Finite Group Databasebeta

← #7652668

Subgroups — #7652668

Order 512.

4400 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42826C214yesmaximal, complemented
2#42826C214yesmaximal, complemented
3#42824C214yesmaximal, complemented
4#42823C214yesmaximal, complemented
5#42000C218yesmaximal
6#39979C214yesmaximal, complemented
7#39978C214yesmaximal, complemented
8#39753C214yesmaximal, complemented
9#39183C214yesmaximal, complemented
10#38449C218yesmaximal
11#35668C211yesmaximal, characteristic
12#35668C211yesmaximal, characteristic
13#35640C211yesmaximal, characteristic
14#35640C211yesmaximal, characteristic
15#35627C211yesmaximal, characteristic
16#35555C211yesmaximal, characteristic
17#35330C211yesmaximal, characteristic
18#35275C211yesmaximal, characteristic
19#35154C211yesmaximal, characteristic
20C2×#2565C211yesmaximal, characteristic
21#34815C211yesmaximal, characteristic
22#34815C211yesmaximal, characteristic
23#34254C211yesmaximal, characteristic
24#34254C211yesmaximal, characteristic
25#34249C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#544C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2868C2212yes—
34#2862C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2855C2214yes—
38#2845C2218yes—
39#2843C2218yes—
40#2806C2218yes—
41#2802C2218yes—
42#2802C2218yes—
43#2792C2218yes—
44#2792C2218yes—
45#2791C2218yes—
46#2791C2218yes—
47#2791C2218yes—
48#2791C2218yes—
49#2774C2218yes—
50#2774C2218yes—
51#2755C2218yes—
52#2755C2218yes—
53#2726C2218yes—
54#2713C2218yes—
55#2713C2218yes—
56#2666C2218yes—
57#2666C2218yes—
58#2666C2218yes—
59#2666C2218yes—
60#2660C2212yes—
61#2660C2212yes—
62#2660C2218yes—
63#2660C2212yes—
64#2660C2212yes—
65#2647C2218yes—
66#2627C2214yes—
67#2612C2218yes—
68#2606C2218yes—
69#2605C2218yes—
70#2583C2214yes—
71#2583C2214yes—
72#2571C2214yes—
73#2570C2218yes—
74#2570C2214yes—
75#2570C2214yes—
76#2570C2218yes—
77#2568C2212yes—
78#2568C2212yes—
79#2567C2212yes—
80#2567C2212yes—
81#2565C2212yes—
82#2565C2214yes—
83#2565C2214yes—
84#2565C2214yes—
85#2565C2214yes—
86#2565C2212yes—
87#2565C2212yes—
88#2565C2212yes—
89#2552C2218yes—
90#2552C2214yes—
91#2552C2214yes—
92#2552C2214yes—
93#2552C2214yes—
94#2552C2214yes—
95#2552C2214yes—
96#2551C2214yes—
97#2550C2214yes—
98#2550C2214yes—
99#2550C2214yes—
100#2550C2214yes—
101#2550C2214yes—
102#2550C2214yes—
103#2549C2218yes—
104#2509C2212yes—
105#2509C2214yes—
106#2509C2212yes—
107#2508C2212yes—
108#2508C2214yes—
109#2508C2212yes—
110#2507C2212yes—
111#2507C2214yes—
112#2507C2212yes—
113#2506C2214yes—
114#2506C2212yes—
115#2506C2212yes—
116#2505C2218yes—
117#2505C2214yes—
118#2505C2214yes—
119#2502C2214yes—
120#2502C2214yes—
121#2473C2214yes—
122#2473C2214yes—
123#2473C2218yes—
124#2453C2214yes—
125#2453C2214yes—
126#2453C2214yes—
127#2453C2214yes—
128#2451C2214yes—
129#2451C2214yes—
130#2451C2214yes—
131#2451C2214yes—
132#2440C2218yes—
133#2438C2218yes—
134#2438C2218yes—
135#2402C2214yes—
136#2402C2214yes—
137C2×#398C2214yes—
138#2356C2214yes—
139#2356C2214yes—
140#2355C2214yes—
141#2355C2214yes—
142#2351C2214yes—
143#2351C2214yes—
144Q8×C4⋊C4C2214yes—
145Q8×C4⋊C4C2214yes—
146#2343C2218yes—
147#2343C2218yes—
148#2331C2218yes—
149#2330C2218yes—
150#2320C2214yes—
151#2320C2214yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2214yes—
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2310C2211yescharacteristic
161#2310C2211yescharacteristic
162C4×#125C2214yes—
163C4×#125C2214yes—
164#2296C2211yescharacteristic
