Finite Group Databasebeta

← #7642940

Subgroups — #7642940

Order 512.

5074 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39977C214yesmaximal, complemented
2#39976C214yesmaximal, complemented
3#39973C214yesmaximal, complemented
4#39972C214yesmaximal, complemented
5#39498C212yesmaximal, complemented
6#39497C212yesmaximal, complemented
7#39370C212yesmaximal, complemented
8#39369C212yesmaximal, complemented
9#38967C212yesmaximal, complemented
10#38966C212yesmaximal, complemented
11#38965C212yesmaximal, complemented
12#38964C212yesmaximal, complemented
13#36750C214yesmaximal, complemented
14#36749C214yesmaximal, complemented
15#36645C211yesmaximal, characteristic, complemented
16#36640C211yesmaximal, characteristic, complemented
17#35585C212yesmaximal, complemented
18#35566C212yesmaximal, complemented
19#35529C212yesmaximal
20#35515C212yesmaximal
21#35253C214yesmaximal, complemented
22#35181C211yesmaximal, characteristic, complemented
23#35167C211yesmaximal, characteristic, complemented
24#35079C214yesmaximal, complemented
25#34186C211yesmaximal, characteristic
26#34181C211yesmaximal, characteristic
27C2×#2293C211yesmaximal, characteristic
28C2×#544C2212yes—
29C2×#544C2214yescomplemented
30C2×#533C2212yes—
31C2×#518C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2212yes—
34#2868C2211yescharacteristic, complemented
35#2868C2211yescharacteristic, complemented
36#2864C2212yescomplemented
37#2864C2212yescomplemented
38#2862C2212yescomplemented
39#2859C2211yescharacteristic, complemented
40#2859C2211yescharacteristic, complemented
41#2859C2211yescharacteristic, complemented
42#2859C2211yescharacteristic, complemented
43#2859C2212yescomplemented
44#2859C2211yescharacteristic, complemented
45#2859C2211yescharacteristic, complemented
46#2857C2212yes—
47#2857C2214yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2851C2212yes—
52#2851C2214yes—
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2807C2218yescomplemented
57#2790C2218yescomplemented
58#2790C2218yescomplemented
59#2788C2218yescomplemented
60#2788C2218yescomplemented
61#2768C2218yescomplemented
62#2768C2218yescomplemented
63#2763C2218yescomplemented
64#2742C2218yescomplemented
65#2729C2218yescomplemented
66#2729C2218yescomplemented
67#2720C2218yescomplemented
68#2720C2218yescomplemented
69#2704C2218yescomplemented
70#2704C2218yescomplemented
71#2677C2218yescomplemented
72#2667C2218yescomplemented
73#2665C2218yescomplemented
74#2659C2214yes—
75#2646C2214yes—
76#2629C2214yescomplemented
77#2629C2214yescomplemented
78#2628C2214yescomplemented
79#2628C2214yescomplemented
80#2584C2214yescomplemented
81#2584C2214yescomplemented
82#2580C2214yes—
83#2580C2214yes—
84#2571C2212yescomplemented
85#2571C2212yescomplemented
86#2570C2214yescomplemented
87#2570C2214yescomplemented
88#2569C2218yes—
89#2567C2214yescomplemented
90#2566C2214yes—
91#2566C2214yes—
92#2563C2214yes—
93#2552C2214yescomplemented
94#2552C2212yescomplemented
95#2552C2212yescomplemented
96#2552C2212yescomplemented
97#2552C2212yescomplemented
98#2551C2214yescomplemented
99#2551C2212yescomplemented
100#2551C2212yescomplemented
101#2550C2214yescomplemented
102#2550C2214yescomplemented
103#2550C2214yescomplemented
104#2550C2214yescomplemented
105#2549C2218yes—
106#2546C2214yescomplemented
107#2542C2214yes—
108#2538C2214yes—
109#2538C2214yes—
110#2509C2214yescomplemented
111#2509C2214yescomplemented
112#2508C2214yescomplemented
113#2508C2214yescomplemented
114#2507C2214yescomplemented
115#2507C2214yescomplemented
116#2506C2214yescomplemented
117#2506C2214yescomplemented
118#2454C2214yes—
119#2454C2214yes—
120#2454C2214yes—
121#2454C2214yes—
122#2452C2214yes—
123#2452C2214yes—
124#2452C2214yes—
125#2452C2214yes—
126#2442C2218yes—
127#2442C2214yescomplemented
128#2442C2214yescomplemented
129#2441C2214yescomplemented
