Finite Group Databasebeta

← #8093598

Subgroups — #8093598

Order 512.

4298 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53091C214yesmaximal, complemented
2#53089C214yesmaximal, complemented
3#53086C214yesmaximal, complemented
4#53082C214yesmaximal, complemented
5#53042C214yesmaximal, complemented
6#53039C214yesmaximal, complemented
7#53003C214yesmaximal, complemented
8#53002C214yesmaximal, complemented
9#52432C218yesmaximal, complemented
10#52399C218yesmaximal, complemented
11#35639C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35629C211yesmaximal, characteristic, complemented
14#35627C211yesmaximal, characteristic, complemented
15#35620C211yesmaximal, characteristic, complemented
16#35618C211yesmaximal, characteristic
17#35592C211yesmaximal, characteristic
18#35576C211yesmaximal, characteristic, complemented
19#35557C211yesmaximal, characteristic, complemented
20#35555C211yesmaximal, characteristic, complemented
21#35532C211yesmaximal, characteristic, complemented
22#35530C211yesmaximal, characteristic
23#34639C211yesmaximal, characteristic, complemented
24#34639C211yesmaximal, characteristic, complemented
25C2×#2660C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32#2841C2218yes—
33#2839C2218yes—
34#2839C2218yes—
35#2838C2218yes—
36#2838C2218yes—
37#2838C2218yes—
38#2837C2218yes—
39#2836C2218yes—
40#2835C2218yes—
41#2833C2218yes—
42#2833C2218yes—
43#2831C2218yes—
44#2827C2218yes—
45#2821C2218yes—
46#2820C2218yes—
47#2814C2218yes—
48#2805C2218yes—
49#2787C2218yes—
50#2776C2218yes—
51#2773C2218yes—
52#2765C2218yes—
53#2762C2218yes—
54#2745C2218yes—
55#2738C2218yes—
56#2729C2218yes—
57#2725C2218yes—
58#2717C2218yes—
59#2715C2218yes—
60#2713C2218yes—
61#2695C2218yes—
62#2690C2218yes—
63#2674C2218yes—
64#2660C2214yes—
65#2660C2214yes—
66#2660C2214yes—
67#2660C2214yes—
68#2645C2212yes—
69#2645C2212yes—
70#2645C2212yes—
71#2645C2212yes—
72#2644C2212yes—
73#2644C2212yes—
74#2644C2212yes—
75#2644C2212yes—
76#2643C2214yes—
77#2643C2214yes—
78#2643C2214yes—
79#2643C2214yes—
80#2591C2214yes—
81#2583C2214yes—
82#2579C2214yes—
83#2579C2214yes—
84#2571C2214yes—
85#2570C2214yes—
86#2570C2214yes—
87#2568C2212yes—
88#2567C2212yes—
89#2566C2212yes—
90#2566C2212yes—
91#2565C2212yes—
92#2565C2212yes—
93#2563C2212yes—
94#2552C2214yes—
95#2551C2214yes—
96#2551C2214yes—
97#2550C2214yes—
98#2550C2214yes—
99#2542C2212yes—
100#2514C2214yes—
101#2513C2214yes—
102#2512C2214yes—
103#2511C2214yes—
104#2510C2218yes—
105#2509C2214yes—
106#2508C2214yes—
107#2507C2214yes—
108#2506C2214yes—
109#2505C2218yes—
110#2504C2212yes—
111#2503C2212yes—
112#2502C2212yes—
113#2501C2212yes—
114#2500C2212yes—
115#2500C2212yes—
116#2499C2212yes—
117#2499C2212yes—
118#2497C2214yes—
119#2496C2214yes—
120#2495C2214yes—
121#2494C2214yes—
122#2492C2214yes—
123#2492C2214yes—
124#2491C2214yes—
125#2491C2214yes—
126#2487C2214yes—
127#2487C2214yes—
128#2481C2218yes—
129#2473C2218yes—
130#2454C2214yes—
131#2454C2214yes—
132#2453C2214yes—
133#2453C2214yes—
134#2450C2218yes—
135#2449C2218yes—
136#2444C2218yes—
137#2443C2218yes—
138#2442C2214yes—
139#2442C2214yes—
140#2442C2214yes—
141#2441C2214yes—
142#2441C2214yes—
143#2441C2214yes—
144#2440C2214yes—
145#2439C2214yes—
146#2436C2214yes—
147#2434C2214yes—
148#2423C2214yes—
149#2422C2214yes—
150#2421C2214yes—
151#2420C2214yes—
152#2401C2214yes—
153#2401C2214yes—
154#2401C2214yes—
155#2401C2214yes—
156C2×#398C2214yes—
157C2×#395C2214yes—
158#2317C2211yescharacteristic
159#2317C2211yescharacteristic
160#2317C2211yescharacteristic
161#2317C2211yescharacteristic
162#2316C2211yescharacteristic
163#2316C2211yescharacteristic
164#2311C2211yescharacteristic
165#2311C2211yescharacteristic
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#384C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#382C2211yescharacteristic
183C2×#382C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190#544—44no—
191#537—44no—
192C2×C4⋊Q8—44no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2318yes—
198C2×#126C2318yes—
199C2×#125—44no—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2314yes—
203C2×#125C2314yes—
204C2×#125C2318yes—
205C2×#124C2318yes—
206C2×#123C2318yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2318yes—
211C2×#121C2314yes—
212C2×#121C2312yes—
213C2×#121C2312yes—
214#520—44no—
215#520—44no—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2312yes—
229C2×#117C2312yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2314yes—
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244#401C2318yes—
245#401C2314yes—
246#401C2314yes—
247#401C2314yes—
248#401C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2314yes—
256#400C2318yes—
257#400C2314yes—
258#400C2314yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2314yes—
292#397C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#396C2314yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#396C2314yes—
317#396C2314yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2318yes—
341#391C2318yes—
342#391C2318yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#390C2311yescharacteristic
348#390C2312yes—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2311yescharacteristic
359#389C2318yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2312yes—
412#386C2312yes—
413#386C2312yes—
414#386C2312yes—
415#386C2314yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2312yes—
427#385C2312yes—
428#385C2318yes—
429#385C2318yes—
430#385C2312yes—
431#385C2312yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2314yes—
442#384C2312yes—
443#384C2314yes—
444#384C2312yes—
445#384C2312yes—
446#383C2318yes—
447#382C2312yes—
448#382C2312yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#382C2312yes—
453#382C2314yes—
454#382C2312yes—
455#382C2314yes—
456#382C2312yes—
457#382C2312yes—
458#381C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊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—
490#376C2312yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#95C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8—44no—
505C22×Q8—84no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2414yes—
509C22×Q8C2418yes—
510C22×D4C2412yes—
511C22×D4C2412yes—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2414yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2411yescharacteristic
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2411yescharacteristic
528C4⋊Q8—48no—
529C4⋊Q8—48no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—88no—
533#126—88no—
534#125—48no—
535#125—48no—
536#125—44no—
537#125—44no—
538#125—88no—
539#124—88no—
540#123—88no—
541C22⋊Q8—48no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544C22⋊Q8—88no—
545#121—44no—
546#121—44no—
547#121—48no—
548C4×Q8—44no—
549C4×Q8—44no—
550C4×D4—44no—
551C4×D4—44no—
552C4×D4—48no—
553C4×D4—48no—
554#117—24no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—24no—
559#117—24no—
560#117—44no—
561#117—44no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4—44no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4—44no—
571C2×C4⋊C4—84no—
572C2×C4⋊C4—84no—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
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×C42—24no—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2418yes—
667#95C2412yes—
668#95C2412yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
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#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715C24C2512yes—
716C24C2512yes—
717C24C2511yescharacteristic
718#41—416no—
719#41—416no—
720C2×Q8—22no—
721C2×Q8—22no—
722C2×Q8—22no—
723C2×Q8—22no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—48no—
727C2×Q8—48no—
728C2×Q8—48no—
729C2×Q8—44no—
730C2×Q8—48no—
731C2×Q8—816no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—44no—
745C2×D4—48no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—24no—
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—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4H(5,𝔽2)14yes—
775C22×C42−1+414yes—
776C22×C42−1+414yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—24no—
878C42—22no—
879C42—22no—
880C42—22no—
881C42—22no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—44no—
887C42—44no—
888C42—48no—
889C42—48no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23C2×H(5,𝔽2)12yes—
903C23C2×2−1+412yes—
904C23C2×2−1+412yes—
905C23C2611yescharacteristic
906Q8—44no—
907Q8—44no—
908Q8—816no—
909Q8—164no—
910D4—48no—
911D4—48no—
912D4—44no—
913D4—44no—
914D4—164no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—48no—
968C2×C4—48no—
969C2×C4—44no—
970C2×C4—44no—
971C2×C4—48no—
972C2×C4—48no—
973C2×C4—84no—
974C2×C4—84no—
975C2×C4—84no—
976C2×C4—84no—
977C2×C4—164no—
978C2×C4—164no—
979C2×C4#563116yes—
980C2×C4C2×H(5,𝔽2)12yes—
981C2×C4C2×H(5,𝔽2)12yes—
982C2×C4C2×2−1+412yes—
983C2×C4C2×2−1+412yes—
984C2×C4C2×2−1+412yes—
985C2×C4C2×2−1+412yes—
986C22—22no—
987C22—24no—
988C22—24no—
989C22—22no—
990C22—42no—
991C22—42no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×#56314yes—
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C22×2−1+411yescharacteristic
1003C22C22×2−1+411yescharacteristic
1004C22H(7,𝔽2)12yes—
1005C222−1+612yes—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—42no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4C2×#56314yes—
1027C4C2×#56314yes—
1028C2—24no—
1029C2—82no—
1030C2—82no—
1031C2C22×#56311yescharacteristic
1032C2#6287611yescharacteristic
1033C2#6287712yes—
1034C2#6287712yes—
1035C2#6288711yescharacteristic
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. #53091C2semidirect
2. #53089C2semidirect
3. #53086C2semidirect
4. #53082C2semidirect
5. #53042C2semidirect
6. #53039C2semidirect
7. #53003C2semidirect
8. #53002C2semidirect
9. #52432C2semidirect
10. #52399C2semidirect
11. #35639C2semidirect
12. #35639C2semidirect
13. #35629C2semidirect
14. #35627C2semidirect
15. #35620C2semidirect
18. #35576C2semidirect
19. #35557C2semidirect
20. #35555C2semidirect
21. #35532C2semidirect
23. #34639C2semidirect
24. #34639C2semidirect
25. C2×#2660C2semidirect

Maximal subgroups

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

subgroupindex
#530912
#530892
#530862
#530822
#530422
#530392
#530032
#530022
#524322
#523992
#356392
#356292
#356272
#356202
#356182
#355922
#355762
#355572
#355552
#355322
#355302
#346392
C2×#26602