Finite Group Databasebeta

← #8425261

Subgroups — #8425261

Order 512.

5271 conjugacy classes of subgroups.

The subgroup lattice has 1011 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59673C211yesmaximal, characteristic, complemented
3#59465C211yesmaximal, characteristic, complemented
4#59080C214yesmaximal, complemented
5#58890C214yesmaximal, complemented
6#58804C214yesmaximal, complemented
7#53106C214yesmaximal, complemented
8#52973C214yesmaximal, complemented
9#52421C214yesmaximal, complemented
10#42607C214yesmaximal, complemented
11#42431C214yesmaximal, complemented
12#40607C214yesmaximal, complemented
13#39386C212yesmaximal, complemented
14#39201C212yesmaximal, complemented
15#39005C214yesmaximal, complemented
16#37792C214yesmaximal, complemented
17#37636C211yesmaximal, characteristic, complemented
18#37626C211yesmaximal, characteristic, complemented
19#37523C214yesmaximal, complemented
20#36595C211yesmaximal, characteristic, complemented
21#36463C212yesmaximal, complemented
22#34925C211yesmaximal, characteristic, complemented
23#34893C212yesmaximal, complemented
24C2×#559C2212yes—
25C2×D4×Q8C2214yes—
26C2×#548C2214yes—
27C2×#540C2214yes—
28C2×#532C2214yes—
29#2867C2211yescharacteristic
30#2858C2211yescharacteristic
31#2858C2211yescharacteristic
32#2854C2214yes—
33#2832C2214yes—
34#2829C2218yes—
35#2828C2214yes—
36#2826C2218yes—
37#2824C2218yes—
38#2819C2214yes—
39#2816C2218yes—
40#2813C2218yes—
41#2813C2214yes—
42#2799C2214yes—
43#2784C2214yes—
44#2757C2218yes—
45#2712C2218yes—
46#2710C2218yes—
47#2710C2218yes—
48#2708C2218yes—
49#2706C2218yes—
50#2687C2218yes—
51#2687C2218yes—
52#2686C2218yes—
53#2683C2214yes—
54#2682C2218yes—
55#2676C2218yes—
56#2676C2218yes—
57#2673C2218yes—
58#2673C2218yes—
59#2672C2218yes—
60#2672C2218yes—
61#2671C2218yes—
62#2663C2214yes—
63#2663C2218yes—
64#2649C2218yes—
65#2649C2218yes—
66#2635C2214yes—
67#2632C2214yes—
68#2632C2214yes—
69#2628C2214yes—
70#2624C2214yes—
71#2624C2214yes—
72#2624C2214yes—
73#2619C2214yes—
74#2619C2214yes—
75#2614C2214yes—
76#2589C2214yes—
77#2587C2214yes—
78#2584C2212yes—
79#2581C2214yes—
80#2580C2214yes—
81#2580C2212yes—
82#2571C2211yescharacteristic
83#2566C2212yes—
84#2564C2214yes—
85#2563C2212yes—
86#2563C2214yes—
87#2557C2218yes—
88#2555C2214yes—
89#2551C2211yescharacteristic
90#2551C2211yescharacteristic
91#2550C2214yes—
92#2550C2212yes—
93#2548C2214yes—
94#2548C2214yes—
95#2548C2212yes—
96#2544C2212yes—
97#2544C2212yes—
98#2541C2212yes—
99#2541C2212yes—
100#2541C2214yes—
101#2541C2214yes—
102#2538C2214yes—
103#2537C2211yescharacteristic
104#2522C2214yes—
105#2513C2214yes—
106#2513C2214yes—
107#2509C2214yes—
108#2509C2212yes—
109#2508C2214yes—
110#2507C2212yes—
111#2495C2214yes—
112#2491C2214yes—
113#2491C2214yes—
114#2491C2214yes—
115#2490C2214yes—
116#2465C2214yes—
117#2463C2218yes—
118#2463C2218yes—
119#2459C2218yes—
120#2455C2218yes—
121#2454C2214yes—
122#2454C2212yes—
123#2452C2214yes—
124#2452C2212yes—
125#2452C2214yes—
126#2452C2214yes—
127#2445C2214yes—
128#2445C2214yes—
129#2445C2214yes—
130#2445C2214yes—
131#2445C2214yes—
132#2445C2214yes—
133#2436C2218yes—
134#2430C2214yes—
135#2428C2214yes—
136#2428C2214yes—
137#2428C2214yes—
138#2428C2214yes—
139#2426C2218yes—
140#2425C2218yes—
141#2422C2214yes—
142#2420C2214yes—
143#2420C2214yes—
144#2409C2214yes—
145#2407C2218yes—
146#2396C2214yes—
147#2396C2214yes—
148#2388C2214yes—
149#2369C2212yes—
150#2366C2212yes—
151#2366C2214yes—
152#2366C2214yes—
153#2366C2212yes—
154#2365C2214yes—
155#2357C2214yes—
156#2349C2214yes—
157#2324C2214yes—
158#2318C2214yes—
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2212yes—
161C4×#127C2211yescharacteristic
162C4×#127C2211yescharacteristic
163C4×#125C2212yes—
164C4×#125C2212yes—
165C4×C22⋊Q8C2214yes—
166C4×#121C2214yes—
167C4×#121C2214yes—
168#2296C2214yes—
169#2293C2212yes—
170#2293C2212yes—
171C42×Q8C2211yescharacteristic
172C42×D4C2212yes—
173C22×#41C2314yes—
174C23×Q8C2314yes—
175#559—48no—
176D4×Q8—416no—
177#548—416no—
178#540—416no—
179#532—416no—
180C2×C4⋊Q8C2311yescharacteristic
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#127C2311yescharacteristic
