Finite Group Databasebeta

← #8097288

Subgroups — #8097288

Order 512.

6117 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53116C216yesmaximal, complemented
2#53080C213yesmaximal, complemented
3#53074C216yesmaximal, complemented
4#52986C213yesmaximal, complemented
5#52301C213yesmaximal, complemented
6#46084C213yesmaximal, complemented
7#46054C216yesmaximal, complemented
8#45645C216yesmaximal, complemented
9#45601C216yesmaximal, complemented
10#45509C216yesmaximal, complemented
11#36583C211yesmaximal, characteristic, complemented
12#36467C212yesmaximal, complemented
13#36429C212yesmaximal, complemented
14#36429C212yesmaximal, complemented
15#36428C212yesmaximal, complemented
16#36049C212yesmaximal, complemented
17#36049C211yesmaximal, characteristic, complemented
18#35910C211yesmaximal, characteristic, complemented
19#35854C212yesmaximal, complemented
20C23×#41C2212yescomplemented
21C2×#557C2212yescomplemented
22C2×#557C2211yescharacteristic, complemented
23C2×#550C2212yes—
24C2×#550C2211yescharacteristic
25C2×#550C2211yescharacteristic
26C2×D4×Q8C2211yescharacteristic
27C2×#548C2212yes—
28C2×#548C2212yes—
29#2861C2216yescomplemented
30#2858C2213yescomplemented
31#2848C2216yescomplemented
32#2847C2216yescomplemented
33#2847C2216yescomplemented
34#2828C2216yescomplemented
35#2828C2216yescomplemented
36#2828C22112yescomplemented
37#2824C22112yescomplemented
38#2824C22112yescomplemented
39#2819C2216yescomplemented
40#2812C22112yescomplemented
41#2804C2216yescomplemented
42#2804C2213yescomplemented
43#2782C2211yescharacteristic
44#2782C2213yescomplemented
45#2782C22112yescomplemented
46#2782C2216yescomplemented
47#2782C2216yescomplemented
48#2782C2216yescomplemented
49#2753C22112yescomplemented
50#2753C22112yescomplemented
51#2753C22112yescomplemented
52#2753C22112yescomplemented
53#2733C2216yescomplemented
54#2712C22112yescomplemented
55#2684C2216yes—
56#2684C22112yescomplemented
57#2684C2216yescomplemented
58#2684C2216yescomplemented
59#2679C2216yes—
60#2679C2213yes—
61#2670C22112yescomplemented
62#2670C22112yescomplemented
63#2642C2213yescomplemented
64#2641C2216yescomplemented
65#2641C2213yescomplemented
66#2640C2216yescomplemented
67#2592C2216yescomplemented
68#2592C2216yescomplemented
69#2568C2213yescomplemented
70#2563C2216yescomplemented
71#2562C2213yes—
72#2562C2216yescomplemented
73#2562C2216yescomplemented
74#2562C2213yescomplemented
75#2548C2213yescomplemented
76#2548C2213yescomplemented
77#2548C2216yescomplemented
78#2547C2213yescomplemented
79#2492C2216yescomplemented
80#2492C2216yescomplemented
81#2491C2216yescomplemented
82#2491C2216yescomplemented
83#2491C2216yescomplemented
84#2491C2216yescomplemented
85#2490C2216yescomplemented
86#2490C2216yescomplemented
87#2490C2216yescomplemented
88#2490C2216yescomplemented
89#2490C2216yescomplemented
90#2490C2216yescomplemented
91#2490C2216yescomplemented
92#2490C2216yescomplemented
93#2489C2216yescomplemented
94#2489C2216yescomplemented
95#2489C2216yescomplemented
96#2489C2216yescomplemented
97#2435C2216yescomplemented
98#2433C2216yescomplemented
99#2433C2216yescomplemented
