Finite Group Databasebeta

← #8095835

Subgroups — #8095835

Order 512.

5913 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53144C216yesmaximal, complemented
2#53144C216yesmaximal, complemented
3#52990C216yesmaximal, complemented
4#52301C213yesmaximal, complemented
5#46073C213yesmaximal, complemented
6#46043C216yesmaximal, complemented
7#45667C216yesmaximal, complemented
8#45645C213yesmaximal, complemented
9#45601C216yesmaximal, complemented
10#45494C213yesmaximal, complemented
11#36575C212yesmaximal, complemented
12Q8×#124C211yesmaximal, characteristic, complemented
13Q8×#120C211yesmaximal, characteristic, complemented
14#36467C212yesmaximal, complemented
15#36428C211yesmaximal, characteristic, complemented
16#36428C212yesmaximal, complemented
17#35948C212yesmaximal, complemented
18#35910C212yesmaximal, complemented
19#35854C212yesmaximal, complemented
20C23×#41C2211yescharacteristic, complemented
21C24×Q8C2211yescharacteristic, complemented
22C2×Q82C2211yescharacteristic, complemented
23C2×#557C2212yescomplemented
24C2×D4×Q8C2212yes—
25C2×D4×Q8C2211yescharacteristic
26C2×#548C2212yes—
27C2×#548C2212yes—
28C2×#548C2212yes—
29#2862C2213yescomplemented
30#2861C2216yescomplemented
31#2848C2213yescomplemented
32#2848C2213yescomplemented
33#2848C2216yescomplemented
34#2847C2216yescomplemented
35#2840C2216yescomplemented
36#2835C22112yescomplemented
37#2832C2216yescomplemented
38#2832C22112yescomplemented
39#2832C22112yescomplemented
40#2824C22112yescomplemented
41#2824C2216yescomplemented
42#2804C2213yes—
43#2804C22112yescomplemented
44#2804C2216yescomplemented
45#2785C2216yescomplemented
46#2782C2216yes—
47#2782C22112yescomplemented
48#2782C2216yescomplemented
49#2782C2216yescomplemented
50#2763C2216yescomplemented
51#2763C22112yescomplemented
52#2763C22112yescomplemented
53#2753C22112yescomplemented
54#2753C22112yescomplemented
55#2736C22112yescomplemented
56#2712C22112yescomplemented
57#2684C22112yes—
58#2684C2211yescharacteristic
59#2684C2213yes—
60#2684C2216yes—
61#2684C2216yescomplemented
62#2679C2213yes—
63#2670C2216yescomplemented
64#2642C2216yescomplemented
65#2640C2216yescomplemented
66#2640C2216yescomplemented
67#2592C2216yescomplemented
68#2592C2216yescomplemented
69#2592C2216yescomplemented
70#2568C2216yescomplemented
71#2568C2213yescomplemented
72#2563C2213yes—
73#2563C2216yescomplemented
74#2562C2216yes—
75#2562C2216yescomplemented
76#2547C2216yescomplemented
77#2492C2216yescomplemented
78#2492C2216yescomplemented
79#2492C2216yescomplemented
80#2492C2216yescomplemented
81#2492C2216yescomplemented
82#2492C2216yescomplemented
83#2492C2216yescomplemented
84#2491C2216yescomplemented
85#2491C2216yescomplemented
86#2491C2216yescomplemented
87#2490C2216yescomplemented
88#2490C2216yescomplemented
89#2490C2216yescomplemented
90#2489C2216yescomplemented
91#2489C2216yescomplemented
92#2489C2216yescomplemented
93#2489C2216yescomplemented
94#2489C2216yescomplemented
95#2436C2216yescomplemented
96#2436C2216yescomplemented
97#2436C2216yescomplemented
98#2435C2216yescomplemented
