Finite Group Databasebeta

← #7688285

Subgroups — #7688285

Order 512.

5337 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59823C212yesmaximal, complemented
3#59809C214yesmaximal, complemented
4#59457C212yesmaximal, complemented
5#59323C214yesmaximal, complemented
6#59036C212yesmaximal, complemented
7#44947C214yesmaximal, complemented
8#43566C218yesmaximal, complemented
9#39980C214yesmaximal, complemented
10#39753C212yesmaximal, complemented
11#39664C214yesmaximal, complemented
12#39618C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36561C212yesmaximal, complemented
15Q8×#127C211yesmaximal, characteristic, complemented
16#36476C212yesmaximal, complemented
17#36274C212yesmaximal, complemented
18#36194C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic, complemented
20#35934C214yesmaximal, complemented
21#34950C211yesmaximal, characteristic, complemented
22#34947C212yesmaximal, complemented
23#34334C212yesmaximal, complemented
24#34330C212yesmaximal
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic
27C2×#554C2211yescharacteristic
28C2×#554C2214yes—
29C2×#550C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×#533C2212yes—
34C2×C4×#41C2212yes—
35#2868C2211yescharacteristic
36#2868C2212yes—
37#2862C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2855C2214yes—
41#2804C2214yes—
42#2791C2218yes—
43#2780C2218yes—
44#2748C2218yes—
45#2748C2218yes—
46#2732C2218yes—
47#2713C2218yes—
48#2692C2218yes—
49#2692C2218yes—
50#2692C2218yes—
51#2692C2218yes—
52#2667C2218yes—
53#2660C2214yes—
54#2607C2218yes—
55#2589C2218yes—
56#2586C2214yes—
57#2582C2212yes—
58#2582C2211yescharacteristic
59#2580C2214yes—
60#2580C2214yes—
61#2580C2214yes—
62#2571C2212yes—
63#2571C2212yes—
64#2570C2214yes—
65#2570C2214yes—
66#2568C2212yes—
67#2567C2211yescharacteristic
68#2567C2211yescharacteristic
69#2566C2214yes—
70#2566C2214yes—
71#2565C2214yes—
72#2564C2218yes—
73#2564C2218yes—
74#2563C2214yes—
75#2563C2212yes—
76#2563C2212yes—
77#2556C2218yes—
78#2556C2218yes—
79#2552C2212yes—
80#2552C2214yes—
81#2551C2211yescharacteristic
82#2550C2214yes—
83#2549C2218yes—
84#2542C2212yes—
85#2542C2214yes—
86#2542C2214yes—
87#2542C2214yes—
88#2542C2212yes—
89#2542C2212yes—
90#2542C2212yes—
91#2538C2212yes—
92#2538C2214yes—
93#2538C2214yes—
94#2538C2214yes—
95#2522C2218yes—
96#2511C2214yes—
97#2507C2212yes—
98#2507C2212yes—
99#2506C2214yes—
100#2497C2218yes—
101#2492C2218yes—
102#2492C2214yes—
103#2487C2214yes—
104#2465C2218yes—
105#2454C2214yes—
106#2454C2218yes—
107#2452C2214yes—
108#2451C2212yes—
109#2451C2214yes—
110#2451C2212yes—
111#2450C2218yes—
112#2450C2218yes—
113#2450C2218yes—
114#2446C2214yes—
115#2441C2214yes—
116#2439C2214yes—
117#2439C2214yes—
118#2438C2218yes—
119#2429C2214yes—
120#2423C2214yes—
121#2423C2214yes—
122#2417C2214yes—
123#2417C2214yes—
124#2417C2214yes—
125#2417C2214yes—
126#2409C2214yes—
127#2409C2214yes—
128#2399C2214yes—
129#2396C2218yes—
130#2370C2212yes—
131#2369C2214yes—
132#2369C2211yescharacteristic
133#2368C2218yes—
134#2368C2214yes—
135#2366C2212yes—
136#2366C2214yes—
137#2366C2211yescharacteristic
138#2366C2212yes—
139#2365C2212yes—
140#2365C2212yes—
141#2364C2218yes—
142#2363C2214yes—
143#2363C2214yes—
144#2363C2212yes—
145#2360C2214yes—
146#2360C2212yes—
147#2357C2214yes—
148#2355C2212yes—
149#2355C2211yescharacteristic
150#2355C2214yes—
151#2355C2212yes—
152#2354C2212yes—
153#2354C2212yes—
154#2354C2211yescharacteristic
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2211yescharacteristic
157#2349C2214yes—
158#2349C2214yes—
159#2349C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2212yes—
163#2345C2212yes—
164#2341C2212yes—
165Q8×C22⋊C4C2214yes—
166#2339C2214yes—
167#2333C2218yes—
168#2331C2214yes—
169#2329C2218yes—
170#2328C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×#127C2212yes—
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#125C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186C4×#121C2214yes—
187#2297C2214yes—
188#2295C2212yes—
189#2295C2212yes—
190C2×#391C2214yes—
