Finite Group Databasebeta

← #7642944

Subgroups — #7642944

Order 512.

4758 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40023C214yesmaximal, complemented
2#40022C214yesmaximal, complemented
3#40001C214yesmaximal, complemented
4#40000C214yesmaximal, complemented
5#39771C212yesmaximal, complemented
6#39761C212yesmaximal, complemented
7#39643C212yesmaximal, complemented
8#39633C212yesmaximal, complemented
9#38985C212yesmaximal, complemented
10#38984C212yesmaximal, complemented
11#38978C212yesmaximal, complemented
12#38977C212yesmaximal, complemented
13#36764C214yesmaximal, complemented
14#36763C214yesmaximal, complemented
15#36645C211yesmaximal, characteristic, complemented
16#36639C211yesmaximal, characteristic
17#35628C212yesmaximal, complemented
18#35619C212yesmaximal, complemented
19#35545C212yesmaximal, complemented
20#35519C212yesmaximal, complemented
21#35270C214yesmaximal, complemented
22#35179C211yesmaximal, characteristic, complemented
23#35178C211yesmaximal, characteristic
24#35083C214yesmaximal, complemented
25#34213C211yesmaximal, characteristic, complemented
26#34206C211yesmaximal, characteristic
27C2×#2295C211yesmaximal, characteristic, complemented
28C2×#536C2212yes—
29C2×#533C2211yescharacteristic
30C2×#533C2212yes—
31C2×#532C2211yescharacteristic
32C2×#520C2212yes—
33C22×C4×Q8C2211yescharacteristic
34#2868C2211yescharacteristic
35#2868C2211yescharacteristic
36#2862C2211yescharacteristic
37#2862C2211yescharacteristic
38#2862C2212yes—
39#2861C2212yes—
40#2861C2212yes—
41#2859C2212yes—
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2858C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2855C2214yes—
51#2854C2214yes—
52#2850C2212yes—
53#2850C2212yes—
54#2850C2212yes—
55#2850C2212yes—
56#2799C2218yes—
57#2796C2218yes—
58#2793C2218yes—
59#2790C2218yes—
60#2777C2218yes—
61#2772C2218yes—
62#2767C2218yes—
63#2765C2218yes—
64#2762C2218yes—
65#2755C2218yes—
66#2751C2218yes—
67#2739C2218yes—
68#2729C2218yes—
69#2716C2218yes—
70#2715C2218yes—
71#2700C2218yes—
72#2654C2218yes—
73#2650C2218yes—
74#2647C2214yes—
75#2645C2214yes—
76#2644C2214yes—
77#2640C2214yes—
78#2627C2214yes—
79#2618C2214yes—
80#2592C2214yes—
81#2592C2214yes—
82#2582C2212yes—
83#2582C2212yes—
84#2582C2214yes—
85#2581C2214yes—
86#2581C2214yes—
87#2580C2214yes—
88#2568C2214yes—
89#2568C2214yes—
90#2568C2212yes—
91#2567C2212yes—
92#2565C2214yes—
93#2548C2212yes—
94#2546C2212yes—
95#2545C2214yes—
96#2538C2212yes—
97#2538C2212yes—
98#2538C2214yes—
99#2536C2214yes—
100#2532C2218yes—
101#2530C2218yes—
102#2529C2218yes—
103#2527C2218yes—
104#2514C2214yes—
105#2513C2214yes—
106#2512C2214yes—
107#2512C2214yes—
108#2511C2214yes—
109#2511C2214yes—
110#2510C2218yes—
111#2509C2214yes—
112#2508C2214yes—
113#2503C2214yes—
114#2502C2214yes—
115#2499C2214yes—
116#2499C2214yes—
117#2497C2214yes—
118#2496C2214yes—
119#2495C2214yes—
120#2494C2214yes—
121#2492C2214yes—
122#2492C2214yes—
123#2489C2214yes—
124#2489C2214yes—
125#2488C2218yes—
126#2488C2218yes—
127#2481C2218yes—
128#2452C2214yes—
129#2451C2214yes—
130#2450C2218yes—
131#2449C2218yes—
132#2448C2214yes—
133#2447C2214yes—
134#2447C2214yes—
135#2447C2214yes—
136#2446C2214yes—
137#2446C2214yes—
138#2442C2214yes—
139#2441C2214yes—
140#2440C2214yes—
141#2439C2214yes—
142#2419C2218yes—
143#2419C2218yes—
144#2370C2214yes—
145#2369C2212yes—
146#2367C2214yes—
147#2366C2212yes—
148#2365C2212yes—
149#2365C2212yes—
150#2355C2214yes—
151#2355C2212yes—
152#2354C2212yes—
153#2352C2214yes—
154Q8×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156#2334C2218yes—
157#2332C2218yes—
158#2331C2214yes—
159#2329C2214yes—
160#2326C2214yes—
161#2325C2214yes—
162#2320C2214yes—
163#2319C2214yes—
164#2317C2212yes—
165#2317C2212yes—
166#2311C2212yes—
