Finite Group Databasebeta

← #8094851

Subgroups — #8094851

Order 512.

5420 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53110C214yesmaximal, complemented
2#53106C214yesmaximal, complemented
3#52973C214yesmaximal, complemented
4#52964C214yesmaximal, complemented
5#52394C218yesmaximal, complemented
6#46088C214yesmaximal, complemented
7#45976C214yesmaximal, complemented
8#45689C214yesmaximal, complemented
9#45610C214yesmaximal, complemented
10#45594C214yesmaximal, complemented
11#45484C214yesmaximal, complemented
12#35541C212yesmaximal, complemented
13#35529C212yesmaximal, complemented
14#35528C212yesmaximal, complemented
15#35256C212yesmaximal, complemented
16#35254C212yesmaximal, complemented
17#35159C211yesmaximal, characteristic, complemented
18#35158C211yesmaximal, characteristic, complemented
19#34952C212yesmaximal, complemented
20C2×#2548C211yesmaximal, characteristic, complemented
21C2×#562C2214yescomplemented
22C2×#544C2211yescharacteristic
23C2×#537C2211yescharacteristic
24C2×#535C2212yes—
25C2×#535C2212yes—
26C22×#127C2211yescharacteristic
27C22×#124C2212yes—
28C2×#518C2212yes—
29C2×C4×#41C2212yes—
30C22×C4×Q8C2211yescharacteristic
31#2856C2214yescomplemented
32#2854C2214yescomplemented
33#2854C2214yescomplemented
34#2851C2214yes—
35#2850C2214yes—
36#2850C2214yescomplemented
37#2837C2218yescomplemented
38#2829C2218yescomplemented
39#2829C2218yescomplemented
40#2827C2218yescomplemented
41#2826C2218yescomplemented
42#2824C2218yescomplemented
43#2820C2214yescomplemented
44#2819C2214yescomplemented
45#2816C2218yescomplemented
46#2813C2218yescomplemented
47#2813C2218yescomplemented
48#2808C2214yescomplemented
49#2779C2218yescomplemented
50#2761C2218yescomplemented
51#2743C2218yescomplemented
52#2732C2214yescomplemented
53#2730C2218yescomplemented
54#2711C2218yescomplemented
55#2710C2218yescomplemented
56#2708C2218yescomplemented
57#2706C2218yescomplemented
58#2701C2218yescomplemented
59#2700C2218yescomplemented
60#2696C2218yescomplemented
61#2686C2218yescomplemented
62#2682C2214yescomplemented
63#2682C2214yescomplemented
64#2681C2218yescomplemented
65#2676C2218yescomplemented
66#2676C2218yescomplemented
67#2672C2218yescomplemented
68#2671C2218yescomplemented
69#2671C2218yescomplemented
70#2646C2214yes—
71#2639C2214yes—
72#2624C2214yescomplemented
73#2624C2214yescomplemented
74#2620C2214yescomplemented
75#2619C2214yescomplemented
76#2582C2212yescomplemented
77#2582C2212yescomplemented
78#2581C2212yescomplemented
79#2581C2212yescomplemented
80#2580C2212yescomplemented
81#2580C2212yescomplemented
82#2579C2214yes—
83#2579C2214yes—
84#2566C2214yescomplemented
85#2566C2214yescomplemented
86#2563C2214yescomplemented
87#2548C2214yes—
88#2548C2214yes—
89#2548C2214yes—
90#2548C2214yes—
91#2544C2214yes—
92#2544C2214yes—
93#2542C2214yescomplemented
94#2541C2214yes—
95#2541C2214yes—
96#2538C2212yescomplemented
97#2538C2212yescomplemented
98#2509C2214yescomplemented
99#2508C2214yescomplemented
100#2507C2214yescomplemented
101#2506C2214yescomplemented
102#2492C2214yescomplemented
103#2491C2214yescomplemented
104#2490C2214yescomplemented
105#2489C2214yescomplemented
106#2487C2214yes—
107#2454C2214yescomplemented
108#2454C2214yescomplemented
109#2452C2214yescomplemented
110#2452C2214yescomplemented
111#2448C2214yescomplemented
112#2448C2214yescomplemented
113#2447C2214yescomplemented
114#2447C2214yescomplemented
115#2445C2214yescomplemented
116#2445C2214yescomplemented
117#2445C2214yescomplemented
118#2445C2214yescomplemented
119#2437C2218yes—
120#2437C2218yes—
121#2428C2214yes—
122#2428C2214yes—
123#2428C2214yes—
124#2428C2214yes—
125#2428C2214yescomplemented
126#2428C2214yescomplemented
