Finite Group Databasebeta

← #7652621

Subgroups — #7652621

Order 512.

5296 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42954C214yesmaximal, complemented
2#42953C214yesmaximal, complemented
3#42818C214yesmaximal, complemented
4#42816C214yesmaximal, complemented
5#41998C218yesmaximal, complemented
6#39985C214yesmaximal, complemented
7#39980C214yesmaximal, complemented
8#39752C214yesmaximal, complemented
9#39179C214yesmaximal, complemented
10#38448C218yesmaximal, complemented
11#35662C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35639C211yesmaximal, characteristic, complemented
14#35639C211yesmaximal, characteristic, complemented
15#35620C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35334C211yesmaximal, characteristic, complemented
18#35280C211yesmaximal, characteristic, complemented
19#35154C211yesmaximal, characteristic, complemented
20C2×#2565C211yesmaximal, characteristic, complemented
21#34745C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34259C211yesmaximal, characteristic
24#34259C211yesmaximal, characteristic
25#34257C211yesmaximal, characteristic
26C22×2−1+4C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2214yes—
38#2855C2214yes—
39#2851C2214yes—
40#2841C2218yes—
41#2841C2218yes—
42#2809C2218yes—
43#2809C2218yes—
44#2806C2218yes—
45#2806C2218yes—
46#2806C2218yes—
47#2799C2218yes—
48#2799C2218yes—
49#2799C2218yes—
50#2784C2218yes—
51#2780C2218yes—
52#2780C2218yes—
53#2748C2218yes—
54#2748C2218yes—
55#2732C2218yes—
56#2692C2218yes—
57#2692C2218yes—
58#2667C2218yes—
59#2667C2218yes—
60#2667C2218yes—
61#2665C2218yes—
62#2659C2218yes—
63#2646C2218yes—
64#2629C2214yes—
65#2628C2214yes—
66#2627C2214yes—
67#2608C2218yes—
68#2607C2218yes—
69#2582C2214yes—
70#2582C2214yes—
71#2582C2214yes—
72#2581C2214yes—
73#2581C2214yes—
74#2581C2214yes—
75#2580C2214yes—
76#2579C2214yes—
77#2579C2214yes—
78#2569C2218yes—
79#2569C2218yes—
80#2569C2218yes—
81#2568C2212yes—
82#2567C2212yes—
83#2566C2212yes—
84#2566C2212yes—
85#2565C2214yes—
86#2565C2212yes—
87#2565C2214yes—
88#2565C2214yes—
89#2565C2214yes—
90#2565C2212yes—
91#2564C2218yes—
92#2563C2212yes—
93#2549C2218yes—
94#2542C2212yes—
95#2538C2214yes—
96#2487C2214yes—
97#2487C2214yes—
98#2454C2214yes—
99#2454C2212yes—
100#2454C2214yes—
101#2454C2212yes—
102#2453C2212yes—
103#2453C2214yes—
104#2453C2214yes—
105#2453C2214yes—
106#2453C2214yes—
107#2453C2212yes—
108#2453C2214yes—
109#2453C2214yes—
110#2452C2212yes—
111#2452C2212yes—
112#2451C2214yes—
113#2451C2214yes—
114#2451C2214yes—
115#2451C2212yes—
116#2451C2214yes—
117#2451C2212yes—
118#2450C2218yes—
119#2450C2214yes—
120#2450C2214yes—
121#2449C2214yes—
122#2449C2214yes—
123#2449C2218yes—
124#2442C2214yes—
125#2442C2214yes—
126#2442C2214yes—
127#2441C2214yes—
128#2441C2214yes—
129#2441C2214yes—
130#2440C2214yes—
131#2439C2214yes—
132#2438C2218yes—
133#2438C2218yes—
134#2417C2218yes—
135#2396C2214yes—
136#2396C2214yes—
137C2×#398C2214yes—
138#2341C2214yes—
139#2341C2214yes—
140Q8×C22⋊C4C2214yes—
141Q8×C22⋊C4C2214yes—
142Q8×C22⋊C4C2214yes—
143Q8×C22⋊C4C2214yes—
144#2339C2218yes—
145#2339C2218yes—
146#2339C2214yes—
147#2339C2214yes—
148#2329C2218yes—
149#2329C2218yes—
150#2317C2211yescharacteristic
151#2317C2211yescharacteristic
152#2316C2211yescharacteristic
153#2316C2211yescharacteristic
154#2316C2211yescharacteristic
155#2311C2211yescharacteristic
156#2311C2211yescharacteristic
157#2311C2214yes—
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2212yes—
161#2311C2212yes—
162#2310C2212yes—
163#2310C2212yes—
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166C4×C22⋊Q8C2214yes—
167C4×C22⋊Q8C2214yes—
168#2297C2211yescharacteristic
169#2297C2212yes—
170#2297C2214yes—
171#2297C2212yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2212yes—
180C2×#391C2212yes—
181C2×#391C2211yescharacteristic
182C2×#391C2211yescharacteristic
183C2×#387C2214yes—
184C2×#384C2211yescharacteristic
