Subgroups — #14268588⋊D₇ #38760430

Order 25284.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27162428	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162426	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#14268588	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×#11744749	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	D₇×D₄₃⋊C₃	—	7	1	no	maximal
10	#14268588⋊C₂	—	7	1	no	maximal
11	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	#14268594	—	7	1	no	—
13	#14268592	—	7	1	no	—
14	#14268588	D₇	1	1	yes	characteristic, complemented
15	(C₄₃⋊C₃)⋊D₇	—	7	1	no	—
16	D₇×C₄₃⋊C₃	—	7	1	no	—
17	C₇×D₄₃⋊C₃	—	14	1	no	—
18	D₇×D₄₃	—	7	1	no	—
19	D₇×D₄₃	—	7	1	no	—
20	D₇×D₄₃	—	21	2	no	—
21	#11744749	C₂×D₇	1	1	yes	characteristic, complemented
22	C₇×C₄₃⋊C₃	—	14	1	no	—
23	D₃₀₁	—	7	1	no	—
24	D₃₀₁	—	7	1	no	—
25	D₃₀₁	—	21	2	no	—
26	C₇×D₄₃	—	3	2	no	—
27	C₇×D₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
28	C₇×D₄₃	C₃×D₇	1	1	yes	characteristic, complemented
29	D₇×C₄₃	—	7	1	no	—
30	D₇×C₄₃	—	7	1	no	—
31	D₇×C₄₃	—	21	2	no	—
32	C₂×ΓL(1,𝔽₈)⋊D₇	—	43	1	no	maximal, Hall
33	C₂×D₄₃⋊C₃	—	49	1	no	Hall
34	C₇×C₄₃	—	3	2	no	—
35	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
37	C₂×C₇×ΓL(1,𝔽₈)	—	43	1	no	—
38	ΓL(1,𝔽₈)⋊D₇	—	43	1	no	—
39	ΓL(1,𝔽₈)⋊D₇	—	86	1	no	—
40	C₂×C₄₃⋊C₃	—	49	1	no	—
41	D₄₃⋊C₃	—	14	1	no	—
42	D₄₃⋊C₃	—	49	1	no	—
43	C₂×C₇⋊D₇	—	43	1	no	Hall
44	C₂×D₄₃	—	49	1	no	Hall
45	C₇×ΓL(1,𝔽₈)	—	86	1	no	Hall
46	C₄₃⋊C₃	—	14	1	no	Hall
47	C₂×C₇²	—	43	1	no	—
48	C₇⋊D₇	—	43	1	no	—
49	C₇⋊D₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
50	C₂×C₄₃	—	49	1	no	—
51	D₄₃	—	49	1	no	—
52	D₄₃	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented
53	C₂×C₃×D₇	—	301	1	no	—
54	C₂×AGL(1,𝔽₇)	—	301	1	no	—
55	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₄₃	C₂×ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃×C₇	—	602	1	no	—
58	C₃×D₇	—	301	1	no	—
59	C₃×D₇	—	602	1	no	—
60	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
61	AGL(1,𝔽₇)	—	301	1	no	—
62	AGL(1,𝔽₇)	—	602	1	no	—
63	C₂×D₇	—	301	1	no	—
64	C₂×D₇	—	301	1	no	—
65	C₂×D₇	—	903	2	no	—
66	C₃×C₇	—	1204	1	no	—
67	ΓL(1,𝔽₈)	—	86	1	no	—
68	C₂×C₇	—	43	1	no	—
69	C₂×C₇	—	43	1	no	—
70	C₂×C₇	—	129	2	no	—
71	D₇	—	7	1	no	—
72	D₇	—	7	1	no	—
73	D₇	—	21	2	no	—
74	D₇	—	301	1	no	—
75	D₇	—	301	1	no	—
76	D₇	—	903	2	no	—
77	C₂²×C₃	—	2107	1	no	Hall
78	C₇	—	3	2	no	—
79	C₇	#14268588⋊C₂	1	1	yes	characteristic, complemented
80	C₇	D₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented
81	C₂×C₃	—	2107	1	no	—
82	C₂×C₃	—	602	1	no	—
83	C₂×C₃	—	4214	1	no	—
84	C₂²	—	2107	1	no	Sylow
85	C₃	—	1204	1	no	Sylow
86	C₂	—	43	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	2107	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #27162428	C₂	semidirect
2. #27162426	C₂	semidirect
3. C₇×#14268588	C₂	semidirect
4. D₄₃×C₇⋊D₇	C₃	semidirect
5. C₇×#11744749	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×D₄₃	C₂×C₃	semidirect
11. C₇²×C₄₃	C₂²×C₃	semidirect
14. #14268588	D₇	semidirect
21. #11744749	C₂×D₇	semidirect
27. C₇×D₄₃	AGL(1,𝔽₇)	semidirect
28. C₇×D₄₃	C₃×D₇	semidirect
35. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
36. C₇×C₄₃	C₂×C₃×D₇	semidirect
49. C₇⋊D₇	D₄₃⋊C₃	semidirect
52. D₄₃	ΓL(1,𝔽₈)⋊D₇	semidirect
55. C₇²	C₂×D₄₃⋊C₃	semidirect
56. C₄₃	C₂×ΓL(1,𝔽₈)⋊D₇	semidirect
79. C₇	#14268588⋊C₂	semidirect
80. C₇	D₇×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#27162428	2
#27162426	2
C₇×#14268588	2
D₄₃×C₇⋊D₇	3
D₇×D₄₃⋊C₃	7
#14268588⋊C₂	7
C₂×ΓL(1,𝔽₈)⋊D₇	43

Subgroups — #14268588⋊D7 #38760430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #14268588⋊D₇ #38760430