Finite Group Databasebeta

← #7987199

Subgroups — #7987199

Order 512.

4783 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59655C212yesmaximal
3#59467C212yesmaximal, complemented
4#59322C212yesmaximal, complemented
5#50702C218yesmaximal, complemented
6#46001C214yesmaximal, complemented
7#45272C214yesmaximal, complemented
8#45086C214yesmaximal
9#42933C214yesmaximal, complemented
10#42823C214yesmaximal, complemented
11#39662C214yesmaximal, complemented
12#39625C212yesmaximal, complemented
13#39617C212yesmaximal
14#39609C212yesmaximal, complemented
15#39369C212yesmaximal
16#36593C211yesmaximal, characteristic, complemented
17Q8×C4⋊Q8C212yesmaximal, complemented
18Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
19#36481C212yesmaximal, complemented
20#36180C211yesmaximal, characteristic
21#35275C212yesmaximal, complemented
22#35208C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic
25#34481C212yesmaximal
26C4×#556C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×Q82C2212yes—
29C2×#557C2212yes—
30C2×#556C2211yescharacteristic
31C2×#554C2212yes—
32C2×#544C2214yes—
33#2868C2211yescharacteristic
34#2868C2214yes—
35#2868C2212yes—
36#2868C2212yes—
37#2863C2214yes—
38#2859C2214yes—
39#2857C2212yes—
40#2843C2218yes—
41#2807C2218yes—
42#2792C2218yes—
43#2792C2218yes—
44#2791C2218yes—
45#2774C2218yes—
46#2742C2218yes—
47#2734C2214yes—
48#2734C2218yes—
49#2729C2218yes—
50#2729C2218yes—
51#2726C2218yes—
52#2720C2218yes—
53#2720C2218yes—
54#2713C2218yes—
55#2677C2218yes—
56#2677C2218yes—
57#2677C2218yes—
58#2666C2218yes—
59#2666C2218yes—
60#2660C2218yes—
61#2660C2214yes—
62#2628C2214yes—
63#2606C2218yes—
64#2590C2218yes—
65#2585C2214yes—
66#2583C2218yes—
67#2582C2212yes—
68#2582C2211yescharacteristic
69#2574C2214yes—
70#2568C2211yescharacteristic
71#2567C2214yes—
72#2567C2212yes—
73#2567C2211yescharacteristic
74#2567C2212yes—
75#2567C2214yes—
76#2567C2214yes—
77#2567C2214yes—
78#2565C2214yes—
79#2563C2211yescharacteristic
80#2556C2218yes—
81#2552C2214yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2212yes—
85#2552C2214yes—
86#2552C2211yescharacteristic
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2552C2214yes—
90#2551C2214yes—
91#2551C2218yes—
92#2551C2218yes—
93#2551C2214yes—
94#2551C2214yes—
95#2551C2212yes—
96#2551C2214yes—
97#2551C2214yes—
98#2551C2212yes—
99#2551C2212yes—
100#2551C2212yes—
101#2550C2214yes—
102#2546C2214yes—
103#2546C2211yescharacteristic
104#2546C2212yes—
105#2546C2214yes—
106#2542C2214yes—
107#2538C2211yescharacteristic
108#2522C2218yes—
109#2511C2212yes—
110#2511C2214yes—
111#2509C2214yes—
112#2509C2212yes—
113#2508C2212yes—
114#2507C2214yes—
115#2507C2214yes—
116#2507C2214yes—
117#2506C2214yes—
118#2502C2214yes—
119#2497C2212yes—
120#2492C2214yes—
121#2462C2218yes—
122#2454C2212yes—
123#2453C2214yes—
124#2453C2214yes—
125#2453C2212yes—
126#2452C2214yes—
127#2451C2214yes—
128#2451C2214yes—
129#2451C2214yes—
130#2446C2212yes—
131#2441C2214yes—
132#2440C2214yes—
133#2440C2214yes—
134#2440C2218yes—
135#2440C2214yes—
136#2440C2214yes—
137#2440C2214yes—
138#2440C2214yes—
139#2429C2218yes—
140#2429C2214yes—
141#2423C2212yes—
142#2423C2214yes—
143#2423C2214yes—
144#2402C2214yes—
145#2396C2214yes—
146#2383C2218yes—
147#2373C2214yes—
148#2370C2214yes—
149#2367C2214yes—
150#2367C2212yes—
151#2365C2211yescharacteristic
152#2365C2212yes—
153#2365C2212yes—
154#2362C2212yes—
155#2360C2214yes—
156#2360C2214yes—
157#2356C2212yes—
158#2355C2211yescharacteristic
159#2354C2211yescharacteristic
160Q8×C4⋊C4C2214yes—
161Q8×C4⋊C4C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168#2347C2212yes—
