Finite Group Databasebeta

← #7711991

Subgroups — #7711991

Order 512.

7172 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59143C214yesmaximal, complemented
2#59124C214yesmaximal, complemented
3#46010C218yesmaximal, complemented
4#39770C212yesmaximal, complemented
5#39770C214yesmaximal, complemented
6#39745C214yesmaximal, complemented
7#39464C218yesmaximal, complemented
8#39386C212yesmaximal, complemented
9#37694C214yesmaximal, complemented
10#37614C212yesmaximal, complemented
11#37319C214yesmaximal, complemented
12C2×#2867C211yesmaximal, characteristic, complemented
13#36635C211yesmaximal, characteristic, complemented
14#36595C212yesmaximal, complemented
15#36128C212yesmaximal, complemented
16#36121C214yesmaximal, complemented
17#35293C212yesmaximal, complemented
18#35278C212yesmaximal, complemented
19#34364C212yesmaximal, complemented
20C4×#529C211yesmaximal, characteristic, complemented
21C2×#559C2214yescomplemented
22C2×#550C2214yescomplemented
23C2×#546C2218yes—
24C2×#540C2214yescomplemented
25C2×#532C2214yescomplemented
26C22×#127C2212yes—
27C22×#127C2214yes—
28C22×#127C2212yes—
29C22×#127C2214yes—
30C22×#127C2212yes—
31C2×#529C2211yescharacteristic
32#2867C2212yes—
33#2867C2214yes—
34#2867C2212yes—
35#2867C2214yes—
36#2867C2212yes—
37#2867C2212yes—
38#2864C2212yescomplemented
39#2863C2214yescomplemented
40#2862C2211yescharacteristic, complemented
41#2859C2211yescharacteristic, complemented
42#2858C2214yescomplemented
43#2857C2212yes—
44#2856C2214yescomplemented
45#2855C2214yes—
46#2851C2212yes—
47#2818C2218yescomplemented
48#2709C22116yescomplemented
49#2709C22116yescomplemented
50#2709C22116yescomplemented
51#2709C22116yescomplemented
52#2673C22116yescomplemented
53#2673C22116yescomplemented
54#2673C22116yescomplemented
55#2673C22116yescomplemented
56#2657C2214yescomplemented
57#2641C2214yescomplemented
58#2641C2214yescomplemented
59#2619C2214yescomplemented
60#2619C2214yescomplemented
61#2619C2214yescomplemented
62#2613C2218yes—
63#2548C2214yescomplemented
64#2548C2214yescomplemented
65#2548C2214yescomplemented
66#2548C2214yescomplemented
67#2544C2218yescomplemented
68#2544C2218yescomplemented
69#2544C2218yescomplemented
70#2544C2218yescomplemented
71#2544C2218yescomplemented
72#2541C2214yescomplemented
73#2541C2214yescomplemented
74#2541C2218yescomplemented
75#2445C2218yescomplemented
76#2445C2218yescomplemented
77#2445C2218yescomplemented
78#2445C2218yescomplemented
79#2445C2218yescomplemented
80#2445C2218yescomplemented
81#2445C2218yescomplemented
82#2445C2218yescomplemented
83#2435C2214yes—
84#2435C2218yes—
85#2433C2214yes—
86#2431C2218yescomplemented
87#2431C2218yescomplemented
88#2431C2218yescomplemented
89#2431C2218yescomplemented
90#2428C2218yescomplemented
91#2428C2218yescomplemented
92#2428C2218yescomplemented
93#2428C2218yescomplemented
94#2428C2218yescomplemented
95#2428C2218yescomplemented
96#2410C22116yes—
97#2408C2218yes—
98#2408C2218yes—
99#2405C22116yes—
100#2380C2218yescomplemented
101#2366C2214yescomplemented
102#2366C2214yescomplemented
103#2366C2214yescomplemented
104#2366C2214yescomplemented
105D4×C22⋊C4C2218yes—
106D4×C22⋊C4C2218yes—
107D4×C22⋊C4C2218yes—
108#2328C2218yescomplemented
109#2328C2214yescomplemented
110#2328C2214yescomplemented
111#2328C2214yescomplemented
112#2308C2218yes—
113C4×C4⋊Q8C2212yescomplemented
114C4×#127C2214yescomplemented
115C4×#125C2212yescomplemented
116C4×#125C2212yescomplemented
117C4×#126C2214yescomplemented
118C4×#124C2212yescomplemented
119C4×C22⋊Q8C2212yes—
120C4×C22⋊Q8C2214yes—
121C4×#123C2214yes—
122C4×#121C2212yes—