99#2435C2213yescomplemented
100#2434C2213yescomplemented
101#2434C2216yescomplemented
102#2432C2216yescomplemented
103#2432C2216yescomplemented
104#2432C2216yescomplemented
105#2409C2216yes—
106#2409C2213yes—
107#2409C2216yescomplemented
108#2409C2216yescomplemented
109#2409C2216yescomplemented
110#2408C2213yes—
111#2408C2216yes—
112#2407C2216yes—
113#2407C2216yes—
114#2407C2216yes—
115#2398C2216yes—
116#2398C2216yescomplemented
117#2398C2216yescomplemented
118#2379C22112yescomplemented
119#2375C2216yes—
120#2341C2212yescomplemented
121#2341C2212yescomplemented
122#2341C2212yescomplemented
123Q8×C22⋊C4C2211yescharacteristic, complemented
124Q8×C22⋊C4C2212yescomplemented
125Q8×C22⋊C4C2211yescharacteristic, complemented
126Q8×C22⋊C4C2212yescomplemented
127Q8×C22⋊C4C2212yescomplemented
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130C4×#124C2213yes—
131C4×#124C2216yescomplemented
132C4×#120C2216yes—
133C4×#120C2213yes—
134C4×#120C2213yes—
135C4×#120C2216yescomplemented
136#2276C2212yescomplemented
137C42×Q8C2211yescharacteristic, complemented
138C22×#41—48no—
139C22×#41—44no—
140C22×#41C2312yes—
141C22×#41C2316yes—
142C23×Q8—48no—
143C23×Q8—44no—
144C23×Q8C2311yescharacteristic
145C23×Q8C2312yes—
146C23×Q8C2311yescharacteristic
147C23×Q8C2316yes—
148C23×Q8C2313yes—
149C23×D4C2313yes—
150C24×C4C2313yes—
151C24×C4C2313yes—
152Q82—44no—
153#557—48no—
154D4×Q8—48no—
155D4×Q8—44no—
156#548—48no—
157#548—48no—
158#548—48no—
159C2×C4⋊Q8C2313yes—
160C2×C4⋊Q8C2316yes—
161C2×C4⋊Q8C2313yes—
162C2×C4⋊Q8C2316yes—
163C2×C4⋊Q8C2316yes—
164C2×#125C2316yes—
165C2×#125C2316yes—
166C2×#124C2311yescharacteristic
167C2×#124C2316yes—
168C2×#124C2316yes—
169C2×#124C2316yes—
170C2×#124C23112yes—
171C2×#124C2316yes—
172C2×C22⋊Q8C2316yes—
173C2×C22⋊Q8C2313yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2313yes—
176C2×C22⋊Q8C2316yes—
177C2×C22⋊Q8C2316yes—
178C2×C22⋊Q8C2316yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#120C2313yes—
183C2×#120C2311yescharacteristic
184C2×#120C2316yes—
185C2×#120C2316yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2316yes—
192C2×C4×Q8C2313yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2313yes—
196C2×C4×D4C2316yes—
197C2×C4×D4C2316yes—
198#400C23112yes—
199#400C23112yes—
200#400C2316yes—
201#400C23112yes—
202#400C23112yes—
203#400C2316yes—
204#400C23112yes—
205#400C2316yes—
206#400C2316yes—
207#400C2316yes—
208#400C2316yes—
209#397C23112yes—
210#397C23112yes—
211#397C23112yes—
212#397C2316yes—
213#397C2316yes—
214#397C23112yes—
215#397C2316yes—
216#397C2316yes—
217#397C2312yes—
218#397C2316yes—
219#395C23112yes—
220#395C2316yes—
221#395C23112yes—
222#394C2316yes—
223#394C23112yes—
224#394C2316yes—
225#394C2316yes—
226#394C23112yes—
227#394C23112yes—
228#394C23112yes—
229#394C23112yes—
230#394C2316yes—
231#394C2312yes—
232#394C2316yes—
233#394C2316yes—
234#393C2316yes—
235#393C2316yes—
236#393C2316yes—
237#393C23112yes—
238#393C2316yes—
239#393C23112yes—
240#393C23112yes—
241#393C23112yes—
242#393C23112yes—
243#393C2316yes—
244#393C2316yes—
245#393C23112yes—
246#393C23112yes—
