Finite Group Databasebeta

← #7674379

Subgroups — #7674379

Order 512.

4986 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45233C214yesmaximal, complemented
2#45213C214yesmaximal, complemented
3#45086C214yesmaximal, complemented
4#45059C214yesmaximal, complemented
5#39675C214yesmaximal, complemented
6#39674C214yesmaximal, complemented
7#39633C214yesmaximal, complemented
8#39630C214yesmaximal, complemented
9#38102C218yesmaximal, complemented
10#38097C218yesmaximal, complemented
11#35668C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35529C211yesmaximal, characteristic
14#35515C211yesmaximal, characteristic
15#35286C211yesmaximal, characteristic, complemented
16#35275C211yesmaximal, characteristic, complemented
17#35174C211yesmaximal, characteristic
18#35154C211yesmaximal, characteristic, complemented
19#34638C211yesmaximal, characteristic, complemented
20#34249C211yesmaximal, characteristic, complemented
21#34248C211yesmaximal, characteristic
22#34211C211yesmaximal, characteristic
23#34211C211yesmaximal, characteristic
24#34074C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#518C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#2868C2212yescomplemented
37#2859C2212yescomplemented
38#2859C2214yescomplemented
39#2855C2214yes—
40#2848C2214yes—
41#2807C2218yescomplemented
42#2807C2218yescomplemented
43#2790C2218yescomplemented
44#2790C2218yescomplemented
45#2790C2218yescomplemented
46#2788C2218yescomplemented
47#2788C2218yescomplemented
48#2788C2218yescomplemented
49#2768C2218yescomplemented
50#2768C2218yescomplemented
51#2763C2218yescomplemented
52#2742C2218yescomplemented
53#2729C2218yescomplemented
54#2729C2218yescomplemented
55#2720C2218yescomplemented
56#2704C2218yescomplemented
57#2660C2212yescomplemented
58#2660C2212yescomplemented
59#2647C2212yescomplemented
60#2647C2212yescomplemented
61#2647C2212yescomplemented
62#2647C2212yescomplemented
63#2647C2214yescomplemented
64#2646C2214yes—
65#2646C2214yes—
66#2627C2214yes—
67#2626C2214yes—
68#2589C2218yescomplemented
69#2587C2218yescomplemented
70#2583C2218yescomplemented
71#2582C2214yescomplemented
72#2581C2214yescomplemented
73#2580C2214yes—
74#2574C2218yescomplemented
75#2571C2214yescomplemented
76#2568C2212yescomplemented
77#2567C2212yescomplemented
78#2566C2212yes—
79#2566C2212yes—
80#2565C2212yescomplemented
81#2565C2212yescomplemented
82#2563C2212yes—
83#2556C2218yescomplemented
84#2552C2214yescomplemented
85#2552C2214yescomplemented
86#2551C2214yescomplemented
87#2549C2218yescomplemented
88#2542C2212yes—
89#2538C2214yes—
90#2522C2218yescomplemented
91#2522C2218yescomplemented
92#2505C2218yescomplemented
93#2505C2218yescomplemented
94#2505C2218yescomplemented
95#2502C2218yescomplemented
96#2497C2218yescomplemented
97#2492C2218yescomplemented
98#2473C2218yescomplemented
99#2454C2214yes—
100#2454C2214yes—
101#2454C2214yes—
102#2454C2214yes—
103#2453C2214yescomplemented
104#2453C2214yescomplemented
105#2453C2214yescomplemented
106#2453C2214yescomplemented
107#2452C2214yes—
108#2452C2214yes—
109#2452C2214yes—
110#2452C2214yes—
111#2451C2214yescomplemented
112#2451C2214yescomplemented
113#2451C2214yescomplemented
114#2451C2214yescomplemented
115#2442C2218yes—
116#2440C2218yes—
117#2440C2218yescomplemented
118#2438C2218yes—
119#2438C2218yes—
120#2437C2218yes—
121#2437C2218yes—
122#2402C2214yescomplemented
123#2402C2214yescomplemented
124#2367C2214yes—
125#2367C2214yes—
126#2367C2214yes—
127#2367C2214yes—
128#2351C2214yescomplemented
129#2351C2214yescomplemented
130Q8×C4⋊C4C2214yescomplemented
131Q8×C4⋊C4C2214yescomplemented
132#2349C2214yes—
133#2349C2214yes—
134D4×C4⋊C4C2214yes—
135D4×C4⋊C4C2214yes—
136#2342C2218yes—
137#2342C2218yes—
138#2331C2212yescomplemented
139#2331C2212yescomplemented
140#2330C2212yescomplemented
141#2330C2212yescomplemented
142#2329C2214yes—
143#2329C2214yes—
144#2326C2214yes—
145#2326C2214yes—
146#2326C2214yes—
147#2326C2214yes—
148#2326C2212yes—
149#2326C2212yes—
150#2326C2214yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2214yes—
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2315C2214yes—
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×#124C2214yes—
164C4×#124C2212yes—
165C4×#124C2212yes—
166#2296C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2214yes—
173#2295C2214yescomplemented
174#2295C2214yescomplemented
175C2×#391C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#388C2214yes—
178C2×#385C2214yes—
179C2×#385C2214yes—
180#2285C2211yescharacteristic
181#2285C2211yescharacteristic
182#2285C2211yescharacteristic
