Subgroups — C₂×Q₈×C₃₂ #512782

Order 512.

362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₃₂	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₃₂	C₂	1	3	yes	maximal
4	C₂×C₄×C₃₂	C₂	1	3	yes	maximal
5	C₂×C₈×Q₈	C₄	1	1	yes	characteristic
6	C₂²×C₃₂	C₂²	1	3	yes	—
7	C₂²×C₃₂	C₂²	1	1	yes	characteristic
8	Q₈×C₁₆	C₄	1	4	yes	—
9	Q₈×C₁₆	C₂²	1	4	yes	—
10	C₂×C₄⋊C₁₆	C₄	1	3	yes	—
11	C₂×C₄×C₁₆	C₂²	1	3	yes	—
12	C₄⋊C₃₂	C₂²	1	12	yes	—
13	C₄×C₃₂	C₂²	1	12	yes	—
14	C₂×C₄×Q₈	C₈	1	1	yes	characteristic
15	C₂²×C₁₆	C₂×C₄	1	3	yes	—
16	C₂²×C₁₆	C₂³	1	1	yes	characteristic
17	C₈×Q₈	C₈	1	4	yes	—
18	C₈×Q₈	C₂×C₄	1	4	yes	—
19	C₂×C₄⋊C₈	C₈	1	3	yes	—
20	C₂×C₄×C₈	C₂×C₄	1	3	yes	—
21	C₂×C₃₂	—	2	6	no	—
22	C₂×C₃₂	Q₈	1	4	yes	direct product factor
23	C₂×C₃₂	C₂³	1	6	yes	—
24	C₂×C₃₂	C₂³	1	2	yes	—
25	C₄⋊C₁₆	C₂×C₄	1	12	yes	—
26	C₄×C₁₆	C₂×C₄	1	6	yes	—
27	C₄×C₁₆	C₂³	1	6	yes	—
28	C₂²×Q₈	C₁₆	1	1	yes	characteristic
29	C₂²×C₈	C₂×C₈	1	3	yes	—
30	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
31	C₄×Q₈	C₁₆	1	4	yes	—
32	C₄×Q₈	C₂×C₈	1	4	yes	—
33	C₂×C₄⋊C₄	C₁₆	1	3	yes	—
34	C₂×C₄²	C₂×C₈	1	3	yes	—
35	C₂×C₁₆	—	2	6	no	—
36	C₂×C₁₆	C₂²×C₄	1	6	yes	—
37	C₂×C₁₆	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Q₈	1	2	yes	—
39	C₂×C₁₆	#41	1	2	yes	—
40	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
41	C₄⋊C₈	C₂×C₈	1	12	yes	—
42	C₄×C₈	C₂×C₈	1	6	yes	—
43	C₄×C₈	C₂²×C₄	1	6	yes	—
44	C₃₂	—	2	6	no	—
45	C₃₂	C₂×Q₈	1	4	yes	direct product factor
46	C₂×Q₈	C₃₂	1	8	yes	direct product factor
47	C₂×Q₈	C₂×C₁₆	1	4	yes	—
48	C₂²×C₄	C₂×C₁₆	1	3	yes	—
49	C₂²×C₄	C₂×C₁₆	1	3	yes	—
50	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
51	C₂×C₈	—	2	6	no	—
52	C₂×C₈	C₄×Q₈	1	2	yes	—
53	C₂×C₈	C₂²×C₈	1	6	yes	—
54	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
55	C₂×C₈	#131	1	2	yes	—
56	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
57	C₄⋊C₄	C₂×C₁₆	1	12	yes	—
58	C₄²	C₂×C₁₆	1	6	yes	—
59	C₄²	C₂²×C₈	1	6	yes	—
60	C₁₆	—	2	6	no	—
61	C₁₆	C₄×Q₈	1	2	yes	—
62	C₁₆	C₂²×Q₈	1	1	yes	characteristic
63	C₁₆	C₂×#41	1	1	yes	characteristic
64	C₂³	C₂²×C₁₆	1	1	yes	characteristic
65	Q₈	C₂×C₃₂	1	16	yes	direct product factor
66	C₂×C₄	—	2	6	no	—
67	C₂×C₄	C₂×C₃₂	1	12	yes	—
68	C₂×C₄	C₈×Q₈	1	2	yes	—
69	C₂×C₄	C₂²×C₁₆	1	6	yes	—
70	C₂×C₄	C₂²×C₁₆	1	1	yes	characteristic
71	C₂×C₄	C₂²×C₁₆	1	6	yes	—
72	C₂×C₄	#504	1	2	yes	—
73	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
74	C₈	—	2	6	no	—
75	C₈	C₈×Q₈	1	2	yes	—
76	C₈	C₂×C₄×Q₈	1	1	yes	characteristic
77	C₈	C₂×#131	1	1	yes	characteristic
78	C₂²	Q₈×C₁₆	1	2	yes	—
79	C₂²	C₂²×C₃₂	1	2	yes	—
80	C₂²	#2258	1	2	yes	—
81	C₂²	C₂³×C₁₆	1	1	yes	characteristic
82	C₄	—	2	6	no	—
83	C₄	Q₈×C₁₆	1	2	yes	—
84	C₄	C₂²×C₃₂	1	12	yes	—
85	C₄	C₂×C₈×Q₈	1	1	yes	characteristic
86	C₄	C₂×#504	1	1	yes	characteristic
87	C₂	Q₈×C₃₂	1	4	yes	direct product factor
88	C₂	C₂×Q₈×C₁₆	1	1	yes	characteristic
89	C₂	C₂³×C₃₂	1	1	yes	characteristic
90	C₂	C₂×#2258	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃₂	C₂²
commutator	C₂	C₂³×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂⁴
socle, prime radical	C₂³	C₂²×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₂ ◁ G
LECS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. Q₈×C₃₂	C₂	direct (N × H)
22. C₂×C₃₂	Q₈	direct (N × H)
45. C₃₂	C₂×Q₈	direct (N × H)
46. C₂×Q₈	C₃₂	direct (N × H)
65. Q₈	C₂×C₃₂	direct (N × H)
87. C₂	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
C₂×Q₈×C₁₆	2
Q₈×C₃₂	2
C₂×C₄⋊C₃₂	2
C₂×C₄×C₃₂	2

Subgroups — C2×Q8×C32 #512782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₃₂ #512782