130#2441C2214yescomplemented
131#2441C2218yescomplemented
132#2440C2218yes—
133#2440C2214yescomplemented
134#2440C2214yescomplemented
135#2439C2214yescomplemented
136#2439C2214yescomplemented
137#2439C2218yescomplemented
138#2438C2218yescomplemented
139#2438C2218yescomplemented
140#2437C2218yes—
141#2437C2218yes—
142#2437C2218yes—
143#2437C2218yes—
144#2357C2214yes—
145#2357C2214yes—
146#2354C2212yes—
147#2354C2212yes—
148#2354C2212yes—
149#2354C2212yes—
150#2349C2214yes—
151#2349C2214yes—
152D4×C4⋊C4C2212yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156#2329C2218yescomplemented
157#2329C2218yescomplemented
158#2317C2212yes—
159#2317C2212yes—
160#2317C2214yescomplemented
161#2317C2214yescomplemented
162#2316C2212yes—
163#2316C2212yes—
164#2316C2214yescomplemented
165#2315C2214yes—
166#2312C2214yes—
167#2309C2212yes—
168C4×C4⋊Q8C2212yescomplemented
169C4×C4⋊Q8C2212yescomplemented
170C4×C4⋊Q8C2212yescomplemented
171C4×C4⋊Q8C2212yescomplemented
172C4×#125C2212yescomplemented
173C4×#125C2212yescomplemented
174C4×#125C2212yescomplemented
175C4×#125C2212yescomplemented
176#2296C2212yes—
177#2296C2212yes—
178#2293C2212yes—
179#2293C2212yes—
180#2293C2212yes—
181#2293C2212yes—
182#2293C2212yes—
183#2293C2212yes—
184#2293C2212yes—
185#2293C2212yes—
186C2×#390C2211yescharacteristic
187C2×#390C2211yescharacteristic
188C2×#389C2211yescharacteristic
189C2×#389C2211yescharacteristic
190C2×#388C2212yes—
191C2×#388C2212yes—
192#2285C2212yes—
193#2285C2211yescharacteristic
194#2285C2211yescharacteristic
195#2285C2211yescharacteristic
196#2285C2211yescharacteristic
197#2280C2214yes—
198C2×#380C2214yes—
199#2274C2212yes—
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×C4×C22⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4C2312yes—
205#544—48no—
206#544—416no—
207#533—48no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2318yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235#518—48no—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4Q8116yescomplemented
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×#117—48no—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4C2318yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#390C2312yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2318yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2314yes—
440#385C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2318yes—
448#384C2314yes—
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2314yes—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2312yes—
459#382C2312yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2312yes—
466#382C2312yes—
467#382C2312yes—
468#382C2314yes—
469#382C2314yes—
470#382C2318yes—
471#382C2312yes—
472#382C2312yes—
473#381C2318yes—
474#380C2318yes—
475#380C2318yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2318yes—
480#380C2318yes—
481#380C2312yes—
482#380C2312yes—
483#380C2318yes—
484#380C2318yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2318yes—
493#380C2314yes—
494#380C2314yes—
495#379C2318yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C2×#95C2312yes—
525C2×#95C2318yes—
526C2×#95C2312yes—
527C2×#95C2312yes—
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C25C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2414yes—
539C22×Q8C2418yes—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4C2×Q818yes—
543C22×D4C2412yes—
544C22×D4C2412yes—
545C23×C4—44no—
546C23×C4—44no—
547C23×C4C2×Q8116yes—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2414yes—
553C23×C4C2411yescharacteristic
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2418yes—
557C23×C4C2418yes—
558C23×C4C2411yescharacteristic
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2411yescharacteristic
562C4⋊Q8—28no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566C4⋊Q8—44no—
