Subgroups — D₇×#10587723 #21439639

Order 7644.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×#63271	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#10587723	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×#63271	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₉₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₉₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₃×D₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×#10587723	—	7	1	no	maximal
10	D₇×D₁₃⋊C₃	—	7	1	no	maximal
11	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	D₇×AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
13	C₂×#63271	—	7	1	no	—
14	#10587723	—	7	1	no	—
15	#10587723	D₇	1	1	yes	characteristic, direct product factor
16	(C₁₃⋊C₃)⋊D₇	—	7	1	no	—
17	D₇×C₁₃⋊C₃	—	7	1	no	—
18	C₇×D₁₃⋊C₃	—	7	1	no	—
19	C₂×D₉₁	—	7	1	no	—
20	D₇×D₁₃	—	7	1	no	—
21	ΓL(1,𝔽₈)⋊D₇	—	13	1	no	—
22	D₇×ΓL(1,𝔽₈)	—	13	1	no	—
23	C₇×AGL(1,𝔽₇)	—	13	1	no	—
24	#63271	C₂×D₇	1	1	yes	characteristic, complemented
25	C₇×C₁₃⋊C₃	—	7	1	no	—
26	D₇²	—	13	1	no	Hall
27	C₂×C₇×C₁₃	—	7	1	no	—
28	D₉₁	—	7	1	no	—
29	D₉₁	—	7	1	no	—
30	D₉₁	—	42	1	no	—
31	D₉₁	C₃×D₇	1	1	yes	characteristic, complemented
32	C₇×D₁₃	—	7	1	no	—
33	C₁₃×D₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₂×D₁₃⋊C₃	—	49	1	no	Hall
35	C₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
36	C₇⋊D₇	—	13	1	no	—
37	C₇×D₇	—	13	1	no	—
38	C₇×D₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₇×C₁₃	—	6	1	no	—
40	C₇×C₁₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
41	C₇×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
42	C₂×C₃×D₇	—	91	1	no	—
43	C₂×AGL(1,𝔽₇)	—	91	1	no	—
44	C₂×C₁₃⋊C₃	—	49	1	no	—
45	D₁₃⋊C₃	—	7	1	no	—
46	D₁₃⋊C₃	—	49	1	no	—
47	C₂×D₁₃	—	49	1	no	Hall
48	C₇²	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	—	91	1	no	—
50	C₃×D₇	—	91	1	no	—
51	C₃×D₇	—	91	1	no	—
52	C₂×ΓL(1,𝔽₈)	—	91	1	no	—
53	AGL(1,𝔽₇)	—	13	1	no	—
54	AGL(1,𝔽₇)	—	91	1	no	—
55	C₁₃⋊C₃	—	7	1	no	Hall
56	C₂×D₇	—	91	1	no	—
57	C₂×D₇	—	91	1	no	—
58	C₂×C₁₃	—	7	1	no	—
59	D₁₃	—	7	1	no	—
60	D₁₃	—	49	1	no	—
61	C₃×C₇	—	91	1	no	—
62	ΓL(1,𝔽₈)	—	13	1	no	—
63	C₂×C₇	—	7	1	no	—
64	C₂×C₇	—	91	1	no	—
65	D₇	—	13	1	no	—
66	D₇	—	546	1	no	—
67	D₇	—	91	1	no	—
68	D₇	—	91	1	no	—
69	D₇	#10587723	1	1	yes	characteristic, direct product factor
70	C₁₃	D₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₃	—	637	1	no	Hall
72	C₇	—	6	1	no	—
73	C₇	D₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
74	C₇	C₂×#10587723	1	1	yes	characteristic, complemented
75	C₂×C₃	—	91	1	no	—
76	C₂×C₃	—	637	1	no	—
77	C₂×C₃	—	637	1	no	—
78	C₂²	—	637	1	no	Sylow
79	C₃	—	91	1	no	Sylow
80	C₂	—	7	1	no	—
81	C₂	—	91	1	no	—
82	C₂	—	637	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇×#63271	C₂	semidirect
2. #16838469	C₂	semidirect
3. C₇×#10587723	C₂	semidirect
4. D₇×D₉₁	C₃	semidirect
5. C₇×#63271	C₂²	semidirect
6. C₇⋊D₉₁	C₂×C₃	semidirect
7. C₇×D₉₁	C₂×C₃	semidirect
8. C₇×C₁₃×D₇	C₂×C₃	semidirect
11. C₇²×C₁₃	C₂²×C₃	semidirect
15. #10587723	D₇	direct (N × H)
24. #63271	C₂×D₇	semidirect
31. D₉₁	C₃×D₇	semidirect
33. C₁₃×D₇	AGL(1,𝔽₇)	semidirect
38. C₇×D₇	D₁₃⋊C₃	semidirect
40. C₇×C₁₃	C₂×AGL(1,𝔽₇)	semidirect
41. C₇×C₁₃	C₂×C₃×D₇	semidirect
48. C₇²	C₂×D₁₃⋊C₃	semidirect
69. D₇	#10587723	direct (N × H)
70. C₁₃	D₇×AGL(1,𝔽₇)	semidirect
73. C₇	D₇×D₁₃⋊C₃	semidirect
74. C₇	C₂×#10587723	semidirect

Subgroups — D7×#10587723 #21439639

Conjugacy classes of subgroups

Complements

Subgroups — D₇×#10587723 #21439639