Subgroups — C₇×Q₈×C₃₂ #13190875

Order 1792.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₃₂	C₂	1	3	yes	maximal
3	C₄×C₇×C₃₂	C₂	1	3	yes	maximal
4	C₇×C₈×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₇×C₃₂	C₂²	1	3	yes	—
6	C₂×C₇×C₃₂	C₂²	1	1	yes	characteristic
7	C₇×C₄⋊C₁₆	C₄	1	3	yes	—
8	C₄×C₇×C₁₆	C₂²	1	3	yes	—
9	Q₈×C₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₄×C₇×Q₈	C₈	1	1	yes	characteristic
11	C₂×C₇×C₁₆	C₂×C₄	1	3	yes	—
12	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
13	C₇×C₄⋊C₈	C₈	1	3	yes	—
14	C₄×C₇×C₈	C₂×C₄	1	3	yes	—
15	C₇×C₃₂	—	2	3	no	—
16	C₇×C₃₂	Q₈	1	2	yes	direct product factor
17	Q₈×C₁₆	C₂×C₇	1	1	yes	characteristic
18	C₄⋊C₃₂	C₂×C₇	1	3	yes	—
19	C₄×C₃₂	C₂×C₇	1	3	yes	—
20	C₂×C₇×Q₈	C₁₆	1	1	yes	characteristic
21	C₂×C₇×C₈	C₂×C₈	1	3	yes	—
22	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
23	C₇×C₄⋊C₄	C₁₆	1	3	yes	—
24	C₄²×C₇	C₂×C₈	1	3	yes	—
25	C₇×C₁₆	—	2	3	no	—
26	C₇×C₁₆	C₂×Q₈	1	1	yes	characteristic
27	C₇×C₁₆	#41	1	1	yes	characteristic
28	C₈×Q₈	C₄×C₇	1	1	yes	characteristic
29	C₂×C₃₂	C₂²×C₇	1	3	yes	—
30	C₂×C₃₂	C₂²×C₇	1	1	yes	characteristic
31	C₄⋊C₁₆	C₄×C₇	1	3	yes	—
32	C₄×C₁₆	C₂²×C₇	1	3	yes	—
33	C₇×Q₈	C₃₂	1	4	yes	direct product factor
34	C₂×C₄×C₇	C₂×C₁₆	1	3	yes	—
35	C₂×C₄×C₇	C₂×C₁₆	1	3	yes	—
36	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
37	C₇×C₈	—	2	3	no	—
38	C₇×C₈	C₄×Q₈	1	1	yes	characteristic
39	C₇×C₈	#131	1	1	yes	characteristic
40	C₄×Q₈	C₇×C₈	1	1	yes	characteristic
41	C₂×C₁₆	C₂×C₄×C₇	1	3	yes	—
42	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
43	C₄⋊C₈	C₇×C₈	1	3	yes	—
44	C₄×C₈	C₂×C₄×C₇	1	3	yes	—
45	C₃₂	—	2	3	no	—
46	C₃₂	C₇×Q₈	1	2	yes	direct product factor
47	C₂²×C₇	C₂²×C₁₆	1	1	yes	characteristic
48	C₄×C₇	—	2	3	no	—
49	C₄×C₇	C₂×C₃₂	1	6	yes	—
50	C₄×C₇	C₈×Q₈	1	1	yes	characteristic
51	C₄×C₇	#504	1	1	yes	characteristic
52	C₂×Q₈	C₇×C₁₆	1	1	yes	characteristic
53	C₂×C₈	C₂×C₇×C₈	1	3	yes	—
54	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
55	C₄⋊C₄	C₇×C₁₆	1	3	yes	—
56	C₄²	C₂×C₇×C₈	1	3	yes	—
57	C₁₆	—	2	3	no	—
58	C₁₆	C₂×C₇×Q₈	1	1	yes	characteristic
59	C₁₆	C₇×#41	1	1	yes	characteristic
60	C₂×C₇	Q₈×C₁₆	1	1	yes	characteristic
61	C₂×C₇	C₂²×C₃₂	1	1	yes	characteristic
62	C₂×C₇	#2258	1	1	yes	characteristic
63	Q₈	C₇×C₃₂	1	4	yes	direct product factor
64	C₂×C₄	C₂×C₇×C₁₆	1	3	yes	—
65	C₂×C₄	C₂×C₇×C₁₆	1	3	yes	—
66	C₂×C₄	C₂²×C₇×C₈	1	1	yes	characteristic
67	C₈	—	2	3	no	—
68	C₈	C₄×C₇×Q₈	1	1	yes	characteristic
69	C₈	C₇×#131	1	1	yes	characteristic
70	C₇	Q₈×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
71	C₂²	C₂²×C₇×C₁₆	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×C₇×C₃₂	1	6	yes	—
74	C₄	C₇×C₈×Q₈	1	1	yes	characteristic
75	C₄	C₇×#504	1	1	yes	characteristic
76	C₂	C₇×Q₈×C₁₆	1	1	yes	characteristic
77	C₂	C₂²×C₇×C₃₂	1	1	yes	characteristic
78	C₂	C₇×#2258	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇×C₃₂	C₂²
commutator	C₂	C₂²×C₇×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂³×C₇
socle, prime radical	C₂²×C₇	C₂²×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
9. Q₈×C₃₂	C₇	direct (N × H)
16. C₇×C₃₂	Q₈	direct (N × H)
33. C₇×Q₈	C₃₂	direct (N × H)
46. C₃₂	C₇×Q₈	direct (N × H)
63. Q₈	C₇×C₃₂	direct (N × H)
70. C₇	Q₈×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
C₇×Q₈×C₁₆	2
C₇×C₄⋊C₃₂	2
C₄×C₇×C₃₂	2
Q₈×C₃₂	7

Subgroups — C7×Q8×C32 #13190875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Q₈×C₃₂ #13190875