Finite Group Databasebeta

← #7679810

Subgroups — #7679810

Order 512.

5030 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C214yesmaximal
2#59642C212yesmaximal, complemented
3#59639C212yesmaximal, complemented
4#59451C212yesmaximal, complemented
5#59450C212yesmaximal, complemented
6#59329C214yesmaximal, complemented
7#45222C214yesmaximal, complemented
8#45201C214yesmaximal, complemented
9#43598C218yesmaximal, complemented
10#39274C214yesmaximal, complemented
11#39271C214yesmaximal, complemented
12#39203C212yesmaximal, complemented
13#39200C212yesmaximal, complemented
14#36476C212yesmaximal, complemented
15#36454C212yesmaximal, complemented
16#35672C212yesmaximal, complemented
17#35644C212yesmaximal, complemented
18#35320C211yesmaximal, characteristic, complemented
19#35311C212yesmaximal, complemented
20#34946C211yesmaximal, characteristic
21C2×#2542C211yesmaximal, characteristic
22#34213C211yesmaximal, characteristic, complemented
23#34209C211yesmaximal, characteristic, complemented
24#34203C212yesmaximal, complemented
25D4×#117C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic, complemented
27C2×#544C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2212yes—
31C22×C22⋊Q8C2212yes—
32C2×#519C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×#117C2212yes—
35#2862C2212yescomplemented
36#2862C2212yescomplemented
37#2855C2214yescomplemented
38#2855C2214yescomplemented
39#2807C2218yescomplemented
40#2798C2218yescomplemented
41#2798C2218yescomplemented
42#2796C2218yes—
43#2794C2218yescomplemented
44#2794C2218yescomplemented
45#2773C2218yescomplemented
46#2773C2218yescomplemented
47#2771C2218yescomplemented
48#2754C2218yescomplemented
49#2754C2218yescomplemented
50#2751C2218yes—
51#2642C2214yescomplemented
52#2625C2214yescomplemented
53#2625C2214yescomplemented
54#2607C2218yescomplemented
55#2596C2218yescomplemented
56#2596C2218yescomplemented
57#2595C2218yes—
58#2592C2214yes—
59#2589C2218yescomplemented
60#2589C2218yescomplemented
61#2582C2214yescomplemented
62#2580C2214yes—
63#2575C2218yescomplemented
64#2575C2218yescomplemented
65#2571C2214yescomplemented
66#2570C2214yescomplemented
67#2570C2214yescomplemented
68#2570C2218yescomplemented
69#2568C2212yescomplemented
70#2568C2212yescomplemented
71#2568C2212yescomplemented
72#2568C2212yescomplemented
73#2563C2211yescharacteristic
74#2563C2211yescharacteristic
75#2562C2212yes—
76#2562C2212yes—
77#2561C2218yes—
78#2561C2214yes—
79#2547C2211yescharacteristic
80#2547C2211yescharacteristic
81#2542C2212yes—
82#2542C2212yes—
83#2542C2212yes—
84#2542C2212yes—
85#2542C2214yes—
86#2542C2214yes—
87#2517C2218yescomplemented
88#2516C2218yes—
89#2513C2214yes—
90#2513C2214yes—
91#2511C2214yescomplemented
92#2511C2214yescomplemented
93#2511C2218yescomplemented
94#2503C2218yes—
95#2503C2214yes—
96#2503C2212yes—
97#2503C2214yes—
98#2503C2214yescomplemented
99#2502C2214yescomplemented
100#2499C2214yescomplemented
101#2499C2214yescomplemented
102#2492C2214yescomplemented
103#2492C2214yescomplemented
104#2492C2214yescomplemented
105#2492C2214yescomplemented
106#2489C2214yescomplemented
107#2489C2214yescomplemented
108#2489C2214yescomplemented
109#2489C2214yescomplemented
110#2484C2218yes—
111#2484C2218yes—
112#2483C2218yes—
113#2482C2218yes—
114#2448C2214yes—
115#2447C2214yes—
116#2435C2212yes—
117#2423C2214yescomplemented
118#2423C2214yescomplemented
119#2423C2214yescomplemented
120#2423C2214yescomplemented
121#2421C2214yescomplemented
122#2421C2214yescomplemented
123#2421C2214yescomplemented
124#2421C2214yescomplemented
125#2398C2214yes—
126C2×#399C2214yes—
127#2370C2214yescomplemented
128#2369C2212yescomplemented
129#2367C2214yes—
130#2365C2212yescomplemented
131#2365C2212yescomplemented
132#2365C2212yescomplemented
133#2365C2212yescomplemented
134#2365C2212yescomplemented
135#2362C2214yescomplemented
136#2362C2214yescomplemented
137#2360C2214yescomplemented
138#2360C2214yescomplemented
139#2357C2214yes—
140#2355C2212yescomplemented
141#2355C2214yescomplemented
142#2355C2214yescomplemented
143#2355C2214yescomplemented
144#2354C2211yescharacteristic
145#2354C2211yescharacteristic
146#2352C2212yes—
147#2352C2212yes—
148Q8×C4⋊C4C2212yescomplemented
149D4×C4⋊C4C2211yescharacteristic
150D4×C4⋊C4C2211yescharacteristic
151#2344C2212yes—
152#2344C2214yes—
153#2344C2218yes—
154#2344C2214yes—
155#2342C2214yes—
156#2342C2218yes—
157D4×C22⋊C4C2212yes—
158#2331C2212yescomplemented
159#2331C2212yescomplemented
160#2330C2212yescomplemented
161#2330C2212yescomplemented
162#2329C2214yes—
163#2329C2214yes—
164#2327C2214yescomplemented
165#2323C2214yescomplemented
166#2323C2214yescomplemented
167#2317C2211yescharacteristic
168#2317C2211yescharacteristic
169#2317C2212yes—
170#2316C2211yescharacteristic
171#2310C2212yes—
172#2310C2212yes—
173#2310C2212yes—