185C2×#127C2311yescharacteristic
186C2×#127C2314yes—
187C2×#127C2314yes—
188C2×#127C2312yes—
189C2×#127C2314yes—
190C2×#127C2314yes—
191C2×#127C2312yes—
192C2×#125C2312yes—
193C2×#125C2312yes—
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#124C2312yes—
197C2×#124C2312yes—
198C2×#124C2318yes—
199C2×#124C2318yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#123C2318yes—
203C2×#123C2314yes—
204C2×#123C2314yes—
205C2×#123C2318yes—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2318yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2318yes—
221C2×#121C2318yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C42C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2318yes—
249#400C2314yes—
250#400C2314yes—
251#400C2318yes—
252#399C2314yes—
253#399C2318yes—
254#399C2314yes—
255#399C2318yes—
256#399C2314yes—
257#399C2314yes—
258#398C2314yes—
259#398C2318yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#396C2314yes—
270#396C2314yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2314yes—
275#396C2314yes—
276#395C2314yes—
277#395C2314yes—
278#395C2314yes—
279#395C2314yes—
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#394C2314yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2314yes—
300#394C2318yes—
301#394C2318yes—
302#393C2314yes—
303#393C2318yes—
304#393C2318yes—
305#393C2318yes—
306#393C2314yes—
307#393C2314yes—
308#393C2318yes—
309#393C2314yes—
310#393C2314yes—
311#393C2314yes—
312#392C2314yes—
313#392C2314yes—
314#392C2318yes—
315#392C2318yes—
316#392C2318yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2318yes—
321#391C2312yes—
322#391C2314yes—
323#391C2318yes—
324#391C2314yes—
325#391C2318yes—
326#390C2314yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2318yes—
347#390C2318yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2314yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#384C2311yescharacteristic
415#384C2312yes—
416#383C2314yes—
417#382C2312yes—
418#382C2312yes—
419#382C2314yes—
420#382C2314yes—
421#382C2314yes—
422#381C2318yes—
423#381C2314yes—
424#380C2318yes—
425#380C2314yes—
426#380C2318yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C2×#95C2314yes—
458C43C2311yescharacteristic
459C43C2311yescharacteristic
460C43C2311yescharacteristic
461C2×#41—48no—
462C2×#41—416no—
463C22×Q8—48no—
464C22×Q8—416no—
465C22×Q8C2414yes—
466C22×Q8C2414yes—
467C22×Q8C2411yescharacteristic
468C22×Q8C2412yes—
469C22×Q8C2414yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2412yes—
476C22×D4C2418yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C22×D4C2414yes—
480C22×D4C2418yes—
481C22×D4C2414yes—
482C22×D4C2418yes—
483C23×C4C2414yes—
484C23×C4C2414yes—
485C23×C4C2414yes—
486C23×C4C2414yes—
487C23×C4C2418yes—
488C23×C4C2418yes—
489C23×C4C2414yes—
490C4⋊Q8—216no—
491C4⋊Q8—28no—
492C4⋊Q8—24no—
493C4⋊Q8—48no—
494#127—24no—
495#127—24no—
496#127—48no—
497#127—48no—
498#127—48no—
499#127—48no—
500#127—44no—
501#127—82no—
502#125—28no—
503#125—44no—
504#124—48no—
505#124—44no—
506#124—44no—
507#124—48no—
508#124—416no—
509#124—416no—
510#124—82no—
511#124—82no—
512#123—416no—
513#123—416no—
514#123—48no—
515#123—48no—
516#123—88no—
517#123—88no—
518C22⋊Q8—216no—
519C22⋊Q8—416no—
520C22⋊Q8—416no—
521C22⋊Q8—48no—
522C22⋊Q8—416no—
523#121—216no—
524#121—48no—
525#121—416no—
526#121—416no—
527#121—416no—
528#121—48no—
529#121—48no—
530#121—48no—
531#121—416no—
532#121—48no—
533#121—88no—
534C4×Q8—24no—
535C4×Q8—44no—
536C4×Q8—48no—
537C4×Q8—44no—
538C4×Q8—48no—
539C4×D4—28no—
540C4×D4—216no—
541C4×D4—216no—
542C4×D4—28no—
543C4×D4—48no—
544C4×D4—44no—
545C4×D4—48no—
546C4×D4—48no—
547C4×D4—48no—
548C4×D4—48no—
549C4×D4—44no—
550C4×D4—44no—
551C4×D4—416no—
552C4×D4—416no—
553#117—48no—
554#117—48no—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C42—48no—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2414yes—
637C2×C42C2412yes—
638C2×C42C2414yes—
639C2×C42C2411yescharacteristic
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2418yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2414yes—
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2412yes—
663#95C2412yes—
664#95C2412yes—
665#95C2414yes—
