Finite Group Databasebeta

← #8093376

Subgroups — #8093376

Order 512.

4402 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46337C218yesmaximal, complemented
2#46336C218yesmaximal, complemented
3#46117C214yesmaximal, complemented
4#46116C214yesmaximal, complemented
5#46109C214yesmaximal, complemented
6#46108C214yesmaximal, complemented
7#46079C214yesmaximal, complemented
8#46078C214yesmaximal, complemented
9#46069C214yesmaximal, complemented
10#46068C214yesmaximal, complemented
11#36641C211yesmaximal, characteristic, complemented
12#36641C211yesmaximal, characteristic, complemented
13C2×#2859C211yesmaximal, characteristic, complemented
14#35649C211yesmaximal, characteristic
15#35640C211yesmaximal, characteristic, complemented
16#35639C211yesmaximal, characteristic, complemented
17#35639C211yesmaximal, characteristic, complemented
18#35629C211yesmaximal, characteristic, complemented
19#35627C211yesmaximal, characteristic, complemented
20#35620C211yesmaximal, characteristic, complemented
21#35618C211yesmaximal, characteristic
22#35557C211yesmaximal, characteristic, complemented
23#35555C211yesmaximal, characteristic, complemented
24#35532C211yesmaximal, characteristic, complemented
25#35530C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C22×#125C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32#2863C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2860C2212yes—
37#2860C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2859C2214yes—
41#2859C2214yes—
42#2859C2214yes—
43#2859C2214yes—
44#2852C2214yes—
45#2852C2214yes—
46#2852C2214yes—
47#2852C2214yes—
48#2839C2218yes—
49#2838C2218yes—
50#2837C2218yes—
51#2836C2218yes—
52#2791C2218yes—
53#2787C2218yes—
54#2777C2218yes—
55#2777C2218yes—
56#2776C2218yes—
57#2775C2218yes—
58#2774C2218yes—
59#2773C2218yes—
60#2771C2218yes—
61#2770C2218yes—
62#2769C2218yes—
63#2766C2218yes—
64#2758C2218yes—
65#2738C2218yes—
66#2727C2218yes—
67#2725C2218yes—
68#2723C2218yes—
69#2722C2218yes—
70#2721C2218yes—
71#2718C2218yes—
72#2707C2218yes—
73#2702C2218yes—
74#2695C2218yes—
75#2689C2218yes—
76#2591C2214yes—
77#2583C2214yes—
78#2579C2214yes—
79#2579C2214yes—
80#2571C2214yes—
81#2570C2214yes—
82#2570C2214yes—
83#2568C2212yes—
84#2567C2212yes—
85#2566C2212yes—
86#2566C2212yes—
87#2565C2212yes—
88#2565C2212yes—
89#2563C2212yes—
90#2552C2214yes—
91#2552C2214yes—
92#2552C2214yes—
93#2550C2214yes—
94#2550C2214yes—
95#2542C2212yes—
96#2514C2214yes—
97#2513C2214yes—
98#2512C2214yes—
99#2511C2214yes—
100#2510C2218yes—
101#2509C2214yes—
102#2508C2214yes—
103#2507C2214yes—
104#2506C2214yes—
105#2505C2218yes—
106#2504C2214yes—
107#2504C2212yes—
108#2503C2212yes—
109#2502C2214yes—
110#2502C2212yes—
111#2501C2212yes—
112#2500C2212yes—
113#2500C2212yes—
114#2499C2212yes—
115#2499C2212yes—
116#2497C2214yes—
117#2496C2214yes—
118#2495C2214yes—
119#2494C2214yes—
120#2490C2214yes—
121#2490C2214yes—
122#2489C2214yes—
123#2489C2214yes—
124#2487C2214yes—
125#2487C2214yes—
126#2481C2218yes—
127#2473C2218yes—
128#2454C2214yes—
129#2454C2214yes—
130#2453C2214yes—
131#2453C2214yes—
132#2450C2218yes—
133#2449C2218yes—
134#2444C2218yes—
135#2443C2218yes—
136#2442C2214yes—
137#2442C2214yes—
138#2442C2214yes—
139#2441C2214yes—
140#2441C2214yes—
141#2441C2214yes—
142#2440C2214yes—
143#2439C2214yes—
144#2423C2214yes—
145#2422C2214yes—
146#2421C2214yes—
147#2420C2214yes—
148#2383C2218yes—
149#2382C2218yes—
150#2378C2218yes—
151#2376C2218yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162C4×#126C2214yes—
163C4×#126C2214yes—
164C4×#126C2214yes—
165C4×#126C2214yes—
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178C2×#389C2214yes—
179C2×#389C2214yes—
180C2×#384C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#382C2211yescharacteristic
183C2×#382C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C43C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189#544—44no—
190#537—44no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×#126C2314yes—
194C2×#126C2314yes—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#126C2318yes—
198C2×#125—44no—
199C2×#125—44no—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2314yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#125C2314yes—
206C2×#125C2318yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×#121C2314yes—
213C2×#121C2312yes—
214C2×#121C2312yes—
215#520—44no—
216#520—44no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C2×#117C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2314yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247C22×C42C2312yes—
248#401C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#399C2318yes—
262#399C2318yes—
263#399C2318yes—
264#399C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#395C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#393C2318yes—
296#391C2311yescharacteristic
297#391C2311yescharacteristic
298#391C2312yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2311yescharacteristic
303#391C2311yescharacteristic
304#391C2318yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2318yes—
310#390C2311yescharacteristic
311#390C2312yes—
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2312yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2311yescharacteristic