174C4×C4⋊Q8C2212yescomplemented
175C4×C4⋊Q8C2212yescomplemented
176C4×C4⋊Q8C2212yescomplemented
177C4×C4⋊Q8C2212yescomplemented
178C4×#125C2212yescomplemented
179C4×#125C2212yescomplemented
180C4×#124C2212yes—
181C4×#124C2212yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2214yescomplemented
185C4×C22⋊Q8C2214yescomplemented
186#2293C2212yes—
187C2×#390C2212yes—
188#2290C2214yes—
189#2285C2211yescharacteristic
190C2×#384C2212yes—
191#2280C2212yes—
192#2280C2212yes—
193#2280C2212yes—
194#2274C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C23×Q8C2312yes—
200C23×D4C2311yescharacteristic
201C24×C4C2312yes—
202#544—28no—
203#533—28no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×C22⋊Q8—216no—
219C2×C22⋊Q8—48no—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231#519—48no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×D4—28no—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×#117—48no—
250C2×#117C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2318yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2311yescharacteristic
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2314yes—
272C22×C22⋊C4C2314yes—
273C22×C22⋊C4C2314yes—
274C22×C42C2314yes—
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#394C2314yes—
312#394C2314yes—
313#393C2314yes—
314#393C2314yes—
315#393C2318yes—
316#393C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2318yes—
337#391C2318yes—
338#391C2314yes—
339#391C2314yes—
340#391C2318yes—
341#391C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2314yes—
347#390C2312yes—
348#390C2318yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2318yes—
367#389C2312yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#385C2314yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2318yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2314yes—
436#384C2318yes—
437#384C2314yes—
438#382C2312yes—
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2318yes—
447#382C2318yes—
448#382C2314yes—
449#382C2312yes—
450#381C2318yes—
451#381C2318yes—
452#381C2314yes—
453#381C2314yes—
454#381C2318yes—
455#381C2318yes—
456#381C2314yes—
457#381C2318yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#379C2314yes—
474#379C2314yes—
475#379C2314yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522#376C2312yes—
523#376C2312yes—
524C2×#95C2312yes—
525C43C2312yes—
526C43C2312yes—
527C25C2412yes—
528C22×Q8—28no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—42no—
539C22×D4C2411yescharacteristic
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C23×C4—28no—
543C23×C4—28no—
544C23×C4—28no—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2412yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—28no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566#125—28no—
567#125—28no—
568#125—28no—
569#124—28no—
570#124—44no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—216no—
574C22⋊Q8—216no—
575C22⋊Q8—216no—
576C22⋊Q8—216no—
577C22⋊Q8—216no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×D4—28no—
591C4×D4—24no—
592C4×D4—28no—
593C4×D4—24no—
594C4×D4—28no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—44no—
598#117—28no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—28no—
603#117—24no—
604#117—48no—
605#117—48no—
606#117—416no—
607#117—44no—
608#117—44no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—216no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4#4118yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C22⋊C4—28no—
669C2×C22⋊C4—216no—
670C2×C22⋊C4—48no—
671C2×C22⋊C4—48no—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C42—48no—
701C2×C42—44no—
702C2×C42#4118yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2418yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775C24—24no—
776C24—24no—
777C24—24no—
778C24—24no—
779C24—42no—
780C24—42no—
781C24—42no—
782C24C2512yes—
783C24C2512yes—
784C24C2511yescharacteristic
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—28no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—28no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—432no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—416no—
809C2×D4—42no—
810C2×D42−1+414yes—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—432no—
845C22×C4C2×#4114yes—
846C22×C4C2×#4114yes—
847C22×C4C2×#4118yes—
848C22×C4C2×#4114yes—
849C22×C4C2×#4114yes—
850C22×C4H(5,𝔽2)14yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2518yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—216no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4C2×#4118yes—
923C4⋊C4C2×#4118yes—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—28no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—216no—
938C22⋊C4—216no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C42—28no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—28no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—28no—
