Subgroups — C₂×D₂₇₅₂ #25017640

Order 11008.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₇₆	C₂	1	2	yes	maximal, complemented
2	D₂₇₅₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₈₈	—	2	2	no	—
5	D₁₃₇₆	—	2	2	no	—
6	D₁₃₇₆	C₂²	1	4	yes	complemented
7	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×C₆₄	C₂²	1	2	yes	complemented
9	C₂×D₃₄₄	—	4	2	no	—
10	D₆₈₈	—	2	4	no	—
11	D₆₈₈	—	4	2	no	—
12	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
13	C₃₂×C₄₃	D₄	1	1	yes	characteristic
14	C₃₂×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×D₁₇₂	—	8	2	no	—
16	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
17	D₃₄₄	—	4	4	no	—
18	D₃₄₄	—	8	2	no	—
19	C₁₆×C₄₃	D₈	1	1	yes	characteristic
20	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×D₄₃	—	16	2	no	—
22	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
23	D₁₇₂	—	8	4	no	—
24	D₁₇₂	—	16	2	no	—
25	C₈×C₄₃	D₁₆	1	1	yes	characteristic
26	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
27	C₂×D₆₄	—	43	1	no	maximal, Sylow
28	C₂²×C₄₃	D₃₂	1	1	yes	characteristic
29	C₂×D₄₃	—	16	4	no	—
30	C₂×D₄₃	—	32	4	no	—
31	C₄×C₄₃	D₃₂	1	1	yes	characteristic
32	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
33	C₂×D₃₂	—	43	2	no	—
34	D₆₄	—	43	4	no	—
35	C₂×C₆₄	D₄₃	1	1	yes	characteristic, complemented
36	C₂×C₄₃	D₆₄	1	2	yes	complemented
37	C₂×C₄₃	C₂×D₃₂	1	1	yes	characteristic
38	D₄₃	—	32	4	no	—
39	C₂×D₁₆	—	86	2	no	—
40	D₃₂	—	43	4	no	—
41	D₃₂	—	86	2	no	—
42	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
43	C₆₄	C₂×D₄₃	1	2	yes	complemented
44	C₄₃	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	172	2	no	—
46	D₁₆	—	86	4	no	—
47	D₁₆	—	172	2	no	—
48	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
49	C₃₂	D₁₇₂	1	1	yes	characteristic
50	C₃₂	C₂²×D₄₃	1	1	yes	characteristic
51	C₂×D₄	—	344	2	no	—
52	D₈	—	344	2	no	—
53	D₈	—	172	4	no	—
54	C₂×C₈	D₃₄₄	1	1	yes	characteristic
55	C₁₆	D₃₄₄	1	1	yes	characteristic
56	C₁₆	C₂×D₁₇₂	1	1	yes	characteristic
57	C₂³	—	688	2	no	—
58	D₄	—	344	4	no	—
59	D₄	—	688	2	no	—
60	C₂×C₄	D₆₈₈	1	1	yes	characteristic
61	C₈	D₆₈₈	1	1	yes	characteristic
62	C₈	C₂×D₃₄₄	1	1	yes	characteristic
63	C₂²	—	1376	4	no	—
64	C₂²	—	688	4	no	—
65	C₂²	D₁₃₇₆	1	1	yes	characteristic
66	C₄	D₁₃₇₆	1	1	yes	characteristic
67	C₄	C₂×D₆₈₈	1	1	yes	characteristic
68	C₂	—	1376	4	no	—
69	C₂	D₂₇₅₂	1	2	yes	direct product factor
70	C₂	C₂×D₁₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃₇₆
commutator, cosocle	C₃₂×C₄₃	C₂³
Frattini	C₃₂	C₂²×D₄₃
Fitting	C₂×C₄₃×C₆₄	C₂
socle	C₂²×C₄₃	D₃₂
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	C₂×D₆₄
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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×D₁₃₇₆	C₂	semidirect
2. D₂₇₅₂	C₂	direct (N × H)
3. C₂×C₄₃×C₆₄	C₂	semidirect
6. D₁₃₇₆	C₂²	semidirect
8. C₄₃×C₆₄	C₂²	semidirect
35. C₂×C₆₄	D₄₃	semidirect
36. C₂×C₄₃	D₆₄	semidirect
43. C₆₄	C₂×D₄₃	semidirect
44. C₄₃	C₂×D₆₄	semidirect
69. C₂	D₂₇₅₂	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×D₁₃₇₆	2
D₂₇₅₂	2
C₂×C₄₃×C₆₄	2
C₂×D₆₄	43

Subgroups — C2×D2752 #25017640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₂₇₅₂ #25017640