Finite Group Databasebeta

← #8094590

Subgroups — #8094590

Order 512.

4468 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53133C214yesmaximal, complemented
2#53113C214yesmaximal, complemented
3#53099C212yesmaximal, complemented
4#53081C212yesmaximal, complemented
5#53033C212yesmaximal, complemented
6#53031C212yesmaximal, complemented
7#52414C214yesmaximal, complemented
8#52413C214yesmaximal, complemented
9#46348C214yesmaximal, complemented
10#46345C212yesmaximal, complemented
11#46343C214yesmaximal, complemented
12#46331C212yesmaximal, complemented
13#46326C214yesmaximal, complemented
14#46196C212yesmaximal, complemented
15#46174C214yesmaximal, complemented
16#46152C212yesmaximal, complemented
17#35574C212yesmaximal, complemented
18#35519C212yesmaximal, complemented
19#35517C212yesmaximal
20#35267C212yesmaximal, complemented
21#35265C212yesmaximal, complemented
22#35160C212yesmaximal, complemented
23#34955C211yesmaximal, characteristic
24#34953C211yesmaximal, characteristic, complemented
25C2×#2567C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C2×#520C2212yes—
30C22×C4×Q8C2211yescharacteristic
31#2864C2214yes—
32#2863C2214yes—
33#2860C2214yes—
34#2859C2214yes—
35#2852C2218yes—
36#2844C2214yes—
37#2843C2214yes—
38#2843C2214yes—
39#2838C2218yes—
40#2838C2218yes—
41#2833C2218yes—
42#2832C2214yes—
43#2831C2218yes—
44#2831C2218yes—
45#2830C2214yes—
46#2823C2214yes—
47#2817C2218yes—
48#2814C2218yes—
49#2809C2214yes—
50#2799C2214yes—
51#2794C2214yes—
52#2793C2218yes—
53#2791C2218yes—
54#2789C2214yes—
55#2774C2218yes—
56#2764C2218yes—
57#2762C2218yes—
58#2759C2218yes—
59#2745C2218yes—
60#2731C2214yes—
61#2723C2218yes—
62#2721C2218yes—
63#2720C2218yes—
64#2720C2218yes—
65#2718C2218yes—
66#2716C2218yes—
67#2715C2218yes—
68#2690C2218yes—
69#2689C2218yes—
70#2683C2214yes—
71#2680C2214yes—
72#2680C2214yes—
73#2647C2214yes—
74#2647C2214yes—
75#2645C2214yes—
76#2644C2214yes—
77#2643C2218yes—
78#2592C2212yes—
79#2592C2212yes—
80#2591C2212yes—
81#2591C2212yes—
82#2584C2212yes—
83#2584C2212yes—
84#2583C2212yes—
85#2583C2212yes—
86#2582C2214yes—
87#2581C2214yes—
88#2580C2214yes—
89#2579C2218yes—
90#2568C2211yescharacteristic
91#2568C2211yescharacteristic
92#2567C2212yes—
93#2567C2212yes—
94#2567C2211yescharacteristic
95#2567C2212yes—
96#2567C2212yes—
97#2567C2211yescharacteristic
98#2567C2212yes—
99#2567C2212yes—
100#2567C2212yes—
101#2567C2212yes—
102#2548C2211yescharacteristic
103#2548C2211yescharacteristic
104#2546C2211yescharacteristic
105#2546C2211yescharacteristic
106#2538C2214yes—
107#2514C2214yes—
108#2513C2214yes—
109#2512C2214yes—
110#2511C2214yes—
111#2510C2218yes—
112#2509C2214yes—
113#2508C2214yes—
114#2507C2214yes—
115#2506C2214yes—
116#2505C2218yes—
117#2504C2212yes—
118#2502C2212yes—
119#2497C2214yes—
120#2497C2214yes—
121#2496C2214yes—
122#2496C2214yes—
123#2495C2214yes—
124#2495C2214yes—
125#2494C2214yes—
126#2494C2214yes—
127#2487C2214yes—
128#2486C2214yes—
129#2485C2214yes—
130#2485C2214yes—
131#2481C2218yes—
132#2473C2218yes—
133#2452C2214yes—
134#2452C2214yes—
135#2451C2214yes—
136#2451C2214yes—
137#2450C2218yes—
138#2449C2218yes—
139#2448C2214yes—
140#2447C2214yes—
141#2446C2214yes—
142#2445C2214yes—
143#2444C2218yes—
144#2443C2218yes—
145#2442C2214yes—
146#2441C2214yes—
147#2440C2214yes—
148#2440C2214yes—
149#2440C2214yes—
150#2439C2214yes—
151#2439C2214yes—
152#2439C2214yes—
153#2436C2212yes—
154#2434C2212yes—
155#2409C2218yes—
156#2399C2212yes—
157#2399C2212yes—
158#2398C2212yes—
159#2398C2212yes—
160C2×#395C2212yes—
161C2×#395C2212yes—
162#2383C2218yes—
163#2381C2214yes—
164#2379C2214yes—
165#2317C2212yes—
166#2317C2212yes—
167#2317C2212yes—
168#2316C2212yes—
169#2311C2212yes—
170#2311C2212yes—
