Finite Group Databasebeta

← #7688381

Subgroups — #7688381

Order 512.

4545 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59653C212yesmaximal
3#59547C214yesmaximal, complemented
4#59508C214yesmaximal, complemented
5#59434C212yesmaximal
6#59067C212yesmaximal, complemented
7#45339C214yesmaximal, complemented
8#44741C218yesmaximal, complemented
9#40191C214yesmaximal
10#40075C214yesmaximal, complemented
11#39157C212yesmaximal, complemented
12#38976C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36563C211yesmaximal, characteristic, complemented
15#36447C212yesmaximal, complemented
16#36312C212yesmaximal
17#36312C212yesmaximal
18#36287C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic
20#35899C214yesmaximal, complemented
21#34951C212yesmaximal, complemented
22#34945C211yesmaximal, characteristic
23#34337C212yesmaximal, complemented
24#34231C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2211yescharacteristic
29C2×#556C2211yescharacteristic
30C2×#533C2212yes—
31#2868C2211yescharacteristic
32#2860C2214yes—
33#2859C2212yes—
34#2859C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2777C2218yes—
38#2773C2218yes—
39#2766C2218yes—
40#2766C2218yes—
41#2762C2218yes—
42#2726C2214yes—
43#2725C2218yes—
44#2721C2218yes—
45#2720C2218yes—
46#2719C2218yes—
47#2689C2218yes—
48#2654C2218yes—
49#2645C2214yes—
50#2612C2218yes—
51#2596C2218yes—
52#2594C2218yes—
53#2585C2218yes—
54#2582C2212yes—
55#2582C2212yes—
56#2582C2212yes—
57#2573C2214yes—
58#2571C2211yescharacteristic
59#2571C2214yes—
60#2568C2211yescharacteristic
61#2567C2212yes—
62#2567C2212yes—
63#2556C2218yes—
64#2552C2212yes—
65#2552C2212yes—
66#2552C2214yes—
67#2552C2212yes—
68#2552C2212yes—
69#2550C2214yes—
70#2550C2214yes—
71#2547C2211yescharacteristic
72#2546C2212yes—
73#2545C2214yes—
74#2542C2212yes—
75#2538C2212yes—
76#2538C2211yescharacteristic
77#2529C2218yes—
78#2529C2218yes—
79#2528C2218yes—
80#2528C2218yes—
81#2524C2218yes—
82#2519C2218yes—
83#2519C2218yes—
84#2519C2218yes—
85#2514C2214yes—
86#2514C2212yes—
87#2511C2214yes—
88#2509C2214yes—
89#2508C2218yes—
90#2508C2214yes—
91#2508C2214yes—
92#2507C2214yes—
93#2507C2214yes—
94#2506C2214yes—
95#2506C2218yes—
96#2506C2214yes—
97#2506C2214yes—
98#2497C2214yes—
99#2496C2214yes—
100#2496C2214yes—
101#2494C2214yes—
102#2494C2212yes—
103#2489C2214yes—
104#2462C2218yes—
105#2453C2214yes—
106#2453C2214yes—
107#2451C2214yes—
108#2451C2214yes—
109#2448C2214yes—
110#2448C2214yes—
111#2447C2212yes—
112#2446C2214yes—
113#2446C2214yes—
114#2446C2214yes—
115#2441C2214yes—
116#2441C2214yes—
117#2441C2214yes—
118#2429C2214yes—
119#2429C2214yes—
120#2423C2214yes—
121#2423C2214yes—
122#2423C2214yes—
123#2421C2212yes—
124#2402C2218yes—
125#2401C2214yes—
126#2373C2214yes—
127#2370C2214yes—
128#2370C2218yes—
129#2370C2212yes—
130#2370C2214yes—
131#2369C2212yes—
132#2369C2212yes—
133#2367C2212yes—
134#2365C2211yescharacteristic
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2362C2214yes—
141#2362C2212yes—
142#2362C2214yes—
143#2362C2214yes—
144#2356C2212yes—
145#2356C2218yes—
146#2355C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2355C2211yescharacteristic
151#2354C2212yes—
152#2354C2211yescharacteristic
153#2351C2214yes—
154#2351C2212yes—
155Q8×C4⋊C4C2214yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2214yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2211yescharacteristic
162#2347C2212yes—
163#2347C2214yes—
164#2346C2214yes—
165#2346C2214yes—
166#2332C2218yes—
167#2330C2214yes—
168#2330C2218yes—
169#2320C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2214yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×#125C2212yes—
178C4×#125C2214yes—
179C4×#125C2214yes—
180C4×#125C2214yes—
181C4×#126C2214yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186#2295C2212yes—
187#2295C2214yes—
188#2295C2214yes—
189#2295C2214yes—
190#2283C2212yes—
191#2276C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—28no—
200#557—216no—
201#556—28no—
202#533—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#125C2314yes—
219C2×#125C2318yes—
220C2×#125C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C22×C42C2312yes—
256#401C2318yes—
257#401C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#399C2318yes—
270#399C2318yes—
271#399C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#396C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#395C2318yes—
294#395C2318yes—
295#391C2312yes—
296#391C2314yes—
297#391C2312yes—
298#391C2314yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2318yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#390C2312yes—
316#390C2312yes—
317#390C2314yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2312yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2314yes—
329#389C2318yes—
330#389C2318yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2312yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#385C2314yes—
416#385C2314yes—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2312yes—
420#384C2312yes—
421#384C2311yescharacteristic
422#384C2314yes—
423#384C2312yes—
424#384C2314yes—
425#384C2314yes—
426#384C2314yes—
427#384C2318yes—
428#384C2312yes—
429#384C2312yes—
430#383C2314yes—
431#383C2314yes—
432#383C2318yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2314yes—
