Finite Group Databasebeta

← #8429307

Subgroups — #8429307

Order 512.

4217 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59672C212yesmaximal, complemented
3#59445C212yesmaximal, complemented
4#59249C212yesmaximal, complemented
5#58614C218yesmaximal, complemented
6#53107C214yesmaximal, complemented
7#53036C214yesmaximal, complemented
8#52965C214yesmaximal, complemented
9#42801C214yesmaximal, complemented
10#42638C214yesmaximal
11#42455C214yesmaximal, complemented
12#39642C212yesmaximal, complemented
13#39514C212yesmaximal
14#39478C212yesmaximal, complemented
15#39379C212yesmaximal
16#39353C212yesmaximal, complemented
17#39183C212yesmaximal, complemented
18#37643C212yesmaximal, complemented
19#37637C212yesmaximal
20#37637C212yesmaximal
21#36593C211yesmaximal, characteristic, complemented
22#36563C211yesmaximal, characteristic, complemented
23#36194C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34941C211yesmaximal, characteristic
26#34941C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#541C2214yes—
29#2868C2212yes—
30#2868C2211yescharacteristic
31#2859C2212yes—
32#2857C2212yes—
33#2845C2218yes—
34#2839C2218yes—
35#2839C2218yes—
36#2836C2218yes—
37#2831C2218yes—
38#2831C2218yes—
39#2822C2218yes—
40#2809C2218yes—
41#2806C2214yes—
42#2802C2218yes—
43#2791C2218yes—
44#2774C2218yes—
45#2767C2218yes—
46#2767C2218yes—
47#2747C2218yes—
48#2725C2218yes—
49#2725C2218yes—
50#2725C2218yes—
51#2722C2218yes—
52#2721C2218yes—
53#2719C2218yes—
54#2719C2218yes—
55#2716C2218yes—
56#2716C2218yes—
57#2713C2218yes—
58#2713C2218yes—
59#2664C2218yes—
60#2647C2214yes—
61#2647C2214yes—
62#2644C2214yes—
63#2637C2218yes—
64#2637C2218yes—
65#2629C2214yes—
66#2629C2214yes—
67#2629C2214yes—
68#2629C2218yes—
69#2629C2214yes—
70#2625C2214yes—
71#2625C2214yes—
72#2585C2214yes—
73#2584C2214yes—
74#2582C2214yes—
75#2582C2211yescharacteristic
76#2582C2212yes—
77#2574C2214yes—
78#2574C2214yes—
79#2571C2212yes—
80#2570C2214yes—
81#2570C2214yes—
82#2568C2211yescharacteristic
83#2567C2212yes—
84#2567C2212yes—
85#2567C2211yescharacteristic
86#2567C2211yescharacteristic
87#2565C2214yes—
88#2565C2218yes—
89#2563C2211yescharacteristic
90#2563C2212yes—
91#2563C2211yescharacteristic
92#2552C2212yes—
93#2552C2212yes—
94#2552C2211yescharacteristic
95#2552C2214yes—
96#2552C2214yes—
97#2552C2214yes—
98#2552C2212yes—
99#2552C2212yes—
100#2552C2212yes—
101#2552C2214yes—
102#2552C2211yescharacteristic
103#2552C2214yes—
104#2552C2211yescharacteristic
105#2552C2214yes—
106#2552C2214yes—
107#2552C2214yes—
108#2550C2214yes—
109#2546C2211yescharacteristic
110#2546C2212yes—
111#2546C2214yes—
112#2538C2211yescharacteristic
113#2538C2212yes—
114#2538C2211yescharacteristic
115#2512C2214yes—
116#2512C2214yes—
117#2512C2214yes—
118#2511C2214yes—
119#2511C2214yes—
120#2511C2214yes—
121#2511C2212yes—
122#2509C2214yes—
123#2509C2212yes—
124#2508C2214yes—
125#2508C2214yes—
126#2508C2214yes—
127#2508C2212yes—
128#2508C2212yes—
129#2507C2214yes—
130#2507C2214yes—
131#2506C2214yes—
132#2506C2214yes—
133#2506C2214yes—
134#2506C2214yes—
135#2497C2214yes—
136#2497C2212yes—
137#2497C2212yes—
138#2496C2214yes—
139#2496C2214yes—
140#2496C2214yes—
141#2496C2214yes—
142#2492C2214yes—
143#2489C2214yes—
144#2489C2214yes—
145#2478C2218yes—
146#2462C2218yes—
147#2454C2212yes—
148#2454C2212yes—
149#2453C2214yes—
150#2453C2212yes—
151#2451C2214yes—
152#2446C2212yes—
153#2446C2214yes—
154#2439C2214yes—
155#2423C2212yes—
156#2423C2212yes—
157#2421C2214yes—
158#2421C2214yes—
159#2402C2214yes—
160#2396C2214yes—
161#2396C2214yes—
162#2370C2214yes—
163#2370C2214yes—
164#2369C2212yes—
165#2369C2212yes—
166#2369C2212yes—
167#2365C2212yes—
168#2355C2212yes—
169#2355C2214yes—
170#2355C2212yes—
171#2354C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174Q8×C4⋊C4C2212yes—
175Q8×C4⋊C4C2212yes—
176#2330C2214yes—
177#2314C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#125C2212yes—
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192#2293C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#557—48no—
200#541—416no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×#126C2318yes—
211C2×#126C2318yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2318yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2314yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C42C2312yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2314yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#400C2314yes—
264#399C2314yes—
265#399C2314yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2314yes—
310#395C2314yes—
311#395C2314yes—
312#395C2318yes—
313#395C2318yes—
314#393C2314yes—
315#393C2314yes—
316#393C2318yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2318yes—
334#391C2312yes—
335#391C2312yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2312yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#385C2314yes—
430#385C2314yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2318yes—
