Subgroups — C₂×D₁₀₈₈ #16955367

Order 4352.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₄₄	C₂	1	2	yes	maximal, complemented
2	D₁₀₈₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₇₂	—	2	2	no	—
5	D₅₄₄	—	2	2	no	—
6	D₅₄₄	C₂²	1	4	yes	complemented
7	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₇×C₆₄	C₂²	1	2	yes	complemented
9	C₂×D₁₃₆	—	4	2	no	—
10	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
11	D₂₇₂	—	2	4	no	—
12	D₂₇₂	—	4	2	no	—
13	C₁₇×C₃₂	D₄	1	1	yes	characteristic
14	C₁₇×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×D₆₈	—	8	2	no	—
16	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
17	D₁₃₆	—	4	4	no	—
18	D₁₃₆	—	8	2	no	—
19	C₁₆×C₁₇	D₈	1	1	yes	characteristic
20	C₁₆×C₁₇	C₂×D₄	1	1	yes	characteristic
21	C₂×D₆₄	—	17	1	no	maximal, Sylow
22	C₂²×D₁₇	—	16	2	no	—
23	C₂×C₄×C₁₇	D₁₆	1	1	yes	characteristic
24	D₆₈	—	8	4	no	—
25	D₆₈	—	16	2	no	—
26	C₈×C₁₇	D₁₆	1	1	yes	characteristic
27	C₈×C₁₇	C₂×D₈	1	1	yes	characteristic
28	C₂×D₃₂	—	17	2	no	—
29	D₆₄	—	17	4	no	—
30	C₂×C₆₄	D₁₇	1	1	yes	characteristic, complemented
31	C₂²×C₁₇	D₃₂	1	1	yes	characteristic
32	C₂×D₁₇	—	16	4	no	—
33	C₂×D₁₇	—	32	4	no	—
34	C₄×C₁₇	D₃₂	1	1	yes	characteristic
35	C₄×C₁₇	C₂×D₁₆	1	1	yes	characteristic
36	C₂×D₁₆	—	34	2	no	—
37	D₃₂	—	17	4	no	—
38	D₃₂	—	34	2	no	—
39	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
40	C₆₄	C₂×D₁₇	1	2	yes	complemented
41	C₂×C₁₇	D₆₄	1	2	yes	complemented
42	C₂×C₁₇	C₂×D₃₂	1	1	yes	characteristic
43	D₁₇	—	32	4	no	—
44	C₂×D₈	—	68	2	no	—
45	D₁₆	—	34	4	no	—
46	D₁₆	—	68	2	no	—
47	C₂×C₁₆	D₆₈	1	1	yes	characteristic
48	C₃₂	D₆₈	1	1	yes	characteristic
49	C₃₂	C₂²×D₁₇	1	1	yes	characteristic
50	C₁₇	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	136	2	no	—
52	D₈	—	68	4	no	—
53	D₈	—	136	2	no	—
54	C₂×C₈	D₁₃₆	1	1	yes	characteristic
55	C₁₆	D₁₃₆	1	1	yes	characteristic
56	C₁₆	C₂×D₆₈	1	1	yes	characteristic
57	C₂³	—	272	2	no	—
58	D₄	—	272	2	no	—
59	D₄	—	136	4	no	—
60	C₂×C₄	D₂₇₂	1	1	yes	characteristic
61	C₈	D₂₇₂	1	1	yes	characteristic
62	C₈	C₂×D₁₃₆	1	1	yes	characteristic
63	C₂²	—	272	4	no	—
64	C₂²	—	544	4	no	—
65	C₂²	D₅₄₄	1	1	yes	characteristic
66	C₄	D₅₄₄	1	1	yes	characteristic
67	C₄	C₂×D₂₇₂	1	1	yes	characteristic
68	C₂	—	544	4	no	—
69	C₂	D₁₀₈₈	1	2	yes	direct product factor
70	C₂	C₂×D₅₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅₄₄
commutator, cosocle	C₁₇×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₇
Fitting	C₂×C₁₇×C₆₄	C₂
socle	C₂²×C₁₇	D₃₂
hypercenter	C₂×C₆₄	D₁₇
hypocenter	C₁₇	C₂×D₆₄
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
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
1. C₂×D₅₄₄	C₂	semidirect
2. D₁₀₈₈	C₂	direct (N × H)
3. C₂×C₁₇×C₆₄	C₂	semidirect
6. D₅₄₄	C₂²	semidirect
8. C₁₇×C₆₄	C₂²	semidirect
30. C₂×C₆₄	D₁₇	semidirect
40. C₆₄	C₂×D₁₇	semidirect
41. C₂×C₁₇	D₆₄	semidirect
50. C₁₇	C₂×D₆₄	semidirect
69. C₂	D₁₀₈₈	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×D₅₄₄	2
D₁₀₈₈	2
C₂×C₁₇×C₆₄	2
C₂×D₆₄	17

Subgroups — C2×D1088 #16955367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₀₈₈ #16955367