Finite Group Databasebeta

← #7654570

Subgroups — #7654570

Order 512.

6712 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42878C214yesmaximal, complemented
4#42312C218yesmaximal, complemented
5#39744C212yesmaximal, complemented
6#39740C214yesmaximal, complemented
7#39595C214yesmaximal, complemented
8#39167C212yesmaximal, complemented
9#39162C214yesmaximal, complemented
10#38047C218yesmaximal, complemented
11#37617C211yesmaximal, characteristic, complemented
12#37537C212yesmaximal, complemented
13#36594C212yesmaximal, complemented
14#36508C212yesmaximal, complemented
15#36427C214yesmaximal, complemented
16#36030C214yesmaximal, complemented
17#35281C211yesmaximal, characteristic, complemented
18#35246C212yesmaximal, complemented
19#35240C211yesmaximal, characteristic, complemented
20#35131C212yesmaximal
21#34965C211yesmaximal, characteristic
22#34953C212yesmaximal, complemented
23#34128C211yesmaximal, characteristic, complemented
24#3523—216no—
25C2×#557C2211yescharacteristic, complemented
26C2×#557C2211yescharacteristic, complemented
27C2×#557C2212yescomplemented
28C2×#556—216no—
29C2×#556C2214yes—
30C2×#556C2212yes—
31C2×#556C2214yes—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#556C2212yes—
35C2×#556C2212yescomplemented
36C2×#556C2211yescharacteristic, complemented
37C2×#552C2212yes—
38C2×#552C2214yes—
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2211yescharacteristic, complemented
41C2×#541C2214yescomplemented
42C2×#541C2212yescomplemented
43C2×#533C2212yes—
44C2×#533C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C2×#529C2212yes—
47C2×#529C2211yescharacteristic
48C22×#126C2214yes—
49C22×#124C2212yes—
50C22×C22⋊Q8C2212yes—
51C2×#519C2212yescomplemented
52C22×C4×Q8C2212yes—
53C22×C4×Q8C2211yescharacteristic
54C22×C4×D4C2211yescharacteristic
55C22×#117C2212yes—
56#2868C2212yescomplemented
57#2862C2212yescomplemented
58#2861C2214yes—
59#2858C2214yes—
60#2853C2218yes—
61#2848C2214yes—
62#2821C2214yescomplemented
63#2820C2218yes—
64#2732C22116yescomplemented
65#2729C22116yescomplemented
66#2727C22116yescomplemented
67#2725C22116yescomplemented
68#2723C22116yescomplemented
69#2721C22116yescomplemented
70#2662C2218yes—
71#2660C2214yescomplemented
72#2658C2214yes—
73#2658C2212yescomplemented
74#2642C2212yescomplemented
75#2640C2214yes—
76#2637C2218yescomplemented
77#2633C2214yes—
78#2632C2218yes—
79#2628C2214yescomplemented
80#2626C2218yes—
81#2623C2214yes—
82#2610C2218yes—
83#2603C2214yes—
84#2599C2218yescomplemented
85#2584C2218yescomplemented
86#2583C2218yes—
87#2579C2218yes—
88#2567C2214yescomplemented
89#2567C2214yescomplemented
90#2566C2212yes—
91#2565C2214yescomplemented
92#2547C2212yes—
93#2547C2212yescomplemented
94#2546C2214yescomplemented
95#2546C2214yescomplemented
96#2546C2212yescomplemented
97#2545C2214yes—
98#2545C2214yes—
99#2545C2214yes—
100#2545C2214yescomplemented
101#2544C2214yes—
102#2544C2212yes—
103#2542C2212yes—
104#2538C2218yescomplemented
105#2536C2214yes—
106#2519C22116yescomplemented
107#2512C22116yescomplemented
108#2504C2211yescharacteristic
109#2502C2214yes—
110#2502C2211yescharacteristic
111#2502C2212yes—
112#2487C2214yes—
113#2482C2218yes—
114#2482C2214yes—
115#2479C22116yescomplemented
116#2479C22116yescomplemented
117#2475C22116yescomplemented
118#2469C22116yescomplemented
119#2441C2218yescomplemented
120#2436C2212yes—
121#2435C2212yes—
122#2435C2211yescharacteristic
123#2434C2212yes—
124#2434C2212yes—
125#2434C2212yes—
126#2433C2211yescharacteristic
127#2429C2218yescomplemented