100#2432C2216yescomplemented
101#2432C2216yescomplemented
102#2431C2216yescomplemented
103#2431C2216yescomplemented
104#2431C2216yescomplemented
105#2431C2216yescomplemented
106#2408C2216yes—
107#2408C2216yescomplemented
108#2408C2216yescomplemented
109#2407C2216yes—
110#2407C2216yes—
111#2407C2216yescomplemented
112#2407C2216yescomplemented
113#2407C2216yescomplemented
114#2407C2216yescomplemented
115#2398C2213yes—
116#2398C2216yescomplemented
117#2398C2216yescomplemented
118#2398C2213yescomplemented
119#2379C2216yescomplemented
120#2375C22112yescomplemented
121#2341C2212yescomplemented
122#2341C2212yescomplemented
123#2341C2212yescomplemented
124#2341C2212yescomplemented
125#2341C2212yescomplemented
126#2341C2212yescomplemented
127Q8×C22⋊C4C2212yescomplemented
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130C4×#124C2213yescomplemented
131C4×#124C2216yescomplemented
132C4×#120C2216yes—
133C4×#120C2216yescomplemented
134C4×#120C2216yescomplemented
135#2276C2211yescharacteristic, complemented
136#2276C2211yescharacteristic, complemented
137C42×Q8C2211yescharacteristic, complemented
138C22×#41—48no—
139C22×#41—48no—
140C22×#41—48no—
141C22×#41C2312yes—
142C22×#41C2312yes—
143C22×#41C2316yes—
144C22×#41C2316yes—
145C23×Q8C2312yes—
146C23×D4C2316yes—
147C24×C4C2316yes—
148#557—48no—
149#557—44no—
150#550—48no—
151#550—44no—
152#550—44no—
153D4×Q8—44no—
154#548—48no—
155#548—48no—
156C2×C4⋊Q8C2316yes—
157C2×C4⋊Q8C2313yes—
158C2×C4⋊Q8C2313yes—
159C2×#127C2313yes—
160C2×#127C2316yes—
161C2×#127C2313yes—
162C2×#125C2313yes—
163C2×#125C2316yes—
164C2×#125C2313yes—
165C2×#125C2316yes—
166C2×#124C2316yes—
167C2×#124C2316yes—
168C2×#124C2313yes—
169C2×#124C2316yes—
170C2×#124C2316yes—
171C2×#124C23112yes—
172C2×#124C2316yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×#121C2316yes—
177C2×#121C2316yes—
178C2×#121C2316yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#120C23112yes—
183C2×#120C2316yes—
184C2×#120C2316yes—
185C2×#120C2316yes—
186C2×#120C23112yes—
187C2×C4×Q8C2311yescharacteristic
188C2×C4×Q8C2311yescharacteristic
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2313yes—
194C2×C4×Q8C2316yes—
195C2×C4×D4C2313yes—
196C2×C4×D4C2316yes—
197C2×C4×D4C2313yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2313yes—
201#400C2316yes—
202#400C2313yes—
203#400C2316yes—
204#400C23112yes—
205#400C2313yes—
206#400C2316yes—
207#400C23112yes—
208#400C2313yes—
209#400C2312yes—
210#400C2311yescharacteristic
211#400C2316yes—
212#397C2316yes—
213#397C23112yes—
214#397C23112yes—
215#397C23112yes—
216#397C2316yes—
217#397C23112yes—
218#397C2316yes—
219#397C2312yes—
220#397C2316yes—
221#397C2316yes—
222#394C2313yes—
223#394C23112yes—
224#394C2316yes—
225#394C23112yes—
226#394C2313yes—
227#394C23112yes—
228#394C2316yes—
229#394C2316yes—
230#394C23112yes—
231#394C23112yes—
232#394C23112yes—
233#394C23112yes—
234#394C23112yes—
235#394C2316yes—
236#394C2313yes—
237#394C2316yes—
238#394C23112yes—
239#394C23112yes—
240#394C2311yescharacteristic
241#394C2316yes—
242#394C2316yes—
243#393C2316yes—
244#393C23112yes—
245#393C2316yes—
246#393C23112yes—
