Finite Group Databasebeta

← #7688615

Subgroups — #7688615

Order 512.

5177 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic
2#59642C212yesmaximal, complemented
3#59461C214yesmaximal, complemented
4#59457C212yesmaximal
5#59413C212yesmaximal, complemented
6#59096C214yesmaximal, complemented
7#45434C214yesmaximal, complemented
8#43558C218yesmaximal, complemented
9#39976C214yesmaximal, complemented
10#39753C212yesmaximal, complemented
11#39656C214yesmaximal, complemented
12#39616C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36593C211yesmaximal, characteristic, complemented
15#36563C212yesmaximal, complemented
16#36562C212yesmaximal, complemented
17Q8×#127C211yesmaximal, characteristic
18#36276C212yesmaximal, complemented
19#36134C212yesmaximal, complemented
20#35934C214yesmaximal, complemented
21#34950C211yesmaximal, characteristic, complemented
22#34929C212yesmaximal, complemented
23#34334C212yesmaximal, complemented
24#34331C212yesmaximal
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#559C211yesmaximal, characteristic
27C2×#559C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#557C2212yes—
30C2×#554C2212yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#533C2214yes—
35#2868C2212yes—
36#2868C2212yes—
37#2868C2211yescharacteristic
38#2862C2212yes—
39#2859C2214yes—
40#2857C2214yes—
41#2807C2218yes—
42#2791C2218yes—
43#2780C2218yes—
44#2768C2218yes—
45#2768C2218yes—
46#2732C2214yes—
47#2720C2218yes—
48#2720C2218yes—
49#2713C2218yes—
50#2704C2218yes—
51#2704C2218yes—
52#2667C2218yes—
53#2660C2214yes—
54#2589C2218yes—
55#2586C2214yes—
56#2582C2211yescharacteristic
57#2582C2212yes—
58#2582C2214yes—
59#2580C2214yes—
60#2571C2212yes—
61#2570C2214yes—
62#2570C2214yes—
63#2568C2212yes—
64#2567C2214yes—
65#2567C2211yescharacteristic
66#2567C2211yescharacteristic
67#2566C2214yes—
68#2566C2214yes—
69#2565C2214yes—
70#2556C2218yes—
71#2556C2218yes—
72#2556C2218yes—
73#2556C2218yes—
74#2552C2214yes—
75#2552C2214yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2214yes—
80#2551C2211yescharacteristic
81#2550C2214yes—
82#2550C2214yes—
83#2550C2214yes—
84#2549C2218yes—
85#2549C2218yes—
86#2549C2218yes—
87#2546C2212yes—
88#2546C2214yes—
89#2542C2212yes—
90#2542C2212yes—
91#2542C2214yes—
92#2542C2214yes—
93#2542C2214yes—
94#2542C2212yes—
95#2542C2212yes—
96#2538C2212yes—
97#2538C2214yes—
98#2538C2214yes—
99#2522C2218yes—
100#2511C2214yes—
101#2507C2218yes—
102#2507C2212yes—
103#2507C2212yes—
104#2506C2214yes—
105#2502C2214yes—
106#2492C2214yes—
107#2465C2218yes—
108#2454C2214yes—
109#2454C2214yes—
110#2452C2214yes—
111#2451C2214yes—
112#2451C2218yes—
113#2451C2212yes—
114#2451C2212yes—
115#2450C2218yes—
116#2446C2214yes—
117#2441C2218yes—
118#2438C2218yes—
119#2434C2214yes—
120#2434C2214yes—
121#2429C2214yes—
122#2429C2214yes—
123#2429C2214yes—
124#2429C2214yes—
125#2423C2214yes—
126#2423C2218yes—
127#2417C2214yes—
128#2399C2214yes—
129#2396C2218yes—
130#2374C2214yes—
131#2370C2214yes—
132#2370C2212yes—
133#2369C2214yes—
134#2368C2218yes—
135#2367C2214yes—
136#2367C2214yes—
137#2367C2212yes—
138#2367C2212yes—
139#2366C2212yes—
140#2366C2211yescharacteristic
141#2365C2212yes—
142#2365C2211yescharacteristic
143#2365C2212yes—
144#2360C2214yes—
145#2360C2214yes—
146#2359C2218yes—
147#2357C2212yes—
148#2357C2212yes—
149#2355C2212yes—
150#2355C2211yescharacteristic
151#2355C2211yescharacteristic
152#2355C2212yes—
153#2355C2211yescharacteristic
154#2355C2212yes—
155#2354C2214yes—
156#2351C2212yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2214yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2211yescharacteristic
161#2349C2214yes—
162#2349C2214yes—
163#2349C2214yes—
164D4×C4⋊C4C2212yes—
165Q8×C22⋊C4C2214yes—
166#2335C2218yes—
167#2331C2214yes—
168#2329C2218yes—
169#2326C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#127C2212yes—
179C4×#127C2211yescharacteristic
180C4×#125C2214yes—
