Subgroups — C₂×D₁₃₇₆ #19136893

Order 5504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²	D₆₈₈
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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×D₆₈₈	C₂	semidirect
2. D₁₃₇₆	C₂	direct (N × H)
3. C₂×C₃₂×C₄₃	C₂	semidirect
6. D₆₈₈	C₂²	semidirect
8. C₃₂×C₄₃	C₂²	semidirect
27. C₂×C₄₃	D₃₂	semidirect
32. C₂×C₃₂	D₄₃	semidirect
33. C₄₃	C₂×D₃₂	semidirect
38. C₃₂	C₂×D₄₃	semidirect
57. C₂	D₁₃₇₆	direct (N × H)

Subgroups — C2×D1376 #19136893

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₃₇₆ #19136893