Subgroups — C₂×#16838473 #21439729

Order 7644.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14274263	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838473	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#14274263	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×D₁₃	C₂×C₃	1	2	yes	complemented
7	C₂×#10587716	—	7	8	no	maximal
8	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×#3861	—	13	1	no	maximal, Hall
10	C₂×#63270	—	7	8	no	—
11	#10587716	—	7	16	no	—
12	C₂×C₇×D₁₃	ΓL(1,𝔽₈)	1	8	yes	complemented
13	C₂×#3861	—	13	2	no	—
14	C₂×#3861	—	13	1	no	—
15	#63270	—	7	8	no	—
16	C₂²×C₇²	—	13	1	no	Hall
17	C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
18	C₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	16	yes	complemented
19	C₂×D₁₃⋊C₃	—	49	1	no	Hall
20	#3861	—	13	1	no	Hall
21	C₂×C₇²	—	13	2	no	—
22	C₂×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
24	C₂²×ΓL(1,𝔽₈)	—	91	8	no	—
25	C₂×C₁₃⋊C₃	—	49	1	no	—
26	D₁₃⋊C₃	—	49	2	no	—
27	C₂×D₁₃	#3861	1	1	yes	characteristic, complemented, Hall
28	C₇²	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×ΓL(1,𝔽₈)	—	91	16	no	—
30	C₂×ΓL(1,𝔽₈)	—	91	8	no	—
31	C₁₃⋊C₃	—	49	1	no	Hall
32	C₂²×C₇	—	13	8	no	—
33	C₂×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented
34	D₁₃	C₂×#3861	1	2	yes	complemented
35	ΓL(1,𝔽₈)	—	91	8	no	—
36	C₂×C₇	—	13	16	no	—
37	C₂×C₇	#10587716	1	8	yes	complemented
38	C₁₃	C₂²×#3861	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	637	1	no	Hall
40	C₇	C₂×#10587716	1	8	yes	complemented
41	C₂×C₃	—	637	2	no	—
42	C₂×C₃	—	637	1	no	—
43	C₂²	—	13	1	no	Sylow
44	C₃	—	637	1	no	Sylow
45	C₂	—	13	2	no	—
46	C₂	#16838473	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#16838473
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×#14274263	C₂	semidirect
2. #16838473	C₂	direct (N × H)
3. C₂×C₇²×D₁₃	C₃	semidirect
4. #14274263	C₂²	semidirect
5. C₂×C₇²×C₁₃	C₂×C₃	semidirect
6. C₇²×D₁₃	C₂×C₃	semidirect
8. C₇²×C₁₃	C₂²×C₃	semidirect
12. C₂×C₇×D₁₃	ΓL(1,𝔽₈)	semidirect
17. C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
18. C₇×D₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₂×C₇²	D₁₃⋊C₃	semidirect
23. C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	semidirect
27. C₂×D₁₃	#3861	semidirect
28. C₇²	C₂×D₁₃⋊C₃	semidirect
33. C₂×C₁₃	C₂×#3861	semidirect
34. D₁₃	C₂×#3861	semidirect
37. C₂×C₇	#10587716	semidirect
38. C₁₃	C₂²×#3861	semidirect
40. C₇	C₂×#10587716	semidirect
46. C₂	#16838473	direct (N × H)

Subgroups — C2×#16838473 #21439729

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16838473 #21439729