Finite Group Databasebeta

← #7657308

Subgroups — #7657308

Order 512.

6488 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic
3#42918C212yesmaximal, complemented
4#42915C212yesmaximal, complemented
5#42891C212yesmaximal, complemented
6#42811C212yesmaximal, complemented
7#42150C214yesmaximal, complemented
8#41939C214yesmaximal, complemented
9#41411C214yesmaximal, complemented
10#40589C214yesmaximal, complemented
11#39855C214yesmaximal, complemented
12#38363C218yesmaximal, complemented
13#37635C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37557C212yesmaximal, complemented
16#37540C211yesmaximal, characteristic, complemented
17#36219C214yesmaximal, complemented
18#36067C212yesmaximal, complemented
19#36042C212yesmaximal, complemented
20#35998C212yesmaximal, complemented
21#35928C212yesmaximal, complemented
22#35248C212yesmaximal, complemented
23#35138C211yesmaximal, characteristic, complemented
24#34627C211yesmaximal, characteristic, complemented
25C2×#2634C212yesmaximal, complemented
26#34195C211yesmaximal, characteristic, complemented
27#3504—216no—
28#3482—216no—
29C2×#557C2211yescharacteristic
30C2×#557C2212yes—
31C2×#557C2212yes—
32C2×#556C2211yescharacteristic
33C2×#556C2212yes—
34C2×#554C2212yes—
35C2×#554C2212yes—
36C2×#554C2214yes—
37C2×#554C2214yes—
38C2×#552C2214yes—
39C2×#552C2212yes—
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#547C2212yes—
43C2×#547C2211yescharacteristic
44C2×#544C2211yescharacteristic
45C2×#544C2212yes—
46C2×#544C2211yescharacteristic
47C2×#544C2212yes—
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#533C2212yes—
51C2×#533C2212yes—
52C2×#529C2212yes—
53C2×#529C2214yes—
54C22×#125C2212yes—
55C22×#125C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#520C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2212yes—
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2212yes—
62#2855C2218yes—
63#2851C2214yes—
64#2822C2214yes—
65#2822C2214yes—
66#2821C2214yes—
67#2821C2214yes—
68#2820C2214yes—
69#2817C2214yes—
70#2721C2218yes—
71#2719C2218yes—
72#2719C2218yes—
73#2716C2218yes—
74#2713C2218yes—
75#2713C2218yes—
76#2700C2218yes—
77#2698C2218yes—
78#2690C2218yes—
79#2689C2218yes—
80#2677C2218yes—
81#2674C2218yes—
82#2664C2214yes—
83#2664C2214yes—
84#2660C2212yes—
85#2660C2212yes—
86#2659C2214yes—
87#2642C2212yes—
88#2642C2212yes—
89#2639C2214yes—
90#2638C2214yes—
91#2634C2212yes—
92#2634C2212yes—
93#2634C2211yescharacteristic
94#2634C2214yes—
95#2634C2212yes—
96#2634C2214yes—
97#2634C2214yes—
98#2634C2212yes—
99#2634C2214yes—
100#2634C2218yes—
101#2634C2214yes—
102#2634C2211yescharacteristic
103#2634C2212yes—
104#2633C2212yes—
105#2633C2211yescharacteristic
106#2633C2211yescharacteristic
107#2632C2214yes—
108#2628C2212yes—
109#2627C2214yes—
110#2625C2212yes—
111#2625C2212yes—
112#2625C2212yes—
113#2623C2214yes—
114#2623C2214yes—
115#2621C2212yes—
116#2616C2212yes—
117#2611C2214yes—
118#2611C2218yes—
119#2599C2218yes—
120#2591C2214yes—
121#2584C2212yes—
122#2583C2214yes—
123#2581C2214yes—
124#2581C2214yes—
125#2581C2214yes—
126#2579C2218yes—
127#2568C2212yes—
128#2568C2214yes—
129#2567C2212yes—
130#2565C2214yes—
131#2564C2218yes—
132#2562C2212yes—
133#2551C2214yes—
134#2550C2214yes—
135#2549C2218yes—
136#2546C2214yes—
137#2503C2212yes—
138#2503C2214yes—
139#2502C2212yes—
140#2499C2214yes—
141#2498C2214yes—
142#2498C2214yes—
143#2492C2214yes—
144#2489C2214yes—
145#2488C2218yes—
146#2488C2218yes—
147#2487C2212yes—
148#2486C2212yes—
149#2484C2212yes—
150#2484C2214yes—
151#2484C2214yes—
152#2484C2214yes—
153#2453C2214yes—
154#2451C2214yes—
155#2450C2218yes—
156#2449C2218yes—
157#2446C2214yes—
158#2446C2214yes—
159#2444C2218yes—
160#2443C2218yes—
161#2441C2214yes—
162#2440C2218yes—
163#2439C2214yes—
164#2438C2218yes—
165#2438C2218yes—
166#2434C2214yes—
167#2423C2214yes—
168#2421C2214yes—
169#2419C2218yes—
170#2419C2218yes—
171#2406C2212yes—
172#2399C2212yes—
173#2398C2212yes—
174#2395C2212yes—
175#2395C2212yes—
176C2×#400C2214yes—
177C2×#400C2214yes—
178C2×#398C2214yes—
179C2×#395C2214yes—