123#2298C2212yescomplemented
124#2295C2214yescomplemented
125#2295C2211yescharacteristic, complemented
126#2293C2211yescharacteristic, complemented
127#2290C2212yes—
128#2283C2212yes—
129#2283C2211yescharacteristic
130C42×Q8C2211yescharacteristic, complemented
131C42×D4C2212yes—
132C42×D4C2211yescharacteristic, complemented
133C4×#117C2212yescomplemented
134C2×C43C2211yescharacteristic
135C22×#41C2318yes—
136C23×D4C2314yes—
137C23×D4C2314yes—
138C23×D4C2314yes—
139C23×D4C2318yes—
140C23×D4C2318yes—
141#559—416no—
142#550—416no—
143#546—432no—
144#540—416no—
145#532—416no—
146C2×C4⋊Q8C2312yes—
147C2×#127—216no—
148C2×#127—48no—
149C2×#127—48no—
150C2×#127—416no—
151C2×#127—416no—
152C2×#127C2314yes—
153C2×#127C2314yes—
154C2×#127C2314yes—
155C2×#127C2314yes—
156C2×#127C2314yes—
157C2×#127C2314yes—
158C2×#127C2314yes—
159C2×#127C2314yes—
160C2×#127C2318yes—
161C2×#127C2318yes—
162C2×#127C2318yes—
163C2×#127C2318yes—
164C2×#127C2314yes—
165C2×#127C2314yes—
166C2×#127C2314yes—
167C2×#127C2318yes—
168C2×#127C2318yes—
169C2×#127C2318yes—
170C2×#127C2314yes—
171C2×#127C2318yes—
172C2×#127C2318yes—
173#529—28no—
174C2×#126C2312yes—
175C2×#125C2311yescharacteristic
176C2×#125C2312yes—
177C2×#124C2311yescharacteristic
178C2×#124C2318yes—
179C2×#124C2318yes—
180C2×#124C2318yes—
181C2×#124C2318yes—
182C2×#123C2312yes—
183C2×#123C23116yes—
184C2×#123C23116yes—
185C2×#123C23116yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2311yescharacteristic
188C2×#121C2311yescharacteristic
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C2318yes—
193C2×#121C2318yes—
194C2×#121C23116yes—
195C2×#121C23116yes—
196C2×#121C23116yes—
197C2×#120C23116yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2312yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2311yescharacteristic
204C2×C4×D4C2312yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2318yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C22×C22⋊C4C23116yes—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221#394C23116yes—
222#394C2318yes—
223#394C2318yes—
224#394C23116yes—
225#394C2318yes—
226#394C2318yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#394C23116yes—
234#394C23116yes—
235#394C23116yes—
236#392C23116yes—
237#392C2318yes—
238#392C2318yes—
239#392C23116yes—
240#392C2318yes—
241#392C2318yes—
242#392C23116yes—
243#392C23116yes—
244#392C23116yes—
245#391C2314yes—
246#391C2314yes—
247#391C2314yes—
248#391C2314yes—
249#391C2312yes—
250#390C2318yes—
251#390C2318yes—
252#390C2318yes—
253#390C2318yes—
254#390C2318yes—
255#390C2318yes—
256#390C2318yes—
257#390C2318yes—
258#390C2318yes—
259#390C2318yes—
260#390C2318yes—
261#390C2318yes—
262#390C2318yes—
263#390C2318yes—
264#390C2312yes—
265#389C2314yes—
266#389C2312yes—
267#389C2312yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#388C2314yes—
274#388C2314yes—
275#388C2314yes—
276#388C2314yes—
277#387C2314yes—
278#387C2314yes—
279#387C2314yes—
280#387C2318yes—
281#387C2314yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#386C23116yes—
286#386C23116yes—
287#386C23116yes—
288#386C23116yes—
289#386C23116yes—
290#386C23116yes—
291#386C23116yes—
292#386C23116yes—
293#386C23116yes—
294#386C23116yes—
295#386C23116yes—
296#386C23116yes—
297#386C23116yes—
298#386C23116yes—
299#386C2314yes—
300#385C2318yes—
301#385C2314yes—
302#384C2312yes—
303#383C2312yes—
304#383C2314yes—
305#382C2312yes—
306#382C2312yes—
307#382C2312yes—
308#382C2312yes—
309#381C2312yes—
310#381C2314yes—
311#380C2312yes—
312#380C2314yes—
313#380C2314yes—
314#379C23116yes—
315#379C23116yes—
316C4×C4⋊C4C2314yes—
317C4×C4⋊C4C2314yes—
