Finite Group Databasebeta

← #8429507

Subgroups — #8429507

Order 512.

4753 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59304C212yesmaximal, complemented
3#59213C212yesmaximal, complemented
4#59136C212yesmaximal, complemented
5#55180C218yesmaximal, complemented
6#53119C214yesmaximal, complemented
7#53023C214yesmaximal, complemented
8#52992C214yesmaximal, complemented
9#42601C214yesmaximal, complemented
10#42512C214yesmaximal, complemented
11#42485C214yesmaximal, complemented
12#39608C212yesmaximal, complemented
13#39126C212yesmaximal, complemented
14#38940C212yesmaximal, complemented
15#38932C212yesmaximal, complemented
16#38931C212yesmaximal, complemented
17#38930C212yesmaximal, complemented
18#37632C212yesmaximal, complemented
19#37624C212yesmaximal, complemented
20#37623C212yesmaximal, complemented
21#36194C211yesmaximal, characteristic, complemented
22#36180C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34943C211yesmaximal, characteristic, complemented
25#34943C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic, complemented
27C2×#554C2212yes—
28C2×#553C2214yes—
29C2×D4×Q8C2212yes—
30C22×C4⋊Q8C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2857C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2843C2218yes—
37#2841C2218yes—
38#2839C2218yes—
39#2836C2218yes—
40#2827C2218yes—
41#2821C2218yes—
42#2814C2218yes—
43#2806C2214yes—
44#2775C2218yes—
45#2770C2218yes—
46#2764C2218yes—
47#2763C2218yes—
48#2758C2218yes—
49#2743C2218yes—
50#2738C2218yes—
51#2737C2218yes—
52#2729C2218yes—
53#2718C2218yes—
54#2708C2218yes—
55#2702C2218yes—
56#2698C2218yes—
57#2698C2218yes—
58#2692C2218yes—
59#2687C2218yes—
60#2681C2218yes—
61#2681C2218yes—
62#2666C2218yes—
63#2660C2214yes—
64#2660C2214yes—
65#2647C2214yes—
66#2647C2214yes—
67#2647C2214yes—
68#2640C2214yes—
69#2638C2218yes—
70#2629C2214yes—
71#2628C2214yes—
72#2628C2214yes—
73#2627C2218yes—
74#2614C2218yes—
75#2584C2214yes—
76#2582C2214yes—
77#2572C2214yes—
78#2572C2214yes—
79#2571C2212yes—
80#2571C2211yescharacteristic
81#2571C2211yescharacteristic
82#2570C2214yes—
83#2567C2212yes—
84#2567C2212yes—
85#2563C2211yescharacteristic
86#2563C2212yes—
87#2563C2211yescharacteristic
88#2563C2211yescharacteristic
89#2563C2214yes—
90#2563C2211yescharacteristic
91#2562C2214yes—
92#2553C2214yes—
93#2552C2212yes—
94#2552C2212yes—
95#2552C2212yes—
96#2552C2211yescharacteristic
97#2552C2212yes—
98#2551C2212yes—
99#2551C2212yes—
100#2550C2214yes—
101#2547C2211yescharacteristic
102#2546C2212yes—
103#2542C2211yescharacteristic
104#2538C2212yes—
105#2537C2211yescharacteristic
106#2537C2214yes—
107#2537C2211yescharacteristic
108#2537C2211yescharacteristic
109#2536C2214yes—
110#2508C2214yes—
111#2507C2214yes—
112#2503C2214yes—
113#2502C2214yes—
114#2501C2214yes—
115#2497C2214yes—
116#2497C2214yes—
117#2496C2214yes—
118#2496C2214yes—
119#2496C2212yes—
120#2495C2212yes—
121#2495C2214yes—
122#2495C2214yes—
123#2495C2212yes—
124#2495C2212yes—
125#2495C2212yes—
126#2492C2214yes—
127#2492C2214yes—
128#2489C2212yes—
129#2487C2214yes—
130#2486C2214yes—
131#2486C2214yes—
132#2485C2214yes—
133#2468C2218yes—
134#2452C2214yes—
135#2443C2218yes—
136#2442C2214yes—
137#2442C2214yes—
138#2442C2214yes—
139#2441C2214yes—
140#2440C2214yes—
141#2440C2214yes—
142#2440C2214yes—
143#2440C2214yes—
144#2440C2214yes—
145#2440C2214yes—
146#2439C2214yes—
147#2439C2214yes—
148#2434C2214yes—
149#2427C2212yes—
150#2426C2214yes—
151#2422C2214yes—
152#2422C2212yes—
153#2421C2214yes—
154#2420C2212yes—
155#2420C2214yes—
156#2420C2212yes—
157#2420C2212yes—
158#2420C2212yes—
159#2417C2214yes—
160#2416C2214yes—
161#2409C2218yes—
162#2398C2214yes—
163#2398C2214yes—
164#2395C2214yes—
165#2369C2212yes—
166#2369C2212yes—
167#2365C2212yes—
168#2361C2214yes—
169#2355C2212yes—
170#2354C2212yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2214yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177#2324C2214yes—
178#2320C2214yes—
179#2319C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C22⋊Q8C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191C2×#384C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#554—48no—
201#553—416no—
202D4×Q8—48no—
203C2×C4⋊Q8—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214#529—48no—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#124C2312yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2318yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×#117C2314yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2312yes—
266C22×C42C2312yes—
267C22×C42C2312yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2318yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2318yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2318yes—
329#394C2314yes—
330#394C2314yes—
331#393C2314yes—
332#393C2318yes—
333#393C2314yes—
334#393C2314yes—
335#393C2314yes—
336#393C2318yes—
337#393C2318yes—
338#393C2318yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2318yes—
346#391C2314yes—
347#391C2314yes—
348#391C2318yes—
349#391C2318yes—
350#390C2312yes—
351#390C2312yes—
352#390C2318yes—
353#390C2314yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#386C2318yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2318yes—
