Finite Group Databasebeta

← #7646795

Subgroups — #7646795

Order 512.

6656 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42301C218yesmaximal, complemented
4#41943C218yesmaximal, complemented
5#38379C218yesmaximal, complemented
6#38375C218yesmaximal, complemented
7#37606C212yesmaximal, complemented
8#37538C212yesmaximal, complemented
9#37258C212yesmaximal, complemented
10#37187C212yesmaximal, complemented
11#36962C211yesmaximal, characteristic, complemented
12#36961C211yesmaximal, characteristic, complemented
13#36708C211yesmaximal, characteristic, complemented
14#36707C211yesmaximal, characteristic, complemented
15#35469C212yesmaximal, complemented
16#35397C212yesmaximal, complemented
17#35302C212yesmaximal, complemented
18#35246C212yesmaximal, complemented
19#35143C212yesmaximal, complemented
20#35092C212yesmaximal, complemented
21#34987C212yesmaximal, complemented
22#34875C212yesmaximal, complemented
23#34187C211yesmaximal, characteristic, complemented
24C2×#556—216no—
25C2×#556C2218yes—
26C2×#556C2218yes—
27#3461—216no—
28C2×#544C2211yescharacteristic
29C2×#542C2214yescomplemented
30C2×#541C2214yescomplemented
31C2×#539C2212yes—
32C2×#539C2212yes—
33C2×#537C2211yescharacteristic
34C2×#536C2212yes—
35C2×#533C2214yescomplemented
36C22×C4⋊Q8C2211yescharacteristic
37C2×#529C2212yes—
38C2×#529C2212yes—
39C2×#529C2214yescomplemented
40C22×#126C2211yescharacteristic
41C22×#126C2211yescharacteristic
42C22×#126C2211yescharacteristic
43C22×#126C2211yescharacteristic
44C22×#124C2211yescharacteristic
45C22×#124C2211yescharacteristic
46C22×C22⋊Q8C2211yescharacteristic
47C22×C22⋊Q8C2211yescharacteristic
48C2×C4×#41C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×Q8C2211yescharacteristic
51C22×C4×Q8C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic
53C22×#117C2211yescharacteristic
54C22×#117C2211yescharacteristic
55#2855C2212yes—
56#2854C2212yes—
57#2853C2214yes—
58#2853C2214yes—
59#2852C2218yescomplemented
60#2848C2212yes—
61#2847C2212yes—
62#2823C2218yescomplemented
63#2820C2214yes—
64#2819C2214yes—
65#2734C2218yescomplemented
66#2733C2218yes—
67#2731C2218yes—
68#2731C2218yescomplemented
69#2730C2218yes—
70#2730C2218yes—
71#2729C2218yescomplemented
72#2729C2218yescomplemented
73#2723C2218yescomplemented
74#2721C2218yescomplemented
75#2716C2218yescomplemented
76#2714C2218yescomplemented
77#2692C2218yescomplemented
78#2690C2218yescomplemented
79#2677C2218yescomplemented
80#2676C2218yescomplemented
81#2664C2214yescomplemented
82#2662C2218yes—
83#2662C2214yescomplemented
84#2637C2214yescomplemented
85#2637C2218yescomplemented
86#2637C2214yescomplemented
87#2636C2214yescomplemented
88#2636C2214yescomplemented
89#2632C2214yes—
90#2631C2214yes—
91#2629C2214yescomplemented
92#2627C2212yes—
93#2626C2212yes—
94#2620C2214yescomplemented
95#2618C2212yes—
96#2617C2212yes—
97#2614C2214yes—
98#2613C2214yes—
99#2610C2218yes—
100#2609C2218yescomplemented
101#2609C2218yescomplemented
102#2604C2214yescomplemented
103#2603C2214yescomplemented
104#2601C2218yescomplemented
105#2601C2218yescomplemented
106#2601C2218yescomplemented
107#2599C2214yescomplemented
108#2599C2218yescomplemented
109#2598C2214yescomplemented
110#2579C2214yes—
111#2579C2214yes—
112#2565C2214yescomplemented
113#2561C2212yes—
114#2561C2212yes—
115#2560C2218yescomplemented
116#2560C2218yescomplemented
117#2556C2218yescomplemented
118#2554C2218yescomplemented
119#2545C2214yescomplemented
120#2539C2212yes—
121#2539C2212yes—
122#2534C2214yes—
123#2534C2214yes—
124#2519C2218yescomplemented
125#2512C2218yescomplemented
126#2504C2212yes—
127#2502C2212yes—
128#2484C2212yes—
129#2484C2212yes—
130#2482C2212yes—
131#2482C2212yes—
132#2469C2218yescomplemented
133#2467C2218yes—
134#2465C2218yescomplemented
135#2463C2218yes—
136#2462C2218yescomplemented
