Finite Group Databasebeta

← #7646391

Subgroups — #7646391

Order 512.

4862 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42700C214yesmaximal, complemented
2#42699C214yesmaximal, complemented
3#42671C214yesmaximal, complemented
4#42666C214yesmaximal, complemented
5#39643C212yesmaximal, complemented
6#39608C212yesmaximal, complemented
7#39515C212yesmaximal, complemented
8#39479C212yesmaximal, complemented
9#39201C212yesmaximal, complemented
10#39158C212yesmaximal, complemented
11#38985C212yesmaximal, complemented
12#38932C212yesmaximal, complemented
13#37505C214yesmaximal, complemented
14#36809C218yesmaximal, complemented
15#35519C212yesmaximal, complemented
16#35517C212yesmaximal, complemented
17#35289C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35230C214yesmaximal, complemented
20#35180C212yesmaximal, complemented
21#35160C212yesmaximal, complemented
22#34938C211yesmaximal, characteristic, complemented
23#34937C211yesmaximal, characteristic
24#34206C211yesmaximal, characteristic, complemented
25C2×#2369C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27C2×#533C2212yes—
28C2×#532C2211yescharacteristic
29C2×#532C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×#520C2212yes—
32C2×C4×#41C2211yescharacteristic
33#2862C2212yes—
34#2858C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2852C2218yes—
38#2850C2218yes—
39#2838C2218yes—
40#2837C2218yes—
41#2799C2218yes—
42#2798C2218yes—
43#2764C2218yes—
44#2763C2218yes—
45#2759C2218yes—
46#2759C2218yes—
47#2755C2218yes—
48#2754C2218yes—
49#2715C2218yes—
50#2712C2218yes—
51#2710C2218yes—
52#2702C2218yes—
53#2700C2218yes—
54#2700C2218yes—
55#2692C2218yes—
56#2687C2218yes—
57#2663C2218yes—
58#2652C2218yes—
59#2651C2218yes—
60#2650C2218yes—
61#2647C2214yes—
62#2644C2214yes—
63#2643C2218yes—
64#2640C2214yes—
65#2639C2218yes—
66#2628C2214yes—
67#2628C2214yes—
68#2624C2214yes—
69#2592C2214yes—
70#2592C2214yes—
71#2582C2214yes—
72#2581C2214yes—
73#2580C2214yes—
74#2568C2214yes—
75#2568C2212yes—
76#2567C2212yes—
77#2563C2212yes—
78#2563C2212yes—
79#2563C2212yes—
80#2563C2214yes—
81#2562C2214yes—
82#2562C2214yes—
83#2552C2211yescharacteristic
84#2552C2211yescharacteristic
85#2551C2211yescharacteristic
86#2551C2211yescharacteristic
87#2550C2212yes—
88#2550C2212yes—
89#2549C2214yes—
90#2548C2214yes—
91#2548C2211yescharacteristic
92#2547C2211yescharacteristic
93#2547C2214yes—
94#2547C2212yes—
95#2547C2212yes—
96#2546C2211yescharacteristic
97#2545C2212yes—
98#2544C2212yes—
99#2543C2214yes—
100#2542C2212yes—
101#2541C2211yescharacteristic
102#2538C2214yes—
103#2521C2218yes—
104#2515C2218yes—
105#2514C2214yes—
106#2513C2214yes—
107#2512C2214yes—
108#2512C2214yes—
109#2511C2214yes—
110#2509C2214yes—
111#2508C2214yes—
112#2504C2214yes—
113#2497C2214yes—
114#2496C2214yes—
115#2495C2214yes—
116#2495C2214yes—
117#2494C2214yes—
118#2494C2214yes—
119#2491C2214yes—
120#2487C2214yes—
121#2487C2214yes—
122#2486C2214yes—
123#2485C2214yes—
124#2485C2214yes—
125#2452C2214yes—
126#2450C2218yes—
127#2449C2218yes—
128#2448C2214yes—
129#2447C2214yes—
130#2446C2214yes—
131#2445C2214yes—
132#2444C2218yes—
133#2443C2218yes—
134#2442C2214yes—
135#2441C2214yes—
136#2440C2212yes—
137#2440C2212yes—
138#2440C2214yes—
139#2439C2214yes—
140#2436C2214yes—
141#2422C2214yes—
142#2416C2212yes—
143#2416C2212yes—
144#2409C2214yes—
145#2399C2214yes—
146#2392C2214yes—
147#2369C2212yes—
148#2369C2212yes—
149#2369C2212yes—
150#2369C2214yes—
151#2369C2212yes—
152#2369C2214yes—
153#2367C2214yes—
154#2366C2212yes—
155#2365C2212yes—
156#2354C2212yes—
157#2352C2214yes—
158D4×C4⋊C4C2212yes—
159#2331C2214yes—
160#2325C2214yes—
161#2324C2214yes—
162#2320C2212yes—
163#2319C2212yes—
164#2319C2214yes—
165#2318C2214yes—
166#2317C2211yescharacteristic
167#2317C2211yescharacteristic
168#2317C2212yes—
169#2314C2212yes—
170#2314C2212yes—
171#2314C2214yes—
172#2311C2211yescharacteristic
