Subgroups — #13089881

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	C₂×D₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624412	C₂	1	1	yes	maximal, characteristic, complemented
6	#10624411	C₂	1	1	yes	maximal, characteristic, complemented
7	#10624409	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented
9	C₂×D₉₁	—	2	2	no	—
10	C₂×D₉₁	C₂²	1	1	yes	characteristic
11	C₂×D₉₁	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₃×D₇	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₇×D₁₃	C₂²	1	1	yes	characteristic, complemented
14	D₇×D₁₃	—	2	2	no	—
15	C₇×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
17	D₄×D₁₃	—	7	1	no	maximal, Hall
18	C₂×C₇×C₁₃	—	2	1	no	—
19	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
20	D₉₁	—	2	1	no	—
21	D₉₁	D₄	1	2	yes	complemented
22	C₇×D₁₃	—	2	1	no	—
23	C₁₃×D₇	—	2	1	no	—
24	D₄×D₇	—	13	1	no	maximal, Hall
25	C₂²×D₁₃	—	7	1	no	—
26	C₂²×D₁₃	—	7	1	no	—
27	D₄×C₁₃	—	7	1	no	—
28	C₂²⋊D₁₃	—	7	1	no	—
29	C₂²⋊D₁₃	D₇	1	1	yes	characteristic, complemented
30	D₅₂	—	7	1	no	—
31	C₄×D₁₃	—	7	1	no	—
32	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
33	C₂²×D₇	—	13	1	no	—
34	C₂²×D₇	—	13	1	no	—
35	C₇×D₄	—	13	1	no	—
36	C₂²⋊D₇	—	13	1	no	—
37	C₂²⋊D₇	D₁₃	1	1	yes	characteristic, complemented
38	D₂₈	—	13	1	no	—
39	C₄×D₇	—	13	1	no	—
40	C₂²×C₁₃	—	7	1	no	—
41	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
42	C₂×D₁₃	—	7	1	no	—
43	C₂×D₁₃	—	7	1	no	—
44	C₂×D₁₃	—	14	2	no	—
45	C₂×D₁₃	—	14	2	no	—
46	C₂×D₁₃	C₂×D₇	1	1	yes	characteristic, complemented
47	C₄×C₁₃	—	7	1	no	—
48	Dic₁₃	C₂×D₇	1	1	yes	characteristic, complemented
49	C₂²×C₇	—	13	1	no	—
50	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic, complemented
51	C₂×D₇	—	13	1	no	—
52	C₂×D₇	—	13	1	no	—
53	C₂×D₇	—	26	2	no	—
54	C₂×D₇	—	26	2	no	—
55	C₂×D₇	C₂×D₁₃	1	1	yes	characteristic, complemented
56	C₄×C₇	—	13	1	no	—
57	Dic₇	C₂×D₁₃	1	1	yes	characteristic, complemented
58	C₂×C₁₃	—	2	1	no	—
59	C₂×C₁₃	—	14	1	no	—
60	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
61	D₁₃	—	2	1	no	—
62	D₁₃	—	7	2	no	—
63	D₁₃	—	14	1	no	—
64	C₂×D₄	—	91	1	no	Sylow
65	C₂×C₇	—	2	1	no	—
66	C₂×C₇	—	26	1	no	—
67	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
68	D₇	—	2	1	no	—
69	D₇	—	13	2	no	—
70	D₇	—	26	1	no	—
71	C₁₃	D₄×D₇	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	91	1	no	—
73	C₂³	—	91	1	no	—
74	D₄	—	7	1	no	—
75	D₄	—	13	1	no	—
76	D₄	—	91	1	no	—
77	D₄	—	91	1	no	—
78	C₂×C₄	—	91	1	no	—
79	C₇	D₄×D₁₃	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	7	1	no	—
81	C₂²	—	13	1	no	—
82	C₂²	—	91	1	no	—
83	C₂²	—	91	1	no	—
84	C₂²	—	182	2	no	—
85	C₂²	—	182	2	no	—
86	C₂²	D₇×D₁₃	1	1	yes	characteristic, complemented
87	C₄	—	7	1	no	—
88	C₄	—	13	1	no	—
89	C₂	—	2	1	no	—
90	C₂	—	14	1	no	—
91	C₂	—	26	1	no	—
92	C₂	—	91	2	no	—
93	C₂	—	182	1	no	—
94	C₂	C₂×D₇×D₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×D₉₁	C₂	semidirect
2. C₂×D₇×D₁₃	C₂	semidirect
3. C₁₃×C₂²⋊D₇	C₂	semidirect
4. C₇×C₂²⋊D₁₃	C₂	semidirect
5. #10624412	C₂	semidirect
6. #10624411	C₂	semidirect
7. #10624409	C₂	semidirect
8. C₂²×C₇×C₁₃	C₂²	semidirect
11. C₂×D₉₁	C₂²	semidirect
12. C₂×C₁₃×D₇	C₂²	semidirect
13. C₂×C₇×D₁₃	C₂²	semidirect
15. C₇×Dic₁₃	C₂²	semidirect
16. C₁₃×Dic₇	C₂²	semidirect
21. D₉₁	D₄	semidirect
29. C₂²⋊D₁₃	D₇	semidirect
32. C₇×C₁₃	C₂×D₄	semidirect
37. C₂²⋊D₇	D₁₃	semidirect
41. C₂²×C₁₃	C₂×D₇	semidirect
46. C₂×D₁₃	C₂×D₇	semidirect
48. Dic₁₃	C₂×D₇	semidirect
50. C₂²×C₇	C₂×D₁₃	semidirect
55. C₂×D₇	C₂×D₁₃	semidirect
57. Dic₇	C₂×D₁₃	semidirect
71. C₁₃	D₄×D₇	semidirect
79. C₇	D₄×D₁₃	semidirect
86. C₂²	D₇×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₉₁	2
C₂×D₇×D₁₃	2
C₁₃×C₂²⋊D₇	2
C₇×C₂²⋊D₁₃	2
#10624412	2
#10624411	2
#10624409	2
D₄×D₁₃	7
D₄×D₇	13