137#2461C2218yescomplemented
138#2460C2218yes—
139#2458C2218yescomplemented
140#2456C2218yes—
141#2452C2218yescomplemented
142#2436C2212yes—
143#2434C2212yes—
144#2413C2214yes—
145#2413C2214yes—
146#2411C2214yes—
147#2411C2214yes—
148#2406C2212yes—
149#2406C2212yes—
150#2404C2212yes—
151#2404C2212yes—
152#2396C2214yescomplemented
153#2392C2214yescomplemented
154#2356C2218yescomplemented
155#2355C2218yescomplemented
156#2327C2214yescomplemented
157#2326C2214yescomplemented
158#2324C2214yescomplemented
159#2323C2214yescomplemented
160#2322C2214yes—
161#2321C2214yes—
162#2313C2212yes—
163#2313C2211yescharacteristic
164#2313C2211yescharacteristic
165#2310C2212yes—
166C4×#123C2214yes—
167C4×#120C2214yes—
168#2290C2218yescomplemented
169#2285C2212yes—
170#2283C2212yes—
171#2283C2212yes—
172#2274C2212yes—
173C22×#41C2312yes—
174C23×Q8C2311yescharacteristic
175C23×Q8C2311yescharacteristic
176C23×Q8C2311yescharacteristic
177C23×D4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180#556—264no—
181#556—264no—
182#544—28no—
183#542—232no—
184#541—232no—
185#539—216no—
186#539—216no—
187#537—28no—
188#536—216no—
189#533—232no—
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8C2318yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2314yes—
195#529—232no—
196#529—216no—
197#529—216no—
198C2×#126—28no—
199C2×#126—28no—
200C2×#126—28no—
201C2×#126—28no—
202C2×#126C2314yes—
203C2×#126C2318yes—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#126C2314yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#126C2314yes—
210C2×#126C2318yes—
211C2×#126C2314yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#124—28no—
218C2×#124—28no—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2314yes—
222C2×#124C2312yes—
223C2×#124C2318yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×C22⋊Q8—28no—
233C2×C22⋊Q8—28no—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#120C2314yes—
249C2×#120C2314yes—
250C4×#41—216no—
251C2×C4×Q8—28no—
252C2×C4×Q8—28no—
253C2×C4×Q8D4116yescomplemented
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2318yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×D4—28no—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2318yes—
271C2×C4×D4C2318yes—
272C2×#117—28no—
273C2×#117—28no—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2314yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C42C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#397C2314yes—
331#397C2318yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yes—
346#395C2318yes—
347#395C2318yes—
348#395C2314yes—
349#395C2314yes—
350#395C2318yes—
351#395C2314yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2314yes—
359#394C2314yes—
360#394C2318yes—
361#394C2314yes—
362#393C2314yes—
363#393C2318yes—
364#393C2314yes—
365#393C2318yes—
366#393C2314yes—
367#393C2314yes—
368#393C2318yes—
369#393C2314yes—
370#392C2318yes—
371#392C2314yes—
372#392C2314yes—
373#392C2314yes—
374#392C2314yes—
375#392C2318yes—
376#392C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2318yes—
381#391C2318yes—
382#391C2314yes—
383#390C2318yes—
384#390C2318yes—
385#390C2318yes—
386#390C2314yes—
387#390C2318yes—
388#390C2314yes—
389#390C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2318yes—
393#389C2314yes—
394#389C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2314yes—
446#385C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#384C2314yes—
452#384C2314yes—
453#383C2314yes—
454#383C2314yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#381C2314yes—
460#381C2314yes—
461#381C2314yes—
462#381C2312yes—
463#381C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#379C2314yes—
470#379C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2314yes—
483#376C2314yes—
484#376C2314yes—
485C25C2411yescharacteristic
