Subgroups — C₂×D₉₆ #69367

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₉₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₃₂	—	3	1	no	maximal, Sylow
5	C₂×D₂₄	—	2	2	no	—
6	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
7	D₄₈	—	2	2	no	—
8	D₄₈	C₂²	1	4	yes	complemented
9	C₃×C₃₂	C₂²	1	2	yes	complemented
10	C₂×D₁₆	—	3	2	no	—
11	D₃₂	—	3	4	no	—
12	C₂×C₃₂	D₃	1	1	yes	characteristic, complemented
13	C₂×D₁₂	—	4	2	no	—
14	C₂×C₃×C₈	D₄	1	1	yes	characteristic
15	D₂₄	—	2	4	no	—
16	D₂₄	—	4	2	no	—
17	C₃×C₁₆	D₄	1	1	yes	characteristic
18	C₃×C₁₆	C₂³	1	1	yes	characteristic
19	C₂×D₈	—	6	2	no	—
20	D₁₆	—	3	4	no	—
21	D₁₆	—	6	2	no	—
22	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
23	C₃₂	C₂×D₃	1	2	yes	complemented
24	C₂²×D₃	—	8	2	no	—
25	C₂×C₃×C₄	D₈	1	1	yes	characteristic
26	D₁₂	—	4	4	no	—
27	D₁₂	—	8	2	no	—
28	C₃×C₈	D₈	1	1	yes	characteristic
29	C₃×C₈	C₂×D₄	1	1	yes	characteristic
30	C₂×D₄	—	12	2	no	—
31	D₈	—	6	4	no	—
32	D₈	—	12	2	no	—
33	C₂×C₈	D₁₂	1	1	yes	characteristic
34	C₁₆	D₁₂	1	1	yes	characteristic
35	C₁₆	C₂²×D₃	1	1	yes	characteristic
36	C₂²×C₃	D₁₆	1	1	yes	characteristic
37	C₂×D₃	—	8	4	no	—
38	C₂×D₃	—	16	4	no	—
39	C₃×C₄	D₁₆	1	1	yes	characteristic
40	C₃×C₄	C₂×D₈	1	1	yes	characteristic
41	C₂³	—	24	2	no	—
42	D₄	—	12	4	no	—
43	D₄	—	24	2	no	—
44	C₂×C₄	D₂₄	1	1	yes	characteristic
45	C₈	D₂₄	1	1	yes	characteristic
46	C₈	C₂×D₁₂	1	1	yes	characteristic
47	C₂×C₃	D₃₂	1	2	yes	complemented
48	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
49	D₃	—	16	4	no	—
50	C₂²	—	24	4	no	—
51	C₂²	—	48	4	no	—
52	C₂²	D₄₈	1	1	yes	characteristic
53	C₄	D₄₈	1	1	yes	characteristic
54	C₄	C₂×D₂₄	1	1	yes	characteristic
55	C₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	48	4	no	—
57	C₂	D₉₆	1	2	yes	direct product factor
58	C₂	C₂×D₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₈
commutator, cosocle	C₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₃
Fitting	C₂×C₃×C₃₂	C₂
socle	C₂²×C₃	D₁₆
hypercenter	C₂×C₃₂	D₃
hypocenter	C₃	C₂×D₃₂
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₄₈	C₂	semidirect
2. C₂×C₃×C₃₂	C₂	semidirect
3. D₉₆	C₂	direct (N × H)
8. D₄₈	C₂²	semidirect
9. C₃×C₃₂	C₂²	semidirect
12. C₂×C₃₂	D₃	semidirect
23. C₃₂	C₂×D₃	semidirect
47. C₂×C₃	D₃₂	semidirect
55. C₃	C₂×D₃₂	semidirect
57. C₂	D₉₆	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×D₄₈	2
C₂×C₃×C₃₂	2
D₉₆	2
C₂×D₃₂	3

Subgroups — C2×D96 #69367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉₆ #69367