Subgroups — Q₈×#10587528 #17982813

Order 4352.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10587528	C₂	1	3	yes	maximal
2	C₄×#10587528	C₂	1	3	yes	maximal
3	Q₈×#63216	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587528	C₂²	1	3	yes	—
5	C₂×#10587528	C₂²	1	1	yes	characteristic
6	C₄⋊#63216	C₄	1	3	yes	—
7	C₄×#63216	C₂²	1	3	yes	—
8	Q₈×#3622	C₄	1	1	yes	characteristic
9	C₄×Q₈×C₁₇	C₈	1	1	yes	characteristic
10	C₂×#63216	C₂×C₄	1	3	yes	—
11	C₂×#63216	C₂³	1	1	yes	characteristic
12	#10587528	—	2	3	no	—
13	#10587528	Q₈	1	2	yes	direct product factor
14	C₄⋊#3622	C₈	1	3	yes	—
15	C₄×#3622	C₂×C₄	1	3	yes	—
16	C₂×Q₈×C₁₇	C₁₆	1	1	yes	characteristic
17	C₄⋊C₄×C₁₇	C₁₆	1	3	yes	—
18	C₄²×C₁₇	C₂×C₈	1	3	yes	—
19	C₂×#3622	C₂×C₈	1	3	yes	—
20	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
21	#63216	—	2	3	no	—
22	#63216	C₂×Q₈	1	1	yes	characteristic
23	#63216	#41	1	1	yes	characteristic
24	Q₈×C₃₂	—	17	1	no	maximal, Sylow
25	Q₈×C₁₇	C₃₂	1	4	yes	complemented
26	C₂×C₄×C₁₇	C₂×C₁₆	1	3	yes	—
27	C₂×C₄×C₁₇	C₂×C₁₆	1	3	yes	—
28	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
29	#3622	—	2	3	no	—
30	#3622	C₄×Q₈	1	1	yes	characteristic
31	#3622	#131	1	1	yes	characteristic
32	Q₈×C₁₆	—	17	1	no	—
33	C₄⋊C₃₂	—	17	3	no	—
34	C₄×C₃₂	—	17	3	no	—
35	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
36	C₄×C₁₇	—	2	3	no	—
37	C₄×C₁₇	C₂×C₃₂	1	6	yes	—
38	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
39	C₄×C₁₇	#504	1	1	yes	characteristic
40	C₈×Q₈	—	17	1	no	—
41	C₂×C₃₂	—	17	1	no	—
42	C₂×C₃₂	—	17	3	no	—
43	C₄⋊C₁₆	—	17	3	no	—
44	C₄×C₁₆	—	17	3	no	—
45	C₂×C₁₇	Q₈×C₁₆	1	1	yes	characteristic
46	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
47	C₂×C₁₇	#2258	1	1	yes	characteristic
48	C₄×Q₈	#3633	1	1	yes	characteristic
49	C₂×C₁₆	—	17	1	no	—
50	C₂×C₁₆	—	17	3	no	—
51	C₄⋊C₈	—	17	3	no	—
52	C₄×C₈	—	17	3	no	—
53	C₃₂	—	17	2	no	—
54	C₃₂	—	34	3	no	—
55	C₁₇	Q₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	#63241	1	1	yes	characteristic
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	—	17	3	no	—
59	C₄⋊C₄	#63241	1	3	yes	—
60	C₄²	C₂×#3633	1	3	yes	—
61	C₁₆	—	17	1	no	—
62	C₁₆	—	17	1	no	—
63	C₁₆	—	34	3	no	—
64	Q₈	#10587528	1	4	yes	direct product factor
65	C₂×C₄	C₂×#63241	1	3	yes	—
66	C₂×C₄	C₂×#63241	1	3	yes	—
67	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
68	C₈	—	17	1	no	—
69	C₈	—	17	1	no	—
70	C₈	—	34	3	no	—
71	C₂²	C₂²×#63241	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×#10587528	1	6	yes	—
74	C₄	Q₈×#3633	1	1	yes	characteristic
75	C₄	#11763931	1	1	yes	characteristic
76	C₂	Q₈×#63241	1	1	yes	characteristic
77	C₂	C₂²×#10587528	1	1	yes	characteristic
78	C₂	#14546017	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator	C₂×C₁₇	C₂²×C₃₂
Fitting	C₄×Q₈×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₂²×C₁₆
cosocle	C₂×#63216	C₂³
hypercenter	C₄×Q₈	#3633
hypocenter	C₁₇	Q₈×C₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
13. #10587528	Q₈	direct (N × H)
25. Q₈×C₁₇	C₃₂	semidirect
55. C₁₇	Q₈×C₃₂	semidirect
64. Q₈	#10587528	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⋊#10587528	2
C₄×#10587528	2
Q₈×#63216	2
Q₈×C₃₂	17

Subgroups — Q8×#10587528 #17982813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#10587528 #17982813