—
83#2546C2211yescharacteristic
84#2533C2218yes—
85#2533C2218yes—
86#2533C2218yes—
87#2530C2218yes—
88#2530C2218yes—
89#2528C2218yes—
90#2524C2218yes—
91#2520C2218yes—
92#2514C2214yes—
93#2514C2214yes—
94#2511C2214yes—
95#2511C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2511C2212yes—
99#2511C2214yes—
100#2509C2212yes—
101#2509C2214yes—
102#2509C2214yes—
103#2508C2214yes—
104#2499C2214yes—
105#2499C2214yes—
106#2499C2214yes—
107#2496C2214yes—
108#2496C2218yes—
109#2496C2218yes—
110#2496C2214yes—
111#2495C2214yes—
112#2494C2214yes—
113#2453C2212yes—
114#2446C2214yes—
115#2446C2214yes—
116#2446C2214yes—
117#2446C2214yes—
118#2446C2212yes—
119#2442C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2402C2218yes—
125#2402C2214yes—
126#2373C2218yes—
127#2373C2214yes—
128#2371C2218yes—
129#2370C2214yes—
130#2370C2212yes—
131#2369C2211yescharacteristic
132#2368C2214yes—
133#2367C2214yes—
134#2367C2212yes—
135#2365C2212yes—
136#2365C2214yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2214yes—
140#2365C2211yescharacteristic
141#2365C2212yes—
142#2362C2214yes—
143#2362C2212yes—
144#2360C2212yes—
145#2356C2214yes—
146#2356C2214yes—
147#2356C2212yes—
148#2356C2214yes—
149#2355C2214yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2355C2211yescharacteristic
153#2355C2212yes—
154#2355C2212yes—
155#2354C2211yescharacteristic
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159#2349C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161#2347C2212yes—
162#2346C2214yes—
163#2345C2214yes—
164#2345C2212yes—
165#2336C2218yes—
166#2334C2218yes—
167#2327C2214yes—
168#2326C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×#125C2214yes—
176C4×#125C2212yes—
177C4×#125C2212yes—
178C4×#125C2214yes—
179C4×#126C2214yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185#2296C2214yes—
186#2295C2212yes—
187#2295C2212yes—
188#2295C2214yes—
189#2285C2212yes—
190#2285C2214yes—
191#2276C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199#557—216no—
200#556—216no—
201#556—28no—
202#554—28no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×#126C2314yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#124C2314yes—
219C2×#124C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2312yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2314yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C42C2312yes—
251C22×C42C2314yes—
252#401C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2314yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#398C2318yes—
273#398C2318yes—
274#398C2314yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2314yes—
283#398C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#395C2318yes—
291#391C2312yes—
292#391C2314yes—
293#391C2312yes—
294#391C2312yes—
295#391C2314yes—
296#391C2312yes—
297#391C2312yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#390C2312yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2314yes—
328#389C2312yes—
329#389C2314yes—
330#389C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2318yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2312yes—
417#384C2311yescharacteristic
418#384C2314yes—
419#384C2312yes—
420#384C2314yes—
421#384C2314yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#384C2314yes—
427#383C2314yes—
428#383C2318yes—
429#383C2318yes—
430#382C2312yes—
431#382C2314yes—
432#382C2314yes—
433#382C2312yes—
434#382C2312yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2318yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2318yes—
445#380C2318yes—
446#380C2314yes—
447#380C2312yes—
448#380C2314yes—
449#380C2312yes—
450#380C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514#376C2314yes—
515#376C2318yes—
516#376C2318yes—
517#376C2314yes—
518C2×#95C2314yes—
519C43C2314yes—
520C43C2312yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2414yes—
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×D4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2414yes—
533C23×C4C2414yes—
534C23×C4C2412yes—
535C4⋊Q8—24no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538C4⋊Q8—216no—
539C4⋊Q8—28no—
540C4⋊Q8—24no—
541C4⋊Q8—44no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544#126—216no—
545#126—232no—
546#125—216no—
547#125—232no—
548#125—28no—
549#125—28no—
550#124—216no—
551#124—28no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C4×Q8—216no—
