Finite Group Databasebeta

← #7687969

Subgroups — #7687969

Order 512.

5385 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59817C212yesmaximal, complemented
3#59809C214yesmaximal, complemented
4#59771C214yesmaximal, complemented
5#59457C212yesmaximal, complemented
6#59214C212yesmaximal, complemented
7#44952C214yesmaximal, complemented
8#43139C218yesmaximal, complemented
9#39981C214yesmaximal, complemented
10#39666C214yesmaximal, complemented
11#39634C212yesmaximal, complemented
12#39181C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15Q8×#121C212yesmaximal, complemented
16#36477C212yesmaximal, complemented
17#36407C212yesmaximal, complemented
18#36274C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#35871C214yesmaximal, complemented
21#34952C212yesmaximal, complemented
22#34951C211yesmaximal, characteristic, complemented
23#34334C212yesmaximal, complemented
24#34330C212yesmaximal
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×#550C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2211yescharacteristic
31C2×D4×Q8C2214yes—
32C2×D4×Q8C2212yes—
33C2×C4×#41C2212yes—
34C22×C4×Q8C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2859C2212yes—
38#2857C2214yes—
39#2857C2212yes—
40#2855C2214yes—
41#2804C2218yes—
42#2784C2218yes—
43#2780C2218yes—
44#2780C2218yes—
45#2780C2218yes—
46#2780C2218yes—
47#2774C2218yes—
48#2713C2218yes—
49#2692C2218yes—
50#2683C2218yes—
51#2683C2214yes—
52#2665C2218yes—
53#2647C2214yes—
54#2608C2218yes—
55#2589C2218yes—
56#2587C2218yes—
57#2587C2218yes—
58#2585C2214yes—
59#2582C2211yescharacteristic
60#2582C2212yes—
61#2581C2214yes—
62#2580C2214yes—
63#2579C2218yes—
64#2574C2218yes—
65#2571C2212yes—
66#2570C2214yes—
67#2568C2211yescharacteristic
68#2567C2212yes—
69#2566C2214yes—
70#2566C2214yes—
71#2566C2214yes—
72#2563C2212yes—
73#2563C2212yes—
74#2556C2218yes—
75#2552C2212yes—
76#2552C2211yescharacteristic
77#2551C2214yes—
78#2551C2212yes—
79#2550C2214yes—
80#2549C2218yes—
81#2546C2214yes—
82#2546C2211yescharacteristic
83#2538C2214yes—
84#2538C2212yes—
85#2538C2214yes—
86#2538C2212yes—
87#2538C2212yes—
88#2538C2212yes—
89#2538C2212yes—
90#2511C2212yes—
91#2509C2214yes—
92#2509C2212yes—
93#2507C2214yes—
94#2497C2214yes—
95#2497C2214yes—
96#2492C2218yes—
97#2492C2214yes—
98#2487C2214yes—
99#2487C2214yes—
100#2454C2214yes—
101#2454C2214yes—
102#2453C2212yes—
103#2452C2214yes—
104#2452C2214yes—
105#2452C2214yes—
106#2452C2214yes—
107#2452C2214yes—
108#2452C2214yes—
109#2452C2218yes—
110#2451C2214yes—
111#2451C2214yes—
112#2450C2218yes—
113#2450C2218yes—
114#2450C2218yes—
115#2446C2212yes—
116#2441C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2438C2218yes—
120#2429C2218yes—
121#2429C2214yes—
122#2417C2218yes—
123#2417C2214yes—
124#2417C2214yes—
125#2409C2214yes—
126#2409C2214yes—
127#2409C2214yes—
128#2402C2214yes—
129#2396C2218yes—
130#2370C2214yes—
131#2369C2214yes—
132#2369C2212yes—
133#2369C2212yes—
134#2368C2218yes—
135#2366C2212yes—
136#2366C2214yes—
137#2366C2211yescharacteristic
138#2366C2212yes—
139#2365C2211yescharacteristic
140#2365C2212yes—
141#2364C2218yes—
142#2363C2214yes—
143#2363C2212yes—
144#2363C2214yes—
145#2360C2214yes—
146#2360C2214yes—
147#2360C2212yes—
148#2357C2214yes—
149#2355C2212yes—
150#2355C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2211yescharacteristic
154Q8×C4⋊C4C2211yescharacteristic
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2211yescharacteristic
157#2349C2214yes—
158#2349C2214yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163#2341C2212yes—
164Q8×C22⋊C4C2214yes—
165Q8×C22⋊C4C2212yes—
166#2339C2214yes—
167#2333C2218yes—
168#2331C2214yes—
169#2329C2218yes—
170#2328C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×#127C2212yes—
177C4×#127C2211yescharacteristic
178C4×#127C2212yes—
179C4×#125C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186C4×#121C2214yes—
187#2297C2214yes—
188#2296C2214yes—
189#2295C2212yes—
190#2295C2212yes—
191C2×#391C2214yes—
192#2285C2212yes—
193#2275C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C42×D4C2211yescharacteristic
199C22×#41C2312yes—
200C23×Q8C2312yes—