247#393C2316yes—
248#393C2316yes—
249#393C2312yes—
250#392C23112yes—
251#392C2316yes—
252#391C2313yes—
253#391C23112yes—
254#391C2316yes—
255#391C2316yes—
256#391C2316yes—
257#391C2316yes—
258#391C2316yes—
259#391C2316yes—
260#391C23112yes—
261#391C2316yes—
262#391C2316yes—
263#391C2316yes—
264#391C2316yes—
265#391C2316yes—
266#391C2316yes—
267#391C23112yes—
268#391C2316yes—
269#390C2313yes—
270#390C23112yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C2316yes—
275#390C2316yes—
276#390C2316yes—
277#390C2316yes—
278#388C23112yes—
279#388C23112yes—
280#388C2316yes—
281#388C23112yes—
282#388C2316yes—
283#388C23112yes—
284#388C23112yes—
285#388C23112yes—
286#388C23112yes—
287#388C23112yes—
288#388C23112yes—
289#388C2316yes—
290#388C2316yes—
291#388C2312yes—
292#388C2316yes—
293#386C2316yes—
294#386C23112yes—
295#386C23112yes—
296#386C23112yes—
297#386C2313yes—
298#386C2316yes—
299#386C2316yes—
300#386C2316yes—
301#386C2316yes—
302#386C2316yes—
303#386C2316yes—
304#386C2312yes—
305#386C2311yescharacteristic
306#385C2313yes—
307#385C23112yes—
308#385C2316yes—
309#385C23112yes—
310#385C23112yes—
311#385C2313yes—
312#385C2316yes—
313#385C23112yes—
314#385C2316yes—
315#385C2316yes—
316#385C2316yes—
317#385C2316yes—
318#385C2316yes—
319#385C2316yes—
320#385C2316yes—
321#382C2316yes—
322#382C23112yes—
323#382C23112yes—
324#382C2313yes—
325#382C2316yes—
326#380C2313yes—
327#380C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2313yes—
335#380C2316yes—
336#379C2313yes—
337#379C23112yes—
338#379C2313yes—
339#379C2316yes—
340#379C2316yes—
341#379C2312yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2313yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C22⋊C4C2313yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357#376C2316yes—
358C43C2313yes—
359C25C2411yescharacteristic
360C25C2413yes—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—28no—
364C2×#41—412no—
365C2×#41—412no—
366C2×#41—412no—
367C2×#41—464no—
368C22×Q8—28no—
369C22×Q8—28no—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8—24no—
373C22×Q8—28no—
374C22×Q8—24no—
375C22×Q8—412no—
376C22×Q8—412no—
377C22×Q8—412no—
378C22×Q8—412no—
379C22×Q8—46no—
380C22×Q8—464no—
381C22×Q8C2416yes—
382C22×Q8C2413yes—
383C22×Q8C2413yes—
384C22×Q8C2411yescharacteristic
385C22×Q8C2416yes—
386C22×Q8C2416yes—
387C22×Q8C2416yes—
388C22×Q8C2411yescharacteristic
389C22×D4—412no—
390C22×D4—46no—
391C22×D4C2416yes—
392C22×D4C2412yes—
393C22×D4C2416yes—
394C22×D4C2416yes—
395C22×D4C2416yes—
396C22×D4C2416yes—
397C22×D4C2411yescharacteristic
398C23×C4—412no—
399C23×C4—46no—
400C23×C4—412no—
401C23×C4—46no—
402C23×C4C2413yes—
403C23×C4C2416yes—
404C23×C4C2413yes—
405C23×C4C2416yes—
406C23×C4C2411yescharacteristic
407C23×C4C2413yes—
408C23×C4C2416yes—
409C23×C4C2416yes—
410C4⋊Q8—412no—
411C4⋊Q8—412no—
412C4⋊Q8—46no—
413C4⋊Q8—412no—
414C4⋊Q8—46no—
415#125—412no—
416#125—412no—
417#124—24no—
418#124—412no—
419#124—412no—
420#124—412no—
421#124—424no—
422#124—412no—
423C22⋊Q8—412no—
424C22⋊Q8—412no—
425C22⋊Q8—412no—
426C22⋊Q8—412no—
427C22⋊Q8—412no—
