Finite Group Databasebeta

← #8093403

Subgroups — #8093403

Order 512.

4572 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52766C214yesmaximal, complemented
2#52528C214yesmaximal, complemented
3#52509C214yesmaximal, complemented
4#52508C214yesmaximal, complemented
5#52491C214yesmaximal, complemented
6#52490C214yesmaximal, complemented
7#52473C214yesmaximal, complemented
8#52470C214yesmaximal, complemented
9#52453C212yesmaximal, complemented
10#52432C214yesmaximal, complemented
11#52431C212yesmaximal, complemented
12#52414C212yesmaximal, complemented
13#52413C212yesmaximal, complemented
14#52399C214yesmaximal, complemented
15#35391C211yesmaximal, characteristic, complemented
16#35377C211yesmaximal, characteristic
17#35370C212yesmaximal, complemented
18#35368C212yesmaximal, complemented
19#35360C212yesmaximal
20#35359C212yesmaximal, complemented
21#35349C212yesmaximal, complemented
22C2×#2659C211yesmaximal, characteristic, complemented
23C2×#2643C212yesmaximal, complemented
24C2×#543C2211yescharacteristic
25C2×#534C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C2×#518C2212yes—
29#2844C2212yescomplemented
30#2843C2212yescomplemented
31#2841C2214yescomplemented
32#2839C2214yescomplemented
33#2839C2214yescomplemented
34#2839C2214yescomplemented
35#2838C2214yescomplemented
36#2838C2214yescomplemented
37#2838C2214yescomplemented
38#2838C2214yescomplemented
39#2838C2214yescomplemented
40#2837C2214yescomplemented
41#2836C2214yescomplemented
42#2836C2214yescomplemented
43#2836C2214yescomplemented
44#2835C2214yescomplemented
45#2834C2214yescomplemented
46#2833C2214yescomplemented
47#2833C2214yescomplemented
48#2833C2212yescomplemented
49#2833C2214yescomplemented
50#2832C2212yescomplemented
51#2831C2214yescomplemented
52#2831C2214yescomplemented
53#2831C2214yescomplemented
54#2830C2212yescomplemented
55#2830C2212yescomplemented
56#2827C2214yescomplemented
57#2827C2214yescomplemented
58#2823C2212yescomplemented
59#2822C2212yescomplemented
60#2821C2214yescomplemented
61#2820C2214yescomplemented
62#2817C2214yescomplemented
63#2814C2214yescomplemented
64#2814C2214yescomplemented
65#2805C2214yescomplemented
66#2799C2212yescomplemented
67#2794C2212yescomplemented
68#2793C2214yescomplemented
69#2789C2212yescomplemented
70#2789C2212yescomplemented
71#2787C2214yescomplemented
72#2776C2214yescomplemented
73#2774C2214yescomplemented
74#2773C2214yescomplemented
75#2770C2214yescomplemented
76#2766C2214yescomplemented
77#2765C2214yescomplemented
78#2765C2214yescomplemented
79#2762C2214yescomplemented
80#2759C2214yescomplemented
81#2745C2214yescomplemented
82#2738C2214yescomplemented
83#2729C2214yescomplemented
84#2728C2212yescomplemented
85#2725C2214yescomplemented
86#2724C2212yescomplemented
87#2723C2214yescomplemented
88#2720C2214yescomplemented
89#2717C2214yescomplemented
90#2715C2214yescomplemented
91#2713C2214yescomplemented
92#2707C2214yescomplemented
93#2698C2214yescomplemented
94#2695C2214yescomplemented
95#2690C2214yescomplemented
96#2690C2214yescomplemented
97#2689C2214yescomplemented
98#2683C2212yescomplemented
99#2680C2212yescomplemented
100#2674C2214yescomplemented
101#2659C2214yescomplemented
102#2659C2214yescomplemented
103#2659C2214yescomplemented
104#2659C2214yescomplemented
105#2643C2214yes—
106#2643C2214yes—
107#2643C2214yes—
108#2643C2214yes—
109#2643C2214yescomplemented
110#2643C2214yescomplemented
111#2643C2214yescomplemented
112#2643C2214yescomplemented
113#2591C2212yes—
114#2591C2212yes—
115#2583C2212yescomplemented
116#2583C2212yescomplemented
117#2579C2214yescomplemented
118#2579C2214yescomplemented
119#2569C2214yescomplemented
120#2569C2214yescomplemented
121#2564C2214yes—
122#2564C2214yes—
123#2549C2214yescomplemented
124#2549C2214yescomplemented
125#2510C2214yes—
126#2510C2214yes—
127#2510C2214yescomplemented
128#2510C2214yescomplemented
129#2505C2214yescomplemented
130#2505C2214yescomplemented
131#2505C2214yescomplemented