169#2347C2214yes—
170#2334C2218yes—
171#2330C2214yes—
172#2326C2214yes—
173#2323C2214yes—
174#2320C2214yes—
175#2317C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2214yes—
183C4×#125C2212yes—
184C4×#125C2212yes—
185C4×#126C2214yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193C2×#384C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199Q82—48no—
200Q82—48no—
201#557—48no—
202#556Q8116yescomplemented
203#554—48no—
204#544—416no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2318yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2318yes—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#126C2314yes—
226C2×#125C2312yes—
227C2×#125C2312yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2318yes—
231C2×#125C2318yes—
232C2×#124C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C42C2312yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2314yes—
276#399C2318yes—
277#399C2314yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#396C2314yes—
301#396C2314yes—
302#396C2318yes—
303#395C2318yes—
304#395C2314yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#393C2314yes—
318#393C2318yes—
319#391C2312yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2318yes—
337#391C2318yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2318yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2314yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2311yescharacteristic
439#384C2314yes—
440#384C2312yes—
441#384C2314yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2318yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2318yes—
454#384C2314yes—
455#384C2312yes—
456#384C2314yes—
457#383C2314yes—
458#383C2318yes—
459#382C2312yes—
460#382C2312yes—
461#382C2318yes—
462#382C2314yes—
463#382C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2314yes—
521C43C2314yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2414yes—
530C22×Q8C2412yes—
531C22×Q8C2418yes—
532C22×Q8C2418yes—
533C22×D4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2418yes—
538C4⋊Q8—28no—
539C4⋊Q8—28no—
540C4⋊Q8—24no—
541C4⋊Q8—24no—
542C4⋊Q8—416no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545C4⋊Q8—44no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—416no—
552C4⋊Q8—416no—
553C4⋊Q8—82no—
554C4⋊Q8—88no—
555C4⋊Q8—84no—
556C4⋊Q8—84no—
557C4⋊Q8C2×Q818yes—
558#126C2×Q8132yes—
559#125—28no—
560#125—216no—
561#125—28no—
562#125—416no—
563#125—48no—
564#125—416no—
565#124C2×Q8116yes—
566C22⋊Q8—28no—
567C22⋊Q8—416no—
568C22⋊Q8—416no—
569C22⋊Q8—416no—
570C22⋊Q8—48no—
571C22⋊Q8—88no—
572C22⋊Q8C2×Q8116yes—
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—24no—
578C4×Q8—28no—
579C4×Q8—24no—
580C4×Q8—24no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8C2×Q8116yes—
589C4×Q8C2×Q818yes—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—48no—
593C4×D4C2×Q818yes—
594#117—28no—
595#117—48no—
596#117C2×Q8116yes—
597C2×C4⋊C4—48no—
598C2×C4⋊C4—48no—
599C2×C4⋊C4—84no—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C42—28no—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2418yes—
704C2×C42C2418yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760C24C2512yes—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—42no—
773C2×Q8—44no—
774C2×Q8—42no—
775C2×Q8—44no—
776C2×Q8—48no—
777C2×Q8—48no—
778C2×Q8—48no—
779C2×Q8—48no—
780C2×Q8—48no—
781C2×Q8—48no—
782C2×Q8C22×Q814yes—
783C2×Q8C22×Q818yes—
