Subgroups — C₇×C₃⋊(ΓL(1,𝔽₈)⋊D₁₃) #26039639

Order 11466.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×ΓL(1,𝔽₈)⋊D₁₃	—	3	1	no	maximal
4	C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₃×ΓL(1,𝔽₈)	—	2	1	no	—
6	C₇×C₁₃×ΓL(1,𝔽₈)	D₃	1	1	yes	characteristic, complemented
7	C₃×C₇×D₃₉	—	7	1	no	maximal
8	C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)	C₇	1	1	yes	maximal, characteristic, direct product factor
9	C₇×D₉₁	—	3	1	no	Hall
10	C₇×C₃⋊AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
11	C₃²×C₇×C₁₃	—	7	1	no	—
12	C₃×C₁₃×ΓL(1,𝔽₈)	C₂×C₇	1	1	yes	characteristic, complemented
13	C₇²×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	D₂₇₃	C₃×C₇	1	1	yes	characteristic, complemented
15	C₇×D₃₉	—	7	1	no	—
16	C₃×C₇×D₁₃	—	21	1	no	—
17	ΓL(1,𝔽₈)⋊D₁₃	—	3	1	no	—
18	C₃×C₇×ΓL(1,𝔽₈)	D₁₃	1	1	yes	characteristic, complemented, Hall
19	C₇×D₂₁	—	13	1	no	—
20	C₇×AGL(1,𝔽₇)	—	39	1	no	—
21	C₃×C₇×C₁₃	—	6	1	no	—
22	C₃×C₇×C₁₃	—	7	1	no	—
23	C₃×C₇×C₁₃	—	14	1	no	—
24	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	C₃×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
26	C₁₃×ΓL(1,𝔽₈)	—	2	1	no	—
27	C₁₃×ΓL(1,𝔽₈)	D₃×C₇	1	1	yes	characteristic, complemented
28	C₃×D₃₉	—	7	1	no	Hall
29	D₉₁	—	3	1	no	—
30	C₇×D₁₃	—	21	1	no	—
31	C₃×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented
32	C₇×ΓL(1,𝔽₈)	—	2	1	no	—
33	C₇×ΓL(1,𝔽₈)	D₃₉	1	1	yes	characteristic, complemented
34	C₃×D₃×C₇	—	91	1	no	—
35	C₃⋊AGL(1,𝔽₇)	—	13	1	no	—
36	C₃²×C₁₃	—	7	1	no	Hall
37	C₇×D₇	—	39	1	no	Hall
38	C₇×C₁₃	—	6	1	no	—
39	C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
40	C₇×C₁₃	C₃×D₃×C₇	1	1	yes	characteristic, complemented
41	D₃₉	—	7	1	no	—
42	C₃×D₁₃	—	21	1	no	—
43	C₃²×C₇	—	7	1	no	—
44	C₃×ΓL(1,𝔽₈)	C₇×D₁₃	1	1	yes	characteristic, complemented
45	C₇²	C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	273	1	no	—
47	D₂₁	—	13	1	no	—
48	D₃×C₇	—	91	1	no	—
49	AGL(1,𝔽₇)	—	39	1	no	—
50	C₃×C₁₃	—	7	1	no	—
51	C₃×C₁₃	—	14	1	no	—
52	C₃×C₁₃	C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
53	D₁₃	—	21	1	no	Hall
54	C₃×C₇	—	6	1	no	—
55	C₃×C₇	—	7	1	no	—
56	C₃×C₇	—	14	1	no	—
57	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
58	C₃×C₇	C₃×C₇×D₁₃	1	1	yes	characteristic, complemented
59	ΓL(1,𝔽₈)	—	2	1	no	—
60	ΓL(1,𝔽₈)	C₇×D₃₉	1	1	yes	characteristic, complemented
61	C₃×D₃	—	91	1	no	Hall
62	C₂×C₇	—	273	1	no	—
63	D₇	—	39	1	no	—
64	C₁₃	C₇×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
65	C₃²	—	7	1	no	Sylow
66	C₇	—	6	1	no	—
67	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)	1	1	yes	characteristic, direct product factor
68	C₇	C₃×C₇×D₃₉	1	1	yes	characteristic, complemented
69	C₂×C₃	—	273	1	no	—
70	D₃	—	91	1	no	—
71	C₃	—	7	1	no	—
72	C₃	—	14	1	no	—
73	C₃	C₇×ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
74	C₂	—	273	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×ΓL(1,𝔽₈)	C₂	semidirect
2. C₇×D₂₇₃	C₃	semidirect
4. C₃×C₇²×C₁₃	C₂×C₃	semidirect
6. C₇×C₁₃×ΓL(1,𝔽₈)	D₃	semidirect
8. C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)	C₇	direct (N × H)
12. C₃×C₁₃×ΓL(1,𝔽₈)	C₂×C₇	semidirect
13. C₇²×C₁₃	C₃×D₃	semidirect
14. D₂₇₃	C₃×C₇	semidirect
18. C₃×C₇×ΓL(1,𝔽₈)	D₁₃	semidirect
24. C₃×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
25. C₃×C₇×C₁₃	C₂×C₃×C₇	semidirect
27. C₁₃×ΓL(1,𝔽₈)	D₃×C₇	semidirect
31. C₃×C₇²	C₃×D₁₃	semidirect
33. C₇×ΓL(1,𝔽₈)	D₃₉	semidirect
39. C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	semidirect
40. C₇×C₁₃	C₃×D₃×C₇	semidirect
44. C₃×ΓL(1,𝔽₈)	C₇×D₁₃	semidirect
45. C₇²	C₃×D₃₉	semidirect
52. C₃×C₁₃	C₇×AGL(1,𝔽₇)	semidirect
57. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₃	semidirect
58. C₃×C₇	C₃×C₇×D₁₃	semidirect
60. ΓL(1,𝔽₈)	C₇×D₃₉	semidirect
64. C₁₃	C₇×C₃⋊AGL(1,𝔽₇)	semidirect
67. C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)	direct (N × H)
68. C₇	C₃×C₇×D₃₉	semidirect
73. C₃	C₇×ΓL(1,𝔽₈)⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×ΓL(1,𝔽₈)	2
C₇×D₂₇₃	3
C₇×ΓL(1,𝔽₈)⋊D₁₃	3
C₃×C₇×D₃₉	7
C₃⋊(ΓL(1,𝔽₈)⋊D₁₃)	7
C₇×C₃⋊AGL(1,𝔽₇)	13

Subgroups — C7×C3⋊(ΓL(1,𝔽8)⋊D13) #26039639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊(ΓL(1,𝔽₈)⋊D₁₃) #26039639