180#2356C2212yes—
181#2353C2214yes—
182#2349C2214yes—
183#2349C2212yes—
184D4×C4⋊C4C2214yes—
185#2347C2212yes—
186#2343C2214yes—
187#2339C2214yes—
188#2339C2214yes—
189#2339C2212yes—
190#2327C2218yes—
191#2322C2214yes—
192#2320C2212yes—
193#2318C2214yes—
194C4×C22⋊Q8C2214yes—
195C2×#387C2218yes—
196#2283C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199C2×#383C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2312yes—
205#557—28no—
206#557—216no—
207#557—216no—
208#556—28no—
209#556—216no—
210#554—216no—
211#554—232no—
212#554—216no—
213#554—232no—
214#552—216no—
215#552—232no—
216D4×Q8—28no—
217#548—216no—
218#547—216no—
219#547—28no—
220#544—216no—
221#544—216no—
222#544—28no—
223#544—28no—
224#533—216no—
225#533—28no—
226#533—216no—
227#533—28no—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2318yes—
241#529—232no—
242#529—216no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125—216no—
247C2×#125—28no—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292#520—28no—
293#520—28no—
294C4×#41—216no—
295C4×#41—28no—
296C4×#41D4116yes—
297C2×C4×Q8—216no—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2311yescharacteristic
336C2×#117C2314yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2314yes—
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2318yes—
354C22×C42C2312yes—
355C22×C42C2314yes—
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358#400C2314yes—
359#400C2314yes—
360#400C2318yes—
361#400C2314yes—
362#400C2318yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2318yes—
368#400C2318yes—
369#400C2312yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#400C2312yes—
376#400C2318yes—
377#400C2318yes—
378#400C2318yes—
379#400C2318yes—
380#399C2318yes—
381#399C2318yes—
382#399C2312yes—
383#399C2314yes—
384#399C2312yes—
385#398C2318yes—
386#398C2318yes—
387#398C2314yes—
388#398C2318yes—
389#398C2314yes—
390#398C2312yes—
391#398C2318yes—
392#398C2318yes—
393#398C2314yes—
394#398C2318yes—
395#398C2314yes—
396#398C2318yes—
397#398C2314yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2318yes—
404#398C2318yes—
405#397C2318yes—
406#397C2318yes—
407#397C2318yes—
408#397C2312yes—
409#397C2318yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#396C2318yes—
416#396C2318yes—
417#395C2314yes—
418#395C2314yes—
419#395C2318yes—
420#395C2318yes—
421#395C2314yes—
422#395C2318yes—
423#395C2312yes—
424#395C2314yes—
425#395C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2318yes—
429#395C2318yes—
430#394C2314yes—
431#394C2312yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#393C2318yes—
436#393C2318yes—
437#393C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2318yes—
444#391C2318yes—
445#391C2318yes—
446#391C2314yes—
447#391C2314yes—
448#391C2318yes—
449#391C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#389C2318yes—
456#389C2318yes—
457#389C2318yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2314yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2314yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2314yes—
491#386C2318yes—
492#386C2318yes—
493#385C2314yes—
494#385C2318yes—
495#385C2318yes—
496#385C2314yes—
497#385C2314yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#384C2314yes—
505#384C2314yes—
506#383C2314yes—
507#383C2314yes—
508#383C2314yes—
509#383C2311yescharacteristic
510#383C2312yes—
511#383C2311yescharacteristic
512#382C2314yes—
513#382C2314yes—
514#382C2312yes—
515#382C2318yes—
516#382C2314yes—
517#382C2312yes—
518#381C2312yes—
519#381C2314yes—
520#381C2314yes—
521#381C2318yes—
522#381C2318yes—
523#381C2312yes—
524#381C2318yes—
525#380C2314yes—
526#380C2314yes—
527#380C2318yes—
528#380C2318yes—
529#380C2312yes—
530#380C2314yes—
531#380C2312yes—
532#380C2314yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C22⋊C4C2314yes—
540C4×C22⋊C4C2312yes—
541C4×C22⋊C4C2312yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2318yes—
545#376C2312yes—
546#376C2314yes—
547#376C2312yes—
548C2×#95C2314yes—
549C2×#95C2314yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41—24no—
