Subgroups — #64423⋊D₄₃ #38760465

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27162418	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#64423	C₂	1	1	yes	maximal, characteristic, complemented
3	#27162408	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄₃×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×ΓL(1,𝔽₈)⋊D₄₃	—	7	1	no	maximal
10	AGL(1,𝔽₇)×D₄₃	—	7	1	no	maximal
11	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×ΓL(1,𝔽₈)×C₄₃	—	7	1	no	—
13	ΓL(1,𝔽₈)⋊D₄₃	—	7	1	no	—
14	ΓL(1,𝔽₈)⋊D₄₃	—	7	1	no	—
15	ΓL(1,𝔽₈)⋊D₄₃	—	7	1	no	—
16	ΓL(1,𝔽₈)⋊D₄₃	—	14	3	no	—
17	AGL(1,𝔽₇)×C₄₃	—	14	1	no	—
18	ΓL(1,𝔽₈)×D₄₃	—	7	1	no	—
19	C₂×D₃₀₁	—	7	1	no	—
20	D₇×D₄₃	—	7	1	no	—
21	ΓL(1,𝔽₈)×C₄₃	—	7	1	no	—
22	ΓL(1,𝔽₈)×C₄₃	—	14	1	no	—
23	ΓL(1,𝔽₈)×C₄₃	—	28	3	no	—
24	C₂×C₇×C₄₃	—	7	1	no	—
25	D₃₀₁	—	7	1	no	—
26	D₃₀₁	—	7	1	no	—
27	D₃₀₁	—	14	3	no	—
28	D₃₀₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₇×D₄₃	—	7	1	no	—
30	D₇×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
31	#64423⋊C₂	—	43	1	no	maximal, Hall
32	C₂×C₃×D₄₃	—	49	1	no	Hall
33	C₇×C₄₃	—	2	3	no	—
34	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
35	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	#64424	—	43	1	no	—
37	#64423	—	43	1	no	—
38	#64423	D₄₃	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄₃	—	98	1	no	—
40	C₃×D₄₃	—	49	1	no	—
41	C₃×D₄₃	—	98	1	no	—
42	D₇²	—	43	1	no	Hall
43	C₂×D₄₃	—	49	1	no	Hall
44	#3861	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
45	C₃×C₄₃	—	196	1	no	Hall
46	C₇⋊D₇	—	43	1	no	—
47	C₇×D₇	—	43	1	no	—
48	C₇×D₇	C₃×D₄₃	1	1	yes	characteristic, complemented
49	C₂×C₄₃	—	7	1	no	—
50	D₄₃	—	7	1	no	—
51	D₄₃	—	49	1	no	—
52	C₂×AGL(1,𝔽₇)	—	301	1	no	—
53	C₂×AGL(1,𝔽₇)	—	301	1	no	—
54	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
55	C₄₃	#64423⋊C₂	1	1	yes	characteristic, complemented, Sylow
56	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
57	C₂×ΓL(1,𝔽₈)	—	301	1	no	—
58	AGL(1,𝔽₇)	—	7	1	no	—
59	AGL(1,𝔽₇)	—	301	1	no	—
60	AGL(1,𝔽₇)	—	301	1	no	—
61	AGL(1,𝔽₇)	—	602	3	no	—
62	AGL(1,𝔽₇)	—	602	1	no	—
63	C₂×D₇	—	301	1	no	—
64	C₂×D₇	—	301	1	no	—
65	ΓL(1,𝔽₈)	—	7	1	no	—
66	ΓL(1,𝔽₈)	—	14	1	no	—
67	ΓL(1,𝔽₈)	—	28	3	no	—
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	301	1	no	—
70	D₇	—	43	1	no	—
71	D₇	—	301	1	no	—
72	D₇	—	301	1	no	—
73	D₇	—	602	3	no	—
74	D₇	ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic, complemented
75	C₂²×C₃	—	2107	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	AGL(1,𝔽₇)×D₄₃	1	1	yes	characteristic, complemented
78	C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic, complemented
79	C₂×C₃	—	2107	1	no	—
80	C₂×C₃	—	98	1	no	—
81	C₂×C₃	—	4214	1	no	—
82	C₂²	—	2107	1	no	Sylow
83	C₃	—	196	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	301	1	no	—
86	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. #27162418	C₂	semidirect
2. C₄₃×#64423	C₂	semidirect
3. #27162408	C₂	semidirect
4. D₇×D₃₀₁	C₃	semidirect
5. C₄₃×#3861	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₇×D₃₀₁	C₂×C₃	semidirect
8. C₇×D₇×C₄₃	C₂×C₃	semidirect
11. C₇²×C₄₃	C₂²×C₃	semidirect
28. D₃₀₁	AGL(1,𝔽₇)	semidirect
30. D₇×C₄₃	AGL(1,𝔽₇)	semidirect
34. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
35. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
38. #64423	D₄₃	semidirect
44. #3861	C₂×D₄₃	semidirect
48. C₇×D₇	C₃×D₄₃	semidirect
54. C₇²	C₂×C₃×D₄₃	semidirect
55. C₄₃	#64423⋊C₂	semidirect
74. D₇	ΓL(1,𝔽₈)⋊D₄₃	semidirect
77. C₇	AGL(1,𝔽₇)×D₄₃	semidirect
78. C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#27162418	2
C₄₃×#64423	2
#27162408	2
D₇×D₃₀₁	3
C₂×ΓL(1,𝔽₈)⋊D₄₃	7
AGL(1,𝔽₇)×D₄₃	7
#64423⋊C₂	43

Subgroups — #64423⋊D43 #38760465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #64423⋊D₄₃ #38760465