Finite Group Databasebeta

← #7634225

Subgroups — #7634225

Order 512.

4858 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52267C214yesmaximal, complemented
2#52237C214yesmaximal, complemented
3#52237C214yesmaximal, complemented
4#52162C214yesmaximal, complemented
5#36756C214yesmaximal, complemented
6#36755C214yesmaximal, complemented
7#36754C214yesmaximal, complemented
8#36753C214yesmaximal, complemented
9#36752C212yesmaximal, complemented
10#36751C212yesmaximal, complemented
11#36750C212yesmaximal, complemented
12#36749C212yesmaximal, complemented
13#36748C214yesmaximal, complemented
14#36747C214yesmaximal
15#36625C212yesmaximal, complemented
16#34966C212yesmaximal, complemented
17#34958C212yesmaximal, complemented
18#34878C212yesmaximal, complemented
19#34739C212yesmaximal, complemented
20#34578C212yesmaximal, complemented
21#34058C211yesmaximal, characteristic
22#34057C211yesmaximal, characteristic
23C2×#2290C211yesmaximal, characteristic
24C2×#533C2212yescomplemented
25C2×#533C2212yescomplemented
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2857C2212yescomplemented
32#2857C2212yescomplemented
33#2855C2214yescomplemented
34#2855C2214yescomplemented
35#2851C2212yes—
36#2851C2212yes—
37#2851C2212yescomplemented
38#2851C2212yescomplemented
39#2848C2214yes—
40#2848C2214yes—
41#2807C2214yescomplemented
42#2807C2214yescomplemented
43#2806C2214yescomplemented
44#2805C2214yescomplemented
45#2804C2214yes—
46#2802C2214yescomplemented
47#2802C2214yescomplemented
48#2792C2214yescomplemented
49#2792C2214yescomplemented
50#2791C2214yescomplemented
51#2791C2214yescomplemented
52#2790C2214yescomplemented
53#2790C2214yescomplemented
54#2790C2214yescomplemented
55#2790C2214yescomplemented
56#2788C2214yescomplemented
57#2788C2214yescomplemented
58#2788C2214yescomplemented
59#2788C2214yescomplemented
60#2784C2214yes—
61#2784C2214yes—
62#2780C2214yes—
63#2780C2214yes—
64#2780C2214yes—
65#2780C2214yes—
66#2774C2214yescomplemented
67#2774C2214yescomplemented
68#2768C2214yescomplemented
69#2768C2214yescomplemented
70#2768C2214yescomplemented
71#2768C2214yescomplemented
72#2763C2214yescomplemented
73#2763C2214yescomplemented
74#2755C2214yescomplemented
75#2755C2214yescomplemented
76#2748C2214yes—
77#2748C2214yes—
78#2742C2214yescomplemented
79#2742C2214yescomplemented
80#2734C2214yescomplemented
81#2732C2214yes—
82#2732C2214yes—
83#2729C2214yescomplemented
84#2729C2214yescomplemented
85#2729C2214yescomplemented
86#2729C2214yescomplemented
87#2726C2214yescomplemented
88#2720C2214yescomplemented
89#2720C2214yescomplemented
90#2720C2214yescomplemented
91#2720C2214yescomplemented
92#2713C2214yescomplemented
93#2713C2214yescomplemented
94#2704C2214yescomplemented
95#2704C2214yescomplemented
96#2704C2214yescomplemented
97#2704C2214yescomplemented
98#2692C2214yes—
99#2692C2214yes—
100#2692C2214yes—
101#2692C2214yes—
102#2683C2214yes—
103#2677C2214yescomplemented
104#2677C2214yescomplemented
105#2667C2214yescomplemented
106#2667C2214yescomplemented
107#2665C2214yescomplemented
108#2665C2214yescomplemented
109#2659C2212yes—
110#2659C2212yes—
111#2646C2212yes—
112#2646C2212yes—
113#2626C2214yes—
114#2626C2214yes—
115#2612C2214yescomplemented
116#2612C2214yescomplemented
117#2608C2212yescomplemented
118#2608C2212yescomplemented
119#2607C2212yescomplemented
120#2607C2212yescomplemented
121#2606C2214yescomplemented
122#2606C2212yescomplemented
123#2606C2212yescomplemented
124#2605C2214yescomplemented
125#2605C2212yescomplemented
126#2605C2212yescomplemented
127#2570C2214yescomplemented
128#2569C2214yes—
129#2569C2214yes—
130#2569C2214yescomplemented
131#2550C2214yescomplemented
132#2549C2214yes—
133#2549C2214yes—
134#2549C2214yescomplemented
135#2442C2214yes—
136#2442C2214yes—
137#2441C2214yescomplemented
138#2440C2214yes—
139#2440C2214yes—
140#2439C2214yescomplemented
141#2438C2214yes—
142#2438C2214yes—
143#2438C2214yes—
144#2438C2214yes—