181C4×#125C2212yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2214yes—
186C4×#123C2214yes—
187#2295C2212yes—
188#2295C2212yes—
189C2×#391C2214yes—
190#2293C2214yes—
191#2275C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2212yes—
199C23×Q8C2314yes—
200#559Q8116yescomplemented
201#557—28no—
202#557—48no—
203#554—48no—
204D4×Q8—216no—
205D4×Q8—48no—
206D4×Q8—48no—
207#533—416no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×#127C2311yescharacteristic
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2314yes—
226C2×#125C2318yes—
227C2×#125C2318yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2318yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×#117C2318yes—
274C22×C4⋊C4C2314yes—
275C22×C42C2314yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#395C2314yes—
307#395C2314yes—
308#395C2318yes—
309#395C2318yes—
310#395C2314yes—
311#395C2314yes—
312#395C2318yes—
313#395C2318yes—
314#393C2318yes—
315#391C2314yes—
316#391C2318yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2318yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2312yes—
387#389C2312yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#386C2318yes—
420#386C2314yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#384C2312yes—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2314yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2314yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2312yes—
450#382C2312yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2312yes—
455#382C2314yes—
456#382C2312yes—
457#381C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2318yes—
462#380C2318yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520C2×#95C2318yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C43C2312yes—
527C22×Q8—216no—
528C22×Q8—48no—
529C22×Q8—48no—
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2414yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C23×C4C2414yes—
542C23×C4C2418yes—
543C23×C4C2414yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—216no—
550C4⋊Q8—28no—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557C4⋊Q8—44no—
558C4⋊Q8—48no—
559#127C2×Q818yes—
560#125—216no—
561#125—28no—
562#125—48no—
563#125—48no—
564#125—416no—
565#125—416no—
566#124C2×Q8116yescomplemented
567#124C2×Q8116yescomplemented
568#123C2×Q8132yescomplemented
569C22⋊Q8—216no—
570C22⋊Q8—232no—
571C22⋊Q8—216no—
572C22⋊Q8—416no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—28no—
587C4×Q8—24no—
588C4×Q8—48no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—42no—
592C4×Q8—48no—
593C4×Q8—416no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8C2×Q818yescomplemented
597C4×Q8C2×Q818yescomplemented
598C4×Q8#4118yes—
599C4×D4—28no—
600C4×D4—216no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—48no—
604C4×D4—44no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—44no—
609C4×D4C2×Q8116yescomplemented
610C4×D4C2×Q8116yescomplemented
611#117—416no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C42—48no—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2412yes—
755#95C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2412yes—
759#95C2412yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770C24C2514yes—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—216no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—28no—
786C2×Q8—22no—
787C2×Q8—44no—
788C2×Q8—42no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—42no—
792C2×Q8—832no—
793C2×Q8C22×Q814yes—
794C2×Q8C22×Q814yes—
795C2×Q8C2×#4114yes—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4C22×Q818yes—
803C2×D4C22×Q818yes—
804C2×D4C22×Q818yes—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—216no—
809C22×C4—28no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—44no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4C22×Q8116yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2511yescharacteristic