165#2296C2211yescharacteristic
166#2296C2214yes—
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2295C2214yes—
174#2295C2214yes—
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#387C2214yes—
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180C2×#384C2211yescharacteristic
181C2×#382C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188#544—44no—
189#544—44no—
190#544—44no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2318yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×#125—44no—
199C2×#125C2314yes—
200C2×#125C2314yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2318yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213#519—44no—
214#519Q8116yescomplemented
215C2×C4×Q8—44no—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2314yes—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2314yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#400C2318yes—
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2314yes—
256#400C2318yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2318yes—
317#391C2318yes—
318#391C2318yes—
319#391C2318yes—
320#391C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2318yes—
333#389C2318yes—
334#389C2312yes—
335#389C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2312yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#385C2312yes—
397#385C2314yes—
398#385C2312yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2312yes—
405#385C2312yes—
406#385C2312yes—
407#385C2314yes—
408#385C2314yes—
409#385C2312yes—
410#385C2312yes—
411#385C2314yes—
412#385C2314yes—
413#385C2312yes—
414#384C2314yes—
415#384C2312yes—
416#384C2311yescharacteristic
417#384C2312yes—
418#384C2311yescharacteristic
419#384C2312yes—
420#384C2312yes—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2318yes—
424#384C2318yes—
425#384C2312yes—
426#384C2318yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2318yes—
431#383C2318yes—
432#383C2318yes—
433#382C2314yes—
434#382C2314yes—
435#382C2314yes—
436#382C2311yescharacteristic
437#382C2312yes—
438#382C2312yes—
439#382C2311yescharacteristic
440#382C2312yes—
441#382C2312yes—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2312yes—
445#382C2312yes—
446#382C2318yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#381C2314yes—
453#381C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489#376C2312yes—
490#376C2312yes—
491#376C2318yes—
492#376C2318yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C2×#95C2314yes—
496C2×#95C2312yes—
497C43C2312yes—
498C43C2312yes—
499C22×Q8—24no—
500C22×Q8—24no—
501C22×Q8C2×Q818yes—
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2414yes—
506C22×Q8C2414yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C4⋊Q8—416no—
517C4⋊Q8—44no—
518C4⋊Q8—44no—
519C4⋊Q8—44no—
520C4⋊Q8—44no—
521C4⋊Q8—44no—
522C4⋊Q8—44no—
523#125—48no—
524#125—48no—
525#125—48no—
526#125—44no—
527#125—44no—
528#125—44no—
529#125—44no—
530#125—44no—
531#125—44no—
532#125—48no—
533#125—416no—
534C22⋊Q8—48no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537C4×Q8—48no—
538C4×Q8—48no—
539C4×Q8—44no—
540C4×Q8—44no—
541C4×Q8—44no—
542C4×Q8—44no—
543C4×Q8C2×Q8132yes—
544C4×Q8C2×Q8132yes—
545#117—24no—
546#117—24no—
547#117—24no—
548#117—24no—
549#117—24no—
550#117—24no—
551#117—48no—
552#117C2×Q8132yes—
553#117C2×Q818yes—
554#117C2×Q818yes—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—44no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4—44no—