201C23×Q8C2314yes—
202#554—48no—
203#550Q8116yescomplemented
204D4×Q8—28no—
205D4×Q8—216no—
206D4×Q8—48no—
207D4×Q8—416no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2318yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C4×#41—48no—
237C2×C4×Q8—48no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2312yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2312yes—
278C22×C42C2312yes—
279C22×C42C2314yes—
280C22×C42C2314yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#399C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2314yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2312yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2312yes—
338#391C2314yes—
339#391C2318yes—
340#390C2314yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#390C2318yes—
355#390C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2318yes—
385#389C2312yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2314yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2312yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2312yes—
453#382C2312yes—
454#382C2314yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#381C2318yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#380C2318yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2312yes—
469#380C2314yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2312yes—
521#376C2314yes—
522C2×#95C2318yes—
523C2×#95C2318yes—
524C43C2312yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—44no—
528C2×#41—44no—
529C2×#41C2×Q8116yescomplemented
530C22×Q8—28no—
531C22×Q8—28no—
532C22×Q8—216no—
533C22×Q8—44no—
534C22×Q8—48no—
535C22×Q8—48no—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2418yes—
542C22×Q8C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2418yes—
555C23×C4C2414yes—
556C23×C4C2418yes—
557C23×C4C2414yes—
558C23×C4C2414yes—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—216no—
562C4⋊Q8—24no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—48no—
566C4⋊Q8—44no—
567C4⋊Q8—416no—
568C4⋊Q8#4118yescomplemented
569#127C2×Q818yescomplemented
570#127C2×Q8116yescomplemented
571#125—44no—
572#125—48no—
573#125—48no—
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—216no—
577C22⋊Q8—216no—
578C22⋊Q8—232no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585#121C2×Q8116yescomplemented
586#121C2×Q8132yescomplemented
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—28no—
590C4×Q8—24no—
591C4×Q8—28no—
592C4×Q8—24no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—44no—
596C4×Q8—44no—
597C4×Q8—42no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8C2×Q818yescomplemented
601C4×D4—28no—
602C4×D4—216no—
603C4×D4—24no—
604C4×D4—28no—
605C4×D4—28no—
606C4×D4—48no—
607C4×D4—44no—
608C4×D4—48no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—42no—
612C4×D4—44no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—416no—
619C4×D4C2×Q818yescomplemented
620C4×D4C2×Q8116yescomplemented
621#117—48no—
622#117—48no—
623#117—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2414yes—
706C2×C42—28no—
707C2×C42—48no—
708C2×C42—48no—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2414yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2414yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2412yes—
758#95C2418yes—
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779C24C2514yes—
780C24C2512yes—
781#41—432no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—216no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—22no—
794C2×Q8—44no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—432no—
801C2×Q8—832no—
802C2×Q8C22×Q814yes—
803C2×Q8C2×#4118yes—
804C2×Q8H(5,𝔽2)14yes—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—42no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4C22×Q814yes—
818C2×D4C22×Q818yes—
819C2×D4C22×Q818yes—
820C2×D4C22×Q8116yes—
821C2×D4C22×Q818yes—
822C2×D4C22×Q8116yes—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—216no—
834C22×C4—24no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—42no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—42no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4C22×Q818yes—