567C4⋊Q8—48no—
568C4⋊Q8—48no—
569C4⋊Q8—48no—
570C4⋊Q8—44no—
571C4⋊Q8—416no—
572#125—28no—
573#125—44no—
574#125—44no—
575#125—44no—
576#125—44no—
577#125—44no—
578#125—48no—
579#125—48no—
580#125—48no—
581#125—416no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—416no—
585C22⋊Q8—416no—
586C22⋊Q8—416no—
587C22⋊Q8—416no—
588C22⋊Q8—416no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4C2×Q8116yes—
596C4×D4C2×Q8116yes—
597C4×D4C2×Q8116yes—
598C4×D4C2×Q8116yes—
599#117—28no—
600#117—28no—
601#117—28no—
602#117—28no—
603#117—216no—
604#117—48no—
605#117—48no—
606#117—48no—
607#117—48no—
608#117—48no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4C2×Q818yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C22⋊C4—44no—
680C2×C22⋊C4—44no—
681C2×C22⋊C4—44no—
682C2×C22⋊C4—44no—
683C2×C22⋊C4—416no—
684C2×C22⋊C4C2×Q8116yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42—44no—
709C2×C42—42no—
710C2×C42—42no—
711C2×C42—42no—
712C2×C42C2×Q818yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2414yes—
736C2×C42C2418yes—
737C2×C42C2418yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24—24no—
786C24—24no—
787C24—42no—
788C24—42no—
789C24—42no—
790C24—42no—
791C24C22×Q818yes—
792C24C2514yes—
793C24C2511yescharacteristic
794C2×Q8—28no—
795C2×Q8—28no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—48no—
801C2×Q8—48no—
802C2×Q8—48no—
803C2×D4—232no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4C22×Q818yes—
809C2×D4C22×Q818yes—
810C22×C4—22no—
811C22×C4—28no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—432no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—44no—
833C22×C4—42no—
834C22×C4—44no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4C22×Q814yes—
846C22×C4C22×Q8116yes—
847C22×C4C22×Q814yes—
848C22×C4C22×Q818yes—
849C22×C4C22×Q8116yes—
850C22×C4C22×Q814yes—
851C22×C4H(5,𝔽2)14yes—
852C22×C42−1+414yes—
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2511yescharacteristic
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—44no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4C22×Q818yes—
940C4⋊C4C22×Q818yes—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4C22×Q8116yes—
960C22⋊C4C22×Q8116yes—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—22no—
968C42—28no—
969C42—28no—
970C42—28no—
971C42—28no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—28no—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42—22no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—44no—
990C42—48no—
991C42—48no—
992C42C22×Q814yes—
993C42C22×Q814yes—
994C42C22×Q814yes—
995C42C22×Q814yes—
996C42H(5,𝔽2)14yes—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—216no—
1008C23—48no—
1009C23—48no—
1010C23—84no—
1011C23—84no—
1012C23—84no—
1013C23—84no—
1014C23C23×Q818yes—
1015C23C23×Q812yes—
1016C23C2×H(5,𝔽2)12yes—
1017C23C2×2−1+412yes—
1018C23C2611yescharacteristic
1019Q8—88no—
1020Q8—88no—
1021Q8—168no—
1022D4—216no—
1023D4—216no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—24no—
1039C2×C4—21no—
1040C2×C4—28no—
1041C2×C4—232no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
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—416no—
1085C2×C4—48no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—84no—
1092C2×C4—84no—
1093C2×C4—168no—
1094C2×C4—168no—
1095C2×C4#544116yescomplemented
1096C2×C4C23×Q812yes—
1097C2×C4C23×Q812yes—
1098C2×C4C23×Q812yes—
1099C2×C4C23×Q818yes—
1100C2×C4C23×Q812yes—
1101C2×C4C23×Q812yes—
1102C2×C4C23×Q812yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×H(5,𝔽2)12yes—
1107C2×C4C2×H(5,𝔽2)12yes—
1108C2×C4C2×2−1+412yes—
1109C2×C4C2×2−1+412yes—
1110C2×C4#58512yes—
1111C2×C4#58512yes—
1112C2×C4#58512yes—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—28no—
1120C22—28no—
1121C22—28no—
1122C22—44no—
1123C22—44no—
1124C22—44no—
1125C22—44no—