428C22⋊Q8—46no—
429C22⋊Q8—46no—
430#121—412no—
431#121—412no—
432#121—412no—
433#120—24no—
434#120—212no—
435#120—412no—
436#120—412no—
437C4×Q8—28no—
438C4×Q8—28no—
439C4×Q8—28no—
440C4×Q8—28no—
441C4×Q8—24no—
442C4×Q8—412no—
443C4×Q8—46no—
444C4×D4—412no—
445C4×D4—412no—
446C4×D4—412no—
447C4×D4—412no—
448C4×D4—46no—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2413yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C2413yes—
463C2×C4⋊C4C2416yes—
464C2×C4⋊C4C24112yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C24112yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C2412yes—
469C2×C22⋊C4C2411yescharacteristic
470C2×C22⋊C4C2413yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2412yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2413yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2413yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C24112yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C24112yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C24112yes—
497C2×C22⋊C4C24112yes—
498C2×C22⋊C4C2411yescharacteristic
499C2×C22⋊C4C2412yes—
500C2×C22⋊C4C2413yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C24112yes—
503C2×C42C2416yes—
504C2×C42C2416yes—
505C2×C42C2416yes—
506C2×C42C2416yes—
507C2×C42C2413yes—
508C2×C42C2411yescharacteristic
509C2×C42C2416yes—
510C2×C42C24112yes—
511C2×C42C2413yes—
512#95C2412yes—
513#95C2416yes—
514#95C2416yes—
515#95C2416yes—
516#95C2412yes—
517#95C2412yes—
518#95C2412yes—
519#95C2416yes—
520#95C2416yes—
521#95C2416yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531#95C2416yes—
532#95C2416yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C24112yes—
538#95C24112yes—
539#95C24112yes—
540#95C24112yes—
541#95C24112yes—
542C24—22no—
543C24—24no—
544C24—26no—
545C24—42no—
546C24—41no—
547C24—41no—
548C24—46no—
549C24—43no—
550C24—46no—
551C24—43no—
552C24C2516yes—
553C24C2511yescharacteristic
554C24C2511yescharacteristic
555C24C2512yes—
556#41—496no—
557#41—432no—
558C2×Q8—212no—
559C2×Q8—212no—
560C2×Q8—212no—
561C2×Q8—212no—
562C2×Q8—26no—
563C2×Q8—212no—
564C2×Q8—26no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—412no—
568C2×Q8—46no—
569C2×Q8—41no—
570C2×Q8—46no—
571C2×Q8—46no—
572C2×Q8—46no—
573C2×Q8—412no—
574C2×Q8—46no—
575C2×Q8—496no—
576C2×Q8—448no—
577C2×Q8—416no—
578C2×Q8—432no—
579C2×Q8—416no—
580C2×Q8H(5,𝔽2)18yes—
581C2×Q8H(5,𝔽2)14yes—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—212no—
585C2×D4—212no—
586C2×D4—212no—
587C2×D4—212no—
588C2×D4—212no—
589C2×D4—212no—
590C2×D4—41no—
591C2×D4—42no—
592C2×D4—412no—
593C2×D4—46no—
594C2×D4—41no—
595C2×D4—46no—
596C2×D4—46no—
597C2×D4—46no—
598C2×D4—46no—
599C2×D4—46no—
600C2×D4—46no—
601C2×D4—448no—
602C2×D42−1+414yes—
603C22×C4—212no—
604C22×C4—212no—
605C22×C4—212no—
606C22×C4—212no—
607C22×C4—26no—
608C22×C4—212no—
609C22×C4—26no—
610C22×C4—212no—
611C22×C4—212no—
612C22×C4—212no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—46no—
616C22×C4—43no—
617C22×C4—46no—
618C22×C4—46no—
619C22×C4—46no—
620C22×C4—46no—
621C22×C4—46no—