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2518yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2511yescharacteristic
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—216no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—216no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—42no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—42no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4C22×Q814yes—
902C4⋊C4C22×Q814yes—
903C4⋊C4C22×Q818yes—
904C4⋊C4C22×Q818yes—
905C4⋊C4C2×#4114yes—
906C4⋊C4C2×#4118yes—
907C4⋊C4H(5,𝔽2)14yes—
908C4⋊C42−1+414yes—
909C22⋊C4—216no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4C22×Q8116yes—
922C22⋊C4C22×Q8116yes—
923C22⋊C4C22×Q8116yes—
924C42—28no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—28no—
929C42—24no—
930C42—22no—
931C42—24no—
932C42—28no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—22no—
937C42—24no—
938C42—24no—
939C42—28no—
940C42—24no—
941C42—22no—
942C42—44no—
943C42—44no—
944C42—44no—
945C42—41no—
946C42—42no—
947C42—42no—
948C42—42no—
949C42—48no—
950C42—44no—
951C42—42no—
952C42—48no—
953C42C22×Q818yes—
954C42C22×Q818yes—
955C42C22×Q814yes—
956C42C2×#4118yes—
957C42C2×#4114yes—
958C42H(5,𝔽2)14yes—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23C23×Q818yes—
966C23C2611yescharacteristic
967Q8—28no—
968Q8—28no—
969Q8—28no—
970Q8—416no—
971Q8—48no—
972Q8—416no—
973Q8—84no—
974Q8—816no—
975D4—216no—
976D4—216no—
977D4—48no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—416no—
1034C2×C4—416no—
1035C2×C4—88no—
1036C2×C4—816no—
1037C2×C4—168no—
1038C2×C4C23×Q814yes—
1039C2×C4C23×Q814yes—
1040C2×C4C23×Q814yes—
1041C2×C4C23×Q814yes—
1042C2×C4C23×Q812yes—
1043C2×C4C23×Q812yes—
1044C2×C4C23×Q812yes—
1045C2×C4C22×#4114yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4114yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C2×H(5,𝔽2)14yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×H(5,𝔽2)12yes—
1055C2×C4C2×2−1+414yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4#58512yes—
1058C22—28no—
1059C22—28no—
1060C22—28no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22C24×Q811yescharacteristic
1066C22C23×#4111yescharacteristic
1067C22C22×H(5,𝔽2)11yescharacteristic
1068C22C22×H(5,𝔽2)11yescharacteristic
1069C22C22×2−1+411yescharacteristic
1070C22C2×#58511yescharacteristic
1071C222−1+611yescharacteristic
1072C4—24no—
1073C4—24no—
1074C4—22no—
1075C4—22no—
1076C4—24no—
1077C4—24no—
1078C4—24no—
1079C4—24no—
1080C4—24no—
1081C4—22no—
1082C4—24no—
1083C4—42no—
1084C4—41no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4—48no—
1089C4—44no—
1090C4—42no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4Q8×#4114yes—
1095C4#350314yes—
1096C4#350814yes—
1097C2—48no—
1098C2C2×Q8×#4111yescharacteristic
1099C2C2×#350311yescharacteristic
1100C2C2×#350811yescharacteristic
1101C2#6293111yescharacteristic
1102C2Q8×H(5,𝔽2)11yescharacteristic
1103C2#6300111yescharacteristic
1104C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59642C2semidirect
3. #59461C2semidirect
5. #59413C2semidirect
6. #59096C2semidirect
7. #45434C2semidirect
8. #43558C2semidirect
9. #39976C2semidirect
10. #39753C2semidirect
11. #39656C2semidirect
12. #39616C2semidirect
13. #36598C2semidirect
14. #36593C2semidirect
15. #36563C2semidirect
16. #36562C2semidirect
18. #36276C2semidirect
19. #36134C2semidirect
20. #35934C2semidirect
21. #34950C2semidirect
22. #34929C2semidirect
23. #34334C2semidirect
25. C4×#557C2semidirect
200. #559Q8semidirect
566. #124C2×Q8semidirect
567. #124C2×Q8semidirect
568. #123C2×Q8semidirect
596. C4×Q8C2×Q8semidirect
597. C4×Q8C2×Q8semidirect
609. C4×D4C2×Q8semidirect
610. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598232
#596422
#594612
#594572
#594132
#590962
#454342
#435582
#399762
#397532
#396562
#396162
#365982
#365932
#365632
#365622
Q8×#1272
#362762
#361342
#359342
#349502
#349292
#343342
#343312
C4×#5572
C4×#5592