1126C22—816no—
1127C22C2×#54414yes—
1128C22C24×Q811yescharacteristic
1129C22C22×H(5,𝔽2)11yescharacteristic
1130C22C22×H(5,𝔽2)11yescharacteristic
1131C22C22×2−1+411yescharacteristic
1132C22C2×#58511yescharacteristic
1133C22C2×#58511yescharacteristic
1134C22C2×#58511yescharacteristic
1135C4—22no—
1136C4—28no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—41no—
1144C4—44no—
1145C4—44no—
1146C4—44no—
1147C4—44no—
1148C4—41no—
1149C4—41no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—41no—
1156C4—44no—
1157C4C2×#54414yes—
1158C4C2×#54414yes—
1159C4#350114yes—
1160C2—24no—
1161C2—48no—
1162C2C22×#54411yescharacteristic
1163C2C2×#350111yescharacteristic
1164C2#6281311yescharacteristic
1165C2#6283011yescharacteristic
1166C2#6283111yescharacteristic
1167C2#6283411yescharacteristic
1168C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39977C2semidirect
2. #39976C2semidirect
3. #39973C2semidirect
4. #39972C2semidirect
5. #39498C2semidirect
6. #39497C2semidirect
7. #39370C2semidirect
8. #39369C2semidirect
9. #38967C2semidirect
10. #38966C2semidirect
11. #38965C2semidirect
12. #38964C2semidirect
13. #36750C2semidirect
14. #36749C2semidirect
15. #36645C2semidirect
16. #36640C2semidirect
17. #35585C2semidirect
18. #35566C2semidirect
21. #35253C2semidirect
22. #35181C2semidirect
23. #35167C2semidirect
24. #35079C2semidirect
29. C2×#544C22semidirect
34. #2868C22semidirect
35. #2868C22semidirect
36. #2864C22semidirect
37. #2864C22semidirect
38. #2862C22semidirect
39. #2859C22semidirect
40. #2859C22semidirect
41. #2859C22semidirect
42. #2859C22semidirect
43. #2859C22semidirect
44. #2859C22semidirect
45. #2859C22semidirect
56. #2807C22semidirect
57. #2790C22semidirect
58. #2790C22semidirect
59. #2788C22semidirect
60. #2788C22semidirect
61. #2768C22semidirect
62. #2768C22semidirect
63. #2763C22semidirect
64. #2742C22semidirect
65. #2729C22semidirect
66. #2729C22semidirect
67. #2720C22semidirect
68. #2720C22semidirect
69. #2704C22semidirect
70. #2704C22semidirect
71. #2677C22semidirect
72. #2667C22semidirect
73. #2665C22semidirect
76. #2629C22semidirect
77. #2629C22semidirect
78. #2628C22semidirect
79. #2628C22semidirect
80. #2584C22semidirect
81. #2584C22semidirect
84. #2571C22semidirect
85. #2571C22semidirect
86. #2570C22semidirect
87. #2570C22semidirect
89. #2567C22semidirect
93. #2552C22semidirect
94. #2552C22semidirect
95. #2552C22semidirect
96. #2552C22semidirect
97. #2552C22semidirect
98. #2551C22semidirect
99. #2551C22semidirect
100. #2551C22semidirect
101. #2550C22semidirect
102. #2550C22semidirect
103. #2550C22semidirect
104. #2550C22semidirect
106. #2546C22semidirect
110. #2509C22semidirect
111. #2509C22semidirect
112. #2508C22semidirect
113. #2508C22semidirect
114. #2507C22semidirect
115. #2507C22semidirect
116. #2506C22semidirect
117. #2506C22semidirect
127. #2442C22semidirect
128. #2442C22semidirect
129. #2441C22semidirect
130. #2441C22semidirect
131. #2441C22semidirect
133. #2440C22semidirect
134. #2440C22semidirect
135. #2439C22semidirect
136. #2439C22semidirect
137. #2439C22semidirect
138. #2438C22semidirect
139. #2438C22semidirect
156. #2329C22semidirect
157. #2329C22semidirect
160. #2317C22semidirect
161. #2317C22semidirect
164. #2316C22semidirect
168. C4×C4⋊Q8C22semidirect
169. C4×C4⋊Q8C22semidirect
170. C4×C4⋊Q8C22semidirect
171. C4×C4⋊Q8C22semidirect
172. C4×#125C22semidirect
173. C4×#125C22semidirect
174. C4×#125C22semidirect
175. C4×#125C22semidirect
238. C2×C4×D4Q8semidirect
1095. C2×C4#544semidirect

Maximal subgroups

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

subgroupindex
#399772
#399762
#399732
#399722
#394982
#394972
#393702
#393692
#389672
#389662
#389652
#389642
#367502
#367492
#366452
#366402
#355852
#355662
#355292
#355152
#352532
#351812
#351672
#350792
#341862
#341812
C2×#22932