128#2423C2218yescomplemented
129#2415C2218yescomplemented
130#2411C2218yes—
131#2411C2214yes—
132#2409C2218yescomplemented
133#2399C2218yescomplemented
134#2392C2214yes—
135#2362C2218yescomplemented
136#2356C2214yescomplemented
137#2356C2212yescomplemented
138#2354C2218yescomplemented
139#2351C2212yescomplemented
140#2344C2212yes—
141#2344C2214yes—
142Q8×C22⋊C4C2212yes—
143#2327C2214yescomplemented
144#2326C2214yes—
145#2326C2214yescomplemented
146#2321C2218yes—
147#2317C2214yes—
148C4×C4⋊Q8C2214yescomplemented
149C4×C4⋊Q8C2214yescomplemented
150C4×#127C2212yes—
151C4×#124C2212yes—
152C4×#120C2214yes—
153#2296C2218yes—
154#2295C2214yescomplemented
155#2295C2212yescomplemented
156#2283C2212yes—
157#2283C2211yescharacteristic
158C42×Q8C2212yescomplemented
159C4×#117C2212yes—
160C4×#117C2211yescharacteristic
161C23×Q8C2312yes—
162C23×Q8C2312yes—
163C23×Q8C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C24×C4C2312yes—
166#557—28no—
167#557—28no—
168#557—216no—
169#556—216no—
170#556—232no—
171#556—216no—
172#556—216no—
173#556—232no—
174#556—216no—
175#556—216no—
176#556—28no—
177#552—216no—
178#552—232no—
179D4×Q8—216no—
180D4×Q8—28no—
181#541—232no—
182#541—216no—
183#533—28no—
184#533—216no—
185C2×C4⋊Q8—28no—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×#127C2312yes—
200#529—28no—
201#529—216no—
202C2×#126—232no—
203C2×#126C2312yes—
204C2×#126C2314yes—
205C2×#126C2318yes—
206C2×#126C2318yes—
207C2×#126C2318yes—
208C2×#126C2318yes—
209C2×#126C2314yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#125C2314yes—
213C2×#125C2312yes—
214C2×#125C2311yescharacteristic
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124—216no—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2311yescharacteristic
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2312yes—
231C2×#123C2314yes—
232C2×#123C2312yes—
233C2×C22⋊Q8—216no—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2318yes—
246C2×#121C2311yescharacteristic
247C2×#120C2314yes—
248#519—216no—
249C2×C4×Q8—216no—
250C2×C4×Q8D4116yescomplemented
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2312yes—
272C2×C4×D4—28no—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2318yes—
282C2×#117—216no—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2318yes—
292C2×#117C2314yes—
293C2×#117C2314yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2314yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C42C2314yes—
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306#400C2318yes—
307#400C2318yes—
308#399C23116yes—
309#399C2318yes—
310#399C2318yes—
311#399C23116yes—
312#399C2318yes—
313#398C23116yes—
314#398C2318yes—
315#398C23116yes—
316#398C2314yes—
317#398C2318yes—
318#398C23116yes—
319#397C23116yes—
320#397C2318yes—
321#397C2314yes—
322#397C2318yes—
323#396C23116yes—
324#396C23116yes—
325#396C2318yes—
326#396C23116yes—
327#396C23116yes—
328#395C2318yes—
329#395C2318yes—
330#395C23116yes—
331#395C2318yes—
332#394C2314yes—
333#394C2318yes—
334#394C2318yes—
335#394C23116yes—
336#393C2318yes—
337#393C23116yes—
338#392C2314yes—
339#391C2312yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2314yes—
347#391C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2312yes—
352#390C23116yes—
353#390C2314yes—
354#390C23116yes—
355#389C23116yes—
356#389C23116yes—
357#389C23116yes—
358#389C23116yes—
359#389C23116yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#388C23116yes—
364#388C23116yes—
365#388C23116yes—
366#388C23116yes—
367#388C23116yes—
368#388C2318yes—
369#388C23116yes—