622C22×C4—46no—
623C22×C4—448no—
624C22×C4—448no—
625C22×C4C2512yes—
626C22×C4C2512yes—
627C22×C4C2512yes—
628C22×C4C2516yes—
629C22×C4C2516yes—
630C22×C4C2516yes—
631C22×C4C2516yes—
632C22×C4C2513yes—
633C22×C4C2512yes—
634C22×C4C2513yes—
635C22×C4C2512yes—
636C22×C4C2516yes—
637C22×C4C2513yes—
638C22×C4C2511yescharacteristic
639C22×C4C2513yes—
640C4⋊C4—212no—
641C4⋊C4—212no—
642C4⋊C4—212no—
643C4⋊C4—212no—
644C4⋊C4—26no—
645C4⋊C4—46no—
646C4⋊C4—46no—
647C4⋊C4—46no—
648C4⋊C4—43no—
649C4⋊C4—46no—
650C4⋊C4—42no—
651C4⋊C4—46no—
652C4⋊C4—46no—
653C4⋊C4—43no—
654C4⋊C4—46no—
655C4⋊C4—412no—
656C4⋊C4—46no—
657C4⋊C4—412no—
658C22⋊C4—26no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—212no—
663C22⋊C4—24no—
664C22⋊C4—212no—
665C22⋊C4—24no—
666C22⋊C4—212no—
667C22⋊C4—412no—
668C22⋊C4—43no—
669C22⋊C4—46no—
670C22⋊C4—42no—
671C22⋊C4—41no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—46no—
676C22⋊C4—46no—
677C22⋊C4—43no—
678C22⋊C4—43no—
679C22⋊C4—46no—
680C22⋊C4—46no—
681C22⋊C4—46no—
682C22⋊C4—46no—
683C22⋊C4—46no—
684C22⋊C4—46no—
685C22⋊C4—46no—
686C22⋊C4—46no—
687C22⋊C4—412no—
688C22⋊C4—412no—
689C22⋊C4—412no—
690C22⋊C4—46no—
691C22⋊C4—412no—
692C22⋊C4—412no—
693C22⋊C4—46no—
694C42—212no—
695C42—212no—
696C42—212no—
697C42—212no—
698C42—26no—
699C42—22no—
700C42—43no—
701C42—46no—
702C42—412no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—22no—
716C23—21no—
717C23—26no—
718C23—26no—
719C23—26no—
720C23—26no—
721C23—26no—
722C23—26no—
723C23—26no—
724C23—48no—
725C23—44no—
726C23—44no—
727C23—48no—
728C23—44no—
729C23—412no—
730C23—812no—
731C23—86no—
732C23—86no—
733C23—812no—
734C23C2×2−1+412yes—
735C23C2×2−1+412yes—
736C23#58514yes—
737C23C2611yescharacteristic
738Q8—44no—
739Q8—424no—
740Q8—412no—
741Q8—424no—
742Q8—412no—
743Q8—812no—
744Q8—166no—
745Q8H(3,𝔽4)116yes—
746D4—44no—
747D4—48no—
748D4—424no—
749D4—424no—
750D4—812no—
751D4—812no—
752D4—812no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—26no—
760C2×C4—26no—
761C2×C4—26no—
762C2×C4—23no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—26no—
771C2×C4—23no—
772C2×C4—26no—
773C2×C4—23no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—26no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—26no—
780C2×C4—26no—
781C2×C4—26no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—26no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—26no—
790C2×C4—22no—
791C2×C4—44no—
792C2×C4—424no—
793C2×C4—412no—
794C2×C4—424no—
795C2×C4—412no—
796C2×C4—412no—
797C2×C4—424no—
798C2×C4—424no—
799C2×C4C2×H(5,𝔽2)112yes—
800C2×C4C2×H(5,𝔽2)16yes—
801C2×C4C2×2−1+412yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—22no—
807C22—22no—
808C22—24no—
809C22—416no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—41no—
820C22—46no—
821C22—46no—
822C22—46no—
823C22—46no—
824C22—46no—
825C22—46no—
826C22—46no—
827C22—824no—
828C22C22×H(5,𝔽2)12yes—
829C22C22×H(5,𝔽2)11yescharacteristic
830C22C22×2−1+411yescharacteristic
831C22C2×#58512yes—
832C222−1+611yescharacteristic
833C4—22no—
834C4—42no—
835C4—42no—
836C4—46no—
837C4—46no—