412#386C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2314yes—
426#384C2314yes—
427#384C2314yes—
428#384C2312yes—
429#384C2314yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#383C2314yes—
437#383C2314yes—
438#383C2314yes—
439#383C2314yes—
440#383C2318yes—
441#382C2314yes—
442#382C2318yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2318yes—
458#381C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2318yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2312yes—
480#380C2318yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522#376C2314yes—
523C43C2311yescharacteristic
524C22×Q8—48no—
525C22×Q8—48no—
526C22×Q8—84no—
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2418yes—
532C22×D4C2411yescharacteristic
533C22×D4C2414yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C22×D4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C4⋊Q8—24no—
550C4⋊Q8—28no—
551C4⋊Q8—24no—
552C4⋊Q8—24no—
553C4⋊Q8—48no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8—82no—
559#126—48no—
560#126—416no—
561#125—44no—
562#125—48no—
563#125—48no—
564#124—44no—
565#123—48no—
566#123—416no—
567#123—88no—
568C22⋊Q8—48no—
569C22⋊Q8—416no—
570C22⋊Q8—416no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—88no—
575C22⋊Q8—84no—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—28no—
580#121—416no—
581#121—44no—
582#121—44no—
583C4×Q8—28no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×Q8—48no—
587C4×D4—24no—
588C4×D4—216no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—42no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—416no—
602#117—48no—
603#117—48no—
604C2×C4⋊C4—48no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—84no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C42—28no—
693C2×C42—28no—
694C2×C42—28no—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2418yes—
711C2×C42C2418yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24C2512yes—
763C24C2512yes—
764C24C2512yes—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—28no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—44no—
775C2×Q8—48no—
776C2×Q8—42no—
777C2×Q8—48no—
778C2×Q8—48no—
779C2×Q8—44no—
780C2×Q8—832no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4H(5,𝔽2)14yes—
798C2×D42−1+414yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—216no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—48no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2518yes—
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—42no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C22⋊C4—216no—
908C22⋊C4—24no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—24no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—42no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—28no—
942C42—28no—
943C42—22no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—22no—
951C42—22no—
952C42—28no—
953C42—48no—
954C42—48no—
955C42—41no—
956C42H(5,𝔽2)14yes—
957C422−1+414yes—
958C422−1+414yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23C2×H(5,𝔽2)14yes—
979C23C2×2−1+414yes—
980C23C2611yescharacteristic
981Q8—48no—
982Q8—48no—
983Q8—84no—
984Q8—88no—
985Q8—816no—
986D4—28no—
987D4—28no—
988D4—416no—
989D4—44no—
990D4—88no—
991D4—88no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—84no—
1058C2×C4—816no—
1059C2×C4—168no—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4#58512yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22C22×H(5,𝔽2)11yescharacteristic
1094C22C22×H(5,𝔽2)11yescharacteristic
1095C22C22×2−1+411yescharacteristic
1096C22C22×2−1+411yescharacteristic
1097C22C22×2−1+411yescharacteristic
1098C22C2×#58511yescharacteristic
1099C22H(7,𝔽2)11yescharacteristic
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—44no—
1110C4—41no—
1111C4—44no—
1112C4—44no—
1113C4—42no—
1114C4—44no—
1115C4—48no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4#354414yes—
1121C4#354714yes—
1122C4#355214yes—
1123C2—44no—
1124C2—44no—
1125C2—82no—
1126C2C2×#355211yescharacteristic
1127C2C2×#354411yescharacteristic
1128C2C2×#354711yescharacteristic
1129C2#6291211yescharacteristic
1130C2#6292911yescharacteristic
1131C2#6294511yescharacteristic
1132C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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. #59304C2semidirect
3. #59213C2semidirect
4. #59136C2semidirect
5. #55180C2semidirect
6. #53119C2semidirect
7. #53023C2semidirect
8. #52992C2semidirect
9. #42601C2semidirect
10. #42512C2semidirect
11. #42485C2semidirect
12. #39608C2semidirect
13. #39126C2semidirect
14. #38940C2semidirect
15. #38932C2semidirect
16. #38931C2semidirect
17. #38930C2semidirect
18. #37632C2semidirect
19. #37624C2semidirect
20. #37623C2semidirect
21. #36194C2semidirect
22. #36180C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34943C2semidirect
25. #34943C2semidirect
26. #34932C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#593042
#592132
#591362
#551802
#531192
#530232
#529922
#426012
#425122
#424852
#396082
#391262
#389402
#389322
#389312
#389302
#376322
#376242
#376232
#361942
#361802
D4×C4⋊Q82
#349432
#349322