132#2505C2214yescomplemented
133#2504C2212yes—
134#2502C2212yescomplemented
135#2498C2214yes—
136#2498C2214yes—
137#2493C2214yescomplemented
138#2493C2214yescomplemented
139#2488C2214yes—
140#2488C2214yes—
141#2487C2214yescomplemented
142#2481C2214yes—
143#2481C2214yes—
144#2481C2214yescomplemented
145#2481C2214yescomplemented
146#2480C2214yescomplemented
147#2480C2214yescomplemented
148#2473C2214yescomplemented
149#2473C2214yescomplemented
150#2473C2214yescomplemented
151#2473C2214yescomplemented
152#2472C2214yes—
153#2472C2214yes—
154#2450C2214yes—
155#2450C2214yes—
156#2450C2214yescomplemented
157#2450C2214yescomplemented
158#2449C2214yes—
159#2449C2214yes—
160#2449C2214yescomplemented
161#2449C2214yescomplemented
162#2444C2214yes—
163#2444C2214yes—
164#2443C2214yes—
165#2443C2214yes—
166#2442C2214yescomplemented
167#2442C2214yescomplemented
168#2440C2214yescomplemented
169#2440C2214yescomplemented
170#2438C2214yescomplemented
171#2438C2214yescomplemented
172#2438C2214yescomplemented
173#2438C2214yescomplemented
174#2437C2214yescomplemented
175#2437C2214yescomplemented
176#2437C2214yescomplemented
177#2437C2214yescomplemented
178#2436C2212yes—
179#2434C2212yescomplemented
180#2419C2214yes—
181#2419C2214yes—
182#2418C2214yes—
183#2418C2214yes—
184#2417C2214yes—
185#2417C2214yes—
186#2412C2214yes—
187#2412C2214yes—
188#2409C2214yescomplemented
189C2×#401C2212yescomplemented
190C2×#400C2212yescomplemented
191C2×#400C2212yescomplemented
192C2×#400C2212yescomplemented
193C2×#398C2211yescharacteristic, complemented
194C2×#398C2212yescomplemented
195C2×#398C2211yescharacteristic, complemented
196C2×#397C2212yescomplemented
197C2×#397C2212yescomplemented
198C2×#397C2212yescomplemented
199C2×#396C2212yescomplemented
200C2×#395C2212yescomplemented
201C2×#395C2211yescharacteristic, complemented
202C2×#395C2211yescharacteristic, complemented
203#2315C2212yes—
204#2315C2212yes—
205#2315C2212yes—
206#2308C2212yes—
207#2308C2212yes—
208C2×#386C2212yes—
209C2×#386C2212yes—
210C2×#386C2212yes—
211C2×#385C2212yes—
212C2×#385C2212yes—
213C2×#385C2212yes—
214C2×#380C2212yes—
215C2×#380C2212yes—
216#2273C2211yescharacteristic
217#2273C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2312yes—
222C24×C4C2311yescharacteristic
223C24×C4C2312yes—
224#543—44no—
225#534—44no—
226C2×C4⋊Q8C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#124C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×C22⋊Q8—44no—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#120C2314yes—
252#518—48no—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2314yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
289#401C2314yes—
290#401C2314yes—
291#401C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2312yes—
424#395C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#390C2312yes—
447#390C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#384C2312yes—
557#384C2312yes—
558#383C2314yes—
559#383C2314yes—
560#382C2314yes—
561#382C2312yes—
562#382C2314yes—
563#382C2312yes—
564#381C2314yes—
565#381C2314yes—
566#381C2314yes—
567#381C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#379C2314yes—
587#379C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C2×#95C2312yes—
597C2×#95C2312yes—
598C2×#95C2312yes—
599C2×#95C2312yes—
600C2×#95C2311yescharacteristic
601C2×#95C2312yes—
602C2×#95C2311yescharacteristic
603C2×#95C2312yes—
604C2×#95C2312yes—
605C2×#95C2312yes—
606C2×#95C2312yes—
607C2×#95C2312yes—
608C2×#95C2312yes—
609C2×#95C2312yes—
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2412yes—
620C25C2411yescharacteristic
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8—82no—
624C22×Q8—82no—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2414yes—
630C22×D4—28no—
631C22×D4—28no—
632C22×D4—28no—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C23×C4—24no—
638C23×C4—28no—
639C23×C4—82no—
640C23×C4—82no—
641C23×C4—82no—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C4⋊Q8—84no—