437#382C2312yes—
438#382C2318yes—
439#382C2318yes—
440#382C2318yes—
441#382C2314yes—
442#382C2314yes—
443#382C2312yes—
444#381C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2318yes—
516#376C2318yes—
517#376C2314yes—
518C43C2314yes—
519C43C2312yes—
520C43C2314yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×D4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C4⋊Q8—28no—
534C4⋊Q8—216no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—44no—
538C4⋊Q8—82no—
539C4⋊Q8#4118yes—
540C4⋊Q8#4118yes—
541#126—216no—
542#126—88no—
543#125—216no—
544#125—216no—
545#125—232no—
546#125—28no—
547#125—216no—
548#125—88no—
549#125—84no—
550#125—84no—
551#124—28no—
552#124—44no—
553C22⋊Q8—216no—
554C22⋊Q8—28no—
555C22⋊Q8—216no—
556C22⋊Q8—28no—
557C22⋊Q8—84no—
558C4×Q8—216no—
559C4×Q8—28no—
560C4×Q8—28no—
561C4×Q8—216no—
562C4×Q8—28no—
563C4×Q8—24no—
564C4×Q8—216no—
565C4×Q8—28no—
566C4×Q8—216no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—44no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—42no—
582#117—216no—
583#117—28no—
584#117—28no—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C42—28no—
661C2×C42C2418yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2411yescharacteristic
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2418yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2411yescharacteristic
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2418yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#95C2414yes—
699#95C2414yes—
700#95C2412yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2412yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2412yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748C24C2512yes—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—24no—
754C2×Q8—28no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—44no—
763C2×Q8—44no—
764C2×Q8C2×#4118yes—
765C2×Q8C2×#4118yes—
766C2×Q82−1+414yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2518yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2511yescharacteristic
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—28no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—216no—
810C4⋊C4—216no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—28no—
822C4⋊C4—216no—
823C4⋊C4—24no—
824C4⋊C4—216no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—22no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—28no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—42no—
848C4⋊C4—48no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4C2×#4118yes—
862C4⋊C4C2×#4118yes—
863C4⋊C4C2×#4118yes—
864C4⋊C4C2×#4118yes—
865C4⋊C42−1+414yes—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—24no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—42no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—216no—
883C42—28no—
884C42—24no—
885C42—28no—
886C42—216no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—28no—
891C42—28no—
892C42—28no—
893C42—24no—
894C42—22no—
895C42—24no—
896C42—22no—
897C42—24no—
898C42—28no—
899C42—24no—
900C42—28no—
901C42—24no—
902C42—22no—
903C42—24no—
904C42—24no—
905C42—44no—
906C42—48no—
907C42—48no—
908C42—42no—
909C42—42no—
910C42—44no—
911C42—44no—
912C42—41no—
913C42C2×#4114yes—
914C42C2×#4114yes—
915C422−1+414yes—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23C2611yescharacteristic
924Q8—216no—
925Q8—216no—
926Q8—28no—
927Q8—44no—
928Q8—48no—
929Q8—88no—
930D4—44no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—28no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—84no—
993C2×C4C22×#4118yes—
994C2×C4C22×#4118yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4C2×2−1+412yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4#58512yes—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22C23×#4111yescharacteristic
1017C22C23×#4111yescharacteristic
1018C22C22×2−1+411yescharacteristic
1019C22C22×2−1+411yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C2×#58511yescharacteristic
1022C22H(7,𝔽2)11yescharacteristic
1023C4—22no—
1024C4—22no—
1025C4—24no—
1026C4—28no—
1027C4—24no—
1028C4—22no—
1029C4—28no—
1030C4—42no—
1031C4—44no—
1032C4—44no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—48no—
1037C4—42no—
1038C4—41no—
1039C4—44no—
1040C4—42no—
1041C4—42no—
1042C4—44no—
1043C4—42no—
1044C4—42no—
1045C4#348214yes—
1046C4#351514yes—
1047C4#352314yes—
1048C2—82no—
1049C2C2×#348211yescharacteristic
1050C2C2×#351511yescharacteristic
1051C2C2×#352311yescharacteristic
1052C2#6294311yescharacteristic
1053C2#6299911yescharacteristic
1054C2#6300611yescharacteristic
1055C2#6303211yescharacteristic
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. #59828C2semidirect
3. #59547C2semidirect
4. #59508C2semidirect
6. #59067C2semidirect
7. #45339C2semidirect
8. #44741C2semidirect
10. #40075C2semidirect
11. #39157C2semidirect
12. #38976C2semidirect
13. #36563C2semidirect
14. #36563C2semidirect
15. #36447C2semidirect
18. #36287C2semidirect
20. #35899C2semidirect
21. #34951C2semidirect
23. #34337C2semidirect
24. #34231C2semidirect
25. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596532
#595472
#595082
#594342
#590672
#453392
#447412
#401912
#400752
#391572
#389762
#365632
#364472
#363122
#362872
#361342
#358992
#349512
#349452
#343372
#342312
C4×#5572
C4×#5562