183C2×#384C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C24×C4C2312yes—
190#544—44no—
191#544—44no—
192#533—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2318yes—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2318yes—
205C2×#124Q8116yescomplemented
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215#519—28no—
216#519—44no—
217#518—28no—
218#518—44no—
219C2×C4×Q8—44no—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×D4—44no—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2314yes—
246C2×#117C2314yes—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2318yes—
252C22×C4⋊C4C2314yes—
253C22×C22⋊C4C2314yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2314yes—
257C22×C22⋊C4C2314yes—
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2312yes—
261C22×C42C2311yescharacteristic
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2318yes—
319#391C2314yes—
320#391C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2314yes—
331#390C2312yes—
332#390C2314yes—
333#390C2312yes—
334#390C2314yes—
335#389C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2318yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2318yes—
367#389C2312yes—
368#389C2318yes—
369#389C2312yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2312yes—
399#385C2312yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2312yes—
405#385C2312yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2312yes—
420#385C2312yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2312yes—
425#385C2312yes—
426#385C2314yes—
427#385C2314yes—
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2318yes—
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2318yes—
442#382C2311yescharacteristic
443#382C2312yes—
444#382C2311yescharacteristic
445#382C2312yes—
446#382C2318yes—
447#382C2312yes—
448#382C2312yes—
449#382C2318yes—
450#382C2312yes—
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#381C2314yes—
454#381C2314yes—
455#380C2318yes—
456#380C2318yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#379C2314yes—
466#379C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490#376C2312yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494#376C2312yes—
495#376C2312yes—
496C2×#95C2312yes—
497C2×#95C2312yes—
498C2×#95C2318yes—
499C2×#95C2314yes—
500C43C2312yes—
501C43C2312yes—
502C25C2412yes—
503C22×Q8—24no—
504C22×Q8—24no—
505C22×Q8C2×Q818yes—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4C2×Q818yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C23×C4—44no—
517C23×C4—84no—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2418yes—
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2418yes—
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C4⋊Q8—28no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535C4⋊Q8—88no—
536#125—28no—
537#125—44no—
538#125—44no—
539#125—44no—
540#125—44no—
541#125—88no—
542#124C2×Q8116yes—
543#124C2×Q8116yes—
544#124C2×Q8132yes—
545C22⋊Q8—216no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548C22⋊Q8—88no—
549C22⋊Q8—88no—
550C22⋊Q8—88no—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—216no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—44no—
559C4×Q8—44no—
560C4×D4—216no—
561C4×D4—216no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—44no—
565C4×D4—44no—
566C4×D4—44no—
567C4×D4—44no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—216no—
576#117—48no—
577#117#4118yes—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—44no—
581C2×C4⋊C4—88no—
582C2×C4⋊C4—84no—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C22⋊C4—216no—
639C2×C22⋊C4—48no—
640C2×C22⋊C4—44no—
641C2×C22⋊C4—84no—
642C2×C22⋊C4C2×Q8132yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2412yes—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—44no—
666C2×C42C2×Q818yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2418yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2412yes—
691#95C2414yes—
692#95C2414yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733C24—24no—
734C24—24no—
735C24—44no—
736C24—44no—
737C24C22×Q818yes—
738C24C2514yes—
739C24C2511yescharacteristic
740C2×Q8—232no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—48no—
751C2×Q8—48no—
752C2×Q8C22×Q818yes—
753C2×Q8C22×Q818yes—
754C2×D4—232no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4C22×Q818yes—
760C2×D4C22×Q818yes—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—216no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—42no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—816no—
787C22×C4C22×Q818yes—
788C22×C4C22×Q818yes—
789C22×C4C22×Q814yes—
790C22×C4C2×#4114yes—