185C2×#382C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—44no—
188C2×2−1+4—44no—
189C2×2−1+4Q8116yescomplemented
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2314yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2312yes—
197C23×Q8C2312yes—
198#544—44no—
199#533—44no—
200#533—44no—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#125—44no—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219#520—44no—
220#520—44no—
221#519—44no—
222C4×#41—44no—
223C4×#41—44no—
224C2×C4×Q8—44no—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2312yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#399C2318yes—
280#399C2314yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2314yes—
304#398C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2314yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2314yes—
314#396C2314yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2314yes—
320#395C2318yes—
321#395C2314yes—
322#393C2318yes—
323#393C2318yes—
324#393C2314yes—
325#393C2314yes—
326#391C2311yescharacteristic
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2311yescharacteristic
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2311yescharacteristic
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2318yes—
347#391C2318yes—
348#391C2311yescharacteristic
349#391C2318yes—
350#391C2318yes—
351#391C2318yes—
352#391C2318yes—
353#391C2314yes—
354#391C2318yes—
355#391C2318yes—
356#391C2318yes—
357#391C2312yes—
358#391C2312yes—
359#391C2318yes—
360#391C2314yes—
361#390C2311yescharacteristic
362#390C2312yes—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#390C2318yes—
369#390C2318yes—
370#390C2312yes—
371#390C2312yes—
372#390C2311yescharacteristic
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2318yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2312yes—
421#386C2314yes—
422#386C2312yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2312yes—
427#386C2318yes—
428#386C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2312yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2312yes—
442#385C2312yes—
443#385C2318yes—
444#385C2314yes—
445#385C2312yes—
446#385C2312yes—
447#385C2314yes—
448#385C2314yes—
449#385C2314yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2312yes—
454#384C2312yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#382C2314yes—
459#382C2312yes—
460#381C2318yes—
461#381C2318yes—
462#381C2314yes—
463#381C2314yes—
464#380C2318yes—
465#380C2314yes—
466#380C2314yes—
467#380C2318yes—
468#380C2318yes—
469#380C2318yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2318yes—
476#380C2314yes—
477#380C2318yes—
478#380C2318yes—
479#380C2314yes—
480#380C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C2×#95C2314yes—
500C2×#95C2318yes—
501C2×#95C2318yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C2×#95C2312yes—
5052−1+4—464no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—48no—
511C2×#41—48no—
512C2×#41—44no—
513C2×#41—44no—
514C2×#41—44no—
515C2×#41—44no—
516C2×#41C2×Q818yes—
517C2×#41C2×Q818yes—
518C2×#41C2×Q8132yes—
519C2×#41C2×Q8116yes—
520C2×#41C2×Q8116yes—
521C22×Q8—24no—
522C22×Q8—24no—
523C22×Q8—44no—
524C22×Q8—44no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8C2×Q818yes—
528C22×Q8C2×Q8116yes—
529C22×Q8C2×Q8116yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2414yes—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2414yes—
556C23×C4C2414yes—
557C23×C4C2414yes—
558C23×C4C2414yes—
559C23×C4C2411yescharacteristic
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564#125—48no—
565#125—48no—
566#125—44no—
567#125—44no—
568#125—44no—
569#125—44no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572C22⋊Q8—48no—
573C22⋊Q8—416no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576C22⋊Q8—416no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—44no—
586C4×Q8—44no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—48no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—44no—