167#2311C2212yes—
168#2310C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×#124C2212yes—
174C4×#124C2212yes—
175C4×#124C2212yes—
176C4×#124C2212yes—
177C4×C22⋊Q8C2214yes—
178C4×#121C2214yes—
179#2297C2212yes—
180#2297C2212yes—
181#2295C2212yes—
182#2295C2212yes—
183#2295C2212yes—
184#2295C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187#2295C2212yes—
188#2295C2212yes—
189C2×#391C2211yescharacteristic
190C2×#391C2211yescharacteristic
191C2×#389C2211yescharacteristic
192C2×#389C2211yescharacteristic
193C2×#387C2212yes—
194C2×#387C2212yes—
195#2285C2212yes—
196#2285C2211yescharacteristic
197#2285C2211yescharacteristic
198#2274C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×#376C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2312yes—
204C23×Q8C2311yescharacteristic
205#536—48no—
206#533—28no—
207#533—48no—
208#532—28no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×#127C2311yescharacteristic
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240#520—48no—
241C2×C4×Q8—28no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2318yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C42C2311yescharacteristic
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277#401C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#399C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#395C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2318yes—
337#391C2318yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2312yes—
355#390C2314yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2312yes—
362#390C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2318yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#384C2314yes—
456#384C2314yes—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2312yes—
463#383C2318yes—
464#382C2314yes—
465#382C2318yes—
466#382C2318yes—
467#382C2314yes—
468#382C2312yes—
469#382C2312yes—
470#382C2312yes—
471#382C2312yes—
472#382C2312yes—
473#382C2312yes—
474#382C2312yes—
475#382C2312yes—
476#381C2318yes—
477#381C2318yes—
478#381C2318yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2318yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2314yes—
489#380C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518#376C2314yes—
519#376C2314yes—
520#376C2314yes—
521C2×#95C2312yes—
522C2×#95C2312yes—
523C2×#95C2312yes—
524C2×#95C2312yes—
525C2×#95C2312yes—
526C2×#95C2312yes—
527C2×#95C2312yes—
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C2×#41—28no—
537C2×#41—28no—
538C2×#41—28no—
539C22×Q8—24no—
540C22×Q8—24no—
541C22×Q8—24no—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2412yes—
546C22×Q8C2414yes—
547C22×Q8C2412yes—
548C22×Q8C2414yes—
549C22×D4C2412yes—
550C22×D4C2414yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2418yes—
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C4⋊Q8—24no—
567C4⋊Q8—24no—
568C4⋊Q8—24no—
569C4⋊Q8—28no—
570C4⋊Q8—44no—
571C4⋊Q8—44no—
572C4⋊Q8—44no—
573C4⋊Q8—44no—
574C4⋊Q8—44no—
575C4⋊Q8—48no—
576#127—24no—
577#126—416no—
578#125—28no—
579#125—44no—
580#125—44no—
581#124—28no—
582#124—28no—
583#124—44no—
584#124—44no—
585#124—44no—
586#124—48no—
587#123—416no—
588C22⋊Q8—28no—
589C22⋊Q8—28no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592C22⋊Q8—416no—
593C22⋊Q8—48no—
594C22⋊Q8—48no—
595#121—28no—
596#121—28no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—28no—
600C4×Q8—28no—
601C4×Q8—28no—
602C4×Q8—28no—
603C4×Q8—48no—
604C4×Q8—48no—
605C4×Q8—48no—
606C4×Q8—48no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—416no—
612#117—28no—
613#117—28no—
614#117—28no—
615#117—48no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C42—28no—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—44no—
697C2×C42—42no—
698C2×C42—42no—
699C2×C42—42no—