318C4×C4⋊C4C2314yes—
319C4×C4⋊C4C2314yes—
320C4×C4⋊C4C2312yes—
321C4×C4⋊C4C2312yes—
322C4×C4⋊C4C2314yes—
323C4×C4⋊C4C2318yes—
324C4×C4⋊C4C2314yes—
325C4×C4⋊C4C2311yescharacteristic
326C4×C4⋊C4C2311yescharacteristic
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2312yes—
329C4×C22⋊C4C2314yes—
330C4×C22⋊C4C2314yes—
331C4×C22⋊C4C2314yes—
332C4×C22⋊C4C2312yes—
333C4×C22⋊C4C2314yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2312yes—
336C4×C22⋊C4C2312yes—
337C4×C22⋊C4C2314yes—
338#376C2312yes—
339#376C2312yes—
340#376C2314yes—
341C43C2312yes—
342C43C2311yescharacteristic
343C43C2312yes—
344C43C2312yes—
345C43C2311yescharacteristic
346C43C2311yescharacteristic
347C43C2311yescharacteristic
348C25C2418yes—
349C2×#41—416no—
350C2×#41—416no—
351C2×#41—416no—
352C22×Q8C2411yescharacteristic
353C22×Q8C2414yes—
354C22×D4—216no—
355C22×D4—216no—
356C22×D4—216no—
357C22×D4—232no—
358C22×D4—48no—
359C22×D4—48no—
360C22×D4—416no—
361C22×D4—416no—
362C22×D4—416no—
363C22×D4—416no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—416no—
367C22×D4C2412yes—
368C22×D4C2411yescharacteristic
369C22×D4C2418yes—
370C22×D4C2418yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C22×D4C2418yes—
374C22×D4C24116yes—
375C22×D4C24116yes—
376C22×D4C2418yes—
377C22×D4C2418yes—
378C22×D4C2418yes—
379C22×D4C2418yes—
380C22×D4C2418yes—
381C22×D4C24116yes—
382C22×D4C24116yes—
383C23×C4C2412yes—
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C24116yes—
391C23×C4C24116yes—
392C4⋊Q8—28no—
393#127—216no—
394#127—216no—
395#127—216no—
396#127—216no—
397#127—216no—
398#127—216no—
399#127—216no—
400#127—216no—
401#127—48no—
402#127—48no—
403#127—416no—
404#127—416no—
405#127—416no—
406#127—48no—
407#127—416no—
408#127—48no—
409#127—416no—
410#127—416no—
411#127—416no—
412#127—416no—
413#127—416no—
414#126—28no—
415#125—24no—
416#125—28no—
417#124—24no—
418#124—416no—
419#124—416no—
420#124—416no—
421#124—416no—
422#123—28no—
423#123—432no—
424#123—432no—
425#123—432no—
426C22⋊Q8—24no—
427C22⋊Q8—216no—
428#121—24no—
429#121—432no—
430#121—432no—
431#121—432no—
432#121—416no—
433#121—416no—
434#121—416no—
435#121—416no—
436#121—416no—
437#120—432no—
438C4×Q8—24no—
439C4×Q8—216no—
440C4×Q8—28no—
441C4×D4—28no—
442C4×D4—216no—
443C4×D4—24no—
444C4×D4—28no—
445C4×D4—416no—
446C4×D4—416no—
447C4×D4—416no—
448C4×D4—416no—
449C4×D4—416no—
450C4×D4—416no—
451C4×D4—416no—
452#117—28no—
453#117—28no—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C22⋊C4—432no—
474C2×C22⋊C4C2414yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2414yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2412yes—
484C2×C22⋊C4C24116yes—
485C2×C22⋊C4C24116yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C24116yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C24116yes—
495C2×C22⋊C4C24116yes—
496C2×C42—28no—
497C2×C42—24no—
498C2×C42—24no—
499C2×C42—28no—
500C2×C42—28no—
501C2×C42#4118yescomplemented
502C2×C42C2412yes—
503C2×C42C2412yes—
504C2×C42C2412yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2418yes—
508C2×C42C2414yes—
509C2×C42C2411yescharacteristic
510C2×C42C2411yescharacteristic
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2412yes—
516C2×C42C2412yes—
517C2×C42C2412yes—
518C2×C42C2412yes—
519C2×C42C2412yes—
520C2×C42C2411yescharacteristic
521C2×C42C2411yescharacteristic
522C2×C42C2411yescharacteristic
523C2×C42C2411yescharacteristic
524C2×C42C2411yescharacteristic
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527#95C2414yes—
528#95C2414yes—
529#95C2414yes—
530#95C2414yes—
531#95C2418yes—
532#95C2414yes—