191#2285C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#554—28no—
202#554—416no—
203#550Q8116yescomplemented
204D4×Q8—216no—
205D4×Q8—48no—
206D4×Q8—48no—
207#533—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×#127C2311yescharacteristic
219C2×#127C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C4×#41—48no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2312yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2312yes—
279C22×C42C2314yes—
280C22×C42C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2314yes—
310#395C2314yes—
311#395C2314yes—
312#395C2314yes—
313#395C2318yes—
314#395C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#391C2314yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2314yes—
339#391C2318yes—
340#391C2314yes—
341#391C2318yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2318yes—
356#390C2314yes—
357#390C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2318yes—
385#389C2312yes—
386#389C2314yes—
387#389C2318yes—
388#389C2312yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2314yes—
414#386C2314yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2312yes—
442#384C2311yescharacteristic
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#384C2312yes—
449#384C2314yes—
450#382C2312yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#381C2318yes—
457#380C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#380C2318yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2312yes—
469#380C2314yes—
470#380C2318yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C2×#95C2318yes—
524C43C2312yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—44no—
528C2×#41—44no—
529C2×#41C2×Q8116yescomplemented
530C22×Q8—216no—
531C22×Q8—48no—
532C22×Q8—48no—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2412yes—
539C22×Q8C2418yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2412yes—
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2418yes—
552C23×C4C2412yes—
553C23×C4C2418yes—
554C23×C4C2414yes—
555C23×C4C2414yes—
556C4⋊Q8—28no—
557C4⋊Q8—216no—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—28no—
562C4⋊Q8—44no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566#127C2×Q818yes—
567#127C2×Q8116yescomplemented
568#125—28no—
569#125—48no—
570#125—416no—
571C22⋊Q8—28no—
572C22⋊Q8—216no—
573C22⋊Q8—232no—
574C22⋊Q8—216no—
575C22⋊Q8—216no—
576C22⋊Q8—416no—
577C22⋊Q8—416no—
578C22⋊Q8—416no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582C22⋊Q8—48no—
583C22⋊Q8—416no—
584#121C2×Q8116yescomplemented
585#121C2×Q8132yescomplemented
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—48no—
592C4×Q8—42no—
593C4×Q8—44no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8C2×Q818yescomplemented
598C4×Q8#4118yescomplemented
599C4×D4—216no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—44no—
607C4×D4—44no—
608C4×D4—42no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—44no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—416no—
617C4×D4C2×Q818yescomplemented
618C4×D4C2×Q8116yescomplemented
619#117—48no—
620#117—44no—
621#117—48no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—48no—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2414yes—
704C2×C42—28no—
705C2×C42—48no—
706C2×C42—48no—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2418yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2418yes—
777C24C2514yes—
778C24C2512yes—
779#41—432no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—216no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—28no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—22no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—44no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8—44no—
798C2×Q8—42no—
799C2×Q8—832no—
800C2×Q8C22×Q814yes—
801C2×Q8C2×#4114yes—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—22no—
807C2×D4—24no—
808C2×D4—42no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4C22×Q818yes—
815C2×D4C22×Q814yes—
816C2×D4C22×Q818yes—
817C2×D4C22×Q818yes—
818C2×D4C22×Q8116yes—