668#126—84no—
669#126—84no—
670#125—84no—
671#125—84no—
672#124—84no—
673#123—48no—
674#123—84no—
675#123—84no—
676C22⋊Q8—48no—
677C22⋊Q8—48no—
678C22⋊Q8—48no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687C22⋊Q8—84no—
688#121—44no—
689#121—44no—
690#120—48no—
691C4×D4—48no—
692C4×D4—48no—
693C4×D4—48no—
694C4×D4—48no—
695#117—48no—
696C2×C4⋊C4—42no—
697C2×C4⋊C4—44no—
698C2×C4⋊C4—42no—
699C2×C4⋊C4—42no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4—82no—
702C2×C4⋊C4—82no—
703C2×C4⋊C4—82no—
704C2×C4⋊C4—82no—
705C2×C4⋊C4—82no—
706C2×C4⋊C4—82no—
707C2×C4⋊C4—82no—
708C2×C4⋊C4—82no—
709C2×C4⋊C4—82no—
710C2×C4⋊C4—82no—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C22⋊C4—28no—
761C2×C22⋊C4—28no—
762C2×C22⋊C4—24no—
763C2×C22⋊C4—24no—
764C2×C22⋊C4—28no—
765C2×C22⋊C4—28no—
766C2×C22⋊C4—48no—
767C2×C22⋊C4—82no—
768C2×C22⋊C4—82no—
769C2×C22⋊C4—82no—
770C2×C22⋊C4—82no—
771C2×C22⋊C4—82no—
772C2×C22⋊C4—82no—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815#95C2411yescharacteristic
816#95C2412yes—
817#95C2412yes—
818#95C2412yes—
819#95C2412yes—
820#95C2412yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2412yes—
824#95C2411yescharacteristic
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2412yes—
858#95C2412yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883C24—24no—
884C24—24no—
885C24—24no—
886C24—42no—
887C24—41no—
888C24—41no—
889C24—42no—
890C24—42no—
891C24—42no—
892C24—42no—
893C24H(5,𝔽2)14yes—
894C242−1+418yes—
895C24C2514yes—
896C24C2512yes—
897C24C2511yescharacteristic
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—44no—
901C2×Q8—44no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—88no—
911C2×Q8—88no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—432no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—24no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—41no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—41no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—41no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—816no—
996C22×C4—88no—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C42—42no—
1101C42—42no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—42no—
1106C42—42no—
1107C42—44no—
1108C23—22no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—21no—
1114C23—22no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—44no—
1123C23—48no—
1124C23—44no—
1125C23—48no—
1126C23—48no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23#563116yes—
1134C23C2×H(5,𝔽2)14yes—
1135C23C2×H(5,𝔽2)12yes—
1136C23C2×2−1+414yes—
1137C23C2×2−1+414yes—
1138C23C2×2−1+414yes—
1139C23C2611yescharacteristic
1140Q8—84no—
1141Q8—84no—
1142Q8—88no—
1143Q8—162no—
1144Q8—162no—
1145D4—416no—
1146D4—416no—
1147D4—162no—
1148D4—162no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—48no—
1206C2×C4—48no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—48no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—82no—
1218C2×C4—82no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—82no—
1227C2×C4—82no—
1228C2×C4—164no—
1229C2×C4—164no—
1230C22—22no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—22no—
1239C22—24no—
1240C22—416no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—168no—
1249C22C2×#56318yes—
1250C22C2×#56314yes—
1251C22C22×H(5,𝔽2)11yescharacteristic
1252C22C22×2−1+412yes—
1253C22H(7,𝔽2)12yes—
1254C22H(7,𝔽2)11yescharacteristic
1255C222−1+611yescharacteristic
1256C4—42no—
1257C4—41no—
1258C4—41no—
1259C4—44no—
1260C4—44no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—42no—
1274C4—42no—
1275C4—44no—
1276C2—28no—
1277C2—24no—
1278C2—84no—
1279C2C22×#56311yescharacteristic
1280C2#6286311yescharacteristic
1281C2#6286412yes—
1282C2#6286512yes—
1283C2#6286611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52766C2semidirect
2. #52528C2semidirect
3. #52509C2semidirect
4. #52508C2semidirect
5. #52491C2semidirect