127#2426C2214yescomplemented
128#2426C2214yescomplemented
129#2424C2218yes—
130#2424C2218yes—
131#2422C2214yescomplemented
132#2422C2214yescomplemented
133#2420C2214yescomplemented
134#2420C2214yescomplemented
135#2418C2218yes—
136#2418C2218yes—
137#2412C2218yes—
138#2412C2218yes—
139#2410C2218yes—
140#2410C2218yes—
141#2409C2214yes—
142#2396C2214yescomplemented
143#2396C2214yescomplemented
144C2×#394C2214yes—
145#2379C2214yescomplemented
146#2377C2218yescomplemented
147#2317C2212yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2311C2212yes—
151#2309C2212yes—
152C4×C22⋊Q8C2214yescomplemented
153C4×C22⋊Q8C2214yescomplemented
154#2297C2212yes—
155#2297C2212yes—
156#2296C2212yes—
157#2296C2212yes—
158C2×#390C2212yes—
159C2×#390C2212yes—
160C2×#390C2212yes—
161#2285C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C22×#41C2312yes—
164C23×Q8C2311yescharacteristic
165C23×D4C2312yes—
166C23×D4C2312yes—
167C23×D4C2312yes—
168#562—416no—
169#544—44no—
170#537—44no—
171#535—48no—
172#535—48no—
173C2×C4⋊Q8C2314yes—
174C2×#127—44no—
175C2×#127C2314yes—
176C2×#127C2314yes—
177C2×#127C2314yes—
178C2×#127C2314yes—
179C2×#125C2314yes—
180C2×#125C2314yes—
181C2×#124—48no—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2318yes—
187C2×#124C2314yes—
188C2×#123C2318yes—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×#123C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2318yes—
206C2×#121C2318yes—
207C2×#121C2318yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#120C2318yes—
211C2×#120C2318yes—
212#518—48no—
213C4×#41—48no—
214C2×C4×Q8—44no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2314yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2312yes—
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2318yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2314yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2314yes—
246#400C2314yes—
247#400C2318yes—
248#400C2314yes—
249#400C2318yes—
250#400C2318yes—
251#399C2314yes—
252#399C2318yes—
253#399C2318yes—
254#399C2318yes—
255#399C2314yes—
256#399C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2314yes—
276#396C2318yes—
277#396C2314yes—
278#396C2314yes—
279#396C2314yes—
280#395C2314yes—
281#395C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#393C2318yes—
304#393C2318yes—
305#393C2318yes—
306#393C2314yes—
307#393C2314yes—
308#392C2318yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2318yes—
313#392C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2318yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2318yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#387C2314yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2314yes—
384#386C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2314yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2314yes—
406#385C2318yes—
407#384C2312yes—
408#384C2314yes—
409#384C2312yes—
410#382C2312yes—
411#382C2314yes—
412#382C2314yes—
413#382C2314yes—
414#382C2312yes—
415#381C2318yes—
416#381C2318yes—
417#380C2318yes—
418#380C2318yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#379C2318yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C2×#95C2312yes—
441C25C2414yes—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—28no—
445C22×Q8—24no—
446C22×Q8—42no—
447C22×Q8—42no—
448C22×Q8C2412yes—
449C22×Q8C2412yes—
450C22×Q8C2411yescharacteristic
451C22×Q8C2414yes—
452C22×Q8C2411yescharacteristic
453C22×D4—28no—
454C22×D4—28no—
455C22×D4—28no—
456C22×D4—44no—
457C22×D4—44no—
458C22×D4—44no—
459C22×D4—44no—
460C22×D4—82no—
461C22×D4—82no—
462C22×D4C2414yes—
463C22×D4C2414yes—
464C22×D4C2414yes—
465C22×D4C2412yes—
466C22×D4C2414yes—
467C22×D4C2414yes—