171#2311C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×#124C2212yes—
175C4×#124C2212yes—
176#2297C2212yes—
177#2297C2212yes—
178#2296C2212yes—
179#2296C2212yes—
180C2×#391C2212yes—
181C2×#389C2212yes—
182C2×#389C2212yes—
183C2×#384C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2312yes—
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190#533—44no—
191#532—44no—
192C2×C4⋊Q8—44no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2311yescharacteristic
202C2×#127C2311yescharacteristic
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#125C2312yes—
206C2×#125C2318yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218#520—48no—
219C2×C4×Q8—44no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2314yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252#401C2318yes—
253#401C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2312yes—
259#400C2312yes—
260#400C2312yes—
261#400C2312yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2318yes—
271#399C2318yes—
272#398C2312yes—
273#398C2318yes—
274#398C2312yes—
275#398C2312yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2312yes—
286#398C2318yes—
287#397C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#395C2312yes—
305#395C2314yes—
306#395C2318yes—
307#395C2318yes—
308#395C2314yes—
309#395C2314yes—
310#395C2314yes—
311#395C2314yes—
312#395C2314yes—
313#395C2314yes—
314#395C2314yes—
315#395C2312yes—
316#395C2312yes—
317#395C2312yes—
318#395C2314yes—
319#395C2318yes—
320#395C2314yes—
321#394C2312yes—
322#394C2318yes—
323#394C2318yes—
324#394C2312yes—
325#394C2312yes—
326#394C2312yes—
327#393C2318yes—
328#393C2314yes—
329#393C2318yes—
330#393C2318yes—
331#393C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2318yes—
350#391C2318yes—
351#391C2318yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2314yes—
440#385C2314yes—
441#385C2318yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#383C2318yes—
452#383C2318yes—
453#382C2312yes—
454#382C2312yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#382C2318yes—
459#381C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490#376C2312yes—
491#376C2312yes—
492C2×#95C2312yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C43C2312yes—
496C43C2312yes—
497C2×#41—28no—
498C2×#41—28no—
499C2×#41—28no—
500C22×Q8—24no—
501C22×Q8—42no—
502C22×Q8—44no—
503C22×Q8—42no—
504C22×Q8—84no—
505C22×Q8C2412yes—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2414yes—
512C22×Q8C2414yes—
513C22×Q8C2411yescharacteristic
514C22×D4C2414yes—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C23×C4C2411yescharacteristic
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2411yescharacteristic
527C23×C4C2418yes—
528C23×C4C2411yescharacteristic
529C4⋊Q8—28no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—42no—
535C4⋊Q8—42no—
536C4⋊Q8—42no—
537C4⋊Q8—44no—
538#127—42no—
539#126—416no—
540#126—88no—
541#125—44no—
542#125—88no—
543#124—28no—
544#124—44no—
545#124—44no—
546#123—88no—
547C22⋊Q8—44no—
548C22⋊Q8—44no—
549C22⋊Q8—88no—
550C22⋊Q8—88no—
551C22⋊Q8—88no—
552#121—44no—
553#121—44no—
554C4×Q8—42no—
555C4×Q8—42no—
556C4×Q8—42no—
557C4×Q8—42no—
558C4×Q8—42no—
559C4×Q8—42no—
560C4×Q8—42no—
561C4×Q8—42no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×Q8—48no—
565C4×D4—48no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—416no—
569#117—28no—
570#117—28no—
571#117—28no—
572#117—48no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—48no—
576C2×C4⋊C4—42no—
577C2×C4⋊C4—42no—
578C2×C4⋊C4—42no—
579C2×C4⋊C4—44no—
580C2×C4⋊C4—84no—
581C2×C4⋊C4—84no—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C42—24no—
654C2×C42—24no—
655C2×C42—24no—