852C22×C4C22×Q8116yes—
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2518yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—216no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—22no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—42no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4C22×Q814yes—
930C4⋊C4C22×Q818yes—
931C4⋊C4C22×Q814yes—
932C4⋊C4C2×#4118yes—
933C4⋊C4C2×#4118yes—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—216no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—42no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4C22×Q818yes—
955C22⋊C4C22×Q8116yes—
956C42—24no—
957C42—28no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—22no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—22no—
971C42—22no—
972C42—44no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—41no—
977C42—42no—
978C42—42no—
979C42—48no—
980C42—48no—
981C42—42no—
982C42C22×Q818yes—
983C42C22×Q814yes—
984C42C2×#4114yes—
985C42H(5,𝔽2)14yes—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23C23×Q814yes—
999C23C23×Q818yes—
1000C23C2611yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—216no—
1004Q8—416no—
1005Q8—48no—
1006Q8—816no—
1007Q8—164no—
1008D4—28no—
1009D4—216no—
1010D4—216no—
1011D4—48no—
1012D4—416no—
1013D4—416no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—216no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—24no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—28no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—416no—
1072C2×C4—48no—
1073C2×C4—416no—
1074C2×C4—84no—
1075C2×C4—816no—
1076C2×C4—88no—
1077C2×C4—88no—
1078C2×C4—168no—
1079C2×C4C23×Q812yes—
1080C2×C4C23×Q814yes—
1081C2×C4C23×Q814yes—
1082C2×C4C23×Q814yes—
1083C2×C4C23×Q812yes—
1084C2×C4C23×Q812yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4118yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)14yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4#58512yes—
1095C2×C4#58512yes—
1096C22—28no—
1097C22—24no—
1098C22—24no—
1099C22—28no—
1100C22—24no—
1101C22—28no—
1102C22—42no—
1103C22—44no—
1104C22—42no—
1105C22—44no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22C24×Q811yescharacteristic
1111C22C23×#4111yescharacteristic
1112C22C22×H(5,𝔽2)11yescharacteristic
1113C22C22×H(5,𝔽2)11yescharacteristic
1114C22C2×#58511yescharacteristic
1115C22C2×#58511yescharacteristic
1116C222−1+611yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—24no—
1121C4—24no—
1122C4—24no—
1123C4—28no—
1124C4—22no—
1125C4—42no—
1126C4—44no—
1127C4—42no—
1128C4—44no—
1129C4—44no—
1130C4—42no—
1131C4—42no—
1132C4—48no—
1133C4—41no—
1134C4—44no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4Q8×#4114yes—
1139C4#350114yes—
1140C4#351914yes—
1141C2—44no—
1142C2—48no—
1143C2C2×Q8×#4111yescharacteristic
1144C2C2×#350111yescharacteristic
1145C2C2×#351911yescharacteristic
1146C2#6296011yescharacteristic
1147C2Q8×H(5,𝔽2)11yescharacteristic
1148C2#6300711yescharacteristic
1149C2#6303511yescharacteristic
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. #59817C2semidirect
2. #59817C2semidirect
3. #59809C2semidirect
4. #59771C2semidirect
5. #59457C2semidirect
6. #59214C2semidirect
7. #44952C2semidirect
8. #43139C2semidirect
9. #39981C2semidirect
10. #39666C2semidirect
11. #39634C2semidirect
12. #39181C2semidirect
13. #36563C2semidirect
14. #36559C2semidirect
15. Q8×#121C2semidirect
16. #36477C2semidirect
17. #36407C2semidirect
18. #36274C2semidirect
19. #36194C2semidirect
20. #35871C2semidirect
21. #34952C2semidirect
22. #34951C2semidirect
23. #34334C2semidirect
25. C4×D4×Q8C2semidirect
203. #550Q8semidirect
529. C2×#41C2×Q8semidirect
568. C4⋊Q8#41semidirect
569. #127C2×Q8semidirect
570. #127C2×Q8semidirect
585. #121C2×Q8semidirect
586. #121C2×Q8semidirect
600. C4×Q8C2×Q8semidirect
619. C4×D4C2×Q8semidirect
620. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598172
#598092
#597712
#594572
#592142
#449522
#431392
#399812
#396662
#396342
#391812
#365632
#365592
Q8×#1212
#364772
#364072
#362742
#361942
#358712
#349522
#349512
#343342
#343302
C4×D4×Q82
C4×#5502