145#2438C2214yescomplemented
146#2438C2214yescomplemented
147#2437C2214yes—
148#2437C2214yes—
149#2437C2214yes—
150#2437C2214yes—
151#2402C2212yescomplemented
152#2402C2214yescomplemented
153#2402C2212yescomplemented
154#2399C2212yescomplemented
155#2399C2214yescomplemented
156#2399C2212yescomplemented
157#2396C2214yescomplemented
158#2396C2214yescomplemented
159#2396C2214yescomplemented
160#2396C2214yescomplemented
161#2396C2214yescomplemented
162#2396C2214yescomplemented
163#2396C2214yescomplemented
164#2396C2214yescomplemented
165#2319C2214yes—
166#2319C2214yes—
167#2318C2214yes—
168#2318C2214yes—
169#2316C2212yes—
170#2315C2212yes—
171#2313C2211yescharacteristic
172#2313C2211yescharacteristic
173#2312C2212yes—
174#2312C2212yes—
175#2312C2211yescharacteristic
176#2312C2211yescharacteristic
177#2309C2212yes—
178#2308C2212yes—
179C4×C4⋊Q8C2214yescomplemented
180C4×#125C2214yescomplemented
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×C22⋊Q8C2214yescomplemented
186C4×C22⋊Q8C2214yescomplemented
187C4×C22⋊Q8C2214yescomplemented
188C4×C22⋊Q8C2214yescomplemented
189#2296C2212yescomplemented
190#2296C2212yescomplemented
191#2296C2212yescomplemented
192#2296C2212yescomplemented
193#2295C2214yescomplemented
194#2295C2214yescomplemented
195#2293C2214yes—
196#2293C2214yes—
197#2290C2214yes—
198#2290C2214yes—
199#2290C2214yes—
200#2290C2214yes—
201#2290C2214yes—
202#2290C2214yes—
203C2×#388C2212yes—
204C2×#387C2212yes—
205C2×#386C2212yes—
206C2×#385C2212yes—
207#2285C2212yescomplemented
208#2285C2212yescomplemented
209#2283C2212yes—
210#2280C2212yes—
211#2280C2212yes—
212#2280C2212yes—
213C4×#117C2212yes—
214C2×C4×C4⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2212yes—
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C24×C4C2312yes—
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223#533—48no—
224#533—48no—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×#125C2314yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4Q8116yescomplemented
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×#117—44no—
253C2×#117C2312yes—
254C2×#117C2314yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C42—44no—
273C22×C42C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284C22×C42C2311yescharacteristic
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#384C2314yes—
526#384C2312yes—
527#384C2312yes—
528#384C2314yes—
529#383C2312yes—
530#383C2312yes—
531#382C2314yes—
532#382C2314yes—
533#382C2312yes—
534#382C2312yes—
535#382C2314yes—
536#381C2312yes—
537#381C2312yes—
538#381C2314yes—
539#381C2314yes—
540#381C2312yes—
541#381C2312yes—
542#380C2314yes—
543#380C2314yes—
544#380C2312yes—
545#380C2312yes—
546#380C2312yes—
547#380C2312yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2312yes—
555#380C2312yes—
556#380C2312yes—
557#380C2312yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#379C2314yes—
566#379C2314yes—
567#379C2312yes—
568#379C2312yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606#376C2312yes—
607#376C2312yes—
608#376C2314yes—
609#376C2312yes—
610#376C2314yes—
611#376C2312yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2314yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C43C2314yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C22×Q8C2414yes—
622C22×Q8C2414yes—
623C22×Q8C2414yes—
624C22×Q8C2414yes—
625C22×D4—44no—
626C22×D4C2×Q818yes—
627C22×D4C2414yes—
628C23×C4—42no—
629C23×C4—42no—
630C23×C4—42no—
631C23×C4—44no—
632C23×C4—42no—
633C23×C4—44no—
634C23×C4—44no—
635C23×C4C2×Q818yes—
636C23×C4C2×Q818yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2412yes—
656C4⋊Q8—44no—
657C4⋊Q8—44no—
658C4⋊Q8—48no—
659C4⋊Q8—48no—
660#125—44no—
661#125—44no—
662#125—48no—
663#125—48no—
664C22⋊Q8—48no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668C22⋊Q8—48no—
669C22⋊Q8—48no—
670C22⋊Q8—48no—
671C22⋊Q8—48no—
672C22⋊Q8—48no—
673C22⋊Q8—48no—
674C22⋊Q8—48no—
675C22⋊Q8—48no—
676C4×Q8—216no—
677C4×Q8—48no—
