Subgroups — C₂×#10624411 #13089876

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10624411	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×D₉₁	—	2	2	no	—
7	C₂×D₉₁	C₂²	1	2	yes	complemented
8	C₂×C₇×D₁₃	—	2	2	no	—
9	C₂×C₇×D₁₃	C₂²	1	2	yes	complemented
10	C₁₃×Dic₇	C₂²	1	2	yes	complemented
11	C₂×D₅₂	—	7	1	no	maximal, Hall
12	C₂×C₇×C₁₃	D₄	1	2	yes	complemented
13	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
14	D₉₁	—	2	2	no	—
15	C₇×D₁₃	—	2	2	no	—
16	C₂×C₂²⋊D₇	—	13	1	no	maximal, Hall
17	C₂²×D₁₃	—	7	1	no	—
18	C₂²×D₁₃	D₇	1	1	yes	characteristic, complemented
19	C₂×C₄×C₁₃	—	7	1	no	—
20	D₅₂	—	7	4	no	—
21	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
22	C₂³×C₇	—	13	1	no	—
23	C₂²×D₇	—	13	1	no	—
24	C₂²⋊D₇	—	13	4	no	—
25	C₂×Dic₇	D₁₃	1	1	yes	characteristic, complemented
26	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
27	C₂×D₁₃	—	2	2	no	—
28	C₂×D₁₃	—	7	2	no	—
29	C₂×D₁₃	—	14	2	no	—
30	C₂×D₁₃	C₂×D₇	1	2	yes	complemented
31	C₄×C₁₃	—	7	2	no	—
32	C₂²×C₇	—	13	2	no	—
33	C₂²×C₇	—	26	2	no	—
34	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
35	C₂×D₇	—	13	2	no	—
36	C₂×D₇	—	26	2	no	—
37	Dic₇	C₂×D₁₃	1	2	yes	complemented
38	C₂×C₁₃	C₂²⋊D₇	1	2	yes	complemented
39	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
40	D₁₃	—	2	2	no	—
41	D₁₃	—	14	2	no	—
42	C₂×D₄	—	91	1	no	Sylow
43	C₂×C₇	—	26	2	no	—
44	C₂×C₇	D₅₂	1	2	yes	complemented
45	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
46	D₇	—	26	2	no	—
47	C₁₃	C₂×C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
48	C₂³	—	13	1	no	—
49	C₂³	—	91	1	no	—
50	D₄	—	91	4	no	—
51	C₂×C₄	—	7	1	no	—
52	C₇	C₂×D₅₂	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	13	2	no	—
54	C₂²	—	26	2	no	—
55	C₂²	—	91	2	no	—
56	C₂²	—	182	2	no	—
57	C₂²	D₇×D₁₃	1	1	yes	characteristic
58	C₄	—	7	2	no	—
59	C₂	—	26	2	no	—
60	C₂	—	182	2	no	—
61	C₂	#10624411	1	2	yes	direct product factor
62	C₂	C₂×D₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₇×D₁₃
commutator, cosocle	C₂×C₇×C₁₃	C₂³
Frattini	C₂	C₂×D₇×D₁₃
Fitting, socle	C₂²×C₇×C₁₃	C₂²
hypocenter	C₇×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₇×C₁₃ ▷ C₇×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₉₁	C₂	semidirect
2. C₂²×C₇×D₁₃	C₂	semidirect
3. C₂×C₁₃×Dic₇	C₂	semidirect
4. #10624411	C₂	direct (N × H)
7. C₂×D₉₁	C₂²	semidirect
9. C₂×C₇×D₁₃	C₂²	semidirect
10. C₁₃×Dic₇	C₂²	semidirect
12. C₂×C₇×C₁₃	D₄	semidirect
18. C₂²×D₁₃	D₇	semidirect
21. C₇×C₁₃	C₂×D₄	semidirect
25. C₂×Dic₇	D₁₃	semidirect
30. C₂×D₁₃	C₂×D₇	semidirect
37. Dic₇	C₂×D₁₃	semidirect
38. C₂×C₁₃	C₂²⋊D₇	semidirect
44. C₂×C₇	D₅₂	semidirect
47. C₁₃	C₂×C₂²⋊D₇	semidirect
52. C₇	C₂×D₅₂	semidirect
61. C₂	#10624411	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₉₁	2
C₂²×C₇×D₁₃	2
C₂×C₁₃×Dic₇	2
#10624411	2
C₂×D₅₂	7
C₂×C₂²⋊D₇	13

Subgroups — C2×#10624411 #13089876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624411 #13089876