Subgroups — C₂×#16838460 #21439716

Order 7644.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838460	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₉₁	C₂×C₃	1	2	yes	complemented
7	C₂×ΓL(1,𝔽₈)⋊D₁₃	—	7	1	no	maximal
8	C₂×ΓL(1,𝔽₈)×D₁₃	—	7	1	no	maximal
9	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×#64423	—	13	1	no	maximal, Hall
11	C₂×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
12	C₂×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
13	C₂×C₁₃×ΓL(1,𝔽₈)	—	14	3	no	—
14	ΓL(1,𝔽₈)⋊D₁₃	—	7	2	no	—
15	ΓL(1,𝔽₈)×D₁₃	—	7	2	no	—
16	C₂×D₉₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
17	C₂×C₇×D₁₃	—	7	1	no	—
18	C₂×#3861	D₁₃	1	1	yes	characteristic, complemented
19	#64423	—	13	2	no	—
20	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
21	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
22	C₁₃×ΓL(1,𝔽₈)	—	14	3	no	—
23	C₂×C₇×D₇	—	13	1	no	Hall
24	C₂×C₇×C₁₃	—	2	3	no	—
25	C₂×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
26	C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
27	D₉₁	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
28	C₇×D₁₃	—	7	2	no	—
29	C₂×C₃×D₁₃	—	49	1	no	Hall
30	#3861	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented
32	C₇×D₇	—	13	2	no	—
33	C₇×C₁₃	—	2	3	no	—
34	C₇×C₁₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
35	C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
36	C₂²×ΓL(1,𝔽₈)	—	91	1	no	—
37	C₂×AGL(1,𝔽₇)	—	91	1	no	—
38	C₂×C₃×C₁₃	—	49	1	no	—
39	C₃×D₁₃	—	49	2	no	—
40	C₂×D₁₃	—	7	1	no	Hall
41	C₇²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
43	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
44	C₂×ΓL(1,𝔽₈)	—	14	3	no	—
45	C₂×ΓL(1,𝔽₈)	—	91	2	no	—
46	AGL(1,𝔽₇)	—	91	2	no	—
47	C₃×C₁₃	—	49	1	no	Hall
48	C₂²×C₇	—	91	1	no	—
49	C₂×D₇	—	13	1	no	—
50	C₂×C₁₃	#64423	1	1	yes	characteristic, complemented
51	D₁₃	—	7	2	no	—
52	ΓL(1,𝔽₈)	—	7	1	no	—
53	ΓL(1,𝔽₈)	—	7	1	no	—
54	ΓL(1,𝔽₈)	—	14	3	no	—
55	C₂×C₇	—	2	3	no	—
56	C₂×C₇	—	91	2	no	—
57	C₂×C₇	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
58	C₂×C₇	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
59	D₇	—	13	2	no	—
60	C₁₃	C₂×#64423	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	—	637	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
64	C₇	C₂×ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
65	C₂×C₃	—	49	1	no	—
66	C₂×C₃	—	637	2	no	—
67	C₂²	—	91	1	no	Sylow
68	C₃	—	49	1	no	Sylow
69	C₂	—	91	2	no	—
70	C₂	#16838460	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#16838460
commutator, hypocenter	C₇²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#3861	C₂	semidirect
2. #16838460	C₂	direct (N × H)
3. C₂×C₇×D₉₁	C₃	semidirect
4. C₁₃×#3861	C₂²	semidirect
5. C₂×C₇²×C₁₃	C₂×C₃	semidirect
6. C₇×D₉₁	C₂×C₃	semidirect
9. C₇²×C₁₃	C₂²×C₃	semidirect
16. C₂×D₉₁	ΓL(1,𝔽₈)	semidirect
18. C₂×#3861	D₁₃	semidirect
25. C₂×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
26. C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
27. D₉₁	C₂×ΓL(1,𝔽₈)	semidirect
30. #3861	C₂×D₁₃	semidirect
31. C₂×C₇²	C₃×D₁₃	semidirect
34. C₇×C₁₃	C₂×AGL(1,𝔽₇)	semidirect
35. C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	semidirect
41. C₇²	C₂×C₃×D₁₃	semidirect
50. C₂×C₁₃	#64423	semidirect
57. C₂×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
58. C₂×C₇	ΓL(1,𝔽₈)⋊D₁₃	semidirect
60. C₁₃	C₂×#64423	semidirect
63. C₇	C₂×ΓL(1,𝔽₈)×D₁₃	semidirect
64. C₇	C₂×ΓL(1,𝔽₈)⋊D₁₃	semidirect
70. C₂	#16838460	direct (N × H)

Subgroups — C2×#16838460 #21439716

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16838460 #21439716