Subgroups — #28382196

Order 14196.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊#92789	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×Dic₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇⋊#92789	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃²	C₂×C₃	1	1	yes	characteristic
5	#14523131	—	7	1	no	maximal, Hall
6	C₇×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₄×#63271	—	13	1	no	maximal
8	#11763957	—	13	1	no	maximal
9	C₂×#92789	—	7	1	no	—
10	C₁₃×Dic₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₂×#63271	—	13	1	no	—
12	C₂×#63270	—	13	1	no	—
13	#92789	—	7	1	no	Hall
14	C₄×C₇×C₁₃	—	13	1	no	—
15	C₇×Dic₁₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂×C₁₃²	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	#63271	—	13	1	no	—
18	#63270	—	13	1	no	—
19	C₂×C₇×C₁₃	—	6	2	no	—
20	C₂×C₇×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic
21	C₂×C₇×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	C₁₃²	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₃⋊C₃	—	91	1	no	—
24	Dic₁₃⋊C₃	—	91	1	no	—
25	C₇×C₁₃	—	6	2	no	—
26	C₇×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₇×C₁₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₄×ΓL(1,𝔽₈)	—	169	1	no	Hall
29	C₂×C₁₃⋊C₃	—	91	1	no	—
30	C₂×C₁₃⋊C₃	—	91	1	no	—
31	C₄×C₁₃	—	13	1	no	—
32	Dic₁₃	#63271	1	1	yes	characteristic, complemented
33	C₂×ΓL(1,𝔽₈)	—	169	1	no	—
34	C₁₃⋊C₃	—	91	1	no	—
35	C₁₃⋊C₃	—	91	1	no	—
36	C₄×C₇	—	13	1	no	Hall
37	C₂×C₁₃	—	6	2	no	—
38	C₂×C₁₃	#10587716	1	1	yes	characteristic
39	C₂×C₁₃	C₂×#63271	1	1	yes	characteristic
40	ΓL(1,𝔽₈)	—	169	1	no	Hall
41	C₂×C₇	#11759818	1	1	yes	characteristic
42	C₁₃	—	6	2	no	—
43	C₁₃	#11763957	1	1	yes	characteristic, complemented
44	C₁₃	C₄×#63271	1	1	yes	characteristic, complemented
45	C₃×C₄	—	1183	1	no	Hall
46	C₇	#14523131	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	1183	1	no	—
48	C₄	—	13	1	no	Sylow
49	C₃	—	1183	1	no	Sylow
50	C₂	#20296924	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#20296924
commutator, hypocenter	C₇×C₁₃²	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₃²	C₂×C₃
prime radical	C₂×C₇⋊#92789	C₂
LCS	G ▷ C₇×C₁₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₃×Dic₁₃	C₃	semidirect
3. C₇⋊#92789	C₄	semidirect
6. C₇×C₁₃²	C₃×C₄	semidirect
10. C₁₃×Dic₁₃	ΓL(1,𝔽₈)	semidirect
15. C₇×Dic₁₃	C₁₃⋊C₃	semidirect
22. C₁₃²	C₄×ΓL(1,𝔽₈)	semidirect
26. C₇×C₁₃	Dic₁₃⋊C₃	semidirect
27. C₇×C₁₃	C₄×C₁₃⋊C₃	semidirect
32. Dic₁₃	#63271	semidirect
43. C₁₃	#11763957	semidirect
44. C₁₃	C₄×#63271	semidirect
46. C₇	#14523131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇⋊#92789	2
C₇×C₁₃×Dic₁₃	3
#14523131	7
C₄×#63271	13
#11763957	13