370#388C23116yes—
371#388C23116yes—
372#387C23116yes—
373#387C23116yes—
374#387C23116yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#386C2318yes—
379#386C23116yes—
380#386C2314yes—
381#386C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C23116yes—
386#385C2318yes—
387#385C23116yes—
388#385C2314yes—
389#385C2318yes—
390#384C2312yes—
391#384C2314yes—
392#384C2318yes—
393#384C2318yes—
394#383C2312yes—
395#383C2314yes—
396#382C2314yes—
397#382C2312yes—
398#382C2318yes—
399#382C2312yes—
400#381C2314yes—
401#381C2312yes—
402#380C2314yes—
403#380C2312yes—
404#380C2318yes—
405#380C2318yes—
406#379C2318yes—
407#379C2314yes—
408C4×C4⋊C4C23116yes—
409C4×C4⋊C4C23116yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2311yescharacteristic
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2312yes—
424#376C2312yes—
425#376C2314yes—
426#376C2312yes—
427#376C2314yes—
428C43C2312yes—
429C43C2314yes—
430C25C2412yes—
431C22×Q8—28no—
432C22×Q8—28no—
433C22×Q8—44no—
434C22×Q8—48no—
435C22×Q8—48no—
436C22×Q8C2×D418yes—
437C22×Q8C2411yescharacteristic
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C22×Q8C2414yes—
441C22×Q8C2411yescharacteristic
442C22×Q8C2411yescharacteristic
443C22×Q8C2414yes—
444C22×Q8C2414yes—
445C22×Q8C2412yes—
446C22×D4—24no—
447C22×D4—44no—
448C22×D4C2412yes—
449C22×D4C2411yescharacteristic
450C22×D4C2412yes—
451C22×D4C2412yes—
452C22×D4C2418yes—
453C23×C4—28no—
454C23×C4—48no—
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2414yes—
465C23×C4C2412yes—
466C4⋊Q8—28no—
467C4⋊Q8—216no—
468C4⋊Q8—28no—
469C4⋊Q8—28no—
470C4⋊Q8—28no—
471C4⋊Q8—28no—
472C4⋊Q8—24no—
473C4⋊Q8—28no—
474C4⋊Q8—24no—
475C4⋊Q8—28no—
476C4⋊Q8—48no—
477C4⋊Q8—48no—
478C4⋊Q8—48no—
479#127—44no—
480#126—232no—
481#126—232no—
482#126—232no—
483#126—232no—
484#126—216no—
485#126—216no—
486#126—216no—
487#126—28no—
488#126—216no—
489#125—216no—
490#125—216no—
491#125—216no—
492#125—28no—
493#125—216no—
494#125—24no—
495#125—28no—
496#125—28no—
497#125—216no—
498#124—216no—
499#124—216no—
500#124—216no—
501#124—216no—
502#124—24no—
503#124—28no—
504#124—48no—
505#124—48no—
506#124—44no—
507#123—216no—
508#123—28no—
509C22⋊Q8—216no—
510C22⋊Q8—216no—
511C22⋊Q8—232no—
512C22⋊Q8—28no—
513C22⋊Q8—216no—
514C22⋊Q8—28no—
515C22⋊Q8—24no—
516C22⋊Q8—28no—
517C22⋊Q8—216no—
518C22⋊Q8—28no—
519C22⋊Q8—216no—
520C22⋊Q8—416no—
521#121—24no—
522#120—216no—
523C4×Q8—28no—
524C4×Q8—28no—
525C4×Q8—216no—
526C4×Q8—216no—
527C4×Q8—216no—
528C4×Q8—216no—
529C4×Q8—216no—
530C4×Q8—28no—
531C4×Q8—216no—
532C4×Q8—24no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—48no—
538C4×Q8C2×D418yes—
539C4×Q8C2×D418yes—
540C4×Q8C2×D4116yes—
541C4×Q8C2×D418yes—
542C4×Q8C2×D418yes—
543C4×Q8C2×D4116yes—
544C4×D4—28no—
545C4×D4—216no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—24no—
551C4×D4—28no—
552C4×D4—416no—
553#117—216no—
554#117—28no—
555#117—216no—
556#117—216no—
557#117—232no—
558#117—28no—
559#117—216no—
560#117—28no—
561#117—216no—
562#117—28no—
563#117—216no—
564C2×C4⋊C4—28no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—216no—
567C2×C4⋊C4—28no—
568C2×C4⋊C4C2×D418yes—
569C2×C4⋊C4C2×D4116yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C24116yes—
604C2×C4⋊C4C24116yes—
605C2×C4⋊C4C24116yes—
606C2×C4⋊C4C24116yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C22⋊C4—216no—
615C2×C22⋊C4—28no—
616C2×C22⋊C4—216no—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C24116yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C24116yes—
640C2×C22⋊C4C24116yes—
641C2×C22⋊C4C2412yes—
