Subgroups — #13089907

Order 1456.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₉₁	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₉₁	C₂	1	2	yes	maximal, complemented
4	C₄×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₈₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₃	C₂²	1	2	yes	—
7	C₂×D₉₁	C₂²	1	1	yes	characteristic
8	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic
9	Dic₉₁	C₂²	1	2	yes	—
10	Dic₉₁	C₂²	1	1	yes	characteristic
11	#6129	—	7	1	no	maximal, Hall
12	C₂×C₇×C₁₃	—	2	2	no	—
13	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
14	D₉₁	—	2	1	no	—
15	#1159	—	13	1	no	maximal, Hall
16	D₄×C₁₃	D₇	1	1	yes	characteristic, complemented
17	C₂²⋊D₁₃	—	7	2	no	—
18	C₂×Dic₁₃	—	7	2	no	—
19	C₄×D₁₃	—	7	1	no	—
20	Dic₂₆	—	7	1	no	—
21	C₇×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
22	C₇×D₄	D₁₃	1	1	yes	characteristic, complemented
23	C₂²⋊D₇	—	13	2	no	—
24	C₂×Dic₇	—	13	2	no	—
25	C₄×D₇	—	13	1	no	—
26	Dic₁₄	—	13	1	no	—
27	C₂²×C₁₃	C₂×D₇	1	2	yes	—
28	C₂×D₁₃	—	7	1	no	—
29	C₄×C₁₃	C₂×D₇	1	1	yes	characteristic
30	Dic₁₃	—	7	2	no	—
31	Dic₁₃	—	7	1	no	—
32	C₂²×C₇	C₂×D₁₃	1	2	yes	—
33	C₂×D₇	—	13	1	no	—
34	C₄×C₇	C₂×D₁₃	1	1	yes	characteristic
35	Dic₇	—	13	2	no	—
36	Dic₇	—	13	1	no	—
37	C₂×C₁₃	—	2	2	no	—
38	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
39	D₁₃	—	14	1	no	—
40	#41	—	91	1	no	Sylow
41	C₂×C₇	—	2	2	no	—
42	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
43	D₇	—	26	1	no	—
44	C₁₃	#1159	1	1	yes	characteristic, complemented, Sylow
45	Q₈	—	91	1	no	—
46	D₄	—	91	2	no	—
47	D₄	D₉₁	1	1	yes	characteristic, complemented
48	C₂×C₄	—	91	2	no	—
49	C₂×C₄	—	91	1	no	—
50	C₇	#6129	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	91	1	no	—
52	C₂²	C₂×D₉₁	1	2	yes	—
53	C₄	—	91	1	no	—
54	C₄	—	91	2	no	—
55	C₄	C₂×D₉₁	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	182	1	no	—
58	C₂	C₂²×D₉₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₉₁
commutator, socle, cosocle	C₂×C₇×C₁₃	C₂³
Fitting	C₇×D₄×C₁₃	C₂
hypercenter	D₄	D₉₁
hypocenter	C₇×C₁₃	#41
LCS	G ▷ C₂×C₇×C₁₃ ▷ C₇×C₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₇×D₄×C₁₃	C₂	semidirect
2. C₂²⋊D₉₁	C₂	semidirect
3. C₂×Dic₉₁	C₂	semidirect
4. C₄×D₉₁	C₂	semidirect
5. Dic₁₈₂	C₂	semidirect
16. D₄×C₁₃	D₇	semidirect
21. C₇×C₁₃	#41	semidirect
22. C₇×D₄	D₁₃	semidirect
44. C₁₃	#1159	semidirect
47. D₄	D₉₁	semidirect
50. C₇	#6129	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₄×C₁₃	2
C₂²⋊D₉₁	2
C₂×Dic₉₁	2
C₄×D₉₁	2
Dic₁₈₂	2
#6129	7
#1159	13