819C2×D4C22×Q8116yes—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—216no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4C22×Q818yes—
849C22×C4C22×Q8116yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2518yes—
860C22×C4C2511yescharacteristic
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—24no—
896C4⋊C4—28no—
897C4⋊C4—216no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4C22×Q814yes—
926C4⋊C4C22×Q818yes—
927C4⋊C4C22×Q814yes—
928C4⋊C4C2×#4114yes—
929C4⋊C4C2×#4118yes—
930C4⋊C4H(5,𝔽2)14yes—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—216no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—42no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4C22×Q818yes—
952C22⋊C4C22×Q8116yes—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—24no—
964C42—22no—
965C42—28no—
966C42—24no—
967C42—22no—
968C42—44no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42—41no—
973C42—42no—
974C42—42no—
975C42—48no—
976C42—48no—
977C42—42no—
978C42C22×Q814yes—
979C42C22×Q818yes—
980C42C2×#4118yes—
981C42C2×#4114yes—
982C42H(5,𝔽2)14yes—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23C23×Q814yes—
996C23C23×Q818yes—
997C23C2611yescharacteristic
998Q8—28no—
999Q8—28no—
1000Q8—48no—
1001Q8—416no—
1002Q8—84no—
1003Q8—88no—
1004Q8—816no—
1005D4—216no—
1006D4—28no—
1007D4—216no—
1008D4—48no—
1009D4—416no—
1010D4—416no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—216no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—28no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—416no—
1067C2×C4—48no—
1068C2×C4—416no—
1069C2×C4—88no—
1070C2×C4—88no—
1071C2×C4—84no—
1072C2×C4—816no—
1073C2×C4—88no—
1074C2×C4—168no—
1075C2×C4C23×Q812yes—
1076C2×C4C23×Q814yes—
1077C2×C4C23×Q814yes—
1078C2×C4C23×Q814yes—
1079C2×C4C23×Q812yes—
1080C2×C4C23×Q812yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4114yes—
1083C2×C4C22×#4114yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)14yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4#58512yes—
1092C2×C4#58512yes—
1093C22—28no—
1094C22—24no—
1095C22—24no—
1096C22—28no—
1097C22—24no—
1098C22—28no—
1099C22—42no—
1100C22—44no—
1101C22—42no—
1102C22—44no—
1103C22—44no—
1104C22—42no—
1105C22—42no—
1106C22—44no—
1107C22C24×Q811yescharacteristic
1108C22C23×#4111yescharacteristic
1109C22C22×H(5,𝔽2)11yescharacteristic
1110C22C22×H(5,𝔽2)11yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C222−1+611yescharacteristic
1114C4—22no—
1115C4—24no—
1116C4—24no—
1117C4—22no—
1118C4—24no—
1119C4—24no—
1120C4—24no—
1121C4—24no—
1122C4—22no—
1123C4—44no—
1124C4—41no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—48no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—44no—
1135C4Q8×#4114yes—
1136C4#350114yes—
1137C4#350814yes—
1138C2—44no—
1139C2—48no—
1140C2C2×Q8×#4111yescharacteristic
1141C2C2×#350111yescharacteristic
1142C2C2×#350811yescharacteristic
1143C2#6292511yescharacteristic
1144C2Q8×H(5,𝔽2)11yescharacteristic
1145C2#6299511yescharacteristic
1146C2#6302411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59864C2semidirect
2. #59823C2semidirect
3. #59809C2semidirect
4. #59457C2semidirect
5. #59323C2semidirect
6. #59036C2semidirect
7. #44947C2semidirect
8. #43566C2semidirect
9. #39980C2semidirect
10. #39753C2semidirect
11. #39664C2semidirect
12. #39618C2semidirect
13. #36598C2semidirect
14. #36561C2semidirect
15. Q8×#127C2semidirect
16. #36476C2semidirect
17. #36274C2semidirect
18. #36194C2semidirect
19. #36134C2semidirect
20. #35934C2semidirect
21. #34950C2semidirect
22. #34947C2semidirect
23. #34334C2semidirect
25. C4×#554C2semidirect
203. #550Q8semidirect
529. C2×#41C2×Q8semidirect
567. #127C2×Q8semidirect
584. #121C2×Q8semidirect
585. #121C2×Q8semidirect
597. C4×Q8C2×Q8semidirect
598. C4×Q8#41semidirect
617. C4×D4C2×Q8semidirect
618. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598642
#598232
#598092
#594572
#593232
#590362
#449472
#435662
#399802
#397532
#396642
#396182
#365982
#365612
Q8×#1272
#364762
#362742
#361942
#361342
#359342
#349502
#349472
#343342
#343302
C4×#5542
C4×#5502