678C4×Q8—48no—
679C4×Q8—48no—
680C4×D4C2×Q8132yes—
681C4×D4C2×Q8132yes—
682#117—28no—
683#117—44no—
684#117—44no—
685#117—44no—
686#117—44no—
687#117—44no—
688#117—44no—
689#117—44no—
690#117—48no—
691#117—48no—
692C2×C4⋊C4—44no—
693C2×C4⋊C4—44no—
694C2×C4⋊C4C2×Q818yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C22⋊C4—44no—
751C2×C22⋊C4—44no—
752C2×C22⋊C4—48no—
753C2×C22⋊C4—44no—
754C2×C22⋊C4C2×Q818yes—
755C2×C22⋊C4C2×Q818yes—
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⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
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×C42—24no—
785C2×C42—28no—
786C2×C42—42no—
787C2×C42—44no—
788C2×C42—44no—
789C2×C42—44no—
790C2×C42—44no—
791C2×C42—42no—
792C2×C42—44no—
793C2×C42—44no—
794C2×C42—42no—
795C2×C42C2×Q818yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2414yes—
802C2×C42C2411yescharacteristic
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824#95C2414yes—
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#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
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#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882C24—24no—
883C24—24no—
884C24—41no—
885C24—41no—
886C24—42no—
887C24—41no—
888C24—42no—
889C24—41no—
890C24C22×Q814yes—
891C24C22×Q814yes—
892C24C2512yes—
893C24C2512yes—
894C24C2511yescharacteristic
895C2×Q8—28no—
896C2×Q8—28no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—44no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—44no—
906C2×Q8—44no—
907C2×D4—416no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4C22×Q8116yes—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—416no—
929C22×C4—416no—
930C22×C4—42no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—41no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—41no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—41no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—432no—
960C22×C4C22×Q814yes—
961C22×C4C22×Q814yes—
962C22×C4C22×Q818yes—
963C22×C4C22×Q818yes—
964C22×C4C22×Q814yes—
965C22×C4C22×Q814yes—
966C22×C4C22×Q814yes—
967C22×C4C22×Q818yes—
968C22×C4C22×Q818yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2511yescharacteristic
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
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⋊C4C22×Q8116yes—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—42no—
1058C22⋊C4—44no—
1059C22⋊C4—42no—
1060C22⋊C4—44no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—42no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4C22×Q8116yes—
1071C22⋊C4C22×Q8116yes—
1072C42—24no—
1073C42—22no—
1074C42—24no—
1075C42—24no—
1076C42—24no—
1077C42—24no—
1078C42—28no—
1079C42—28no—
1080C42—28no—
1081C42—24no—
1082C42—28no—
1083C42—41no—
1084C42—41no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42C22×Q818yes—
1098C42C22×Q818yes—
1099C42H(5,𝔽2)14yes—
1100C23—21no—
1101C23—22no—
1102C23—21no—
1103C23—22no—
1104C23—22no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—24no—
1113C23—28no—
1114C23—28no—
1115C23—44no—
1116C23—44no—
1117C23—44no—
1118C23—44no—
1119C23—48no—
1120C23—48no—
1121C23—84no—
1122C23—84no—
1123C23C23×Q814yes—
1124C23C23×Q814yes—
1125C23C23×Q812yes—
1126C23#58514yes—
1127C23C2611yescharacteristic
1128Q8—88no—
1129Q8—88no—
1130Q8—88no—
1131Q8—88no—
1132D4—416no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—28no—
1146C2×C4—28no—
1147C2×C4—216no—
1148C2×C4—216no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—48no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—48no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4C23×Q814yes—
1201C2×C4C23×Q814yes—
1202C2×C4C23×Q812yes—
1203C2×C4C23×Q814yes—
1204C2×C4C23×Q814yes—
1205C2×C4C23×Q812yes—
1206C2×C4C2×H(5,𝔽2)14yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4#58514yes—
1209C2×C4#58512yes—
1210C22—24no—
1211C22—24no—
1212C22—22no—
