Subgroups — C₂×Dic₁₃₇₆ #25017647

Order 11008.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₈₈	C₂	1	2	yes	maximal
2	Dic₁₃₇₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₄₄	—	2	2	no	—
5	Dic₆₈₈	—	2	2	no	—
6	Dic₆₈₈	C₂²	1	4	yes	—
7	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×C₆₄	C₂²	1	2	yes	—
9	C₂×Dic₁₇₂	—	4	2	no	—
10	Dic₃₄₄	—	2	4	no	—
11	Dic₃₄₄	—	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×Dic₈₆	—	8	2	no	—
16	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
17	Dic₁₇₂	—	4	4	no	—
18	Dic₁₇₂	—	8	2	no	—
19	C₁₆×C₄₃	D₈	1	1	yes	characteristic
20	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
22	C₂×Dic₄₃	—	16	2	no	—
23	Dic₈₆	—	8	4	no	—
24	Dic₈₆	—	16	2	no	—
25	C₈×C₄₃	D₁₆	1	1	yes	characteristic
26	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
27	C₂×Q₁₂₈	—	43	1	no	maximal, Sylow
28	C₂²×C₄₃	D₃₂	1	1	yes	characteristic
29	C₄×C₄₃	D₃₂	1	1	yes	characteristic
30	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
31	Dic₄₃	—	16	4	no	—
32	C₂×Q₆₄	—	43	2	no	—
33	Q₁₂₈	—	43	4	no	—
34	C₂×C₆₄	D₄₃	1	1	yes	characteristic
35	C₂×C₄₃	Q₁₂₈	1	2	yes	complemented
36	C₂×C₄₃	C₂×D₃₂	1	1	yes	characteristic
37	C₂×Q₃₂	—	86	2	no	—
38	Q₆₄	—	43	4	no	—
39	Q₆₄	—	86	2	no	—
40	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
41	C₆₄	C₂×D₄₃	1	2	yes	—
42	C₄₃	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₁₆	—	172	2	no	—
44	Q₃₂	—	86	4	no	—
45	Q₃₂	—	172	2	no	—
46	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
47	C₃₂	D₁₇₂	1	1	yes	characteristic
48	C₃₂	C₂²×D₄₃	1	1	yes	characteristic
49	C₂×Q₈	—	344	2	no	—
50	Q₁₆	—	344	2	no	—
51	Q₁₆	—	172	4	no	—
52	C₂×C₈	D₃₄₄	1	1	yes	characteristic
53	C₁₆	D₃₄₄	1	1	yes	characteristic
54	C₁₆	C₂×D₁₇₂	1	1	yes	characteristic
55	Q₈	—	344	4	no	—
56	Q₈	—	688	2	no	—
57	C₂×C₄	—	688	2	no	—
58	C₂×C₄	D₆₈₈	1	1	yes	characteristic
59	C₈	D₆₈₈	1	1	yes	characteristic
60	C₈	C₂×D₃₄₄	1	1	yes	characteristic
61	C₂²	D₁₃₇₆	1	1	yes	characteristic
62	C₄	—	688	4	no	—
63	C₄	D₁₃₇₆	1	1	yes	characteristic
64	C₄	C₂×D₆₈₈	1	1	yes	characteristic
65	C₂	Dic₁₃₇₆	1	2	yes	direct product factor
66	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, prime radical	C₂²×C₄₃	D₃₂
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	C₂×Q₁₂₈
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
2. Dic₁₃₇₆	C₂	direct (N × H)
35. C₂×C₄₃	Q₁₂₈	semidirect
42. C₄₃	C₂×Q₁₂₈	semidirect
65. C₂	Dic₁₃₇₆	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×Dic₆₈₈	2
Dic₁₃₇₆	2
C₂×C₄₃×C₆₄	2
C₂×Q₁₂₈	43

Subgroups — C2×Dic1376 #25017647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₃₇₆ #25017647