533#95C2414yes—
534#95C2412yes—
535#95C2414yes—
536#95C2414yes—
537#95C2414yes—
538#95C2414yes—
539#95C2414yes—
540#95C2414yes—
541#95C2412yes—
542#95C2414yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547C24—216no—
548C24—232no—
549C24—416no—
550C24—48no—
551C24—48no—
552C24C25116yes—
553C24C2512yes—
554C24C2511yescharacteristic
555#41—864no—
556C2×Q8—22no—
557C2×Q8—24no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×D4—24no—
562C2×D4—28no—
563C2×D4—22no—
564C2×D4—216no—
565C2×D4—216no—
566C2×D4—216no—
567C2×D4—216no—
568C2×D4—216no—
569C2×D4—216no—
570C2×D4—24no—
571C2×D4—216no—
572C2×D4—216no—
573C2×D4—216no—
574C2×D4—216no—
575C2×D4—216no—
576C2×D4—216no—
577C2×D4—216no—
578C2×D4—216no—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—232no—
583C2×D4—232no—
584C2×D4—216no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—416no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—48no—
596C2×D4—416no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—48no—
600C2×D4—48no—
601C2×D4—48no—
602C2×D4—416no—
603C2×D4—416no—
604C2×D4—416no—
605C2×D4—832no—
606C2×D4—832no—
607C2×D4—864no—
608C2×D4—832no—
609C2×D4—864no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—28no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—416no—
626C22×C4—416no—
627C22×C4—416no—
628C22×C4—416no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4C2×#4114yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4H(5,𝔽2)18yes—
635C22×C4C2514yes—
636C22×C4C2518yes—
637C22×C4C2514yes—
638C22×C4C2518yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2512yes—
642C22×C4C2511yescharacteristic
643C22×C4C2511yescharacteristic
644C22×C4C2511yescharacteristic
645C22×C4C2511yescharacteristic
646C22×C4C2512yes—
647C22×C4C2512yes—
648C22×C4C2512yes—
649C22×C4C2511yescharacteristic
650C22×C4C2511yescharacteristic
651C22×C4C2512yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—24no—
658C4⋊C4—28no—
659C4⋊C4—24no—
660C4⋊C4—28no—
661C4⋊C4—24no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—216no—
668C4⋊C4—28no—
669C4⋊C4—216no—
670C4⋊C4—216no—
671C22⋊C4—24no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—416no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—416no—
688C22⋊C4—416no—
689C22⋊C4—416no—
690C22⋊C4—416no—
691C22⋊C4—416no—
692C22⋊C4—416no—
693C42—24no—
694C42—24no—
695C42—28no—
696C42—24no—
697C42—24no—
698C42—24no—
699C42—24no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—24no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—24no—
708C42—28no—
709C42—28no—
710C42—216no—
711C42C2×#4114yes—
712C42C2×#4114yes—
713C42C2×#4114yes—
714C42C2×#4114yes—
715C42H(5,𝔽2)14yes—
716C42H(5,𝔽2)14yes—
717C42H(5,𝔽2)18yes—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—216no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—216no—
727C23—216no—
728C23—216no—
729C23—216no—
730C23—216no—
731C23—216no—
732C23—22no—
733C23—432no—
734C23—832no—
735C23—816no—
736C23—816no—
737C23—832no—
738C23C22×#4112yes—
739C23C2×H(5,𝔽2)14yes—
740C23C2611yescharacteristic
741Q8—44no—
742Q8—416no—
743D4—48no—
744D4—44no—
745D4—432no—
746D4—432no—
747D4—432no—
748D4—432no—
749D4—832no—
750D4—816no—
751D4—816no—
752D4—816no—
753D4—816no—
754D4—816no—
755D4—832no—
756D4—816no—
757D4—832no—
758D4—1616no—
759C2×C4—216no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—216no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—48no—
795C2×C4—416no—
796C2×C4—832no—
797C2×C4—1616no—
798C2×C4C22×#4112yes—
799C2×C4C22×#4112yes—
800C2×C4C22×#4112yes—
801C2×C4C22×#4112yes—
802C2×C4C22×#4112yes—
803C2×C4C22×#4112yes—
