Finite Group Databasebeta

← #7720023

Subgroups — #7720023

Order 512.

6354 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C211yesmaximal, characteristic
2C2×#3563C211yesmaximal, characteristic, complemented
3#51545C214yesmaximal, complemented
4#51544C214yesmaximal, complemented
5#51422C218yesmaximal, complemented
6#44761C218yesmaximal, complemented
7#44448C214yesmaximal, complemented
8#43496C214yesmaximal, complemented
9#39619C212yesmaximal, complemented
10#39613C212yesmaximal, complemented
11#37871C212yesmaximal, complemented
12#37865C212yesmaximal, complemented
13#37865C212yesmaximal, complemented
14#37863C212yesmaximal, complemented
15#37423C212yesmaximal, complemented
16#37392C212yesmaximal, complemented
17#36181C212yesmaximal, complemented
18#36164C212yesmaximal, complemented
19#35330C212yesmaximal, complemented
20#35326C211yesmaximal, characteristic, complemented
21#35320C211yesmaximal, characteristic, complemented
22#35318C212yesmaximal, complemented
23#35139C211yesmaximal, characteristic, complemented
24C2×#2660C211yesmaximal, characteristic, complemented
25#34149C211yesmaximal, characteristic, complemented
26#3563—216no—
27#3544—216no—
28C2×#564C2212yes—
29C2×#563C2212yes—
30C2×#563C2214yes—
31C2×Q82C2211yescharacteristic
32C2×#557C2212yes—
33C2×#555C2211yescharacteristic
34C2×#554C2212yes—
35C2×#554C2211yescharacteristic
36C2×#554C2211yescharacteristic
37C2×#552C2212yes—
38C2×#552C2214yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×#547C2212yes—
43C2×#547C2212yes—
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#544C2212yes—
47C2×#544C2212yes—
48C2×#542C2212yes—
49C2×#542C2212yes—
50C2×#541C2212yes—
51C2×#541C2214yes—
52C2×#539C2212yes—
53C2×#536C2214yes—
54C2×#533C2211yescharacteristic
55C22×C4⋊Q8C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic
59#2862C2212yes—
60#2862C2212yes—
61#2862C2212yes—
62#2861C2212yes—
63#2859C2212yes—
64#2859C2212yes—
65#2857C2212yes—
66#2857C2212yes—
67#2850C2212yes—
68#2850C2212yes—
69#2729C2218yes—
70#2720C2218yes—
71#2719C2218yes—
72#2719C2218yes—
73#2719C2218yes—
74#2718C2218yes—
75#2716C2218yes—
76#2715C2218yes—
77#2713C2218yes—
78#2713C2218yes—
79#2713C2218yes—
80#2708C2218yes—
81#2704C2218yes—
82#2700C2218yes—
83#2698C2218yes—
84#2698C2218yes—
85#2698C2218yes—
86#2690C2218yes—
87#2689C2218yes—
88#2687C2218yes—
89#2664C2214yes—
90#2660C2211yescharacteristic
91#2660C2212yes—
92#2660C2212yes—
93#2660C2212yes—
94#2660C2212yes—
95#2660C2214yes—
96#2660C2212yes—
97#2660C2212yes—
98#2660C2214yes—
99#2658C2211yescharacteristic
100#2642C2211yescharacteristic
101#2642C2214yes—
102#2640C2211yescharacteristic
103#2621C2212yes—
104#2620C2212yes—
105#2611C2214yes—
106#2611C2214yes—
107#2604C2214yes—
108#2568C2212yes—
109#2568C2212yes—
110#2568C2212yes—
111#2568C2212yes—
112#2568C2214yes—
113#2567C2212yes—
114#2566C2212yes—
115#2566C2212yes—
116#2565C2212yes—
117#2565C2212yes—
118#2565C2212yes—
119#2565C2212yes—
120#2564C2214yes—
121#2563C2212yes—
122#2556C2218yes—
123#2553C2218yes—
124#2550C2218yes—
125#2550C2218yes—
126#2549C2218yes—
127#2549C2218yes—
128#2521C2218yes—
129#2519C2218yes—
130#2506C2218yes—
131#2504C2212yes—
132#2504C2211yescharacteristic
133#2503C2212yes—
134#2503C2212yes—
135#2503C2211yescharacteristic
136#2503C2212yes—
137#2503C2214yes—