247#393C2316yes—
248#393C2316yes—
249#393C2316yes—
250#393C2316yes—
251#392C23112yes—
252#392C23112yes—
253#392C23112yes—
254#392C23112yes—
255#392C23112yes—
256#392C23112yes—
257#392C23112yes—
258#391C2316yes—
259#391C2316yes—
260#391C2316yes—
261#391C2316yes—
262#391C2316yes—
263#391C2316yes—
264#391C2316yes—
265#391C2313yes—
266#391C2316yes—
267#390C23112yes—
268#390C2313yes—
269#390C23112yes—
270#390C2316yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C2316yes—
275#390C2316yes—
276#390C2316yes—
277#390C2316yes—
278#390C2316yes—
279#390C2316yes—
280#390C2316yes—
281#390C2316yes—
282#390C2316yes—
283#390C23112yes—
284#390C2316yes—
285#388C23112yes—
286#388C2316yes—
287#388C23112yes—
288#388C23112yes—
289#388C23112yes—
290#388C23112yes—
291#388C2316yes—
292#388C23112yes—
293#388C23112yes—
294#388C23112yes—
295#388C23112yes—
296#388C2316yes—
297#388C2316yes—
298#388C2312yes—
299#388C2316yes—
300#386C2316yes—
301#386C23112yes—
302#386C23112yes—
303#386C23112yes—
304#386C2316yes—
305#386C2316yes—
306#386C23112yes—
307#386C2316yes—
308#386C2316yes—
309#386C2312yes—
310#386C2316yes—
311#386C2316yes—
312#386C2316yes—
313#385C2316yes—
314#385C23112yes—
315#385C2316yes—
316#385C23112yes—
317#385C2316yes—
318#385C2316yes—
319#385C2316yes—
320#385C2316yes—
321#385C2316yes—
322#385C2312yes—
323#385C2312yes—
324#382C23112yes—
325#382C2316yes—
326#382C2316yes—
327#382C2311yescharacteristic
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#380C2316yes—
337#379C23112yes—
338#379C2316yes—
339#379C2316yes—
340#379C2316yes—
341C4×C4⋊C4C2313yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2313yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2313yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356#376C2313yes—
357#376C2313yes—
358C43C2313yes—
359C25C2416yes—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—28no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—412no—
367C2×#41—412no—
368C2×#41—412no—
369C2×#41—412no—
370C2×#41—412no—
371C2×#41—412no—
372C2×#41—4128no—
373C22×Q8—28no—
374C22×Q8—28no—
375C22×Q8—28no—
376C22×Q8C2416yes—
377C22×Q8C2413yes—
378C22×Q8C2416yes—
379C22×Q8C2411yescharacteristic
380C22×D4—412no—
381C22×D4—412no—
382C22×D4—412no—
383C22×D4C2416yes—
384C22×D4C2416yes—
385C22×D4C2411yescharacteristic
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2413yes—
389C22×D4C2416yes—
390C22×D4C2413yes—
391C22×D4C24112yes—
392C22×D4C2416yes—
393C22×D4C2416yes—
394C22×D4C24112yes—
395C23×C4—412no—
396C23×C4—412no—
397C23×C4—412no—
398C23×C4C2416yes—
399C23×C4C2416yes—
400C23×C4C2416yes—
401C23×C4C2412yes—
402C23×C4C2416yes—
403C23×C4C2416yes—
404C4⋊Q8—412no—
405C4⋊Q8—46no—
406C4⋊Q8—46no—
407#127—412no—
408#127—46no—
409#127—46no—
410#125—412no—
411#125—46no—
412#125—412no—
413#125—46no—
414#124—46no—
415#124—412no—
416#124—412no—
417#124—412no—
418#124—412no—
419#124—86no—
420#124—812no—
421C22⋊Q8—412no—
422C22⋊Q8—412no—
423C22⋊Q8—412no—
424#121—412no—
425#121—412no—
426#121—412no—
427#121—412no—
428#121—412no—
429#121—412no—
430#120—412no—
431#120—412no—
432#120—424no—
433#120—412no—
434#120—812no—
435C4×Q8—28no—