6. #52490C2semidirect
7. #52473C2semidirect
8. #52470C2semidirect
9. #52453C2semidirect
10. #52432C2semidirect
11. #52431C2semidirect
12. #52414C2semidirect
13. #52413C2semidirect
14. #52399C2semidirect
15. #35391C2semidirect
17. #35370C2semidirect
18. #35368C2semidirect
20. #35359C2semidirect
21. #35349C2semidirect
22. C2×#2659C2semidirect
23. C2×#2643C2semidirect
29. #2844C22semidirect
30. #2843C22semidirect
31. #2841C22semidirect
32. #2839C22semidirect
33. #2839C22semidirect
34. #2839C22semidirect
35. #2838C22semidirect
36. #2838C22semidirect
37. #2838C22semidirect
38. #2838C22semidirect
39. #2838C22semidirect
40. #2837C22semidirect
41. #2836C22semidirect
42. #2836C22semidirect
43. #2836C22semidirect
44. #2835C22semidirect
45. #2834C22semidirect
46. #2833C22semidirect
47. #2833C22semidirect
48. #2833C22semidirect
49. #2833C22semidirect
50. #2832C22semidirect
51. #2831C22semidirect
52. #2831C22semidirect
53. #2831C22semidirect
54. #2830C22semidirect
55. #2830C22semidirect
56. #2827C22semidirect
57. #2827C22semidirect
58. #2823C22semidirect
59. #2822C22semidirect
60. #2821C22semidirect
61. #2820C22semidirect
62. #2817C22semidirect
63. #2814C22semidirect
64. #2814C22semidirect
65. #2805C22semidirect
66. #2799C22semidirect
67. #2794C22semidirect
68. #2793C22semidirect
69. #2789C22semidirect
70. #2789C22semidirect
71. #2787C22semidirect
72. #2776C22semidirect
73. #2774C22semidirect
74. #2773C22semidirect
75. #2770C22semidirect
76. #2766C22semidirect
77. #2765C22semidirect
78. #2765C22semidirect
79. #2762C22semidirect
80. #2759C22semidirect
81. #2745C22semidirect
82. #2738C22semidirect
83. #2729C22semidirect
84. #2728C22semidirect
85. #2725C22semidirect
86. #2724C22semidirect
87. #2723C22semidirect
88. #2720C22semidirect
89. #2717C22semidirect
90. #2715C22semidirect
91. #2713C22semidirect
92. #2707C22semidirect
93. #2698C22semidirect
94. #2695C22semidirect
95. #2690C22semidirect
96. #2690C22semidirect
97. #2689C22semidirect
98. #2683C22semidirect
99. #2680C22semidirect
100. #2674C22semidirect
101. #2659C22semidirect
102. #2659C22semidirect
103. #2659C22semidirect
104. #2659C22semidirect
109. #2643C22semidirect
110. #2643C22semidirect
111. #2643C22semidirect
112. #2643C22semidirect
115. #2583C22semidirect
116. #2583C22semidirect
117. #2579C22semidirect
118. #2579C22semidirect
119. #2569C22semidirect
120. #2569C22semidirect
123. #2549C22semidirect
124. #2549C22semidirect
127. #2510C22semidirect
128. #2510C22semidirect
129. #2505C22semidirect
130. #2505C22semidirect
131. #2505C22semidirect
132. #2505C22semidirect
134. #2502C22semidirect
137. #2493C22semidirect
138. #2493C22semidirect
141. #2487C22semidirect
144. #2481C22semidirect
145. #2481C22semidirect
146. #2480C22semidirect
147. #2480C22semidirect
148. #2473C22semidirect
149. #2473C22semidirect
150. #2473C22semidirect
151. #2473C22semidirect
156. #2450C22semidirect
157. #2450C22semidirect
160. #2449C22semidirect
161. #2449C22semidirect
166. #2442C22semidirect
167. #2442C22semidirect
168. #2440C22semidirect
169. #2440C22semidirect
170. #2438C22semidirect
171. #2438C22semidirect
172. #2438C22semidirect
173. #2438C22semidirect
174. #2437C22semidirect
175. #2437C22semidirect
176. #2437C22semidirect
177. #2437C22semidirect
179. #2434C22semidirect
188. #2409C22semidirect
189. C2×#401C22semidirect
190. C2×#400C22semidirect
191. C2×#400C22semidirect
192. C2×#400C22semidirect
193. C2×#398C22semidirect
194. C2×#398C22semidirect
195. C2×#398C22semidirect
196. C2×#397C22semidirect
197. C2×#397C22semidirect
198. C2×#397C22semidirect
199. C2×#396C22semidirect
200. C2×#395C22semidirect
201. C2×#395C22semidirect
202. C2×#395C22semidirect

Maximal subgroups

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

subgroupindex
#527662
#525282
#525092
#525082
#524912
#524902
#524732
#524702
#524532
#524322
#524312
#524142
#524132
#523992
#353912
#353772
#353702
#353682
#353602
#353592
#353492
C2×#26592
C2×#26432