Subgroups — C₂×Dic₃₅₂ #14674823

Order 2816.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₆	C₂	1	2	yes	maximal
2	Dic₃₅₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈	—	2	2	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	Dic₁₇₆	—	2	2	no	—
7	Dic₁₇₆	C₂²	1	4	yes	—
8	C₁₁×C₆₄	C₂²	1	2	yes	—
9	C₂×Dic₄₄	—	4	2	no	—
10	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
11	Dic₈₈	—	2	4	no	—
12	Dic₈₈	—	4	2	no	—
13	C₁₁×C₃₂	D₄	1	1	yes	characteristic
14	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×Q₁₂₈	—	11	1	no	maximal, Sylow
16	C₂×Dic₂₂	—	8	2	no	—
17	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
18	Dic₄₄	—	4	4	no	—
19	Dic₄₄	—	8	2	no	—
20	C₁₁×C₁₆	D₈	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
22	C₂×Q₆₄	—	11	2	no	—
23	Q₁₂₈	—	11	4	no	—
24	C₂×C₆₄	D₁₁	1	1	yes	characteristic
25	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
26	C₂×Dic₁₁	—	16	2	no	—
27	Dic₂₂	—	8	4	no	—
28	Dic₂₂	—	16	2	no	—
29	C₈×C₁₁	D₁₆	1	1	yes	characteristic
30	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
31	C₂×Q₃₂	—	22	2	no	—
32	Q₆₄	—	11	4	no	—
33	Q₆₄	—	22	2	no	—
34	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
35	C₆₄	C₂×D₁₁	1	2	yes	—
36	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
37	C₄×C₁₁	D₃₂	1	1	yes	characteristic
38	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
39	Dic₁₁	—	16	4	no	—
40	C₂×Q₁₆	—	44	2	no	—
41	Q₃₂	—	22	4	no	—
42	Q₃₂	—	44	2	no	—
43	C₂×C₁₆	D₄₄	1	1	yes	characteristic
44	C₃₂	D₄₄	1	1	yes	characteristic
45	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
46	C₂×C₁₁	Q₁₂₈	1	2	yes	complemented
47	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
48	C₂×Q₈	—	88	2	no	—
49	Q₁₆	—	44	4	no	—
50	Q₁₆	—	88	2	no	—
51	C₂×C₈	D₈₈	1	1	yes	characteristic
52	C₁₆	D₈₈	1	1	yes	characteristic
53	C₁₆	C₂×D₄₄	1	1	yes	characteristic
54	C₁₁	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	88	4	no	—
56	Q₈	—	176	2	no	—
57	C₂×C₄	—	176	2	no	—
58	C₂×C₄	D₁₇₆	1	1	yes	characteristic
59	C₈	D₁₇₆	1	1	yes	characteristic
60	C₈	C₂×D₈₈	1	1	yes	characteristic
61	C₂²	D₃₅₂	1	1	yes	characteristic
62	C₄	—	176	4	no	—
63	C₄	D₃₅₂	1	1	yes	characteristic
64	C₄	C₂×D₁₇₆	1	1	yes	characteristic
65	C₂	Dic₃₅₂	1	2	yes	direct product factor
66	C₂	C₂×D₃₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₅₂
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle, prime radical	C₂²×C₁₁	D₃₂
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	C₂×Q₁₂₈
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₃₅₂	C₂	direct (N × H)
46. C₂×C₁₁	Q₁₂₈	semidirect
54. C₁₁	C₂×Q₁₂₈	semidirect
65. C₂	Dic₃₅₂	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×Dic₁₇₆	2
Dic₃₅₂	2
C₂×C₁₁×C₆₄	2
C₂×Q₁₂₈	11

Subgroups — C2×Dic352 #14674823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃₅₂ #14674823