436C4×Q8—28no—
437C4×Q8—24no—
438C4×Q8—28no—
439C4×Q8—24no—
440C4×Q8—24no—
441C4×Q8—412no—
442C4×Q8—46no—
443C4×D4—412no—
444C4×D4—412no—
445C4×D4—46no—
446C4×D4—412no—
447C4×D4—46no—
448C4×D4—46no—
449C2×C4⋊C4C2413yes—
450C2×C4⋊C4C2413yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2413yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2416yes—
460C2×C4⋊C4C2413yes—
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2413yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2413yes—
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C24112yes—
469C2×C4⋊C4C2416yes—
470C2×C22⋊C4C2412yes—
471C2×C22⋊C4C2412yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C24112yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C24112yes—
494C2×C22⋊C4C24112yes—
495C2×C22⋊C4C24112yes—
496C2×C22⋊C4C24112yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C24112yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C24112yes—
505C2×C42C2416yes—
506C2×C42C2416yes—
507C2×C42C2413yes—
508C2×C42C2416yes—
509C2×C42C2413yes—
510C2×C42C2413yes—
511C2×C42C2411yescharacteristic
512C2×C42C2413yes—
513C2×C42C2416yes—
514C2×C42C2416yes—
515C2×C42C2416yes—
516#95C2411yescharacteristic
517#95C2411yescharacteristic
518#95C2416yes—
519#95C2416yes—
520#95C2413yes—
521#95C2413yes—
522#95C2412yes—
523#95C2412yes—
524#95C2412yes—
525#95C2412yes—
526#95C2412yes—
527#95C2412yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531#95C2416yes—
532#95C2416yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C2416yes—
538#95C2416yes—
539#95C2416yes—
540#95C2416yes—
541#95C24112yes—
542#95C24112yes—
543#95C24112yes—
544C24—212no—
545C24—46no—
546C24—46no—
547C24—46no—
548C24—46no—
549C24—46no—
550C24—46no—
551C24C2516yes—
552C24C2516yes—
553C24C2512yes—
554#41—496no—
555#41—496no—
556#41—432no—
557#41—432no—
558C2×Q8—212no—
559C2×Q8—212no—
560C2×Q8—212no—
561C2×Q8—26no—
562C2×Q8—43no—
563C2×Q8—46no—
564C2×Q8—46no—
565C2×Q8—43no—
566C2×Q8—46no—
567C2×Q8—432no—
568C2×Q8H(5,𝔽2)18yes—
569C2×Q8H(5,𝔽2)14yes—
570C2×D4—24no—
571C2×D4—212no—
572C2×D4—212no—
573C2×D4—212no—
574C2×D4—212no—
575C2×D4—212no—
576C2×D4—212no—
577C2×D4—212no—
578C2×D4—212no—
579C2×D4—26no—
580C2×D4—41no—
581C2×D4—412no—
582C2×D4—412no—
583C2×D4—412no—
584C2×D4—46no—
585C2×D4—46no—
586C2×D4—43no—
587C2×D4—46no—
588C2×D4—43no—
589C2×D4—46no—
590C2×D4—46no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—46no—
594C2×D4—43no—
595C2×D4—412no—
596C2×D4—412no—
597C2×D4—46no—
598C2×D4—412no—
599C2×D4—46no—
600C2×D4—412no—
601C2×D4—46no—
602C2×D4—46no—
603C2×D4—496no—
604C22×C4—212no—
605C22×C4—212no—
606C22×C4—212no—
607C22×C4—212no—
608C22×C4—212no—
609C22×C4—212no—
610C22×C4—212no—
611C22×C4—212no—
612C22×C4—212no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—46no—
617C22×C4—46no—
618C22×C4—46no—
619C22×C4—46no—
620C22×C4—46no—
621C22×C4—46no—
622C22×C4—496no—
623C22×C4C2511yescharacteristic
624C22×C4C2512yes—
625C22×C4C2512yes—
626C22×C4C2512yes—
627C22×C4C2516yes—
628C22×C4C2512yes—
629C22×C4C2513yes—
630C22×C4C2513yes—
631C22×C4C2516yes—
632C22×C4C2511yescharacteristic
633C22×C4C2516yes—