486C25C2411yescharacteristic
487C2×#41—28no—
488C2×#41—48no—
489C22×Q8—24no—
490C22×Q8—24no—
491C22×Q8—44no—
492C22×Q8—44no—
493C22×Q8—44no—
494C22×Q8C2×D418yes—
495C22×Q8C2414yes—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×Q8C2414yes—
501C22×D4—24no—
502C22×D4—44no—
503C22×D4C2414yes—
504C22×D4C2412yes—
505C22×D4C2414yes—
506C22×D4C2412yes—
507C22×D4C2412yes—
508C22×D4C2418yes—
509C22×D4C2418yes—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—44no—
513C23×C4—44no—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2414yes—
518C23×C4C2414yes—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C4⋊Q8—232no—
533C4⋊Q8—216no—
534C4⋊Q8—216no—
535C4⋊Q8—48no—
536#126—232no—
537#126—232no—
538#126—216no—
539#126—216no—
540#126—216no—
541#126—216no—
542#126—216no—
543#126—216no—
544#126—216no—
545#126—216no—
546#125—216no—
547#125—216no—
548#125—216no—
549#125—28no—
550#125—28no—
551#124—232no—
552#124—216no—
553#124—216no—
554#124—216no—
555#124—28no—
556#124—28no—
557#124—48no—
558#123—216no—
559#123—216no—
560#123—216no—
561#123—216no—
562#123—48no—
563#123—48no—
564C22⋊Q8—216no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—28no—
568C22⋊Q8—232no—
569C22⋊Q8—232no—
570C22⋊Q8—216no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—48no—
574#121—28no—
575#121—28no—
576#121—216no—
577#121—48no—
578#120—48no—
579#120—48no—
580C4×Q8—232no—
581C4×Q8—216no—
582C4×Q8—216no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8C2×D4132yes—
588C4×Q8C2×D4132yes—
589C4×D4—216no—
590C4×D4—216no—
591C4×D4—232no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—416no—
597#117—28no—
598#117—216no—
599#117—216no—
600#117—216no—
601#117—216no—
602#117—216no—
603#117—216no—
604#117—216no—
605#117—48no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4C2×D418yes—
616C2×C4⋊C4C2×D418yes—
617C2×C4⋊C4C2×D418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—24no—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C42—24no—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42—216no—
706C2×C42C2×D418yes—
707C2×C42C2×D418yes—
708C2×C42C2×D418yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750C24—22no—
751C24—22no—
752C24—24no—
753C24—24no—
754C24—42no—
755C24—42no—
756C24—42no—
757C24—42no—
758C24C2512yes—
759C24C2512yes—
760C24C2514yes—
761C24C2511yescharacteristic
762#41—432no—
763C2×Q8—28no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—416no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—48no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—416no—
778C2×Q8—416no—
779C2×Q8C22×D4116yes—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—24no—
784C2×D4—28no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—48no—
788C2×D4—44no—
789C2×D4—416no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—48no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—42no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—48no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—48no—
830C22×C4—416no—
831C22×C4—416no—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D414yes—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D414yes—
838C22×C4C22×D414yes—
839C22×C4C2518yes—
840C22×C4C2518yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2512yes—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—216no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4C22×D4116yes—
894C4⋊C4C22×D4116yes—
895C4⋊C4C22×D4116yes—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C42—28no—
932C42—28no—
933C42—28no—
934C42—28no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—48no—
939C42—48no—
940C42—44no—
941C42—44no—
942C42C22×D418yes—
943C42C22×D418yes—
944C42C22×D418yes—
945C42C22×D418yes—
946C42C22×D418yes—
947C42C22×D418yes—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—28no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—28no—