784C2×Q82−1+414yes—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4C22×Q814yes—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—42no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4C22×Q818yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2518yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—22no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—216no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—42no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—42no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4C22×Q814yes—
887C4⋊C4C22×Q818yes—
888C4⋊C4C22×Q814yes—
889C4⋊C4C22×Q8116yes—
890C4⋊C4C22×Q818yes—
891C4⋊C4C22×Q818yes—
892C4⋊C4H(5,𝔽2)14yes—
893C4⋊C42−1+414yes—
894C22⋊C4—28no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4C22×Q8116yes—
904C22⋊C4C22×Q818yes—
905C22⋊C4C22×Q8116yes—
906C42—28no—
907C42—24no—
908C42—28no—
909C42—28no—
910C42—24no—
911C42—22no—
912C42—24no—
913C42—28no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—22no—
918C42—28no—
919C42—24no—
920C42—24no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—48no—
927C42—48no—
928C42—48no—
929C42—41no—
930C42—42no—
931C42—44no—
932C42—42no—
933C42C22×Q8116yes—
934C42C22×Q814yes—
935C42C22×Q818yes—
936C42H(5,𝔽2)14yes—
937C422−1+414yes—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23C23×Q814yes—
945C23C2611yescharacteristic
946Q8—28no—
947Q8—216no—
948Q8—28no—
949Q8—48no—
950Q8—88no—
951Q8—84no—
952Q8—168no—
953Q8—168no—
954D4—28no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—216no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—21no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—48no—
1013C2×C4—48no—
1014C2×C4—168no—
1015C2×C4C23×Q814yes—
1016C2×C4C23×Q814yes—
1017C2×C4C23×Q812yes—
1018C2×C4C23×Q818yes—
1019C2×C4C23×Q814yes—
1020C2×C4C23×Q812yes—
1021C2×C4C23×Q812yes—
1022C2×C4C2×H(5,𝔽2)14yes—
1023C2×C4C2×H(5,𝔽2)12yes—
1024C2×C4C2×H(5,𝔽2)12yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+414yes—
1029C2×C4C2×2−1+414yes—
1030C2×C4C2×2−1+412yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4C2×2−1+412yes—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22C24×Q811yescharacteristic
1042C22C22×H(5,𝔽2)11yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×2−1+411yescharacteristic
1045C22C22×2−1+411yescharacteristic
1046C22C22×2−1+411yescharacteristic
1047C22H(7,𝔽2)11yescharacteristic
1048C4—22no—
1049C4—24no—
1050C4—24no—
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—28no—
1055C4—22no—
1056C4—22no—
1057C4—24no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—42no—
1062C4—41no—
1063C4—44no—
1064C4—48no—
1065C4—44no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4#350314yes—
1071C4#350314yes—
1072C4#355214yes—
1073C2—44no—
1074C2C2×#355211yescharacteristic
1075C2C2×#350311yescharacteristic
1076C2C2×#350311yescharacteristic
1077C2#6291611yescharacteristic
1078C2#6294511yescharacteristic
1079C2Q8×2−1+411yescharacteristic
1080C2#6303711yescharacteristic
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. #59832C2semidirect
3. #59467C2semidirect
4. #59322C2semidirect
5. #50702C2semidirect
6. #46001C2semidirect
7. #45272C2semidirect
9. #42933C2semidirect
10. #42823C2semidirect
11. #39662C2semidirect
12. #39625C2semidirect
14. #39609C2semidirect
16. #36593C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×C4⋊Q8C2semidirect
19. #36481C2semidirect
21. #35275C2semidirect
22. #35208C2semidirect
23. #34951C2semidirect
202. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#596552
#594672
#593222
#507022
#460012
#452722
#450862
#429332
#428232
#396622
#396252
#396172
#396092
#393692
#365932
Q8×C4⋊Q82
#364812
#361802
#352752
#352082
#349512
#349412
#344812
C4×#5562