468C22×D4C2418yes—
469C22×D4C2418yes—
470C22×D4C2418yes—
471C22×D4C2418yes—
472C22×D4C2414yes—
473C22×D4C2418yes—
474C23×C4C2411yescharacteristic
475C23×C4C2414yes—
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2414yes—
482C23×C4C2418yes—
483C23×C4C2418yes—
484C23×C4C2414yes—
485C23×C4C2411yescharacteristic
486C4⋊Q8—48no—
487#127—48no—
488#127—48no—
489#127—48no—
490#127—48no—
491#125—48no—
492#125—48no—
493#124—216no—
494#124—48no—
495#124—48no—
496#124—48no—
497#124—48no—
498#124—416no—
499#123—416no—
500#123—416no—
501#123—88no—
502#123—88no—
503C22⋊Q8—216no—
504C22⋊Q8—48no—
505C22⋊Q8—416no—
506C22⋊Q8—48no—
507C22⋊Q8—48no—
508C22⋊Q8—88no—
509#121—416no—
510#121—416no—
511#121—416no—
512#121—48no—
513#121—48no—
514#121—48no—
515#121—48no—
516#121—48no—
517#121—48no—
518#121—88no—
519#121—88no—
520#121—88no—
521#120—416no—
522#120—416no—
523C4×Q8—44no—
524C4×Q8—44no—
525C4×Q8—44no—
526C4×Q8—44no—
527C4×Q8—44no—
528C4×Q8—44no—
529C4×D4—44no—
530C4×D4—44no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—48no—
537#117—28no—
538#117—28no—
539#117—28no—
540#117—48no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—42no—
544C2×C4⋊C4—44no—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C22⋊C4—48no—
584C2×C22⋊C4—48no—
585C2×C22⋊C4—416no—
586C2×C22⋊C4—84no—
587C2×C22⋊C4—84no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C42—28no—
623C2×C42—24no—
624C2×C42—48no—
625C2×C42—44no—
626C2×C42C2412yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666C24—28no—
667C24—28no—
668C24—28no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24C2518yes—
674C24C2514yes—
675C24C2511yescharacteristic
676#41—432no—
677C2×Q8—24no—
678C2×Q8—24no—
679C2×Q8—24no—
680C2×Q8—22no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—41no—
684C2×Q8—42no—
685C2×Q8—41no—
686C2×Q8—41no—
687C2×Q8—41no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—416no—
692C2×Q8H(5,𝔽2)14yes—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—28no—
700C2×D4—24no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—28no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—432no—
730C2×D4—816no—
731C2×D4—816no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4H(5,𝔽2)14yes—
766C22×C4H(5,𝔽2)14yes—
767C22×C42−1+414yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—42no—
798C4⋊C4—42no—
799C4⋊C4—41no—
800C4⋊C4—42no—
801C4⋊C4—41no—
802C4⋊C4—42no—
803C4⋊C4—42no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—216no—
827C22⋊C4—216no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—24no—
861C42—24no—
862C42—24no—
863C42—28no—
864C42—28no—
865C42—28no—
866C42—28no—
867C42—44no—
868C42—44no—
869C42—44no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—28no—
875C23—24no—
876C23—28no—
877C23—24no—
878C23—24no—
879C23—28no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—28no—
884C23—24no—
885C23—28no—
886C23—28no—
887C23—24no—
888C23—416no—
889C23—88no—
890C23—88no—
891C23—88no—
892C23—88no—
893C23—88no—
894C23—88no—
895C23C2×H(5,𝔽2)12yes—
896C23C2×H(5,𝔽2)12yes—
897C23C2×2−1+412yes—
898C23C2611yescharacteristic
899Q8—44no—
900Q8—48no—
901Q8—44no—
902Q8—48no—
903Q8—164no—
904D4—416no—
905D4—416no—
906D4—416no—
907D4—48no—
908D4—88no—
909D4—88no—
910D4—816no—
911D4—168no—
912D4—168no—
913D4—164no—
914D4—168no—
915D4—168no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—48no—
963C2×C4—44no—
964C2×C4—416no—
965C2×C4—88no—
966C2×C4—84no—
967C2×C4—84no—
968C2×C4—84no—
969C2×C4—88no—
970C2×C4—168no—
971C2×C4—168no—
972C2×C4#562116yescomplemented
973C2×C4C2×H(5,𝔽2)12yes—
974C2×C4C2×H(5,𝔽2)14yes—
975C2×C4C2×H(5,𝔽2)14yes—
976C2×C4C2×H(5,𝔽2)14yes—
977C2×C4C2×2−1+414yes—