173#2311C2211yescharacteristic
174#2311C2212yes—
175#2311C2212yes—
176#2311C2212yes—
177#2311C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182C4×#121C2214yes—
183#2297C2212yes—
184#2296C2212yes—
185#2295C2212yes—
186C2×#391C2214yes—
187#2293C2212yes—
188C2×#389C2212yes—
189C2×#389C2212yes—
190#2290C2214yes—
191#2285C2212yes—
192#2285C2211yescharacteristic
193#2283C2212yes—
194C4×#117C2211yescharacteristic
195C2×C4×C4⋊C4C2211yescharacteristic
196C2×C4×C4⋊C4C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×Q8C2312yes—
202#533—48no—
203#532—28no—
204#532—48no—
205C2×C4⋊Q8—28no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×#127C2311yescharacteristic
217C2×#127C2312yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#123C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239#520—48no—
240C4×#41—28no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2318yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2311yescharacteristic
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2314yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2314yes—
276C22×C42C2311yescharacteristic
277#401C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2314yes—
312#396C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2314yes—
316#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2314yes—
322#394C2318yes—
323#394C2314yes—
324#394C2314yes—
325#394C2318yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#392C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2312yes—
340#391C2314yes—
341#391C2318yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2318yes—
347#391C2314yes—
348#391C2314yes—
349#391C2318yes—
350#391C2318yes—
351#391C2318yes—
352#391C2318yes—
353#390C2314yes—
354#390C2314yes—
355#390C2318yes—
356#390C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#390C2312yes—
366#390C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2318yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2314yes—
445#385C2318yes—
446#384C2312yes—
447#384C2312yes—
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#383C2314yes—
454#383C2318yes—
455#382C2314yes—
456#382C2318yes—
457#382C2314yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#381C2314yes—
464#381C2318yes—
465#380C2312yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2318yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2312yes—
519#376C2314yes—
520C2×#95C2312yes—
521C2×#95C2314yes—
522C2×#95C2314yes—
523C2×#95C2312yes—
524C43C2312yes—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—28no—
531C22×Q8—28no—
532C22×Q8—82no—
533C22×Q8—82no—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C22×Q8C2414yes—
539C22×Q8C2414yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2418yes—
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—28no—
564C4⋊Q8—28no—
565C4⋊Q8—28no—
566C4⋊Q8—24no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570C4⋊Q8—44no—
571#127—24no—
572#127—44no—
573#126—88no—
574#125—44no—
575#125—44no—
576#124—28no—
577#124—44no—
578#124—44no—
579#124—88no—
580#124—84no—
581#124—84no—
582#123—88no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—88no—
586C22⋊Q8—84no—
587C22⋊Q8—84no—
588#121—28no—
589#121—28no—
590#121—28no—
591#121—44no—
592#121—48no—
593#121—48no—
594C4×Q8—24no—
595C4×Q8—24no—
596C4×Q8—48no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—416no—
610#117—24no—
611#117—28no—
612#117—24no—
613#117—24no—
614#117—28no—
615#117—48no—
616#117—48no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—42no—
623C2×C4⋊C4—48no—
624C2×C4⋊C4—84no—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C42—28no—
706C2×C42—28no—
707C2×C42—44no—
708C2×C42—84no—
709C2×C42#4118yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2418yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2418yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775C24C2512yes—