642C2×C42—216no—
643C2×C42C2×D418yes—
644C2×C42C2×D4116yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2418yes—
649C2×C42C2418yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2418yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2418yes—
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667#95C2412yes—
668#95C2414yes—
669#95C2412yes—
670#95C2414yes—
671#95C2418yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2414yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C24116yes—
681#95C24116yes—
682#95C24116yes—
683#95C24116yes—
684#95C24116yes—
685C24—24no—
686C24—28no—
687C24—44no—
688C24—44no—
689C24C2514yes—
690C24C2512yes—
691C24C2511yescharacteristic
692C2×Q8—22no—
693C2×Q8—24no—
694C2×Q8—28no—
695C2×Q8—24no—
696C2×Q8—28no—
697C2×Q8—28no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—28no—
701C2×Q8—28no—
702C2×Q8—24no—
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—44no—
706C2×Q8—48no—
707C2×Q8—48no—
708C2×Q8—416no—
709C2×Q8—432no—
710C2×Q8—432no—
711C2×Q8C22×D414yes—
712C2×Q8C22×D414yes—
713C2×Q8C22×D418yes—
714C2×D4—24no—
715C2×D4—28no—
716C2×D4—22no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—216no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—44no—
724C2×D4—416no—
725C2×D4—48no—
726C2×D4—48no—
727C22×C4—24no—
728C22×C4—28no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—216no—
739C22×C4—48no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—48no—
743C22×C4—48no—
744C22×C4—432no—
745C22×C4C22×D418yes—
746C22×C4C22×D414yes—
747C22×C4C22×D414yes—
748C22×C4C22×D414yes—
749C22×C4C22×D418yes—
750C22×C4C2514yes—
751C22×C4C2518yes—
752C22×C4C2512yes—
753C22×C4C2514yes—
754C22×C4C2518yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2514yes—
759C22×C4C2511yescharacteristic
760C22×C4C2512yes—
761C22×C4C2511yescharacteristic
762C22×C4C2512yes—
763C22×C4C2511yescharacteristic
764C22×C4C2512yes—
765C22×C4C2511yescharacteristic
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—216no—
775C4⋊C4—216no—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—24no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—28no—
787C4⋊C4—24no—
788C4⋊C4—22no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—22no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—416no—
804C4⋊C4—416no—
805C4⋊C4—416no—
806C4⋊C4—416no—
807C4⋊C4C22×D414yes—
808C4⋊C4C22×D414yes—
809C4⋊C4C22×D418yes—
810C4⋊C4C22×D418yes—
811C4⋊C4C22×D418yes—
812C4⋊C4C22×D418yes—
813C4⋊C4C22×D418yes—
814C22⋊C4—28no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—28no—
818C22⋊C4—216no—
819C22⋊C4—216no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—216no—
824C22⋊C4—24no—
825C22⋊C4—28no—
826C22⋊C4—24no—
827C22⋊C4—28no—
828C22⋊C4—24no—
829C22⋊C4—28no—
830C22⋊C4—24no—
831C22⋊C4—216no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—416no—
835C22⋊C4—416no—
836C22⋊C4—416no—
837C22⋊C4—48no—
838C22⋊C42−1+418yes—
839C42—216no—
840C42—216no—
841C42—28no—
842C42—28no—
843C42—28no—
844C42—28no—
845C42—24no—
846C42—216no—
847C42—28no—
848C42—28no—
849C42—28no—
850C42—24no—
851C42—24no—
852C42—48no—
853C42C22×D414yes—
854C42C22×D418yes—
855C42C22×D414yes—
856C42C22×D414yes—
857C42C22×D414yes—
858C42C22×D418yes—
859C42C22×D418yes—
860C42C22×D418yes—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—24no—
865C23—28no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—28no—
870C23—24no—
871C23—24no—
872C23—48no—
873C23—48no—
874C23—48no—
875C23—816no—
876C23C23×D412yes—
877C23C2×2−1+414yes—
878C23C2611yescharacteristic
879Q8—28no—
