Subgroups — C₂×#10624413 #13089878

Order 1456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#10624413	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
6	Dic₉₁	C₂²	1	2	yes	—
7	C₇×Dic₁₃	C₂²	1	2	yes	—
8	C₁₃×Dic₇	C₂²	1	2	yes	—
9	C₂×Dic₂₆	—	7	1	no	maximal, Hall
10	C₂×C₇×C₁₃	Q₈	1	2	yes	complemented
11	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×Dic₁₄	—	13	1	no	maximal, Hall
13	C₂×C₄×C₁₃	—	7	1	no	—
14	C₂×Dic₁₃	—	7	1	no	—
15	C₂×Dic₁₃	D₇	1	1	yes	characteristic
16	Dic₂₆	—	7	4	no	—
17	C₇×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄×C₇	—	13	1	no	—
19	C₂×Dic₇	—	13	1	no	—
20	C₂×Dic₇	D₁₃	1	1	yes	characteristic
21	Dic₁₄	—	13	4	no	—
22	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
23	C₄×C₁₃	—	7	2	no	—
24	Dic₁₃	—	7	2	no	—
25	Dic₁₃	C₂×D₇	1	2	yes	—
26	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
27	C₄×C₇	—	13	2	no	—
28	Dic₇	—	13	2	no	—
29	Dic₇	C₂×D₁₃	1	2	yes	—
30	C₂×C₁₃	Dic₁₄	1	2	yes	complemented
31	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
32	C₂×Q₈	—	91	1	no	Sylow
33	C₂×C₇	Dic₂₆	1	2	yes	complemented
34	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
35	C₁₃	C₂×Dic₁₄	1	1	yes	characteristic, complemented, Sylow
36	Q₈	—	91	4	no	—
37	C₂×C₄	—	7	1	no	—
38	C₂×C₄	—	13	1	no	—
39	C₂×C₄	—	91	1	no	—
40	C₇	C₂×Dic₂₆	1	1	yes	characteristic, complemented, Sylow
41	C₂²	D₇×D₁₃	1	1	yes	characteristic
42	C₄	—	7	2	no	—
43	C₄	—	13	2	no	—
44	C₄	—	91	2	no	—
45	C₂	#10624413	1	2	yes	direct product factor
46	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, prime radical	C₂²×C₇×C₁₃	C₂²
hypocenter	C₇×C₁₃	C₂×Q₈
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
4. #10624413	C₂	direct (N × H)
10. C₂×C₇×C₁₃	Q₈	semidirect
17. C₇×C₁₃	C₂×Q₈	semidirect
30. C₂×C₁₃	Dic₁₄	semidirect
33. C₂×C₇	Dic₂₆	semidirect
35. C₁₃	C₂×Dic₁₄	semidirect
40. C₇	C₂×Dic₂₆	semidirect
45. C₂	#10624413	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×Dic₉₁	2
C₂×C₁₃×Dic₇	2
C₂×C₇×Dic₁₃	2
#10624413	2
C₂×Dic₂₆	7
C₂×Dic₁₄	13

Subgroups — C2×#10624413 #13089878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624413 #13089878