776C24C2514yes—
777C24C2511yescharacteristic
778#41—416no—
779#41—432no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—24no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—816no—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—28no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—24no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—42no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4C2×#4114yes—
858C22×C4C2×#4114yes—
859C22×C4C2×#4114yes—
860C22×C4H(5,𝔽2)14yes—
861C22×C42−1+414yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2518yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2512yes—
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—42no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C42−1+414yes—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—28no—
977C42—24no—
978C42—44no—
979C42—48no—
980C42—48no—
981C42—48no—
982C42—42no—
983C42—42no—
984C42C2×#4114yes—
985C42C2×#4114yes—
986C42C2×#4114yes—
987C42C2×#4114yes—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—22no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23C22×#4112yes—
1007C23C2×H(5,𝔽2)12yes—
1008C23C2×2−1+412yes—
1009C23C2611yescharacteristic
1010Q8—44no—
1011Q8—48no—
1012Q8—88no—
1013Q8—88no—
1014Q8—88no—
1015Q8—88no—
1016D4—48no—
1017D4—416no—
1018D4—44no—
1019D4—48no—
1020D4—48no—
1021D4—84no—
1022D4—88no—
1023D4—88no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—28no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—44no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—416no—
1085C2×C4—48no—
1086C2×C4—416no—
1087C2×C4—48no—
1088C2×C4—84no—
1089C2×C4—84no—
1090C2×C4—84no—
1091C2×C4—168no—
1092C2×C4#542116yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4112yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×H(5,𝔽2)12yes—
1101C2×C4C2×2−1+414yes—
1102C2×C4C2×2−1+412yes—
1103C2×C4C2×2−1+412yes—
1104C2×C4C2×2−1+412yes—
1105C2×C4#58512yes—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—42no—
1113C22—44no—
1114C22—42no—
1115C22—44no—
1116C22—42no—
1117C22—44no—
1118C22—44no—
1119C22—42no—
1120C22—42no—
1121C22—44no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22C2×#54214yes—
1127C22C23×#4111yescharacteristic
1128C22C22×H(5,𝔽2)11yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C22C22×2−1+411yescharacteristic
1131C22C2×#58511yescharacteristic
1132C22H(7,𝔽2)11yescharacteristic
1133C22H(7,𝔽2)11yescharacteristic
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—24no—
1138C4—42no—
1139C4—48no—
1140C4—42no—
1141C4—42no—
1142C4—44no—
1143C4—44no—
1144C4—42no—
1145C4—42no—
1146C4—44no—
1147C4—42no—
1148C4—42no—
1149C4—44no—
1150C4—42no—
1151C4—42no—
1152C4—44no—
1153C4—42no—
1154C4C2×#54214yes—
1155C4C2×#54214yes—
1156C4#350714yes—
1157C2—24no—
1158C2—82no—
1159C2—84no—
1160C2C22×#54211yescharacteristic
1161C2C2×#350711yescharacteristic
1162C2#6285511yescharacteristic
1163C2#6292611yescharacteristic
1164C2#6293011yescharacteristic
1165C2#6294311yescharacteristic
1166C2#6294411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42700C2semidirect
2. #42699C2semidirect
3. #42671C2semidirect
4. #42666C2semidirect
5. #39643C2semidirect
6. #39608C2semidirect
7. #39515C2semidirect
8. #39479C2semidirect
9. #39201C2semidirect
10. #39158C2semidirect
11. #38985C2semidirect
12. #38932C2semidirect
13. #37505C2semidirect
14. #36809C2semidirect
15. #35519C2semidirect
16. #35517C2semidirect
17. #35289C2semidirect
18. #35279C2semidirect
19. #35230C2semidirect
20. #35180C2semidirect
21. #35160C2semidirect
22. #34938C2semidirect
24. #34206C2semidirect
25. C2×#2369C2semidirect
26. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#427002
#426992
#426712
#426662
#396432
#396082
#395152
#394792
#392012
#391582
#389852
#389322
#375052
#368092
#355192
#355172
#352892
#352792
#352302
#351802
#351602
#349382
#349372
#342062
C2×#23692
#340602