138#2503C2212yes—
139#2502C2212yes—
140#2502C2211yescharacteristic
141#2501C2211yescharacteristic
142#2500C2212yes—
143#2499C2212yes—
144#2499C2212yes—
145#2499C2212yes—
146#2498C2214yes—
147#2496C2218yes—
148#2489C2218yes—
149#2488C2218yes—
150#2488C2218yes—
151#2486C2218yes—
152#2475C2218yes—
153#2474C2218yes—
154#2473C2218yes—
155#2465C2218yes—
156#2451C2218yes—
157#2446C2218yes—
158#2438C2218yes—
159#2438C2218yes—
160#2419C2218yes—
161#2419C2218yes—
162#2413C2214yes—
163#2413C2218yes—
164#2406C2218yes—
165C2×#398C2214yes—
166C2×#395C2214yes—
167#2373C2214yes—
168#2372C2212yes—
169#2371C2212yes—
170#2368C2212yes—
171#2364C2212yes—
172#2359C2214yes—
173#2344C2218yes—
174#2339C2218yes—
175#2327C2212yes—
176#2327C2212yes—
177#2326C2212yes—
178#2326C2212yes—
179#2322C2214yes—
180#2317C2212yes—
181#2317C2212yes—
182#2310C2214yes—
183C4×C4⋊Q8C2212yes—
184C4×#124C2212yes—
185#2298C2212yes—
186#2295C2212yes—
187#2290C2212yes—
188#2290C2212yes—
189#2285C2212yes—
190C2×#384C2212yes—
191C2×#382C2212yes—
192C2×#382C2212yes—
193C42×D4C2212yes—
194C4×#117C2212yes—
195C4×#117C2211yescharacteristic
196C2×#376C2211yescharacteristic
197C22×#41C2314yes—
198C23×Q8C2312yes—
199#564—216no—
200#563—232no—
201#563—216no—
202Q82—28no—
203#557—216no—
204#555—28no—
205#554—28no—
206#554—28no—
207#554—216no—
208#552—232no—
209#552—216no—
210#552—216no—
211#552—216no—
212#552—216no—
213#547—216no—
214#547—216no—
215#544—216no—
216#544—216no—
217#544—216no—
218#544—216no—
219#542—216no—
220#542—216no—
221#541—232no—
222#541—216no—
223#539—216no—
224#536—232no—
225#533—28no—
226C2×C4⋊Q8—28no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242#529—28no—
243#529D4116yes—
244C2×#126C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#125—28no—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2311yescharacteristic
273C2×#124C2312yes—
274C2×#124C2311yescharacteristic
275C2×#124C2314yes—
276C2×#124C2314yes—
277C2×#124C2311yescharacteristic
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×#121C2311yescharacteristic
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2314yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2318yes—
347C22×C42C2312yes—
348C22×C42C2312yes—
349C22×C42C2311yescharacteristic
350#400C2314yes—
351#400C2318yes—
352#400C2318yes—
353#400C2318yes—
354#400C2318yes—
355#400C2318yes—
356#400C2318yes—
357#400C2314yes—
358#400C2314yes—
359#400C2318yes—
360#400C2318yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2314yes—
369#398C2314yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#398C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#397C2314yes—
379#397C2314yes—
380#397C2318yes—
381#397C2318yes—
382#397C2318yes—
383#397C2318yes—
384#397C2318yes—
385#396C2318yes—
386#396C2318yes—
387#396C2318yes—
388#395C2314yes—
389#395C2318yes—
390#395C2318yes—
391#395C2318yes—
392#395C2318yes—
393#395C2318yes—
394#395C2318yes—
395#395C2318yes—
396#394C2318yes—
397#394C2318yes—
398#393C2318yes—
399#393C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2318yes—
408#391C2318yes—
409#391C2318yes—
410#391C2318yes—
411#391C2312yes—
412#391C2312yes—
413#391C2318yes—
414#391C2318yes—
415#391C2318yes—
416#391C2318yes—
417#391C2318yes—
418#391C2314yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#389C2318yes—
423#389C2318yes—