804C2×C4C2×H(5,𝔽2)14yes—
805C2×C4C2×H(5,𝔽2)14yes—
806C2×C4C2×H(5,𝔽2)14yes—
807C2×C4C2×H(5,𝔽2)14yes—
808C2×C4C2×H(5,𝔽2)12yes—
809C2×C4C2×H(5,𝔽2)12yes—
810C2×C4C2×H(5,𝔽2)14yes—
811C2×C4C2×H(5,𝔽2)14yes—
812C2×C4C2×H(5,𝔽2)14yes—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—24no—
817C22—44no—
818C22—416no—
819C22—416no—
820C22—42no—
821C22—416no—
822C22—416no—
823C22—42no—
824C22—42no—
825C22—416no—
826C22—416no—
827C22—416no—
828C22—44no—
829C22—1632no—
830C22#350814yes—
831C22C23×#4111yescharacteristic
832C22C22×H(5,𝔽2)11yescharacteristic
833C22C22×H(5,𝔽2)12yes—
834C22C22×H(5,𝔽2)12yes—
835C22C22×H(5,𝔽2)11yescharacteristic
836C4—24no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—24no—
842C4—24no—
843C4—44no—
844C4—48no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—48no—
850C4#350814yes—
851C4#350814yes—
852C4#354318yes—
853C2—24no—
854C2—82no—
855C2—816no—
856C2C2×#354312yes—
857C2C2×#350811yescharacteristic
858C2C2×#350811yescharacteristic
859C2C2×#350811yescharacteristic
860C2#6283212yes—
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. #59143C2semidirect
2. #59124C2semidirect
3. #46010C2semidirect
4. #39770C2semidirect
5. #39770C2semidirect
6. #39745C2semidirect
7. #39464C2semidirect
8. #39386C2semidirect
9. #37694C2semidirect
10. #37614C2semidirect
11. #37319C2semidirect
12. C2×#2867C2semidirect
13. #36635C2semidirect
14. #36595C2semidirect
15. #36128C2semidirect
16. #36121C2semidirect
17. #35293C2semidirect
18. #35278C2semidirect
19. #34364C2semidirect
20. C4×#529C2semidirect
21. C2×#559C22semidirect
22. C2×#550C22semidirect
24. C2×#540C22semidirect
25. C2×#532C22semidirect
38. #2864C22semidirect
39. #2863C22semidirect
40. #2862C22semidirect
41. #2859C22semidirect
42. #2858C22semidirect
44. #2856C22semidirect
47. #2818C22semidirect
48. #2709C22semidirect
49. #2709C22semidirect
50. #2709C22semidirect
51. #2709C22semidirect
52. #2673C22semidirect
53. #2673C22semidirect
54. #2673C22semidirect
55. #2673C22semidirect
56. #2657C22semidirect
57. #2641C22semidirect
58. #2641C22semidirect
59. #2619C22semidirect
60. #2619C22semidirect
61. #2619C22semidirect
63. #2548C22semidirect
64. #2548C22semidirect
65. #2548C22semidirect
66. #2548C22semidirect
67. #2544C22semidirect
68. #2544C22semidirect
69. #2544C22semidirect
70. #2544C22semidirect
71. #2544C22semidirect
72. #2541C22semidirect
73. #2541C22semidirect
74. #2541C22semidirect
75. #2445C22semidirect
76. #2445C22semidirect
77. #2445C22semidirect
78. #2445C22semidirect
79. #2445C22semidirect
80. #2445C22semidirect
81. #2445C22semidirect
82. #2445C22semidirect
86. #2431C22semidirect
87. #2431C22semidirect
88. #2431C22semidirect
89. #2431C22semidirect
90. #2428C22semidirect
91. #2428C22semidirect
92. #2428C22semidirect
93. #2428C22semidirect
94. #2428C22semidirect
95. #2428C22semidirect
100. #2380C22semidirect
101. #2366C22semidirect
102. #2366C22semidirect
103. #2366C22semidirect
104. #2366C22semidirect
108. #2328C22semidirect
109. #2328C22semidirect
110. #2328C22semidirect
111. #2328C22semidirect
113. C4×C4⋊Q8C22semidirect
114. C4×#127C22semidirect
115. C4×#125C22semidirect
116. C4×#125C22semidirect
117. C4×#126C22semidirect
118. C4×#124C22semidirect
123. #2298C22semidirect
124. #2295C22semidirect
125. #2295C22semidirect
126. #2293C22semidirect
130. C42×Q8C22semidirect
132. C42×D4C22semidirect
133. C4×#117C22semidirect
501. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#591432
#591242
#460102
#397702
#397452
#394642
#393862
#376942
#376142
#373192
C2×#28672
#366352
#365952
#361282
#361212
#352932
#352782
#343642
C4×#5292