558C2×#41—44no—
559C2×#41C2×D418yes—
560C22×Q8—28no—
561C22×Q8—48no—
562C22×Q8C2411yescharacteristic
563C22×Q8C2412yes—
564C22×Q8C2414yes—
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×Q8C2414yes—
571C22×D4C2414yes—
572C22×D4C2412yes—
573C22×D4C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2411yescharacteristic
576C23×C4C2414yes—
577C23×C4C2412yes—
578C23×C4C2414yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2411yescharacteristic
582C23×C4C2414yes—
583C23×C4C2412yes—
584C23×C4C2414yes—
585C23×C4C2412yes—
586C23×C4C2418yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2412yes—
592C4⋊Q8—28no—
593C4⋊Q8—28no—
594C4⋊Q8—28no—
595C4⋊Q8—216no—
596C4⋊Q8—28no—
597C4⋊Q8—216no—
598C4⋊Q8—24no—
599C4⋊Q8—24no—
600C4⋊Q8—28no—
601C4⋊Q8—28no—
602C4⋊Q8—24no—
603C4⋊Q8—24no—
604C4⋊Q8—416no—
605#126—216no—
606#126—216no—
607#126—216no—
608#125—216no—
609#125—216no—
610#125—28no—
611#125—216no—
612#125—28no—
613#125—216no—
614#125—24no—
615#125—28no—
616#125—28no—
617#125—28no—
618#125—28no—
619#125—28no—
620#125—216no—
621#125—28no—
622#125—216no—
623#125—28no—
624#125—24no—
625#125—28no—
626#124—216no—
627#124—28no—
628#123—216no—
629#123—216no—
630#123—216no—
631#123—48no—
632C22⋊Q8—28no—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—216no—
637C22⋊Q8—216no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—48no—
650#121—216no—
651#121—28no—
652C4×Q8—28no—
653C4×Q8—28no—
654C4×Q8—28no—
655C4×Q8—24no—
656C4×Q8—216no—
657C4×Q8—28no—
658C4×Q8—28no—
659C4×Q8—28no—
660C4×Q8—216no—
661C4×Q8—28no—
662C4×Q8—24no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8—28no—
666C4×Q8—216no—
667C4×Q8C2×D418yes—
668C4×Q8C2×D418yes—
669C4×D4—28no—
670C4×D4—216no—
671C4×D4—216no—
672C4×D4—28no—
673C4×D4—28no—
674C4×D4—216no—
675C4×D4—28no—
676C4×D4—216no—
677C4×D4—28no—
678C4×D4—216no—
679C4×D4—24no—
680C4×D4—24no—
681C4×D4C2×D418yes—
682C4×D4C2×D4116yes—
683C4×D4C2×D418yes—
684C4×D4C2×D4116yes—
685#117—24no—
686#117—28no—
687#117—28no—
688#117—24no—
689#117—24no—
690#117—28no—
691#117—28no—
692#117—216no—
693#117—28no—
694#117—216no—
695#117C2×D4116yes—
696#117C2×D418yes—
697C2×C4⋊C4—28no—
698C2×C4⋊C4—216no—
699C2×C4⋊C4—28no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4—24no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—216no—
704C2×C4⋊C4—216no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—28no—
707C2×C4⋊C4—416no—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C42—216no—
792C2×C42—28no—
793C2×C42C2×D4116yes—
794C2×C42C2×D418yes—
795C2×C42C2412yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2418yes—
807C2×C42C2414yes—
808C2×C42C2411yescharacteristic
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815#95C2412yes—
816#95C2412yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2412yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2412yes—
837#95C2412yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854C24C2512yes—
855C24C2511yescharacteristic
856C24C2512yes—
857#41—232no—
858#41—416no—
859#41—432no—
860C2×Q8—22no—
861C2×Q8—28no—
862C2×Q8—24no—
863C2×Q8—24no—
864C2×Q8—28no—
865C2×Q8—24no—
866C2×Q8—24no—
867C2×Q8—28no—
868C2×Q8—24no—
869C2×Q8—28no—
870C2×Q8—24no—
871C2×Q8—28no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—48no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—44no—
879C2×Q8—44no—
880C2×Q8—432no—
881C2×Q8C22×D414yes—
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—24no—
885C2×D4—216no—
886C2×D4—22no—
887C2×D4—24no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4C22×D418yes—
891C2×D4C22×D414yes—
892C2×D42−1+418yes—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—216no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—216no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—28no—
907C22×C4—28no—
908C22×C4—24no—
909C22×C4—42no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—44no—
919C22×C4—48no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4C22×D418yes—
924C22×C4C22×D414yes—
925C22×C4C22×D418yes—
926C22×C4C22×D418yes—
927C22×C4C22×D414yes—
928C22×C4C22×D414yes—