634C22×C4C2516yes—
635C22×C4C2512yes—
636C22×C4C2513yes—
637C22×C4C2511yescharacteristic
638C22×C4C2513yes—
639C4⋊C4—26no—
640C4⋊C4—212no—
641C4⋊C4—26no—
642C4⋊C4—212no—
643C4⋊C4—212no—
644C4⋊C4—26no—
645C4⋊C4—41no—
646C4⋊C4—42no—
647C4⋊C4—41no—
648C4⋊C4—46no—
649C4⋊C4—46no—
650C4⋊C4—43no—
651C4⋊C4—41no—
652C4⋊C4—42no—
653C4⋊C4—46no—
654C4⋊C4—43no—
655C4⋊C4—46no—
656C4⋊C4—43no—
657C4⋊C4—46no—
658C4⋊C4—412no—
659C4⋊C4—46no—
660C22⋊C4—24no—
661C22⋊C4—212no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—212no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—46no—
668C22⋊C4—46no—
669C22⋊C4—46no—
670C22⋊C4—46no—
671C22⋊C4—46no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—46no—
675C22⋊C4—412no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C22⋊C4—46no—
679C22⋊C4—46no—
680C22⋊C4—412no—
681C22⋊C4—46no—
682C22⋊C4—46no—
683C22⋊C4—412no—
684C22⋊C4—412no—
685C22⋊C4—412no—
686C22⋊C4—412no—
687C22⋊C4—46no—
688C22⋊C4—46no—
689C22⋊C4—46no—
690C22⋊C4—412no—
691C22⋊C4—46no—
692C22⋊C4—412no—
693C22⋊C4—46no—
694C22⋊C4—46no—
695C42—212no—
696C42—212no—
697C42—212no—
698C42—26no—
699C42—26no—
700C42—26no—
701C42—22no—
702C42—46no—
703C42—46no—
704C42—43no—
705C42—46no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—26no—
713C23—26no—
714C23—26no—
715C23—26no—
716C23—26no—
717C23—26no—
718C23—26no—
719C23—26no—
720C23—26no—
721C23—26no—
722C23—26no—
723C23—26no—
724C23—26no—
725C23—26no—
726C23—424no—
727C23—812no—
728C23—812no—
729C23—812no—
730C23—812no—
731C23—812no—
732C23—812no—
733C23#58514yes—
734C23C2611yescharacteristic
735Q8—424no—
736Q8—86no—
737Q8—812no—
738Q8H(3,𝔽4)116yes—
739D4—44no—
740D4—448no—
741D4—424no—
742D4—424no—
743D4—86no—
744D4—812no—
745D4—812no—
746D4—812no—
747D4—86no—
748D4—166no—
749D4—1612no—
750D4—166no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—26no—
759C2×C4—23no—
760C2×C4—23no—
761C2×C4—26no—
762C2×C4—26no—
763C2×C4—23no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—26no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—26no—
776C2×C4—23no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—22no—
784C2×C4—26no—
785C2×C4—22no—
786C2×C4—23no—
787C2×C4—23no—
788C2×C4—26no—
789C2×C4—26no—
790C2×C4—23no—
791C2×C4—22no—
792C2×C4—48no—
793C2×C4—424no—
794C2×C4—424no—
795C2×C4—424no—
796C2×C4—424no—
797C2×C4—424no—
798C2×C4C2×H(5,𝔽2)112yes—
799C2×C4C2×H(5,𝔽2)16yes—
800C2×C4#58512yes—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—46no—
809C22—46no—
810C22—46no—
811C22—46no—
812C22—46no—
813C22—46no—
814C22—46no—
815C22—46no—
816C22—46no—
817C22—46no—
818C22—46no—
819C22—46no—
820C22—46no—
821C22—46no—
822C22—848no—
823C22C22×H(5,𝔽2)12yes—
824C22C22×H(5,𝔽2)11yescharacteristic
825C22C2×#58511yescharacteristic
826C22C2×#58512yes—
827C22H(7,𝔽2)11yescharacteristic
828C4—22no—
829C4—42no—
830C4—46no—
831C4—42no—
832C4—41no—
833C4—41no—
834C4—43no—
835C4—46no—
836C4—43no—
837C4—46no—
838C4—43no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—46no—
843C4C2×H(3,𝔽4)112yes—
844C2—44no—
845C2—86no—
846C2—86no—
847C2C22×H(3,𝔽4)11yescharacteristic
848C2#6289911yescharacteristic
849C2#6289912yes—
850C2#6301912yes—
851C2#6302011yescharacteristic
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. #53116C2semidirect
2. #53080C2semidirect
3. #53074C2semidirect
4. #52986C2semidirect
5. #52301C2semidirect
6. #46084C2semidirect
7. #46054C2semidirect
8. #45645C2semidirect
9. #45601C2semidirect
10. #45509C2semidirect
11. #36583C2semidirect
12. #36467C2semidirect
13. #36429C2semidirect
14. #36429C2semidirect
15. #36428C2semidirect
16. #36049C2semidirect
17. #36049C2semidirect
18. #35910C2semidirect
19. #35854C2semidirect
20. C23×#41C22semidirect
21. C2×#557C22semidirect
22. C2×#557C22semidirect
29. #2861C22semidirect
30. #2858C22semidirect
31. #2848C22semidirect
32. #2847C22semidirect
33. #2847C22semidirect
34. #2828C22semidirect
35. #2828C22semidirect
36. #2828C22semidirect
37. #2824C22semidirect
38. #2824C22semidirect
39. #2819C22semidirect
40. #2812C22semidirect
41. #2804C22semidirect
42. #2804C22semidirect
44. #2782C22semidirect
45. #2782C22semidirect
46. #2782C22semidirect
47. #2782C22semidirect
48. #2782C22semidirect
49. #2753C22semidirect
50. #2753C22semidirect
51. #2753C22semidirect
52. #2753C22semidirect
53. #2733C22semidirect
54. #2712C22semidirect
56. #2684C22semidirect
57. #2684C22semidirect
58. #2684C22semidirect
61. #2670C22semidirect
62. #2670C22semidirect
63. #2642C22semidirect
64. #2641C22semidirect
65. #2641C22semidirect
66. #2640C22semidirect
67. #2592C22semidirect
68. #2592C22semidirect
69. #2568C22semidirect
70. #2563C22semidirect
72. #2562C22semidirect
73. #2562C22semidirect
74. #2562C22semidirect
75. #2548C22semidirect
76. #2548C22semidirect
77. #2548C22semidirect
78. #2547C22semidirect
79. #2492C22semidirect
80. #2492C22semidirect
81. #2491C22semidirect
82. #2491C22semidirect
83. #2491C22semidirect
84. #2491C22semidirect
85. #2490C22semidirect
86. #2490C22semidirect
87. #2490C22semidirect
88. #2490C22semidirect
89. #2490C22semidirect
90. #2490C22semidirect
91. #2490C22semidirect
92. #2490C22semidirect
93. #2489C22semidirect
94. #2489C22semidirect
95. #2489C22semidirect
96. #2489C22semidirect
97. #2435C22semidirect
98. #2433C22semidirect
99. #2433C22semidirect
100. #2432C22semidirect
101. #2432C22semidirect
102. #2431C22semidirect
103. #2431C22semidirect
104. #2431C22semidirect
105. #2431C22semidirect
107. #2408C22semidirect
108. #2408C22semidirect
111. #2407C22semidirect
112. #2407C22semidirect
113. #2407C22semidirect
114. #2407C22semidirect
116. #2398C22semidirect
117. #2398C22semidirect
118. #2398C22semidirect
119. #2379C22semidirect
120. #2375C22semidirect
121. #2341C22semidirect
122. #2341C22semidirect
123. #2341C22semidirect
124. #2341C22semidirect
125. #2341C22semidirect
126. #2341C22semidirect
127. Q8×C22⋊C4C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. C4×#124C22semidirect
131. C4×#124C22semidirect
133. C4×#120C22semidirect
134. C4×#120C22semidirect
135. #2276C22semidirect
136. #2276C22semidirect
137. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#531162
#530802
#530742
#529862
#523012
#460842
#460542
#456452
#456012
#455092
#365832
#364672
#364292
#364282
#360492
#359102
#358542