557C4×Q8—216no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—28no—
561C4×Q8—24no—
562C4×Q8—216no—
563C4×Q8—28no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—44no—
567C4×Q8—48no—
568C4×Q8—42no—
569C4×Q8—48no—
570C4×Q8—44no—
571C4×Q8#4118yes—
572C4×D4—28no—
573C4×D4—24no—
574C4×D4—44no—
575C4×D4—42no—
576C4×D4#4118yes—
577#117—216no—
578#117—28no—
579#117—44no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2412yes—
653C2×C42—28no—
654C2×C42—48no—
655C2×C42C2414yes—
656C2×C42C2418yes—
657C2×C42C2412yes—
658C2×C42C2411yescharacteristic
659C2×C42C2412yes—
660C2×C42C2411yescharacteristic
661C2×C42C2412yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2418yes—
680C2×C42C2414yes—
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#95C2412yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2412yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2412yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2412yes—
719#95C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744C24C2512yes—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—28no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—28no—
758C2×Q8—24no—
759C2×Q8—22no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8C2×#4114yes—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4C2×#4114yes—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—44no—
780C22×C4C2×#4118yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2518yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—216no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—216no—
819C4⋊C4—216no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—42no—
845C4⋊C4—44no—
846C4⋊C4—42no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—42no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4C2×#4114yes—
863C4⋊C4C2×#4114yes—
864C4⋊C4C2×#4118yes—
865C4⋊C42−1+414yes—
866C22⋊C4—28no—
867C22⋊C4—216no—
868C22⋊C4—216no—
869C22⋊C4—28no—
870C22⋊C4—24no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—42no—
875C22⋊C4—44no—
876C22⋊C4C2×#4118yes—
877C42—28no—
878C42—216no—
879C42—24no—
880C42—28no—
881C42—216no—
882C42—28no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—22no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—28no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—44no—
898C42—44no—
899C42—41no—
900C42—42no—
901C42—42no—
902C42—44no—
903C42—44no—
904C42—42no—
905C42—48no—
906C42—48no—
907C42—44no—
908C42C2×#4118yes—
909C42C2×#4114yes—
910C42C2×#4114yes—
911C422−1+414yes—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23C22×#4114yes—
919C23C2611yescharacteristic
920Q8—28no—
921Q8—416no—
922Q8—48no—
923Q8—44no—
924Q8—48no—
925Q8—84no—
926D4—28no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—216no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—48no—
988C2×C4—88no—
989C2×C4—88no—
990C2×C4—84no—
991C2×C4C22×#4114yes—
992C2×C4C22×#4114yes—
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+412yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4#58512yes—
1006C2×C4#58512yes—
1007C22—24no—
1008C22—24no—
1009C22—24no—
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—24no—
1022C4—22no—
1023C4—22no—
1024C4—24no—
1025C4—24no—
1026C4—24no—
1027C4—22no—
1028C4—44no—
1029C4—44no—
1030C4—42no—
1031C4—44no—
1032C4—42no—
1033C4—41no—
1034C4—44no—
1035C4—42no—
1036C4—44no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—44no—
1042C4—48no—
1043C4#348014yes—
1044C4#350914yes—
1045C4#351514yes—
1046C2—44no—
1047C2C2×#348011yescharacteristic
1048C2C2×#351511yescharacteristic
1049C2C2×#350911yescharacteristic
1050C2#6295911yescharacteristic
1051C2#6299511yescharacteristic
1052C2#6300111yescharacteristic
1053C2#6302511yescharacteristic
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. #59870C2semidirect
2. #59511C2semidirect
3. #59443C2semidirect
5. #59330C2semidirect
6. #59256C2semidirect
8. #43752C2semidirect
9. #40028C2semidirect
10. #39769C2semidirect
11. #39250C2semidirect
13. #36599C2semidirect
14. #36598C2semidirect
15. #36593C2semidirect
16. #36556C2semidirect
17. #36314C2semidirect
20. #35870C2semidirect
21. #34951C2semidirect
22. #34948C2semidirect
23. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#595112
#594432
#594372
#593302
#592562
#452212
#437522
#400282
#397692
#392502
#391732
#365992
#365982
#365932
#365562
#363142
#361882
#358702
#349512
#349482
#343282
#343242
C4×#5542
C4×#5562