929C22×C4C2514yes—
930C22×C4C2518yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2511yescharacteristic
943C22×C4C2512yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2511yescharacteristic
950C22×C4C2512yes—
951C22×C4C2511yescharacteristic
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—24no—
980C4⋊C4—22no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—216no—
997C4⋊C4—28no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—48no—
1001C4⋊C4—48no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4C22×D414yes—
1008C4⋊C4C22×D418yes—
1009C4⋊C4C22×D414yes—
1010C4⋊C4C22×D418yes—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—24no—
1017C22⋊C4—28no—
1018C22⋊C4—216no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—48no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—48no—
1032C22⋊C4C22×D418yes—
1033C22⋊C4C22×D418yes—
1034C22⋊C4C22×D418yes—
1035C42—24no—
1036C42—24no—
1037C42—28no—
1038C42—28no—
1039C42—24no—
1040C42—28no—
1041C42—28no—
1042C42—28no—
1043C42—24no—
1044C42—24no—
1045C42—28no—
1046C42—44no—
1047C42—48no—
1048C42C22×D414yes—
1049C42C22×D414yes—
1050C42C22×D414yes—
1051C42C22×D418yes—
1052C42C22×D418yes—
1053C42C22×D414yes—
1054C42C22×D418yes—
1055C23—24no—
1056C23—24no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—22no—
1063C23—22no—
1064C23—24no—
1065C23C23×D412yes—
1066C23C23×D414yes—
1067C23C2×2−1+418yes—
1068C23C2611yescharacteristic
1069Q8—28no—
1070Q8—28no—
1071Q8—416no—
1072Q8—48no—
1073Q8—48no—
1074Q8—84no—
1075Q8—88no—
1076Q8—84no—
1077Q8—88no—
1078D4—216no—
1079D4—48no—
1080D4—44no—
1081D4—416no—
1082D4#536116yes—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—216no—
1094C2×C4—28no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—28no—
1108C2×C4—24no—
1109C2×C4—28no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—28no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—48no—
1129C2×C4—44no—
1130C2×C4—48no—
1131C2×C4—44no—
1132C2×C4—48no—
1133C2×C4—416no—
1134C2×C4—48no—
1135C2×C4—416no—
1136C2×C4—48no—
1137C2×C4—88no—
1138C2×C4—84no—
1139C2×C4—88no—
1140C2×C4—84no—
1141C2×C4—816no—
1142C2×C4C23×D412yes—
1143C2×C4C23×D414yes—
1144C2×C4C23×D414yes—
1145C2×C4C23×D412yes—
1146C2×C4C23×D412yes—
1147C2×C4C23×D412yes—
1148C2×C4C23×D412yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D412yes—
1151C2×C4C2×2−1+414yes—
1152C2×C4#58514yes—
1153C22—24no—
1154C22—24no—
1155C22—216no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—44no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—44no—
1164C22—44no—
1165C22C2×#53618yes—
1166C22C24×D411yescharacteristic
1167C22C22×2−1+412yes—
1168C22C2×#58512yes—
1169C222−1+612yes—
1170C4—22no—
1171C4—22no—
1172C4—24no—
1173C4—24no—
1174C4—22no—
1175C4—22no—
1176C4—24no—
1177C4—22no—
1178C4—24no—
1179C4—44no—
1180C4—42no—
1181C4—44no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—44no—
1186C4—42no—
1187C4—42no—
1188C4—44no—
1189C4—44no—
1190C4—48no—
1191C4—44no—
1192C4C2×#53614yes—
1193C2—28no—
1194C2—42no—
1195C2—82no—
1196C2C22×#53611yescharacteristic
1197C2#6281111yescharacteristic
1198C2#6285911yescharacteristic
1199C2#6295014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3482C2
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×#3504C2semidirect
3. #42918C2semidirect
4. #42915C2semidirect
5. #42891C2semidirect
6. #42811C2semidirect
7. #42150C2semidirect
8. #41939C2semidirect
9. #41411C2semidirect
10. #40589C2semidirect
11. #39855C2semidirect
12. #38363C2semidirect
13. #37635C2semidirect
14. #37607C2semidirect
15. #37557C2semidirect
16. #37540C2semidirect
17. #36219C2semidirect
18. #36067C2semidirect
19. #36042C2semidirect
20. #35998C2semidirect
21. #35928C2semidirect
22. #35248C2semidirect
23. #35138C2semidirect
24. #34627C2semidirect
25. C2×#2634C2semidirect
26. #34195C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#34822
#429182
#429152
#428912
#428112
#421502
#419392
#414112
#405892
#398552
#383632
#376352
#376072
#375572
#375402
#362192
#360672
#360422
#359982
#359282
#352482
#351382
#346272
C2×#26342
#341952