838C4—43no—
839C4—42no—
840C4—46no—
841C4—46no—
842C4—42no—
843C4—42no—
844C4—43no—
845C4—43no—
846C4—46no—
847C4C2×H(3,𝔽4)112yes—
848C2—44no—
849C2—42no—
850C2—42no—
851C2—86no—
852C2C22×H(3,𝔽4)11yescharacteristic
853C2#6289311yescharacteristic
854C2#6289712yes—
855C2#6301512yes—
856C2#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. #53144C2semidirect
2. #53144C2semidirect
3. #52990C2semidirect
4. #52301C2semidirect
5. #46073C2semidirect
6. #46043C2semidirect
7. #45667C2semidirect
8. #45645C2semidirect
9. #45601C2semidirect
10. #45494C2semidirect
11. #36575C2semidirect
12. Q8×#124C2semidirect
13. Q8×#120C2semidirect
14. #36467C2semidirect
15. #36428C2semidirect
16. #36428C2semidirect
17. #35948C2semidirect
18. #35910C2semidirect
19. #35854C2semidirect
20. C23×#41C22semidirect
21. C24×Q8C22semidirect
22. C2×Q82C22semidirect
23. C2×#557C22semidirect
29. #2862C22semidirect
30. #2861C22semidirect
31. #2848C22semidirect
32. #2848C22semidirect
33. #2848C22semidirect
34. #2847C22semidirect
35. #2840C22semidirect
36. #2835C22semidirect
37. #2832C22semidirect
38. #2832C22semidirect
39. #2832C22semidirect
40. #2824C22semidirect
41. #2824C22semidirect
43. #2804C22semidirect
44. #2804C22semidirect
45. #2785C22semidirect
47. #2782C22semidirect
48. #2782C22semidirect
49. #2782C22semidirect
50. #2763C22semidirect
51. #2763C22semidirect
52. #2763C22semidirect
53. #2753C22semidirect
54. #2753C22semidirect
55. #2736C22semidirect
56. #2712C22semidirect
61. #2684C22semidirect
63. #2670C22semidirect
64. #2642C22semidirect
65. #2640C22semidirect
66. #2640C22semidirect
67. #2592C22semidirect
68. #2592C22semidirect
69. #2592C22semidirect
70. #2568C22semidirect
71. #2568C22semidirect
73. #2563C22semidirect
75. #2562C22semidirect
76. #2547C22semidirect
77. #2492C22semidirect
78. #2492C22semidirect
79. #2492C22semidirect
80. #2492C22semidirect
81. #2492C22semidirect
82. #2492C22semidirect
83. #2492C22semidirect
84. #2491C22semidirect
85. #2491C22semidirect
86. #2491C22semidirect
87. #2490C22semidirect
88. #2490C22semidirect
89. #2490C22semidirect
90. #2489C22semidirect
91. #2489C22semidirect
92. #2489C22semidirect
93. #2489C22semidirect
94. #2489C22semidirect
95. #2436C22semidirect
96. #2436C22semidirect
97. #2436C22semidirect
98. #2435C22semidirect
99. #2435C22semidirect
100. #2434C22semidirect
101. #2434C22semidirect
102. #2432C22semidirect
103. #2432C22semidirect
104. #2432C22semidirect
107. #2409C22semidirect
108. #2409C22semidirect
109. #2409C22semidirect
116. #2398C22semidirect
117. #2398C22semidirect
118. #2379C22semidirect
120. #2341C22semidirect
121. #2341C22semidirect
122. #2341C22semidirect
123. Q8×C22⋊C4C22semidirect
124. Q8×C22⋊C4C22semidirect
125. Q8×C22⋊C4C22semidirect
126. Q8×C22⋊C4C22semidirect
127. Q8×C22⋊C4C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
131. C4×#124C22semidirect
135. C4×#120C22semidirect
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
#531442
#529902
#523012
#460732
#460432
#456672
#456452
#456012
#454942
#365752
Q8×#1242
Q8×#1202
#364672
#364282
#359482
#359102
#358542