656C2×C42—44no—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2418yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2414yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
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#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723C24C2514yes—
724C24C2511yescharacteristic
725#41—432no—
726C2×Q8—24no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—22no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—41no—
736C2×Q8—41no—
737C2×Q8—41no—
738C2×Q8—41no—
739C2×Q8—41no—
740C2×Q8—41no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8—44no—
744C2×Q8—48no—
745C2×Q8—48no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—42no—
749C2×Q8—416no—
750C2×Q8—816no—
751C2×Q82−1+414yes—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—44no—
762C2×D4—42no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4H(5,𝔽2)14yes—
791C22×C42−1+418yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2518yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2518yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2514yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—48no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C42—22no—
887C42—22no—
888C42—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—28no—
899C42—28no—
900C42—28no—
901C42—24no—
902C42—24no—
903C42—28no—
904C42—44no—
905C42—48no—
906C42—42no—
907C42—44no—
908C42—44no—
909C42—42no—
910C23—21no—
911C23—21no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23C2×H(5,𝔽2)12yes—
921C23C2×2−1+414yes—
922C23C2611yescharacteristic
923Q8—44no—
924Q8—44no—
925Q8—44no—
926Q8—44no—
927Q8—48no—
928Q8—84no—
929Q8—84no—
930Q8—88no—
931Q8—88no—
932D4—416no—
933D4—48no—
934D4—84no—
935D4—84no—
936C2×C4—28no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—21no—
973C2×C4—24no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—28no—
987C2×C4—28no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—416no—
993C2×C4—44no—
994C2×C4—416no—
995C2×C4—82no—
996C2×C4—82no—
997C2×C4—88no—
998C2×C4—168no—
999C2×C4#563116yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+414yes—
1006C2×C4C2×2−1+414yes—
1007C2×C4#58512yes—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—24no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22C2×#56314yes—
1020C22C22×H(5,𝔽2)11yescharacteristic
1021C22C22×2−1+411yescharacteristic
1022C22C22×2−1+412yes—
1023C22C2×#58511yescharacteristic
1024C22H(7,𝔽2)12yes—
1025C4—22no—
1026C4—22no—
1027C4—22no—
1028C4—22no—
1029C4—41no—
1030C4—41no—
1031C4—44no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—48no—
1037C4—41no—
1038C4—41no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—48no—
1043C4—44no—
1044C4—44no—
1045C4—44no—
1046C4C2×#56314yes—
1047C4C2×#56314yes—
1048C2—24no—
1049C2—84no—
1050C2C22×#56311yescharacteristic
1051C2#6281911yescharacteristic
1052C2#6287411yescharacteristic
1053C2#6292612yes—
1054C2#6294312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53133C2semidirect
2. #53113C2semidirect
3. #53099C2semidirect
4. #53081C2semidirect
5. #53033C2semidirect
6. #53031C2semidirect
7. #52414C2semidirect
8. #52413C2semidirect
9. #46348C2semidirect
10. #46345C2semidirect
11. #46343C2semidirect
12. #46331C2semidirect
13. #46326C2semidirect
14. #46196C2semidirect
15. #46174C2semidirect
16. #46152C2semidirect
17. #35574C2semidirect
18. #35519C2semidirect
20. #35267C2semidirect
21. #35265C2semidirect
22. #35160C2semidirect
24. #34953C2semidirect
25. C2×#2567C2semidirect

Maximal subgroups

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

subgroupindex
#531332
#531132
#530992
#530812
#530332
#530312
#524142
#524132
#463482
#463452
#463432
#463312
#463262
#461962
#461742
#461522
#355742
#355192
#355172
#352672
#352652
#351602
#349552
#349532
C2×#25672