424#389C2318yes—
425#389C2318yes—
426#389C2318yes—
427#389C2318yes—
428#389C2318yes—
429#389C2318yes—
430#389C2318yes—
431#389C2318yes—
432#389C2314yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2318yes—
444#388C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2318yes—
462#386C2318yes—
463#386C2314yes—
464#386C2318yes—
465#386C2318yes—
466#386C2314yes—
467#386C2314yes—
468#385C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2314yes—
474#385C2318yes—
475#385C2314yes—
476#385C2314yes—
477#385C2318yes—
478#384C2312yes—
479#384C2312yes—
480#384C2312yes—
481#384C2312yes—
482#384C2312yes—
483#384C2312yes—
484#384C2312yes—
485#384C2318yes—
486#382C2312yes—
487#382C2312yes—
488#382C2312yes—
489#382C2312yes—
490#382C2312yes—
491#382C2312yes—
492#382C2312yes—
493#382C2312yes—
494#382C2318yes—
495#382C2312yes—
496#382C2312yes—
497#382C2312yes—
498#382C2318yes—
499#382C2318yes—
500#381C2318yes—
501#381C2318yes—
502#381C2314yes—
503#381C2318yes—
504#381C2318yes—
505#380C2318yes—
506#380C2318yes—
507#380C2318yes—
508#380C2318yes—
509C4×C4⋊C4C2318yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2318yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2311yescharacteristic
527C4×C22⋊C4C2311yescharacteristic
528#376C2312yes—
529#376C2312yes—
530#376C2312yes—
531#376C2312yes—
532#376C2312yes—
533#376C2311yescharacteristic
534#376C2311yescharacteristic
535C2×#95C2312yes—
536C2×#95C2318yes—
537C2×#95C2318yes—
538C2×#95C2312yes—
539C43C2312yes—
540C43C2312yes—
541C2×#41—216no—
542C2×#41—416no—
543C22×Q8—28no—
544C22×Q8—48no—
545C22×Q8C2411yescharacteristic
546C22×Q8C2412yes—
547C22×Q8C2412yes—
548C22×Q8C2414yes—
549C22×Q8C2412yes—
550C22×Q8C2414yes—
551C22×Q8C2414yes—
552C22×Q8C2412yes—
553C22×Q8C2411yescharacteristic
554C22×D4C2411yescharacteristic
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2414yes—
558C22×D4C2411yescharacteristic
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2414yes—
562C23×C4C2411yescharacteristic
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2414yes—
568C23×C4C2414yes—
569C23×C4C2414yes—
570C23×C4C2414yes—
571C23×C4C2411yescharacteristic
572C4⋊Q8—216no—
573C4⋊Q8—216no—
574C4⋊Q8—216no—
575C4⋊Q8—216no—
576C4⋊Q8—28no—
577C4⋊Q8—28no—
578C4⋊Q8—28no—
579C4⋊Q8—24no—
580C4⋊Q8—24no—
581C4⋊Q8—28no—
582C4⋊Q8—24no—
583C4⋊Q8—24no—
584C4⋊Q8—28no—
585C4⋊Q8—28no—
586C4⋊Q8—28no—
587#126—216no—
588#126—216no—
589#126—216no—
590#126—216no—
591#126—216no—
592#126—216no—
593#126—28no—
594#126C2×D4116yes—
595#125—216no—
596#125—216no—
597#125—216no—
598#125—216no—
599#125—216no—
600#125—216no—
601#125—28no—
602#125—216no—
603#125—216no—
604#125—216no—
605#125—216no—
606#125—28no—
607#125—28no—
608#125—28no—
609#125—28no—
610#125—24no—
611#125—28no—
612#125—28no—
613#125—28no—
614#125C2×D418yes—
615#124—216no—
616#124—216no—
617#124—24no—
618#124—28no—
619#124C2×D418yes—
620#123—216no—
621#123—216no—
622#123—216no—
623#123—28no—
624#123—216no—
625#123—216no—
626#123—216no—
627#123—48no—
628#123C2×D4116yes—
629C22⋊Q8—28no—
630C22⋊Q8—24no—
631C22⋊Q8—28no—
632C22⋊Q8—28no—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—216no—
637C22⋊Q8—216no—
638C22⋊Q8—216no—
639C22⋊Q8—216no—
640C22⋊Q8—216no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8C2×D418yes—
647#121—28no—
648#121—24no—
649#121—28no—