791C22×C4H(5,𝔽2)14yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C4⋊C4—24no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4C2×#4118yes—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—216no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4C22×Q8132yes—
888C22⋊C4C22×Q8132yes—
889C22⋊C4C2×#4118yes—
890C42—24no—
891C42—22no—
892C42—22no—
893C42—24no—
894C42—216no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—48no—
904C42—44no—
905C42—44no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—44no—
910C42C22×Q814yes—
911C42C22×Q814yes—
912C42C22×Q818yes—
913C42C2×#4118yes—
914C23—22no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—28no—
919C23—28no—
920C23—216no—
921C23—416no—
922C23—84no—
923C23—88no—
924C23—84no—
925C23C23×Q818yes—
926C23C23×Q812yes—
927C23C22×#4112yes—
928C23C2×H(5,𝔽2)12yes—
929C23C2611yescharacteristic
930Q8—216no—
931Q8—216no—
932Q8—88no—
933Q8—164no—
934Q8—164no—
935D4—216no—
936D4—216no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—216no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—816no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—816no—
995C2×C4—164no—
996C2×C4—164no—
997C2×C4#554116yes—
998C2×C4C23×Q814yes—
999C2×C4C23×Q814yes—
1000C2×C4C23×Q818yes—
1001C2×C4C23×Q812yes—
1002C2×C4C23×Q812yes—
1003C2×C4C22×#4118yes—
1004C2×C4C22×#4112yes—
1005C2×C4C22×#4112yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C22—24no—
1009C22—24no—
1010C22—22no—
1011C22—22no—
1012C22—216no—
1013C22—28no—
1014C22—48no—
1015C22—44no—
1016C22—44no—
1017C22—816no—
1018C22C2×#55414yes—
1019C22C24×Q811yescharacteristic
1020C22C23×#4111yescharacteristic
1021C22C22×H(5,𝔽2)11yescharacteristic
1022C22H(7,𝔽2)12yes—
1023C222−1+612yes—
1024C4—24no—
1025C4—24no—
1026C4—28no—
1027C4—28no—
1028C4—44no—
1029C4—42no—
1030C4—44no—
1031C4—42no—
1032C4—44no—
1033C4—42no—
1034C4—44no—
1035C4—44no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4C2×#55414yes—
1046C4C2×#55414yes—
1047C2—24no—
1048C2—48no—
1049C2C22×#55411yescharacteristic
1050C2#6285412yes—
1051C2#6285712yes—
1052C2#6287611yescharacteristic
1053C2#6288711yescharacteristic
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. #45233C2semidirect
2. #45213C2semidirect
3. #45086C2semidirect
4. #45059C2semidirect
5. #39675C2semidirect
6. #39674C2semidirect
7. #39633C2semidirect
8. #39630C2semidirect
9. #38102C2semidirect
10. #38097C2semidirect
11. #35668C2semidirect
12. #35662C2semidirect
15. #35286C2semidirect
16. #35275C2semidirect
18. #35154C2semidirect
19. #34638C2semidirect
20. #34249C2semidirect
24. #34074C2semidirect
36. #2868C22semidirect
37. #2859C22semidirect
38. #2859C22semidirect
41. #2807C22semidirect
42. #2807C22semidirect
43. #2790C22semidirect
44. #2790C22semidirect
45. #2790C22semidirect
46. #2788C22semidirect
47. #2788C22semidirect
48. #2788C22semidirect
49. #2768C22semidirect
50. #2768C22semidirect
51. #2763C22semidirect
52. #2742C22semidirect
53. #2729C22semidirect
54. #2729C22semidirect
55. #2720C22semidirect
56. #2704C22semidirect
57. #2660C22semidirect
58. #2660C22semidirect
59. #2647C22semidirect
60. #2647C22semidirect
61. #2647C22semidirect
62. #2647C22semidirect
63. #2647C22semidirect
68. #2589C22semidirect
69. #2587C22semidirect
70. #2583C22semidirect
71. #2582C22semidirect
72. #2581C22semidirect
74. #2574C22semidirect
75. #2571C22semidirect
76. #2568C22semidirect
77. #2567C22semidirect
80. #2565C22semidirect
81. #2565C22semidirect
83. #2556C22semidirect
84. #2552C22semidirect
85. #2552C22semidirect
86. #2551C22semidirect
87. #2549C22semidirect
90. #2522C22semidirect
91. #2522C22semidirect
92. #2505C22semidirect
93. #2505C22semidirect
94. #2505C22semidirect
95. #2502C22semidirect
96. #2497C22semidirect
97. #2492C22semidirect
98. #2473C22semidirect
103. #2453C22semidirect
104. #2453C22semidirect
105. #2453C22semidirect
106. #2453C22semidirect
111. #2451C22semidirect
112. #2451C22semidirect
113. #2451C22semidirect
114. #2451C22semidirect
117. #2440C22semidirect
122. #2402C22semidirect
123. #2402C22semidirect
128. #2351C22semidirect
129. #2351C22semidirect
130. Q8×C4⋊C4C22semidirect
131. Q8×C4⋊C4C22semidirect
138. #2331C22semidirect
139. #2331C22semidirect
140. #2330C22semidirect
141. #2330C22semidirect
173. #2295C22semidirect
174. #2295C22semidirect
205. C2×#124Q8semidirect

Maximal subgroups

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

subgroupindex
#452332
#452132
#450862
#450592
#396752
#396742
#396332
#396302
#381022
#380972
#356682
#356622
#355292
#355152
#352862
#352752
#351742
#351542
#346382
#342492
#342482
#342112
#340742
C2×#23262