666#95C2414yes—
667#95C2418yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680C24C2514yes—
681C24C2514yes—
682C24C2514yes—
683#41—832no—
684C2×Q8—22no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—216no—
688C2×Q8—24no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—44no—
694C2×Q8—48no—
695C2×Q8—42no—
696C2×Q8—832no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—216no—
702C2×D4—24no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4—48no—
732C2×D4—48no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—216no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—48no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4C2512yes—
753C22×C4C2514yes—
754C22×C4C2514yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2512yes—
759C22×C4C2511yescharacteristic
760C22×C4C2511yescharacteristic
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2511yescharacteristic
765C22×C4C2512yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2512yes—
772C4⋊C4—24no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—216no—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—42no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—42no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4H(5,𝔽2)14yes—
809C4⋊C4H(5,𝔽2)18yes—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—216no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—48no—
823C22⋊C4—44no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C42—24no—
845C42—28no—
846C42—24no—
847C42—28no—
848C42—28no—
849C42—22no—
850C42—22no—
851C42—24no—
852C42—22no—
853C42—24no—
854C42—28no—
855C42—24no—
856C42—24no—
857C42—44no—
858C42—44no—
859C42—48no—
860C42—41no—
861C42—41no—
862C42—41no—
863C422−1+414yes—
864C23—24no—
865C23—24no—
866C23—28no—
867C23—24no—
868C23—24no—
869C23—28no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—28no—
876C23—24no—
877C23—28no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23C2611yescharacteristic
882Q8—416no—
883Q8—416no—
884Q8—44no—
885Q8—84no—
886Q8—88no—
887D4—416no—
888D4—48no—
889D4—416no—
890D4—88no—
891D4—84no—
892D4—84no—
893D4—816no—
894D4—816no—
895D4—816no—
896D4—88no—
897D4—164no—
898D4—168no—
899D4—168no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—21no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—21no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—416no—
946C2×C4—416no—
947C2×C4—816no—
948C2×C4—88no—
949C2×C4—88no—
950C2×C4—88no—
951C2×C4—168no—
952C2×C4C2×H(5,𝔽2)12yes—
953C2×C4C2×H(5,𝔽2)12yes—
954C2×C4C2×H(5,𝔽2)12yes—
955C2×C4C2×H(5,𝔽2)18yes—
956C2×C4C2×H(5,𝔽2)14yes—
957C2×C4C2×2−1+412yes—
958C2×C4C2×2−1+414yes—
959C2×C4#58514yes—
960C22—44no—
961C22—48no—
962C22—44no—
963C22—48no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—48no—
975C22—44no—
976C22—48no—
977C22C22×H(5,𝔽2)12yes—
978C22C22×H(5,𝔽2)11yescharacteristic
979C22C22×2−1+411yescharacteristic
980C22C2×#58512yes—
981C22H(7,𝔽2)11yescharacteristic
982C4—22no—
983C4—28no—
984C4—22no—
985C4—22no—
986C4—22no—
987C4—44no—
988C4—44no—
989C4—44no—
990C4—41no—
991C4—44no—
992C4—41no—
993C4—41no—
994C4—44no—
995C4—42no—
996C4—42no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—42no—
1001C4#355418yes—
1002C2—84no—
1003C2—84no—
1004C2—84no—
1005C2C2×#355412yes—
1006C2#6275911yescharacteristic
1007C2#6291711yescharacteristic
1008C2#6292312yes—
1009C2#6301111yescharacteristic
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. #59817C2semidirect
2. #59673C2semidirect
3. #59465C2semidirect
4. #59080C2semidirect
5. #58890C2semidirect
6. #58804C2semidirect
7. #53106C2semidirect
8. #52973C2semidirect
9. #52421C2semidirect
10. #42607C2semidirect
11. #42431C2semidirect
12. #40607C2semidirect
13. #39386C2semidirect
14. #39201C2semidirect
15. #39005C2semidirect
16. #37792C2semidirect
17. #37636C2semidirect
18. #37626C2semidirect
19. #37523C2semidirect
20. #36595C2semidirect
21. #36463C2semidirect
22. #34925C2semidirect
23. #34893C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596732
#594652
#590802
#588902
#588042
#531062
#529732
#524212
#426072
#424312
#406072
#393862
#392012
#390052
#377922
#376362
#376262
#375232
#365952
#364632
#349252
#348932