650#121C2×D418yes—
651C4×Q8—28no—
652C4×Q8—216no—
653C4×Q8—24no—
654C4×Q8—28no—
655C4×Q8—28no—
656C4×Q8—28no—
657C4×Q8—28no—
658C4×Q8—28no—
659C4×Q8C2×D418yes—
660C4×D4—216no—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—24no—
664C4×D4—28no—
665C4×D4—48no—
666C4×D4C2×D4116yes—
667C4×D4C2×D418yes—
668#117—28no—
669#117—28no—
670#117—28no—
671#117—28no—
672#117—216no—
673#117—216no—
674#117—216no—
675#117—28no—
676#117—28no—
677#117—44no—
678#117C2×D4116yes—
679C2×C4⋊C4—28no—
680C2×C4⋊C4—24no—
681C2×C4⋊C4—28no—
682C2×C4⋊C4—24no—
683C2×C4⋊C4—28no—
684C2×C4⋊C4—28no—
685C2×C4⋊C4—28no—
686C2×C4⋊C4—28no—
687C2×C4⋊C4—28no—
688C2×C4⋊C4—416no—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2418yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2418yes—
766C2×C22⋊C4C2418yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2418yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C42—28no—
775C2×C42—28no—
776C2×C42C2×D418yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2412yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2412yes—
799#95C2418yes—
800#95C2412yes—
801#95C2412yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2418yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810#95C2418yes—
811#95C2418yes—
812#95C2412yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2414yes—
818#95C2414yes—
819#95C2418yes—
820#95C2414yes—
821#95C2418yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2414yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834C24C2512yes—
835C24C2512yes—
836C24C2511yescharacteristic
837#41—832no—
838C2×Q8—22no—
839C2×Q8—24no—
840C2×Q8—24no—
841C2×Q8—28no—
842C2×Q8—24no—
843C2×Q8—28no—
844C2×Q8—28no—
845C2×Q8—24no—
846C2×Q8—24no—
847C2×Q8—24no—
848C2×Q8—24no—
849C2×Q8—42no—
850C2×Q8—48no—
851C2×Q8—44no—
852C2×Q8—44no—
853C2×Q8—44no—
854C2×Q8—48no—
855C2×Q8—48no—
856C2×Q8—816no—
857C2×Q8C22×D414yes—
858C2×D4—28no—
859C2×D4—24no—
860C2×D4—28no—
861C2×D4—28no—
862C2×D4—22no—
863C2×D4—24no—
864C2×D4—42no—
865C2×D4—48no—
866C2×D4C22×D418yes—
867C2×D4C22×D414yes—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—216no—
877C22×C4—24no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—24no—
881C22×C4—28no—
882C22×C4—28no—
883C22×C4—28no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4C22×D414yes—
894C22×C4C22×D414yes—
895C22×C4C22×D418yes—
896C22×C4C22×D414yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2512yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2511yescharacteristic
910C22×C4C2512yes—
911C22×C4C2511yescharacteristic
912C22×C4C2512yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2511yescharacteristic
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—24no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—24no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—24no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—28no—
950C4⋊C4—24no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—28no—
960C4⋊C4—216no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—48no—
964C4⋊C4—48no—
965C4⋊C4—48no—
966C4⋊C4—44no—
967C4⋊C4—48no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—48no—
971C4⋊C4C22×D414yes—
972C4⋊C4C22×D414yes—
973C4⋊C4C22×D418yes—
974C4⋊C4C22×D418yes—
975C4⋊C4C22×D418yes—
976C4⋊C4C22×D418yes—
977C22⋊C4—28no—
