Finite Group Databasebeta

← #7715425

Subgroups — #7715425

Order 512.

6392 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic
2C2×#3563C211yesmaximal, characteristic, complemented
3#51209C214yesmaximal, complemented
4#50895C214yesmaximal, complemented
5#48832C218yesmaximal, complemented
6#47722C218yesmaximal, complemented
7#46426C214yesmaximal, complemented
8#46358C214yesmaximal, complemented
9#39616C212yesmaximal, complemented
10#39613C212yesmaximal, complemented
11#39489C212yesmaximal, complemented
12#39485C212yesmaximal, complemented
13#37871C212yesmaximal, complemented
14#37871C212yesmaximal, complemented
15#37863C212yesmaximal, complemented
16#37862C212yesmaximal, complemented
17#37635C211yesmaximal, characteristic, complemented
18#37539C211yesmaximal, characteristic, complemented
19#37392C212yesmaximal, complemented
20#37304C212yesmaximal, complemented
21#35335C211yesmaximal, characteristic, complemented
22#35332C212yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35275C212yesmaximal, complemented
25#34081C211yesmaximal, characteristic, complemented
26#3563—216no—
27#3547—216no—
28C2×#564C2212yes—
29C2×#563C2212yes—
30C2×#562C2214yes—
31C2×#557C2212yes—
32C2×#555C2212yes—
33C2×#555C2211yescharacteristic
34C2×#554C2212yes—
35C2×#554C2211yescharacteristic
36C2×#553C2212yes—
37C2×#552C2212yes—
38C2×#552C2214yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×D4×Q8C2211yescharacteristic
42C2×#548C2212yes—
43C2×#547C2211yescharacteristic
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#544C2212yes—
47C2×#542C2214yes—
48C2×#541C2212yes—
49C2×#541C2214yes—
50C2×#540C2212yes—
51C2×#539C2212yes—
52C2×#537C2212yes—
53C2×#536C2212yes—
54C2×#533C2211yescharacteristic
55C2×#533C2211yescharacteristic
56C2×#532C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic
59#2868C2212yes—
60#2868C2211yescharacteristic
61#2862C2211yescharacteristic
62#2859C2212yes—
63#2859C2212yes—
64#2859C2212yes—
65#2858C2211yescharacteristic
66#2858C2211yescharacteristic
67#2850C2212yes—
68#2850C2212yes—
69#2820C2214yes—
70#2817C2214yes—
71#2729C2218yes—
72#2725C2218yes—
73#2721C2218yes—
74#2720C2218yes—
75#2720C2218yes—
76#2720C2218yes—
77#2719C2218yes—
78#2718C2218yes—
79#2715C2218yes—
80#2715C2218yes—
81#2713C2218yes—
82#2708C2218yes—
83#2708C2218yes—
84#2704C2218yes—
85#2701C2218yes—
86#2698C2218yes—
87#2694C2218yes—
88#2689C2218yes—
89#2681C2218yes—
90#2680C2218yes—
91#2674C2218yes—
92#2674C2218yes—
93#2674C2218yes—
94#2672C2218yes—
95#2660C2212yes—
96#2660C2212yes—
97#2660C2212yes—
98#2660C2212yes—
99#2660C2212yes—
100#2660C2212yes—
101#2642C2212yes—
102#2641C2212yes—
103#2634C2214yes—
104#2633C2214yes—
105#2625C2214yes—
106#2620C2212yes—
107#2620C2212yes—
108#2620C2212yes—
109#2620C2212yes—
110#2618C2214yes—
111#2584C2214yes—
112#2584C2214yes—
113#2583C2214yes—
114#2583C2214yes—
115#2581C2214yes—
116#2568C2212yes—
117#2568C2212yes—
118#2567C2212yes—
119#2567C2212yes—
120#2566C2214yes—
121#2566C2212yes—
122#2566C2212yes—
123#2566C2212yes—
124#2566C2212yes—
125#2565C2212yes—
126#2565C2212yes—
127#2563C2212yes—
128#2559C2218yes—
129#2559C2218yes—
130#2558C2218yes—
131#2558C2218yes—
132#2552C2218yes—
133#2551C2218yes—
134#2545C2214yes—
135#2542C2212yes—
136#2504C2211yescharacteristic
137#2504C2211yescharacteristic
138#2504C2212yes—
139#2503C2212yes—
140#2502C2212yes—
141#2501C2211yescharacteristic
142#2501C2212yes—
143#2501C2211yescharacteristic
144#2500C2212yes—
145#2500C2212yes—
146#2500C2214yes—
147#2499C2212yes—
148#2499C2212yes—
149#2499C2212yes—
150#2499C2212yes—
151#2475C2218yes—
152#2475C2218yes—
153#2474C2218yes—
154#2474C2218yes—
155#2473C2218yes—
156#2470C2218yes—
157#2466C2218yes—
158#2465C2218yes—
159#2449C2218yes—
160#2443C2218yes—
161#2441C2218yes—
162#2440C2218yes—
163#2440C2218yes—
164#2434C2218yes—
165#2432C2214yes—
166#2429C2218yes—
167#2422C2218yes—
168#2413C2218yes—
169#2406C2218yes—
170#2406C2214yes—
171#2337C2212yes—
172#2336C2212yes—
173#2335C2214yes—