978C2×C4#58512yes—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—44no—
986C22—48no—
987C22—44no—
988C22—48no—
989C22—48no—
990C22—44no—
991C22—44no—
992C22—48no—
993C22—44no—
994C22—48no—
995C22—48no—
996C22—44no—
997C22—44no—
998C22—48no—
999C22—1616no—
1000C22C2×#56214yes—
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C22×H(5,𝔽2)11yescharacteristic
1004C22C22×2−1+411yescharacteristic
1005C22C2×#58511yescharacteristic
1006C22H(7,𝔽2)11yescharacteristic
1007C22H(7,𝔽2)11yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—24no—
1011C4—42no—
1012C4—44no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—44no—
1024C4C2×#56218yes—
1025C2—24no—
1026C2—84no—
1027C2—88no—
1028C2C22×#56211yescharacteristic
1029C2#6281811yescharacteristic
1030C2#6287411yescharacteristic
1031C2#6291611yescharacteristic
1032C2#6291711yescharacteristic
1033C2#6296111yescharacteristic
1034C2#6296211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53110C2semidirect
2. #53106C2semidirect
3. #52973C2semidirect
4. #52964C2semidirect
5. #52394C2semidirect
6. #46088C2semidirect
7. #45976C2semidirect
8. #45689C2semidirect
9. #45610C2semidirect
10. #45594C2semidirect
11. #45484C2semidirect
12. #35541C2semidirect
13. #35529C2semidirect
14. #35528C2semidirect
15. #35256C2semidirect
16. #35254C2semidirect
17. #35159C2semidirect
18. #35158C2semidirect
19. #34952C2semidirect
20. C2×#2548C2semidirect
21. C2×#562C22semidirect
31. #2856C22semidirect
32. #2854C22semidirect
33. #2854C22semidirect
36. #2850C22semidirect
37. #2837C22semidirect
38. #2829C22semidirect
39. #2829C22semidirect
40. #2827C22semidirect
41. #2826C22semidirect
42. #2824C22semidirect
43. #2820C22semidirect
44. #2819C22semidirect
45. #2816C22semidirect
46. #2813C22semidirect
47. #2813C22semidirect
48. #2808C22semidirect
49. #2779C22semidirect
50. #2761C22semidirect
51. #2743C22semidirect
52. #2732C22semidirect
53. #2730C22semidirect
54. #2711C22semidirect
55. #2710C22semidirect
56. #2708C22semidirect
57. #2706C22semidirect
58. #2701C22semidirect
59. #2700C22semidirect
60. #2696C22semidirect
61. #2686C22semidirect
62. #2682C22semidirect
63. #2682C22semidirect
64. #2681C22semidirect
65. #2676C22semidirect
66. #2676C22semidirect
67. #2672C22semidirect
68. #2671C22semidirect
69. #2671C22semidirect
72. #2624C22semidirect
73. #2624C22semidirect
74. #2620C22semidirect
75. #2619C22semidirect
76. #2582C22semidirect
77. #2582C22semidirect
78. #2581C22semidirect
79. #2581C22semidirect
80. #2580C22semidirect
81. #2580C22semidirect
84. #2566C22semidirect
85. #2566C22semidirect
86. #2563C22semidirect
93. #2542C22semidirect
96. #2538C22semidirect
97. #2538C22semidirect
98. #2509C22semidirect
99. #2508C22semidirect
100. #2507C22semidirect
101. #2506C22semidirect
102. #2492C22semidirect
103. #2491C22semidirect
104. #2490C22semidirect
105. #2489C22semidirect
107. #2454C22semidirect
108. #2454C22semidirect
109. #2452C22semidirect
110. #2452C22semidirect
111. #2448C22semidirect
112. #2448C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2445C22semidirect
116. #2445C22semidirect
117. #2445C22semidirect
118. #2445C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2426C22semidirect
128. #2426C22semidirect
131. #2422C22semidirect
132. #2422C22semidirect
133. #2420C22semidirect
134. #2420C22semidirect
142. #2396C22semidirect
143. #2396C22semidirect
145. #2379C22semidirect
146. #2377C22semidirect
152. C4×C22⋊Q8C22semidirect
153. C4×C22⋊Q8C22semidirect
972. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531102
#531062
#529732
#529642
#523942
#460882
#459762
#456892
#456102
#455942
#454842
#355412
#355292
#355282
#352562
#352542
#351592
#351582
#349522
C2×#25482