978C22⋊C4—24no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—28no—
988C22⋊C4—24no—
989C22⋊C4—28no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—28no—
993C22⋊C4—216no—
994C22⋊C4—48no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4C22×D418yes—
1000C22⋊C4C22×D418yes—
1001C22⋊C4C22×D418yes—
1002C22⋊C4C22×D418yes—
1003C22⋊C4C22×D418yes—
1004C42—28no—
1005C42—28no—
1006C42—28no—
1007C42—24no—
1008C42—28no—
1009C42—28no—
1010C42—28no—
1011C42—28no—
1012C42—28no—
1013C42—24no—
1014C42—24no—
1015C42—24no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C42C22×D414yes—
1021C42C22×D414yes—
1022C42C22×D414yes—
1023C42C22×D414yes—
1024C42C22×D418yes—
1025C422−1+418yes—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—22no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23C23×D414yes—
1037C23C23×D412yes—
1038C23#58514yes—
1039C23C2611yescharacteristic
1040Q8—44no—
1041Q8—44no—
1042Q8—48no—
1043Q8—84no—
1044Q8—88no—
1045Q8—84no—
1046Q8—88no—
1047Q8—84no—
1048Q8—88no—
1049D4—216no—
1050D4—44no—
1051D4—48no—
1052D4—44no—
1053D4—88no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—216no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—28no—
1088C2×C4—28no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—28no—
1094C2×C4—28no—
1095C2×C4—24no—
1096C2×C4—44no—
1097C2×C4—416no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—416no—
1101C2×C4—88no—
1102C2×C4—88no—
1103C2×C4—84no—
1104C2×C4—88no—
1105C2×C4—88no—
1106C2×C4C23×D412yes—
1107C2×C4C23×D414yes—
1108C2×C4C23×D414yes—
1109C2×C4C23×D412yes—
1110C2×C4C23×D414yes—
1111C2×C4C23×D412yes—
1112C2×C4C23×D412yes—
1113C2×C4C23×D412yes—
1114C2×C4C23×D412yes—
1115C2×C4C2×2−1+418yes—
1116C2×C4C2×2−1+414yes—
1117C22—22no—
1118C22—22no—
1119C22—28no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—44no—
1124C22—44no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—48no—
1129C22#350014yes—
1130C22C24×D411yescharacteristic
1131C22C22×2−1+412yes—
1132C22C2×#58512yes—
1133C222−1+612yes—
1134C4—22no—
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—24no—
1139C4—22no—
1140C4—22no—
1141C4—24no—
1142C4—28no—
1143C4—42no—
1144C4—44no—
1145C4—44no—
1146C4—44no—
1147C4—44no—
1148C4—42no—
1149C4—42no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4#349914yes—
1156C2—24no—
1157C2—44no—
1158C2—82no—
1159C2C2×#349911yescharacteristic
1160C2C2×#350011yescharacteristic
1161C2#6285911yescharacteristic
1162C2#6292814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3544C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3563C2semidirect
3. #51545C2semidirect
4. #51544C2semidirect
5. #51422C2semidirect
6. #44761C2semidirect
7. #44448C2semidirect
8. #43496C2semidirect
9. #39619C2semidirect
10. #39613C2semidirect
11. #37871C2semidirect
12. #37865C2semidirect
13. #37865C2semidirect
14. #37863C2semidirect
15. #37423C2semidirect
16. #37392C2semidirect
17. #36181C2semidirect
18. #36164C2semidirect
19. #35330C2semidirect
20. #35326C2semidirect
21. #35320C2semidirect
22. #35318C2semidirect
23. #35139C2semidirect
24. C2×#2660C2semidirect
25. #34149C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
C2×#35632
#515452
#515442
#514222
#447612
#444482
#434962
#396192
#396132
#378712
#378652
#378632
#374232
#373922
#361812
#361642
#353302
#353262
#353202
#353182
#351392
C2×#26602
#341492