438#384C2314yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#384C2312yes—
451#382C2312yes—
452#382C2312yes—
453#382C2312yes—
454#382C2314yes—
455#382C2314yes—
456#382C2318yes—
457#382C2318yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2314yes—
472#380C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518C43C2312yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C22×Q8C2412yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2414yes—
526C22×Q8C2412yes—
527C22×D4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C4⋊Q8—28no—
532C4⋊Q8—24no—
533C4⋊Q8—24no—
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—44no—
537C4⋊Q8—48no—
538C4⋊Q8—82no—
539C4⋊Q8—84no—
540#126—416no—
541#126—416no—
542#126—88no—
543#125—28no—
544#125—28no—
545#125—44no—
546#125—48no—
547#125—48no—
548#125—416no—
549#125—48no—
550#125—416no—
551#125—416no—
552#125—88no—
553C22⋊Q8—28no—
554C22⋊Q8—44no—
555C22⋊Q8—48no—
556C4×Q8—216no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—28no—
562C4×Q8—24no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—48no—
566C4×Q8—42no—
567C4×Q8—48no—
568C4×Q8—84no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572#117—48no—
573#117—48no—
574#117—84no—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C42—28no—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2412yes—
666C2×C42C2411yescharacteristic
667C2×C42C2418yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2412yes—
680C2×C42C2418yes—
681C2×C42C2418yes—
682C2×C42C2412yes—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2412yes—
700#95C2412yes—
701#95C2414yes—
702#95C2414yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738C24C2512yes—
739C2×Q8—24no—
740C2×Q8—22no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—22no—
744C2×Q8—22no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—28no—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—42no—
756C2×Q8H(5,𝔽2)14yes—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—22no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—42no—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2518yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—216no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—42no—
836C4⋊C4—44no—
837C4⋊C4—42no—
838C4⋊C4—44no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C42−1+414yes—
864C22⋊C4—28no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C42—24no—
878C42—28no—
879C42—24no—
880C42—22no—
881C42—216no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—22no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—28no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—28no—
895C42—22no—
896C42—48no—
897C42—42no—
898C42—48no—
899C42—42no—
900C42—48no—
901C42—41no—
902C42—42no—
903C422−1+414yes—
904C422−1+414yes—
905C422−1+414yes—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23C2611yescharacteristic
914Q8—28no—
915Q8—48no—
916Q8—48no—
917Q8—44no—
918Q8—84no—
919Q8—88no—
920D4—44no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—28no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4C2×H(5,𝔽2)14yes—
986C2×C4C2×H(5,𝔽2)12yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+412yes—
989C2×C4C2×2−1+412yes—
990C2×C4C2×2−1+414yes—
991C2×C4C2×2−1+412yes—
992C2×C4C2×2−1+412yes—
993C2×C4C2×2−1+412yes—
994C2×C4C2×2−1+412yes—
995C2×C4C2×2−1+412yes—
996C2×C4C2×2−1+412yes—
997C2×C4C2×2−1+412yes—
998C2×C4#58512yes—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22C22×H(5,𝔽2)11yescharacteristic
1007C22C22×2−1+411yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C22×2−1+411yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C2×#58511yescharacteristic
1012C22H(7,𝔽2)11yescharacteristic
1013C4—24no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—44no—
1023C4—42no—
1024C4—41no—
1025C4—42no—
1026C4—44no—
1027C4—42no—
1028C4—44no—
1029C4—48no—
1030C4—42no—
1031C4—44no—
1032C4—44no—
1033C4—42no—
1034C4—42no—
1035C4#354414yes—
1036C4#355514yes—
1037C4#355614yes—
1038C2—82no—
1039C2C2×#354411yescharacteristic
1040C2C2×#355511yescharacteristic
1041C2C2×#355611yescharacteristic
1042C2#6291711yescharacteristic
1043C2#6292611yescharacteristic
1044C2#6294511yescharacteristic
1045C2#6303911yescharacteristic
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. #59871C2semidirect
2. #59672C2semidirect
3. #59445C2semidirect
4. #59249C2semidirect
5. #58614C2semidirect
6. #53107C2semidirect
7. #53036C2semidirect
8. #52965C2semidirect
9. #42801C2semidirect
11. #42455C2semidirect
12. #39642C2semidirect
14. #39478C2semidirect
16. #39353C2semidirect
17. #39183C2semidirect
18. #37643C2semidirect
21. #36593C2semidirect
22. #36563C2semidirect
24. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#596722
#594452
#592492
#586142
#531072
#530362
#529652
#428012
#426382
#424552
#396422
#395142
#394782
#393792
#393532
#391832
#376432
#376372
#365932
#365632
#361942
#349512
#349412