Finite Group Databasebeta

← #7652153

Subgroups — #7652153

Order 512.

4776 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42717C214yesmaximal, complemented
2#42672C214yesmaximal, complemented
3#42635C214yesmaximal, complemented
4#42457C214yesmaximal, complemented
5#40838C218yesmaximal, complemented
6#40179C214yesmaximal, complemented
7#39925C214yesmaximal, complemented
8#39660C214yesmaximal, complemented
9#39609C214yesmaximal, complemented
10#38575C218yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35628C211yesmaximal, characteristic, complemented
13#35592C211yesmaximal, characteristic
14#35576C211yesmaximal, characteristic, complemented
15#35532C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic
17#35312C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic
19#35182C211yesmaximal, characteristic, complemented
20C2×#2567C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2862C2212yes—
36#2861C2212yes—
37#2857C2212yes—
38#2853C2214yes—
39#2850C2212yes—
40#2838C2218yes—
41#2838C2218yes—
42#2801C2218yes—
43#2777C2218yes—
44#2774C2218yes—
45#2774C2218yes—
46#2773C2218yes—
47#2772C2218yes—
48#2763C2218yes—
49#2762C2218yes—
50#2759C2218yes—
51#2755C2218yes—
52#2742C2218yes—
53#2742C2218yes—
54#2729C2218yes—
55#2717C2218yes—
56#2702C2218yes—
57#2674C2218yes—
58#2666C2218yes—
59#2663C2218yes—
60#2655C2218yes—
61#2650C2218yes—
62#2642C2212yes—
63#2640C2212yes—
64#2632C2218yes—
65#2628C2218yes—
66#2623C2214yes—
67#2621C2212yes—
68#2620C2212yes—
69#2592C2214yes—
70#2591C2214yes—
71#2583C2214yes—
72#2568C2214yes—
73#2567C2214yes—
74#2567C2214yes—
75#2567C2214yes—
76#2567C2214yes—
77#2567C2212yes—
78#2566C2212yes—
79#2565C2212yes—
80#2551C2214yes—
81#2551C2214yes—
82#2550C2214yes—
83#2550C2214yes—
84#2542C2212yes—
85#2525C2218yes—
86#2514C2212yes—
87#2514C2214yes—
88#2514C2214yes—
89#2513C2212yes—
90#2512C2212yes—
91#2511C2212yes—
92#2511C2214yes—
93#2511C2214yes—
94#2510C2214yes—
95#2509C2218yes—
96#2502C2212yes—
97#2501C2212yes—
98#2500C2212yes—
99#2499C2212yes—
100#2493C2218yes—
101#2492C2214yes—
102#2492C2214yes—
103#2492C2214yes—
104#2492C2214yes—
105#2491C2214yes—
106#2491C2214yes—
107#2489C2214yes—
108#2489C2214yes—
109#2488C2218yes—
110#2488C2218yes—
111#2481C2214yes—
112#2474C2218yes—
113#2470C2218yes—
114#2465C2218yes—
115#2454C2212yes—
116#2453C2212yes—
117#2452C2212yes—
118#2451C2218yes—
119#2451C2212yes—
120#2450C2214yes—
121#2449C2218yes—
122#2449C2214yes—
123#2448C2214yes—
124#2446C2214yes—
125#2443C2218yes—
126#2441C2214yes—
127#2440C2214yes—
128#2436C2214yes—
129#2434C2214yes—
130#2429C2214yes—
131#2427C2214yes—
132#2425C2218yes—
133#2423C2214yes—
134#2423C2214yes—
135#2422C2214yes—
136#2421C2214yes—
137#2401C2214yes—
138#2396C2214yes—
139C2×#395C2214yes—
140#2367C2214yes—
141#2365C2214yes—
142#2362C2214yes—
143#2360C2218yes—
144#2360C2214yes—
145#2355C2214yes—
146#2355C2214yes—
147#2354C2214yes—
148#2352C2218yes—
149Q8×C4⋊C4C2214yes—
150#2334C2218yes—
151#2330C2214yes—
152#2323C2218yes—
153#2322C2214yes—
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2314C2214yes—
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163C4×C4⋊Q8C2214yes—
164C4×#126C2214yes—
165C4×C22⋊Q8C2214yes—
166C4×#123C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#389C2214yes—
178#2285C2211yescharacteristic
179#2285C2214yes—
180C2×#384C2211yescharacteristic
181C2×#384C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2312yes—
191#544—44no—
192#537—44no—
193#536—28no—
194#536—44no—
195#533—28no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2318yes—
205C2×#126C2314yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2318yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2318yes—
224C2×#121C2314yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227#520—44no—
228C4×#41—28no—
229C2×C4×Q8—44no—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2318yes—
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C42C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2312yes—
263#401C2314yes—
264#401C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#399C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2314yes—
297#396C2318yes—
298#396C2314yes—
299#396C2318yes—
300#396C2314yes—
301#396C2314yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2314yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2314yes—
319#391C2318yes—
320#391C2311yescharacteristic
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2311yescharacteristic
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2314yes—
336#391C2312yes—
337#391C2318yes—
338#391C2311yescharacteristic
339#391C2318yes—
340#391C2312yes—
341#391C2311yescharacteristic
342#391C2318yes—
343#391C2318yes—
344#391C2312yes—
345#391C2314yes—
346#390C2311yescharacteristic
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2312yes—
354#390C2311yescharacteristic
355#390C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2312yes—
417#386C2312yes—
418#386C2312yes—
419#386C2318yes—
420#386C2312yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2312yes—
429#385C2318yes—
430#385C2312yes—
431#385C2312yes—
432#385C2318yes—
433#385C2312yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2314yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#383C2314yes—
448#383C2318yes—
449#382C2312yes—