961C42—24no—
962C42—24no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—42no—
967C42—42no—
968C42—48no—
969C42—42no—
970C42—42no—
971C42—48no—
972C42—48no—
973C42—48no—
974C42C2×#4114yes—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C42C2×#4114yes—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—48no—
996C23—48no—
997C23—48no—
998C23—48no—
999C23—84no—
1000C23—84no—
1001C23—84no—
1002C23C22×#4112yes—
1003C23C22×#4112yes—
1004C23C2×H(5,𝔽2)12yes—
1005C23C2×2−1+414yes—
1006C23C2611yescharacteristic
1007Q8—416no—
1008Q8—416no—
1009Q8—48no—
1010Q8—88no—
1011Q8—84no—
1012D4—28no—
1013D4—48no—
1014D4—44no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—24no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—28no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—48no—
1073C2×C4—44no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—416no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—88no—
1082C2×C4—88no—
1083C2×C4#559116yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4118yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4#58512yes—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—816no—
1118C22C2×#55914yes—
1119C22C23×#4111yescharacteristic
1120C22C23×#4111yescharacteristic
1121C22C22×H(5,𝔽2)11yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C222−1+611yescharacteristic
1125C222−1+611yescharacteristic
1126C4—28no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—44no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—48no—
1146C4C2×#55914yes—
1147C4C2×#55914yes—
1148C4#349514yes—
1149C2—24no—
1150C2—44no—
1151C2—82no—
1152C2C22×#55911yescharacteristic
1153C2C2×#349511yescharacteristic
1154C2#6286011yescharacteristic
1155C2#6292511yescharacteristic
1156C2#6294211yescharacteristic
1157C2#6299111yescharacteristic
1158C2#6299811yescharacteristic
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
2. #59642C2semidirect
3. #59639C2semidirect
4. #59451C2semidirect
5. #59450C2semidirect
6. #59329C2semidirect
7. #45222C2semidirect
8. #45201C2semidirect
9. #43598C2semidirect
10. #39274C2semidirect
11. #39271C2semidirect
12. #39203C2semidirect
13. #39200C2semidirect
14. #36476C2semidirect
15. #36454C2semidirect
16. #35672C2semidirect
17. #35644C2semidirect
18. #35320C2semidirect
19. #35311C2semidirect
22. #34213C2semidirect
23. #34209C2semidirect
24. #34203C2semidirect
26. C4×#544C2semidirect
35. #2862C22semidirect
36. #2862C22semidirect
37. #2855C22semidirect
38. #2855C22semidirect
39. #2807C22semidirect
40. #2798C22semidirect
41. #2798C22semidirect
43. #2794C22semidirect
44. #2794C22semidirect
45. #2773C22semidirect
46. #2773C22semidirect
47. #2771C22semidirect
48. #2754C22semidirect
49. #2754C22semidirect
51. #2642C22semidirect
52. #2625C22semidirect
53. #2625C22semidirect
54. #2607C22semidirect
55. #2596C22semidirect
56. #2596C22semidirect
59. #2589C22semidirect
60. #2589C22semidirect
61. #2582C22semidirect
63. #2575C22semidirect
64. #2575C22semidirect
65. #2571C22semidirect
66. #2570C22semidirect
67. #2570C22semidirect
68. #2570C22semidirect
69. #2568C22semidirect
70. #2568C22semidirect
71. #2568C22semidirect
72. #2568C22semidirect
87. #2517C22semidirect
91. #2511C22semidirect
92. #2511C22semidirect
93. #2511C22semidirect
98. #2503C22semidirect
99. #2502C22semidirect
100. #2499C22semidirect
101. #2499C22semidirect
102. #2492C22semidirect
103. #2492C22semidirect
104. #2492C22semidirect
105. #2492C22semidirect
106. #2489C22semidirect
107. #2489C22semidirect
108. #2489C22semidirect
109. #2489C22semidirect
117. #2423C22semidirect
118. #2423C22semidirect
119. #2423C22semidirect
120. #2423C22semidirect
121. #2421C22semidirect
122. #2421C22semidirect
123. #2421C22semidirect
124. #2421C22semidirect
127. #2370C22semidirect
128. #2369C22semidirect
130. #2365C22semidirect
131. #2365C22semidirect
132. #2365C22semidirect
133. #2365C22semidirect
134. #2365C22semidirect
135. #2362C22semidirect
136. #2362C22semidirect
137. #2360C22semidirect
138. #2360C22semidirect
140. #2355C22semidirect
141. #2355C22semidirect
142. #2355C22semidirect
143. #2355C22semidirect
148. Q8×C4⋊C4C22semidirect
158. #2331C22semidirect
159. #2331C22semidirect
160. #2330C22semidirect
161. #2330C22semidirect
164. #2327C22semidirect
165. #2323C22semidirect
166. #2323C22semidirect
174. C4×C4⋊Q8C22semidirect
175. C4×C4⋊Q8C22semidirect
176. C4×C4⋊Q8C22semidirect
177. C4×C4⋊Q8C22semidirect
178. C4×#125C22semidirect
179. C4×#125C22semidirect
184. C4×C22⋊Q8C22semidirect
185. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#596422
#596392
#594512
#594502
#593292
#452222
#452012
#435982
#392742
#392712
#392032
#392002
#364762
#364542
#356722
#356442
#353202
#353112
#349462
C2×#25422
#342132
#342092
#342032
D4×#1172
C4×#5442