602#117—44no—
603#117—48no—
604#117—44no—
605#117—44no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—24no—
691C2×C42—44no—
692C2×C42—44no—
693C2×C42—44no—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2418yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24C2512yes—
754C24C2512yes—
755C24C2511yescharacteristic
756#41—232no—
757#41—232no—
758#41—464no—
759#41—432no—
760#41—432no—
761C2×Q8—232no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—28no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—48no—
780C2×Q8—432no—
781C2×Q8—432no—
782C2×Q8C22×Q818yes—
783C2×Q8C22×Q818yes—
784C2×Q8C22×Q814yes—
785C2×Q8C22×Q814yes—
786C2×Q8C22×Q8116yes—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4C22×Q818yes—
798C2×D4C22×Q818yes—
799C2×D4C22×Q814yes—
800C2×D4C22×Q814yes—
801C2×D4C22×Q8116yes—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—42no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4C22×Q818yes—
839C22×C4C22×Q818yes—
840C22×C4C22×Q818yes—
841C22×C4C22×Q8116yes—
842C22×C4C22×Q8116yes—
843C22×C4C22×Q814yes—
844C22×C4H(5,𝔽2)14yes—
845C22×C4H(5,𝔽2)14yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—216no—
885C4⋊C4—28no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—44no—
955C42—44no—
956C42—48no—
957C42—44no—
958C42—44no—
959C42—48no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23C23×Q814yes—
971C23C23×Q814yes—
972C23C23×Q812yes—
973C23C2×H(5,𝔽2)12yes—
974C23C2×H(5,𝔽2)12yes—
975C23C2611yescharacteristic
976Q8—216no—
977Q8—216no—
978Q8—28no—
979Q8—28no—
980Q8—416no—
981Q8—88no—
982Q8—88no—
983Q8—164no—
984D4—216no—
985D4—216no—
986D4—28no—
987D4—28no—
988D4—416no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—216no—
998C2×C4—216no—
999C2×C4—216no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—28no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—416no—
1042C2×C4—416no—
1043C2×C4—48no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—88no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—88no—
1052C2×C4—164no—
1053C2×C4—164no—
1054C2×C4#543116yes—
1055C2×C4C23×Q814yes—
1056C2×C4C23×Q814yes—
1057C2×C4C23×Q818yes—
1058C2×C4C23×Q812yes—
1059C2×C4C23×Q812yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4#58514yes—
1065C22—24no—
1066C22—22no—
1067C22—22no—
1068C22—24no—
1069C22—28no—
1070C22—28no—
1071C22—24no—
1072C22—24no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—44no—
1078C22—44no—
1079C22C2×#54314yes—
1080C22C24×Q811yescharacteristic
1081C22C22×H(5,𝔽2)11yescharacteristic
1082C22C22×H(5,𝔽2)11yescharacteristic
1083C22C2×#58512yes—
1084C222−1+612yes—
1085C4—24no—
1086C4—24no—
1087C4—28no—
1088C4—24no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—44no—
1101C4—44no—
1102C4—42no—
1103C4—44no—
1104C4—44no—
1105C4C2×#54314yes—
1106C4C2×#54314yes—
1107C2—24no—
1108C2—44no—
1109C2—44no—
1110C2C22×#54311yescharacteristic
1111C2#6283611yescharacteristic
1112C2#6288711yescharacteristic
1113C2#6292712yes—
1114C2#6300412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×2−1+4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42954C2semidirect
2. #42953C2semidirect
3. #42818C2semidirect
4. #42816C2semidirect
5. #41998C2semidirect
6. #39985C2semidirect
7. #39980C2semidirect
8. #39752C2semidirect
9. #39179C2semidirect
10. #38448C2semidirect
11. #35662C2semidirect
12. #35662C2semidirect
13. #35639C2semidirect
14. #35639C2semidirect
15. #35620C2semidirect
16. #35532C2semidirect
17. #35334C2semidirect
18. #35280C2semidirect
19. #35154C2semidirect
20. C2×#2565C2semidirect
21. #34745C2semidirect
22. #34745C2semidirect
189. C2×2−1+4Q8semidirect

Maximal subgroups

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

subgroupindex
#429542
#429532
#428182
#428162
#419982
#399852
#399802
#397522
#391792
#384482
#356622
#356392
#356202
#355322
#353342
#352802
#351542
C2×#25652
#347452
#342592
#342572