174#2334C2214yes—
175#2333C2212yes—
176#2332C2212yes—
177#2326C2212yes—
178#2326C2212yes—
179#2326C2212yes—
180#2326C2212yes—
181#2317C2212yes—
182#2317C2212yes—
183#2317C2212yes—
184#2317C2212yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187#2298C2212yes—
188#2295C2212yes—
189#2293C2212yes—
190#2290C2212yes—
191#2290C2212yes—
192#2285C2212yes—
193C2×#384C2212yes—
194#2283C2211yescharacteristic
195C4×#117C2212yes—
196C4×#117C2211yescharacteristic
197C22×#41C2312yes—
198C22×#41C2312yes—
199C23×Q8C2312yes—
200#564—216no—
201#563—216no—
202#562—232no—
203#557—216no—
204#555—216no—
205#555—28no—
206#554—28no—
207#554—216no—
208#553—216no—
209#552—216no—
210#552—232no—
211#552—216no—
212#552—216no—
213D4×Q8—28no—
214#548—216no—
215#547—28no—
216#544—216no—
217#544—216no—
218#544—216no—
219#542—232no—
220#541—232no—
221#541—216no—
222#540—216no—
223#539—216no—
224#537—216no—
225#536—216no—
226#533—28no—
227#533—28no—
228#532—28no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2318yes—
240C2×C4⋊Q8C2314yes—
241C2×#127C2311yescharacteristic
242#529D4116yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2312yes—
249C2×#125—28no—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#125C2311yescharacteristic
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#124C2311yescharacteristic
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2318yes—
285C2×#123C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2318yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×#121C2311yescharacteristic
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2318yes—
352C22×C42C2312yes—
353C22×C42C2311yescharacteristic
354#400C2318yes—
355#400C2318yes—
356#400C2318yes—
357#400C2318yes—
358#400C2318yes—
359#399C2314yes—
360#399C2314yes—
361#399C2318yes—
362#399C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#397C2318yes—
373#397C2318yes—
374#397C2314yes—
375#397C2314yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#396C2318yes—
383#396C2318yes—
384#396C2318yes—
385#396C2318yes—
386#396C2318yes—
387#395C2318yes—
388#395C2318yes—
389#395C2318yes—
390#395C2318yes—
391#395C2318yes—
392#395C2318yes—
393#395C2318yes—
394#395C2318yes—
395#394C2318yes—
396#394C2318yes—
397#394C2318yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#393C2318yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2318yes—
411#391C2318yes—
412#391C2314yes—
413#391C2314yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#389C2318yes—
425#389C2318yes—
426#389C2318yes—
427#389C2318yes—
428#389C2318yes—
429#389C2318yes—
430#389C2318yes—
431#389C2318yes—
432#389C2318yes—
433#389C2318yes—
434#389C2314yes—
435#389C2314yes—
436#389C2318yes—
437#389C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2318yes—
465#387C2318yes—
466#386C2314yes—
467#386C2314yes—
468#386C2318yes—
469#386C2318yes—
470#386C2314yes—
471#386C2314yes—
472#386C2318yes—
473#385C2318yes—
474#385C2318yes—
475#385C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2314yes—
486#385C2314yes—
487#385C2318yes—
488#384C2312yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#384C2314yes—
493#384C2312yes—
494#384C2312yes—
495#384C2312yes—
496#384C2312yes—
497#384C2312yes—
498#384C2312yes—
499#384C2318yes—
500#384C2318yes—
501#383C2312yes—
502#382C2312yes—
503#382C2312yes—
504#382C2312yes—
505#382C2312yes—
506#382C2312yes—
507#382C2312yes—
508#382C2312yes—
509#382C2314yes—
510#382C2312yes—
511#382C2312yes—
512#381C2312yes—
513#381C2318yes—
514#380C2318yes—
515#380C2312yes—
516#380C2318yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2318yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2318yes—
530C4×C22⋊C4C2318yes—
531C4×C22⋊C4C2311yescharacteristic
532C4×C22⋊C4C2311yescharacteristic
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2312yes—
535#376C2312yes—
536#376C2312yes—
537#376C2312yes—
538C43C2311yescharacteristic
539C43C2311yescharacteristic
540C43C2312yes—
541C2×#41—28no—
542C2×#41—28no—
543C2×#41—84no—
544C2×#41—84no—