450#382C2318yes—
451#382C2312yes—
452#382C2312yes—
453#382C2312yes—
454#382C2318yes—
455#382C2318yes—
456#381C2314yes—
457#381C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2318yes—
464#380C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497C2×#95C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C43C2312yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—44no—
511C22×Q8—84no—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2414yes—
517C22×Q8C2414yes—
518C22×Q8C2418yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2414yes—
524C23×C4C2411yescharacteristic
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2411yescharacteristic
535C23×C4C2414yes—
536C23×C4C2411yescharacteristic
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—88no—
545#126—216no—
546#125—28no—
547#125—44no—
548#125—44no—
549#124—28no—
550#124—44no—
551#124—88no—
552#123—216no—
553#123—48no—
554#123—88no—
555C22⋊Q8—216no—
556C22⋊Q8—216no—
557C22⋊Q8—216no—
558C22⋊Q8—48no—
559C22⋊Q8—44no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—88no—
564#121—44no—
565#121—44no—
566#121—48no—
567C4×Q8—28no—
568C4×Q8—216no—
569C4×Q8—48no—
570C4×Q8—48no—
571C4×Q8—44no—
572C4×Q8—88no—
573C4×D4—28no—
574C4×D4—216no—
575C4×D4—44no—
576C4×D4—48no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—24no—
582#117—28no—
583#117—44no—
584#117—88no—
585#117#4118yes—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—84no—
594C2×C4⋊C4—84no—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C42—24no—
669C2×C42—24no—
670C2×C42—24no—
671C2×C42—28no—
672C2×C42—44no—
673C2×C42C2411yescharacteristic
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2418yes—
691C2×C42C2414yes—
692C2×C42C2418yes—
693C2×C42C2418yes—
694C2×C42C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2418yes—
710#95C2414yes—
711#95C2418yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736C24C2512yes—
737C24C2512yes—
738C24C2511yescharacteristic
739#41—416no—
740#41—416no—
741C2×Q8—22no—
742C2×Q8—28no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—28no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—44no—
756C2×Q8—48no—
757C2×Q8—48no—
758C2×Q8—48no—
759C2×Q8—44no—
760C2×Q8—48no—
761C2×Q8—416no—
762C2×Q8—816no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—44no—
776C2×D4—48no—
777C22×C4—22no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4C2×#4114yes—
808C22×C4H(5,𝔽2)14yes—
809C22×C42−1+414yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4C2×#4118yes—
878C4⋊C42−1+418yes—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—28no—
885C22⋊C4—216no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4C2×#4118yes—
905C42—22no—
906C42—22no—
907C42—24no—
908C42—28no—
909C42—24no—
910C42—22no—
911C42—22no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—28no—
920C42—48no—
921C42—44no—
922C42—48no—
923C42—48no—
924C42—44no—
925C42—48no—
926C42C2×#4118yes—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23C22×#4112yes—
940C23C2×H(5,𝔽2)12yes—
941C23C2×2−1+412yes—
942C23C2611yescharacteristic
943Q8—416no—
944Q8—48no—
945Q8—48no—
946Q8—44no—
947Q8—44no—
948Q8—816no—
949Q8—164no—
950D4—48no—
951D4—48no—
952D4—44no—
953D4—44no—
954D4—164no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—416no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—44no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—84no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—164no—
1016C2×C4#542116yes—
1017C2×C4C22×#4118yes—
1018C2×C4C22×#4112yes—
1019C2×C4C22×#4112yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×H(5,𝔽2)12yes—
1022C2×C4C2×2−1+414yes—
1023C2×C4C2×2−1+414yes—
1024C2×C4C2×2−1+414yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4C2×2−1+412yes—
1027C22—24no—
1028C22—22no—
1029C22—22no—
1030C22—24no—
1031C22—44no—
1032C22—44no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—44no—
1040C22—44no—
1041C22C2×#54214yes—
1042C22C23×#4111yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×2−1+412yes—
1045C22C22×2−1+411yescharacteristic
1046C22H(7,𝔽2)12yes—
1047C4—24no—
1048C4—28no—
1049C4—24no—
1050C4—24no—
1051C4—42no—
1052C4—42no—
1053C4—44no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—42no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4C2×#54214yes—
1068C4C2×#54214yes—
1069C2—24no—
1070C2—82no—
1071C2—82no—
1072C2C22×#54211yescharacteristic
1073C2#6283311yescharacteristic
1074C2#6287611yescharacteristic
1075C2#6294312yes—
1076C2#6300012yes—
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. #42717C2semidirect
2. #42672C2semidirect
3. #42635C2semidirect
4. #42457C2semidirect
5. #40838C2semidirect
6. #40179C2semidirect
7. #39925C2semidirect
8. #39660C2semidirect
9. #39609C2semidirect
10. #38575C2semidirect
11. #35630C2semidirect
12. #35628C2semidirect
14. #35576C2semidirect
15. #35532C2semidirect
17. #35312C2semidirect
19. #35182C2semidirect
20. C2×#2567C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34266C2semidirect
24. #34214C2semidirect
25. #34188C2semidirect

Maximal subgroups

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

subgroupindex
#427172
#426722
#426352
#424572
#408382
#401792
#399252
#396602
#396092
#385752
#356302
#356282
#355922
#355762
#355322
#355302
#353122
#353082
#351822
C2×#25672
#348162
#347452
#342662
#342142
#341882