562C2×C4⋊C4—44no—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C42—24no—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—44no—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2418yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2418yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714C24C2511yescharacteristic
715C2×Q8—232no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—24no—
720C2×Q8—44no—
721C2×Q8—44no—
722C2×Q8—44no—
723C2×Q8—48no—
724C2×Q8—48no—
725C2×Q8—48no—
726C2×Q8C22×Q818yes—
727C2×Q8C22×Q818yes—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—42no—
745C22×C4—44no—
746C22×C4C22×Q818yes—
747C22×C4C22×Q814yes—
748C22×C4H(5,𝔽2)14yes—
749C22×C42−1+414yes—
750C22×C4C2512yes—
751C22×C4C2512yes—
752C22×C4C2512yes—
753C22×C4C2514yes—
754C22×C4C2514yes—
755C22×C4C2512yes—
756C22×C4C2512yes—
757C22×C4C2512yes—
758C22×C4C2514yes—
759C22×C4C2512yes—
760C22×C4C2512yes—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2512yes—
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—216no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—42no—
797C4⋊C4—48no—
798C4⋊C4—42no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—48no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4C22×Q8132yes—
838C4⋊C4C22×Q818yes—
839C4⋊C4C22×Q818yes—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4C22×Q818yes—
847C22⋊C4C22×Q818yes—
848C42—24no—
849C42—24no—
850C42—24no—
851C42—24no—
852C42—24no—
853C42—24no—
854C42—22no—
855C42—24no—
856C42—22no—
857C42—22no—
858C42—22no—
859C42—24no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—48no—
864C42—44no—
865C42—48no—
866C42—44no—
867C42—44no—
868C42—44no—
869C42—48no—
870C42—44no—
871C42C22×Q8132yes—
872C42C22×Q818yes—
873C42C22×Q818yes—
874C23—22no—
875C23—22no—
876C23C23×Q812yes—
877C23C2×H(5,𝔽2)12yes—
878C23C2×2−1+412yes—
879C23C2611yescharacteristic
880Q8—216no—
881Q8—216no—
882Q8—164no—
883Q8—164no—
884Q8—164no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—216no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—48no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4—84no—
941C2×C4—84no—
942C2×C4—84no—
943C2×C4—84no—
944C2×C4#544116yes—
945C2×C4C23×Q818yes—
946C2×C4C23×Q818yes—
947C2×C4C23×Q818yes—
948C2×C4C23×Q812yes—
949C2×C4C23×Q812yes—
950C2×C4C2×H(5,𝔽2)12yes—
951C2×C4C2×H(5,𝔽2)12yes—
952C2×C4C2×2−1+412yes—
953C2×C4C2×2−1+412yes—
954C2×C4#58514yes—
955C22—24no—
956C22—22no—
957C22—22no—
958C22—24no—
959C22C2×#54414yes—
960C22C24×Q811yescharacteristic
961C22C22×H(5,𝔽2)11yescharacteristic
962C22C22×2−1+411yescharacteristic
963C22C2×#58512yes—
964C222−1+612yes—
965C4—28no—
966C4—28no—
967C4—24no—
968C4—28no—
969C4—42no—
970C4—42no—
971C4—44no—
972C4—44no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—44no—
980C4—42no—
981C4—42no—
982C4—44no—
983C4—44no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4C2×#54414yes—
988C4C2×#54414yes—
989C2—24no—
990C2C22×#54411yescharacteristic
991C2#6283611yescharacteristic
992C2#6288711yescharacteristic
993C2#6292812yes—
994C2#6300412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42826C2semidirect
2. #42826C2semidirect
3. #42824C2semidirect
4. #42823C2semidirect
6. #39979C2semidirect
7. #39978C2semidirect
8. #39753C2semidirect
9. #39183C2semidirect
214. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#428262
#428242
#428232
#420002
#399792
#399782
#397532
#391832
#384492
#356682
#356402
#356272
#355552
#353302
#352752
#351542
C2×#25652
#348152
#342542
#342492