1213C22—22no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—416no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—88no—
1228C22#345814yes—
1229C22C24×Q811yescharacteristic
1230C22C22×H(5,𝔽2)11yescharacteristic
1231C22C2×#58512yes—
1232C22C2×#58512yes—
1233C22C2×#58511yescharacteristic
1234C4—24no—
1235C4—24no—
1236C4—22no—
1237C4—24no—
1238C4—24no—
1239C4—24no—
1240C4—24no—
1241C4—42no—
1242C4—42no—
1243C4—44no—
1244C4—44no—
1245C4—44no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C4#350114yes—
1254C2—24no—
1255C2—44no—
1256C2—44no—
1257C2C2×#345811yescharacteristic
1258C2#6272912yes—
1259C2#6274312yes—
1260C2C2×#350111yescharacteristic
1261C2#6281311yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52267C2semidirect
2. #52237C2semidirect
3. #52237C2semidirect
4. #52162C2semidirect
5. #36756C2semidirect
6. #36755C2semidirect
7. #36754C2semidirect
8. #36753C2semidirect
9. #36752C2semidirect
10. #36751C2semidirect
11. #36750C2semidirect
12. #36749C2semidirect
13. #36748C2semidirect
15. #36625C2semidirect
16. #34966C2semidirect
17. #34958C2semidirect
18. #34878C2semidirect
19. #34739C2semidirect
20. #34578C2semidirect
24. C2×#533C22semidirect
25. C2×#533C22semidirect
31. #2857C22semidirect
32. #2857C22semidirect
33. #2855C22semidirect
34. #2855C22semidirect
37. #2851C22semidirect
38. #2851C22semidirect
41. #2807C22semidirect
42. #2807C22semidirect
43. #2806C22semidirect
44. #2805C22semidirect
46. #2802C22semidirect
47. #2802C22semidirect
48. #2792C22semidirect
49. #2792C22semidirect
50. #2791C22semidirect
51. #2791C22semidirect
52. #2790C22semidirect
53. #2790C22semidirect
54. #2790C22semidirect
55. #2790C22semidirect
56. #2788C22semidirect
57. #2788C22semidirect
58. #2788C22semidirect
59. #2788C22semidirect
66. #2774C22semidirect
67. #2774C22semidirect
68. #2768C22semidirect
69. #2768C22semidirect
70. #2768C22semidirect
71. #2768C22semidirect
72. #2763C22semidirect
73. #2763C22semidirect
74. #2755C22semidirect
75. #2755C22semidirect
78. #2742C22semidirect
79. #2742C22semidirect
80. #2734C22semidirect
83. #2729C22semidirect
84. #2729C22semidirect
85. #2729C22semidirect
86. #2729C22semidirect
87. #2726C22semidirect
88. #2720C22semidirect
89. #2720C22semidirect
90. #2720C22semidirect
91. #2720C22semidirect
92. #2713C22semidirect
93. #2713C22semidirect
94. #2704C22semidirect
95. #2704C22semidirect
96. #2704C22semidirect
97. #2704C22semidirect
103. #2677C22semidirect
104. #2677C22semidirect
105. #2667C22semidirect
106. #2667C22semidirect
107. #2665C22semidirect
108. #2665C22semidirect
115. #2612C22semidirect
116. #2612C22semidirect
117. #2608C22semidirect
118. #2608C22semidirect
119. #2607C22semidirect
120. #2607C22semidirect
121. #2606C22semidirect
122. #2606C22semidirect
123. #2606C22semidirect
124. #2605C22semidirect
125. #2605C22semidirect
126. #2605C22semidirect
127. #2570C22semidirect
130. #2569C22semidirect
131. #2550C22semidirect
134. #2549C22semidirect
137. #2441C22semidirect
140. #2439C22semidirect
145. #2438C22semidirect
146. #2438C22semidirect
151. #2402C22semidirect
152. #2402C22semidirect
153. #2402C22semidirect
154. #2399C22semidirect
155. #2399C22semidirect
156. #2399C22semidirect
157. #2396C22semidirect
158. #2396C22semidirect
159. #2396C22semidirect
160. #2396C22semidirect
161. #2396C22semidirect
162. #2396C22semidirect
163. #2396C22semidirect
164. #2396C22semidirect
179. C4×C4⋊Q8C22semidirect
180. C4×#125C22semidirect
185. C4×C22⋊Q8C22semidirect
186. C4×C22⋊Q8C22semidirect
187. C4×C22⋊Q8C22semidirect
188. C4×C22⋊Q8C22semidirect
189. #2296C22semidirect
190. #2296C22semidirect
191. #2296C22semidirect
192. #2296C22semidirect
193. #2295C22semidirect
194. #2295C22semidirect
207. #2285C22semidirect
208. #2285C22semidirect
249. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#522672
#522372
#521622
#367562
#367552
#367542
#367532
#367522
#367512
#367502
#367492
#367482
#367472
#366252
#349662
#349582
#348782
#347392
#345782
#340582
#340572
C2×#22902