700C2×C42#4118yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2418yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2414yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783C24C2514yes—
784C24C2511yescharacteristic
785#41—432no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—28no—
799C2×Q8—24no—
800C2×Q8—28no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8—416no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—42no—
819C2×D4—42no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—28no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4C2×#4114yes—
855C22×C4C2×#4114yes—
856C22×C4C2×#4114yes—
857C22×C4H(5,𝔽2)14yes—
858C22×C42−1+414yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2511yescharacteristic
873C22×C4C2514yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—28no—
912C4⋊C4—44no—
913C4⋊C4—44no—
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—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—42no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—44no—
932C4⋊C4—42no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C42—28no—
954C42—28no—
955C42—28no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—28no—
961C42—28no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—22no—
968C42—22no—
969C42—28no—
970C42—22no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—41no—
981C42—41no—
982C42—44no—
983C42—48no—
984C42—48no—
985C42—48no—
986C42C2×#4114yes—
987C42C2×#4114yes—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C422−1+414yes—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23C22×#4112yes—
1003C23C2×H(5,𝔽2)12yes—
1004C23C2×2−1+412yes—
1005C23C2611yescharacteristic
1006Q8—48no—
1007Q8—48no—
1008Q8—48no—
1009Q8—48no—
1010Q8—84no—
1011Q8—88no—
1012Q8—88no—
1013D4—416no—
1014D4—48no—
1015D4—48no—
1016D4—84no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—416no—
1085C2×C4—84no—
1086C2×C4—84no—
1087C2×C4—168no—
1088C2×C4#542116yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×2−1+412yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4#58512yes—
1103C2×C4#58512yes—
1104C2×C4#58512yes—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22C2×#54214yes—
1119C22C23×#4111yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C22C2×#58511yescharacteristic
1125C22C2×#58511yescharacteristic
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4—41no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—41no—
1141C4—44no—
1142C4—41no—
1143C4—44no—
1144C4—44no—
1145C4—41no—
1146C4—44no—
1147C4—44no—
1148C4C2×#54214yes—
1149C4C2×#54214yes—
1150C4#350714yes—
1151C2—24no—
1152C2—84no—
1153C2C22×#54211yescharacteristic
1154C2C2×#350711yescharacteristic
1155C2#6281511yescharacteristic
1156C2#6283011yescharacteristic
1157C2#6283111yescharacteristic
1158C2#6283511yescharacteristic
1159C2#6283711yescharacteristic
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. #40023C2semidirect
2. #40022C2semidirect
3. #40001C2semidirect
4. #40000C2semidirect
5. #39771C2semidirect
6. #39761C2semidirect
7. #39643C2semidirect
8. #39633C2semidirect
9. #38985C2semidirect
10. #38984C2semidirect
11. #38978C2semidirect
12. #38977C2semidirect
13. #36764C2semidirect
14. #36763C2semidirect
15. #36645C2semidirect
17. #35628C2semidirect
18. #35619C2semidirect
19. #35545C2semidirect
20. #35519C2semidirect
21. #35270C2semidirect
22. #35179C2semidirect
24. #35083C2semidirect
25. #34213C2semidirect
27. C2×#2295C2semidirect

Maximal subgroups

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

subgroupindex
#400232
#400222
#400012
#400002
#397712
#397612
#396432
#396332
#389852
#389842
#389782
#389772
#367642
#367632
#366452
#366392
#356282
#356192
#355452
#355192
#352702
#351792
#351782
#350832
#342132
#342062
C2×#22952