545C22×Q8—28no—
546C22×Q8—84no—
547C22×Q8C2412yes—
548C22×Q8C2414yes—
549C22×Q8C2412yes—
550C22×Q8C2412yes—
551C22×Q8C2412yes—
552C22×Q8C2414yes—
553C22×Q8C2412yes—
554C22×Q8C2411yescharacteristic
555C22×D4C2411yescharacteristic
556C22×D4C2411yescharacteristic
557C22×D4C2414yes—
558C22×D4C2412yes—
559C22×D4C2412yes—
560C22×D4C2414yes—
561C22×D4C2412yes—
562C22×D4C2412yes—
563C22×D4C2412yes—
564C22×D4C2411yescharacteristic
565C23×C4C2412yes—
566C23×C4C2411yescharacteristic
567C23×C4C2412yes—
568C23×C4C2414yes—
569C23×C4C2412yes—
570C23×C4C2414yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2414yes—
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C4⋊Q8—216no—
579C4⋊Q8—216no—
580C4⋊Q8—216no—
581C4⋊Q8—24no—
582C4⋊Q8—24no—
583C4⋊Q8—24no—
584C4⋊Q8—24no—
585C4⋊Q8—24no—
586C4⋊Q8—28no—
587C4⋊Q8—28no—
588C4⋊Q8—84no—
589C4⋊Q8—88no—
590#127—24no—
591#126—216no—
592#126—216no—
593#126—216no—
594#126—216no—
595#126—216no—
596#126C2×D4116yes—
597#125—216no—
598#125—216no—
599#125—216no—
600#125—216no—
601#125—216no—
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—28no—
611#125—28no—
612#125—28no—
613#125—28no—
614#125C2×D418yes—
615#124—216no—
616#124—216no—
617#124—216no—
618#124—28no—
619#124—28no—
620#124—28no—
621#124—84no—
622#124C2×D418yes—
623#123—216no—
624#123—216no—
625#123—216no—
626#123—216no—
627#123—216no—
628#123—216no—
629#123—84no—
630#123—84no—
631#123—88no—
632#123C2×D4116yes—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—88no—
651C22⋊Q8C2×D418yes—
652#121—28no—
653#121—216no—
654#121—216no—
655#121—24no—
656#121—24no—
657#121—28no—
658#121—28no—
659#121—28no—
660#121—216no—
661#121—216no—
662#121C2×D418yes—
663C4×Q8—216no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8C2×D418yes—
671C4×D4—216no—
672C4×D4—216no—
673C4×D4—24no—
674C4×D4—28no—
675C4×D4—24no—
676C4×D4—28no—
677C4×D4—28no—
678C4×D4C2×D418yes—
679C4×D4C2×D4116yes—
680#117—28no—
681#117—28no—
682#117—28no—
683#117—28no—
684#117—28no—
685#117—216no—
686#117—216no—
687#117—216no—
688#117—28no—
689#117—28no—
690#117C2×D4116yes—
691C2×C4⋊C4—28no—
692C2×C4⋊C4—24no—
693C2×C4⋊C4—28no—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—28no—
696C2×C4⋊C4—28no—
697C2×C4⋊C4—28no—
698C2×C4⋊C4—88no—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2418yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2418yes—
743C2×C4⋊C4C2418yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2418yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C42—28no—
789C2×C42C2×D418yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806C2×C42C2411yescharacteristic
807C2×C42C2412yes—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2418yes—
819#95C2412yes—
820#95C2412yes—
821#95C2418yes—
822#95C2418yes—
823#95C2414yes—
824#95C2414yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839C24C2512yes—
840C24C2512yes—
841C24C2511yescharacteristic
842C24C2512yes—
843#41—816no—
844#41—816no—
845C2×Q8—24no—
846C2×Q8—24no—
847C2×Q8—24no—
848C2×Q8—24no—
849C2×Q8—28no—
850C2×Q8—28no—
851C2×Q8—24no—
852C2×Q8—24no—
853C2×Q8—24no—
854C2×Q8—42no—
855C2×Q8—44no—
856C2×Q8—48no—
857C2×Q8—44no—
858C2×Q8—48no—
859C2×Q8—44no—
860C2×Q8—44no—
861C2×Q8—816no—
862C2×Q8C22×D414yes—
863C2×D4—28no—
864C2×D4—24no—
865C2×D4—28no—
866C2×D4—24no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—24no—
872C2×D4—24no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—44no—
876C2×D4—48no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—48no—
881C2×D4C22×D418yes—
882C2×D4C22×D414yes—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—28no—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—28no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—42no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—42no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—48no—
907C22×C4C22×D414yes—
908C22×C4C22×D418yes—
909C22×C4C22×D414yes—
910C22×C4C22×D414yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2511yescharacteristic