962C23—24no—
963C23—22no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23—44no—
969C23—44no—
970C23—88no—
971C23—88no—
972C23C23×D412yes—
973C23#58514yes—
974C23C2611yescharacteristic
975Q8—416no—
976Q8—416no—
977Q8—416no—
978Q8—48no—
979Q8—84no—
980Q8—84no—
981D4—416no—
982D4—48no—
983D4—416no—
984D4—84no—
985D4—84no—
986D4—816no—
987D4—168no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—416no—
1031C2×C4—416no—
1032C2×C4—416no—
1033C2×C4—416no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—88no—
1040C2×C4C23×D412yes—
1041C2×C4C23×D414yes—
1042C2×C4C23×D414yes—
1043C2×C4C23×D414yes—
1044C2×C4C23×D414yes—
1045C2×C4C23×D412yes—
1046C2×C4C23×D414yes—
1047C2×C4C23×D414yes—
1048C2×C4#58514yes—
1049C22—22no—
1050C22—22no—
1051C22—28no—
1052C22—42no—
1053C22—42no—
1054C22—44no—
1055C22—44no—
1056C22—42no—
1057C22—42no—
1058C22—48no—
1059C22—48no—
1060C22—44no—
1061C22—48no—
1062C22—44no—
1063C22—44no—
1064C22—42no—
1065C22—42no—
1066C22—88no—
1067C22—88no—
1068C22#344914yes—
1069C22C24×D411yescharacteristic
1070C22C2×#58512yes—
1071C22C2×#58512yes—
1072C222−1+612yes—
1073C4—24no—
1074C4—24no—
1075C4—24no—
1076C4—24no—
1077C4—22no—
1078C4—22no—
1079C4—24no—
1080C4—24no—
1081C4—24no—
1082C4—42no—
1083C4—44no—
1084C4—42no—
1085C4—44no—
1086C4—42no—
1087C4—48no—
1088C4—48no—
1089C4—44no—
1090C4—42no—
1091C4—42no—
1092C2—24no—
1093C2—84no—
1094C2—82no—
1095C2—82no—
1096C2C2×#344911yescharacteristic
1097C2#6281111yescharacteristic
1098C2#6284811yescharacteristic
1099C2#6291114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#556C2semidirect
2. C2×#3461C2semidirect
3. #42301C2semidirect
4. #41943C2semidirect
5. #38379C2semidirect
6. #38375C2semidirect
7. #37606C2semidirect
8. #37538C2semidirect
9. #37258C2semidirect
10. #37187C2semidirect
11. #36962C2semidirect
12. #36961C2semidirect
13. #36708C2semidirect
14. #36707C2semidirect
15. #35469C2semidirect
16. #35397C2semidirect
17. #35302C2semidirect
18. #35246C2semidirect
19. #35143C2semidirect
20. #35092C2semidirect
21. #34987C2semidirect
22. #34875C2semidirect
23. #34187C2semidirect
29. C2×#542C22semidirect
30. C2×#541C22semidirect
35. C2×#533C22semidirect
39. C2×#529C22semidirect
59. #2852C22semidirect
62. #2823C22semidirect
65. #2734C22semidirect
68. #2731C22semidirect
71. #2729C22semidirect
72. #2729C22semidirect
73. #2723C22semidirect
74. #2721C22semidirect
75. #2716C22semidirect
76. #2714C22semidirect
77. #2692C22semidirect
78. #2690C22semidirect
79. #2677C22semidirect
80. #2676C22semidirect
81. #2664C22semidirect
83. #2662C22semidirect
84. #2637C22semidirect
85. #2637C22semidirect
86. #2637C22semidirect
87. #2636C22semidirect
88. #2636C22semidirect
91. #2629C22semidirect
94. #2620C22semidirect
100. #2609C22semidirect
101. #2609C22semidirect
102. #2604C22semidirect
103. #2603C22semidirect
104. #2601C22semidirect
105. #2601C22semidirect
106. #2601C22semidirect
107. #2599C22semidirect
108. #2599C22semidirect
109. #2598C22semidirect
112. #2565C22semidirect
115. #2560C22semidirect
116. #2560C22semidirect
117. #2556C22semidirect
118. #2554C22semidirect
119. #2545C22semidirect
124. #2519C22semidirect
125. #2512C22semidirect
132. #2469C22semidirect
134. #2465C22semidirect
136. #2462C22semidirect
137. #2461C22semidirect
139. #2458C22semidirect
141. #2452C22semidirect
152. #2396C22semidirect
153. #2392C22semidirect
154. #2356C22semidirect
155. #2355C22semidirect
156. #2327C22semidirect
157. #2326C22semidirect
158. #2324C22semidirect
159. #2323C22semidirect
168. #2290C22semidirect
253. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#34612
#423012
#419432
#383792
#383752
#376062
#375382
#372582
#371872
#369622
#369612
#367082
#367072
#354692
#353972
#353022
#352462
#351432
#350922
#349872
#348752
#341872