322#390C2318yes—
323#389C2318yes—
324#389C2312yes—
325#389C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2312yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2318yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#386C2312yes—
407#386C2312yes—
408#386C2312yes—
409#386C2314yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2312yes—
414#386C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2314yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2312yes—
422#385C2312yes—
423#385C2318yes—
424#385C2318yes—
425#385C2312yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2312yes—
430#385C2314yes—
431#385C2318yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2312yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2318yes—
443#383C2314yes—
444#383C2314yes—
445#383C2314yes—
446#383C2314yes—
447#383C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2312yes—
453#382C2314yes—
454#382C2312yes—
455#382C2318yes—
456#382C2314yes—
457#382C2312yes—
458#382C2312yes—
459#382C2318yes—
460#381C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#380C2318yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C2×#95C2314yes—
493C2×#95C2314yes—
494C43C2312yes—
495C43C2312yes—
496C43C2312yes—
497C43C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2414yes—
507C22×D4C2412yes—
508C22×D4C2412yes—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2414yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2412yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2411yescharacteristic
525C4⋊Q8—44no—
526C4⋊Q8—44no—
527#126—48no—
528#126—48no—
529#126—48no—
530#126—48no—
531#126—416no—
532#125—48no—
533#125—48no—
534#125—48no—
535#125—48no—
536#125—44no—
537#125—44no—
538#125—416no—
539#123—416no—
540C22⋊Q8—48no—
541C22⋊Q8—416no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544#121—44no—
545#121—44no—
546#121—48no—
547C4×Q8—44no—
548C4×Q8—44no—
549C4×D4—44no—
550C4×D4—44no—
551C4×D4—48no—
552C4×D4—48no—
553#117—24no—
554#117—24no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—24no—
559#117—44no—
560#117—44no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—48no—
566C2×C4⋊C4—48no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4—44no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4—44no—
571C2×C4⋊C4—44no—
572C2×C4⋊C4—44no—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42—24no—
650C2×C42—44no—
651C2×C42—44no—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2418yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718C24C2512yes—
719C24C2512yes—
720C24C2511yescharacteristic
721#41—416no—
722#41—416no—
723C2×Q8—22no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—44no—
730C2×Q8—48no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—44no—
744C2×D4—48no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4H(5,𝔽2)14yes—
774C22×C42−1+414yes—
775C22×C42−1+414yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—22no—
879C42—24no—
880C42—22no—
881C42—22no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—44no—
895C42—44no—
896C42—48no—
897C42—48no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23C2×H(5,𝔽2)12yes—
911C23C2×2−1+412yes—
912C23C2×2−1+412yes—
913C23C2611yescharacteristic
914Q8—44no—
915Q8—44no—
916Q8—164no—
917D4—48no—
918D4—48no—
919D4—44no—
920D4—44no—
921D4—164no—
922C2×C4—216no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—48no—
976C2×C4—48no—
977C2×C4—48no—
978C2×C4—84no—
979C2×C4—84no—
980C2×C4—84no—
981C2×C4—84no—
982C2×C4—164no—
983C2×C4—164no—
984C2×C4#563116yes—
985C2×C4C2×H(5,𝔽2)12yes—
986C2×C4C2×H(5,𝔽2)12yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+412yes—
989C2×C4C2×2−1+412yes—
990C2×C4C2×2−1+412yes—
991C2×C4#58514yes—
992C2×C4#58514yes—
993C22—24no—
994C22—22no—
995C22—22no—
996C22—24no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—44no—
1004C22—44no—
1005C22—42no—
1006C22—42no—
1007C22C2×#56314yes—
1008C22C22×H(5,𝔽2)11yescharacteristic
1009C22C22×2−1+411yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C2×#58512yes—
1012C22C2×#58512yes—
1013C4—24no—
1014C4—24no—
1015C4—44no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—44no—
1028C4—44no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4C2×#56314yes—
1034C4C2×#56314yes—
1035C2—24no—
1036C2—82no—
1037C2—82no—
1038C2C22×#56311yescharacteristic
1039C2#6282512yes—
1040C2#6283611yescharacteristic
1041C2#6283611yescharacteristic
1042C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46337C2semidirect
2. #46336C2semidirect
3. #46117C2semidirect
4. #46116C2semidirect
5. #46109C2semidirect
6. #46108C2semidirect
7. #46079C2semidirect
8. #46078C2semidirect
9. #46069C2semidirect
10. #46068C2semidirect
11. #36641C2semidirect
12. #36641C2semidirect
13. C2×#2859C2semidirect
15. #35640C2semidirect
16. #35639C2semidirect
17. #35639C2semidirect
18. #35629C2semidirect
19. #35627C2semidirect
20. #35620C2semidirect
22. #35557C2semidirect
23. #35555C2semidirect
24. #35532C2semidirect

Maximal subgroups

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

subgroupindex
#463372
#463362
#461172
#461162
#461092
#461082
#460792
#460782
#460692
#460682
#366412
C2×#28592
#356492
#356402
#356392
#356292
#356272
#356202
#356182
#355572
#355552
#355322
#355302