923C22×C4C2512yes—
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2512yes—
929C22×C4C2512yes—
930C22×C4C2514yes—
931C22×C4C2511yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—24no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—48no—
977C4⋊C4—44no—
978C4⋊C4—48no—
979C4⋊C4—48no—
980C4⋊C4—48no—
981C4⋊C4—48no—
982C4⋊C4C22×D414yes—
983C4⋊C4C22×D414yes—
984C4⋊C4C22×D418yes—
985C4⋊C4C22×D418yes—
986C4⋊C4C22×D418yes—
987C4⋊C4C22×D418yes—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—24no—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—24no—
998C22⋊C4—28no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—24no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—216no—
1005C22⋊C4—216no—
1006C22⋊C4—48no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—44no—
1012C22⋊C4—42no—
1013C22⋊C4—48no—
1014C22⋊C4—42no—
1015C22⋊C4—48no—
1016C22⋊C4C22×D418yes—
1017C22⋊C4C22×D418yes—
1018C22⋊C4C22×D418yes—
1019C22⋊C4C22×D418yes—
1020C22⋊C4C22×D418yes—
1021C42—28no—
1022C42—28no—
1023C42—28no—
1024C42—28no—
1025C42—28no—
1026C42—28no—
1027C42—28no—
1028C42—24no—
1029C42—24no—
1030C42—24no—
1031C42—42no—
1032C42—44no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—44no—
1037C42C22×D414yes—
1038C42C22×D414yes—
1039C42C22×D414yes—
1040C42C22×D414yes—
1041C42C22×D418yes—
1042C422−1+418yes—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—24no—
1048C23—24no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23C23×D414yes—
1059C23C23×D412yes—
1060C23C2611yescharacteristic
1061Q8—44no—
1062Q8—48no—
1063Q8—48no—
1064Q8—84no—
1065Q8—88no—
1066Q8—84no—
1067Q8—88no—
1068Q8—84no—
1069D4—48no—
1070D4—44no—
1071D4—44no—
1072D4—44no—
1073D4—84no—
1074D4—84no—
1075D4—88no—
1076D4—84no—
1077D4—84no—
1078D4—88no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—216no—
1091C2×C4—28no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—28no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—28no—
1117C2×C4—28no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—416no—
1121C2×C4—48no—
1122C2×C4—48no—
1123C2×C4—48no—
1124C2×C4—88no—
1125C2×C4—88no—
1126C2×C4—84no—
1127C2×C4—88no—
1128C2×C4—88no—
1129C2×C4C23×D412yes—
1130C2×C4C23×D412yes—
1131C2×C4C23×D414yes—
1132C2×C4C23×D414yes—
1133C2×C4C23×D414yes—
1134C2×C4C23×D412yes—
1135C2×C4C23×D412yes—
1136C2×C4C23×D412yes—
1137C2×C4C23×D412yes—
1138C2×C4C2×2−1+418yes—
1139C2×C4C2×2−1+414yes—
1140C22—22no—
1141C22—24no—
1142C22—22no—
1143C22—24no—
1144C22—22no—
1145C22—24no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—48no—
1156C22—48no—
1157C22C24×D411yescharacteristic
1158C22C22×2−1+412yes—
1159C22H(7,𝔽2)12yes—
1160C222−1+612yes—
1161C4—24no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—24no—
1166C4—22no—
1167C4—22no—
1168C4—24no—
1169C4—28no—
1170C4—44no—
1171C4—42no—
1172C4—42no—
1173C4—44no—
1174C4—44no—
1175C4—44no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4—44no—
1180C4—44no—
1181C4#349914yes—
1182C2—42no—
1183C2—44no—
1184C2—82no—
1185C2—82no—
1186C2C2×#349911yescharacteristic
1187C2#6285211yescharacteristic
1188C2#6285911yescharacteristic
1189C2#6287714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3547C2
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. #51209C2semidirect
4. #50895C2semidirect
5. #48832C2semidirect
6. #47722C2semidirect
7. #46426C2semidirect
8. #46358C2semidirect
9. #39616C2semidirect
10. #39613C2semidirect
11. #39489C2semidirect
12. #39485C2semidirect
13. #37871C2semidirect
14. #37871C2semidirect
15. #37863C2semidirect
16. #37862C2semidirect
17. #37635C2semidirect
18. #37539C2semidirect
19. #37392C2semidirect
20. #37304C2semidirect
21. #35335C2semidirect
22. #35332C2semidirect
23. #35298C2semidirect
24. #35275C2semidirect
25. #34081C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
C2×#35632
#512092
#508952
#488322
#477222
#464262
#463582
#396162
#396132
#394892
#394852
#378712
#378632
#378622
#376352
#375392
#373922
#373042
#353352
#353322
#352982
#352752
#340812