880Q8—28no—
881Q8—48no—
882Q8—416no—
883Q8—416no—
884Q8—48no—
885Q8—44no—
886Q8—48no—
887Q8—416no—
888D4—48no—
889D4—48no—
890D4—44no—
891D4—48no—
892D4—816no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—216no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—48no—
929C2×C4—416no—
930C2×C4—416no—
931C2×C4—48no—
932C2×C4—416no—
933C2×C4—416no—
934C2×C4—48no—
935C2×C4C23×D414yes—
936C2×C4C23×D414yes—
937C2×C4C23×D412yes—
938C2×C4C23×D414yes—
939C2×C4C23×D412yes—
940C2×C4C23×D412yes—
941C2×C4C23×D414yes—
942C2×C4C23×D412yes—
943C2×C4C23×D412yes—
944C2×C4C23×D412yes—
945C2×C4C2×2−1+418yes—
946C2×C4#58514yes—
947C2×C4#58514yes—
948C22—28no—
949C22—22no—
950C22—22no—
951C22—48no—
952C22—48no—
953C22—48no—
954C22—44no—
955C22—42no—
956C22—42no—
957C22—44no—
958C22—42no—
959C22—44no—
960C22—816no—
961C22#349914yes—
962C22C24×D411yescharacteristic
963C22C22×2−1+412yes—
964C22C2×#58512yes—
965C22C2×#58512yes—
966C4—28no—
967C4—22no—
968C4—24no—
969C4—22no—
970C4—24no—
971C4—22no—
972C4—22no—
973C4—24no—
974C4—24no—
975C4—44no—
976C4—48no—
977C4—48no—
978C4—42no—
979C4—44no—
980C4—42no—
981C4—44no—
982C4—42no—
983C4—44no—
984C4#344914yes—
985C4#348714yes—
986C2—24no—
987C2—82no—
988C2—84no—
989C2C2×#344911yescharacteristic
990C2C2×#348711yescharacteristic
991C2C2×#349911yescharacteristic
992C2#6302514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2433C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. C22×#556C2semidirect
3. #42878C2semidirect
4. #42312C2semidirect
5. #39744C2semidirect
6. #39740C2semidirect
7. #39595C2semidirect
8. #39167C2semidirect
9. #39162C2semidirect
10. #38047C2semidirect
11. #37617C2semidirect
12. #37537C2semidirect
13. #36594C2semidirect
14. #36508C2semidirect
15. #36427C2semidirect
16. #36030C2semidirect
17. #35281C2semidirect
18. #35246C2semidirect
19. #35240C2semidirect
22. #34953C2semidirect
23. #34128C2semidirect
25. C2×#557C22semidirect
26. C2×#557C22semidirect
27. C2×#557C22semidirect
35. C2×#556C22semidirect
36. C2×#556C22semidirect
40. C2×D4×Q8C22semidirect
41. C2×#541C22semidirect
42. C2×#541C22semidirect
51. C2×#519C22semidirect
56. #2868C22semidirect
57. #2862C22semidirect
62. #2821C22semidirect
64. #2732C22semidirect
65. #2729C22semidirect
66. #2727C22semidirect
67. #2725C22semidirect
68. #2723C22semidirect
69. #2721C22semidirect
71. #2660C22semidirect
73. #2658C22semidirect
74. #2642C22semidirect
76. #2637C22semidirect
79. #2628C22semidirect
84. #2599C22semidirect
85. #2584C22semidirect
88. #2567C22semidirect
89. #2567C22semidirect
91. #2565C22semidirect
93. #2547C22semidirect
94. #2546C22semidirect
95. #2546C22semidirect
96. #2546C22semidirect
100. #2545C22semidirect
104. #2538C22semidirect
106. #2519C22semidirect
107. #2512C22semidirect
115. #2479C22semidirect
116. #2479C22semidirect
117. #2475C22semidirect
118. #2469C22semidirect
119. #2441C22semidirect
127. #2429C22semidirect
128. #2423C22semidirect
129. #2415C22semidirect
132. #2409C22semidirect
133. #2399C22semidirect
135. #2362C22semidirect
136. #2356C22semidirect
137. #2356C22semidirect
138. #2354C22semidirect
139. #2351C22semidirect
143. #2327C22semidirect
145. #2326C22semidirect
148. C4×C4⋊Q8C22semidirect
149. C4×C4⋊Q8C22semidirect
154. #2295C22semidirect
155. #2295C22semidirect
158. C42×Q8C22semidirect
250. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C22×#5562
#428782
#423122
#397442
#397402
#395952
#391672
#391622
#380472
#376172
#375372
#365942
#365082
#364272
#360302
#352812
#352462
#352402
#351312
#349652
#349532
#341282