Subgroups — #64422⋊D₅₃ #44528417

Order 31164.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊#64422	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#64422	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃⋊#64425	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₇₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₇₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₇×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×ΓL(1,𝔽₈)⋊D₅₃	—	7	1	no	maximal
10	AGL(1,𝔽₇)×D₅₃	—	7	1	no	maximal
11	C₇²×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)⋊D₅₃	—	7	1	no	—
13	ΓL(1,𝔽₈)⋊D₅₃	—	7	1	no	—
14	ΓL(1,𝔽₈)⋊D₅₃	—	7	1	no	—
15	AGL(1,𝔽₇)×C₅₃	—	7	1	no	—
16	ΓL(1,𝔽₈)×D₅₃	—	7	1	no	—
17	C₂×ΓL(1,𝔽₈)×C₅₃	—	7	1	no	—
18	C₂×D₃₇₁	—	7	1	no	—
19	D₇×D₅₃	—	7	1	no	—
20	ΓL(1,𝔽₈)×C₅₃	—	7	1	no	—
21	ΓL(1,𝔽₈)×C₅₃	—	7	1	no	—
22	C₂×C₇×C₅₃	—	7	1	no	—
23	D₃₇₁	—	7	1	no	—
24	D₃₇₁	—	7	1	no	—
25	D₃₇₁	—	42	1	no	—
26	D₃₇₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
27	C₇×D₅₃	—	7	1	no	—
28	D₇×C₅₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₂×C₃×D₅₃	—	49	1	no	Hall
30	#64422⋊C₂	—	53	1	no	maximal, Hall
31	C₇×C₅₃	—	6	1	no	—
32	C₇×C₅₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	C₇×C₅₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅₃	—	49	1	no	—
35	C₃×D₅₃	—	49	1	no	—
36	C₃×D₅₃	—	49	1	no	—
37	#64425	—	53	1	no	—
38	#64422	—	53	1	no	—
39	#64422	D₅₃	1	1	yes	characteristic, complemented
40	C₂×D₅₃	—	49	1	no	Hall
41	D₇²	—	53	1	no	Hall
42	C₃×C₅₃	—	49	1	no	Hall
43	#3862	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅₃	—	7	1	no	—
45	D₅₃	—	7	1	no	—
46	D₅₃	—	49	1	no	—
47	C₇⋊D₇	—	53	1	no	—
48	C₇×D₇	—	53	1	no	—
49	C₇×D₇	C₃×D₅₃	1	1	yes	characteristic, complemented
50	C₂×AGL(1,𝔽₇)	—	371	1	no	—
51	C₂×AGL(1,𝔽₇)	—	371	1	no	—
52	C₅₃	#64422⋊C₂	1	1	yes	characteristic, complemented, Sylow
53	C₇²	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
55	C₂×ΓL(1,𝔽₈)	—	371	1	no	—
56	AGL(1,𝔽₇)	—	7	1	no	—
57	AGL(1,𝔽₇)	—	371	1	no	—
58	AGL(1,𝔽₇)	—	371	1	no	—
59	AGL(1,𝔽₇)	—	371	1	no	—
60	C₂×D₇	—	371	1	no	—
61	C₂×D₇	—	371	1	no	—
62	ΓL(1,𝔽₈)	—	7	1	no	—
63	ΓL(1,𝔽₈)	—	7	1	no	—
64	C₂×C₇	—	7	1	no	—
65	C₂×C₇	—	371	1	no	—
66	D₇	—	53	1	no	—
67	D₇	—	371	1	no	—
68	D₇	—	371	1	no	—
69	D₇	—	2226	1	no	—
70	D₇	ΓL(1,𝔽₈)⋊D₅₃	1	1	yes	characteristic, complemented
71	C₂²×C₃	—	2597	1	no	Hall
72	C₇	—	6	1	no	—
73	C₇	AGL(1,𝔽₇)×D₅₃	1	1	yes	characteristic, complemented
74	C₇	C₂×ΓL(1,𝔽₈)⋊D₅₃	1	1	yes	characteristic, complemented
75	C₂×C₃	—	2597	1	no	—
76	C₂×C₃	—	2597	1	no	—
77	C₂×C₃	—	49	1	no	—
78	C₂²	—	2597	1	no	Sylow
79	C₃	—	49	1	no	Sylow
80	C₂	—	7	1	no	—
81	C₂	—	2597	1	no	—
82	C₂	—	371	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₅₃	C₂²×C₃
LCS	G ▷ C₇²×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅₃⋊#64422	C₂	semidirect
2. C₅₃×#64422	C₂	semidirect
3. C₅₃⋊#64425	C₂	semidirect
4. D₇×D₃₇₁	C₃	semidirect
5. C₅₃×#3862	C₂²	semidirect
6. C₇⋊D₃₇₁	C₂×C₃	semidirect
7. C₇×D₃₇₁	C₂×C₃	semidirect
8. C₇×D₇×C₅₃	C₂×C₃	semidirect
11. C₇²×C₅₃	C₂²×C₃	semidirect
26. D₃₇₁	AGL(1,𝔽₇)	semidirect
28. D₇×C₅₃	AGL(1,𝔽₇)	semidirect
32. C₇×C₅₃	C₂×AGL(1,𝔽₇)	semidirect
33. C₇×C₅₃	C₂×AGL(1,𝔽₇)	semidirect
39. #64422	D₅₃	semidirect
43. #3862	C₂×D₅₃	semidirect
49. C₇×D₇	C₃×D₅₃	semidirect
52. C₅₃	#64422⋊C₂	semidirect
53. C₇²	C₂×C₃×D₅₃	semidirect
70. D₇	ΓL(1,𝔽₈)⋊D₅₃	semidirect
73. C₇	AGL(1,𝔽₇)×D₅₃	semidirect
74. C₇	C₂×ΓL(1,𝔽₈)⋊D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃⋊#64422	2
C₅₃×#64422	2
C₅₃⋊#64425	2
D₇×D₃₇₁	3
C₂×ΓL(1,𝔽₈)⋊D₅₃	7
AGL(1,𝔽₇)×D₅₃	7
#64422⋊C₂	53

Subgroups — #64422⋊D53 #44528417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #64422⋊D₅₃ #44528417