Subgroups — Q₈×C₄₇⋊C₃₂ #26136909

Order 12032.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₃₂)	C₂	1	3	yes	maximal
2	C₄×C₄₇⋊C₃₂	C₂	1	3	yes	maximal
3	Q₈×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₃₂	C₂²	1	3	yes	—
5	C₂×C₄₇⋊C₃₂	C₂²	1	1	yes	characteristic
6	C₈×Q₈×C₄₇	C₄	1	1	yes	characteristic
7	C₄₇×C₄⋊C₁₆	C₄	1	3	yes	—
8	C₄×C₁₆×C₄₇	C₂²	1	3	yes	—
9	C₄₇⋊C₃₂	—	2	3	no	—
10	C₄₇⋊C₃₂	Q₈	1	2	yes	direct product factor
11	C₄×Q₈×C₄₇	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₂×C₄	1	3	yes	—
13	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
14	C₄⋊C₈×C₄₇	C₈	1	3	yes	—
15	C₄×C₈×C₄₇	C₂×C₄	1	3	yes	—
16	C₂×Q₈×C₄₇	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂×C₈	1	3	yes	—
18	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₄₇	C₁₆	1	3	yes	—
20	C₄²×C₄₇	C₂×C₈	1	3	yes	—
21	C₁₆×C₄₇	—	2	3	no	—
22	C₁₆×C₄₇	C₂×Q₈	1	1	yes	characteristic
23	C₁₆×C₄₇	#41	1	1	yes	characteristic
24	Q₈×C₄₇	C₃₂	1	4	yes	complemented
25	C₂×C₄×C₄₇	C₂×C₁₆	1	3	yes	—
26	C₂×C₄×C₄₇	C₂×C₁₆	1	3	yes	—
27	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
28	C₈×C₄₇	—	2	3	no	—
29	C₈×C₄₇	C₄×Q₈	1	1	yes	characteristic
30	C₈×C₄₇	#131	1	1	yes	characteristic
31	Q₈×C₃₂	—	47	1	no	maximal, Sylow
32	C₂²×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
33	C₄×C₄₇	—	2	3	no	—
34	C₄×C₄₇	C₂×C₃₂	1	6	yes	—
35	C₄×C₄₇	C₈×Q₈	1	1	yes	characteristic
36	C₄×C₄₇	#504	1	1	yes	characteristic
37	Q₈×C₁₆	D₄₇	1	1	yes	characteristic
38	C₄⋊C₃₂	—	47	3	no	—
39	C₄×C₃₂	—	47	3	no	—
40	C₂×C₄₇	Q₈×C₁₆	1	1	yes	characteristic
41	C₂×C₄₇	C₂²×C₃₂	1	1	yes	characteristic
42	C₂×C₄₇	#2258	1	1	yes	characteristic
43	C₈×Q₈	Dic₄₇	1	1	yes	characteristic
44	C₂×C₃₂	—	47	1	no	—
45	C₂×C₃₂	—	47	3	no	—
46	C₄⋊C₁₆	Dic₄₇	1	3	yes	—
47	C₄×C₁₆	C₂×D₄₇	1	3	yes	—
48	C₄₇	Q₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
49	C₄×Q₈	C₄₇⋊C₈	1	1	yes	characteristic
50	C₂×C₁₆	C₂×Dic₄₇	1	3	yes	—
51	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
52	C₄⋊C₈	C₄₇⋊C₈	1	3	yes	—
53	C₄×C₈	C₂×Dic₄₇	1	3	yes	—
54	C₃₂	—	47	2	no	—
55	C₃₂	—	94	3	no	—
56	C₂×Q₈	C₄₇⋊C₁₆	1	1	yes	characteristic
57	C₂×C₈	C₂×C₄₇⋊C₈	1	3	yes	—
58	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
59	C₄⋊C₄	C₄₇⋊C₁₆	1	3	yes	—
60	C₄²	C₂×C₄₇⋊C₈	1	3	yes	—
61	C₁₆	—	2	3	no	—
62	C₁₆	Q₈×D₄₇	1	1	yes	characteristic
63	C₁₆	#10625354	1	1	yes	characteristic
64	Q₈	C₄₇⋊C₃₂	1	4	yes	direct product factor
65	C₂×C₄	C₂×C₄₇⋊C₁₆	1	3	yes	—
66	C₂×C₄	C₂×C₄₇⋊C₁₆	1	3	yes	—
67	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
68	C₈	—	2	3	no	—
69	C₈	Q₈×Dic₄₇	1	1	yes	characteristic
70	C₈	#13094031	1	1	yes	characteristic
71	C₂²	C₂²×C₄₇⋊C₁₆	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×C₄₇⋊C₃₂	1	6	yes	—
74	C₄	Q₈×C₄₇⋊C₈	1	1	yes	characteristic
75	C₄	#15689540	1	1	yes	characteristic
76	C₂	Q₈×C₄₇⋊C₁₆	1	1	yes	characteristic
77	C₂	C₂²×C₄₇⋊C₃₂	1	1	yes	characteristic
78	C₂	#20245682	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₄₇
commutator	C₂×C₄₇	C₂²×C₃₂
Fitting	Q₈×C₁₆×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂²×C₁₆
cosocle	C₂×C₁₆×C₄₇	C₂³
hypercenter	Q₈×C₁₆	D₄₇
hypocenter	C₄₇	Q₈×C₃₂
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₆ ◁ Q₈×C₁₆

Complements

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

N	H ≅ G/N	type
10. C₄₇⋊C₃₂	Q₈	direct (N × H)
24. Q₈×C₄₇	C₃₂	semidirect
48. C₄₇	Q₈×C₃₂	semidirect
64. Q₈	C₄₇⋊C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊(C₄₇⋊C₃₂)	2
C₄×C₄₇⋊C₃₂	2
Q₈×C₁₆×C₄₇	2
Q₈×C₃₂	47

Subgroups — Q8×C47⋊C32 #26136909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₄₇⋊C₃₂ #26136909