Subgroups — #28382182

Order 14196.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813074	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×Dic₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16813074	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃²	C₂×C₃	1	1	yes	characteristic
5	C₄×#92788	—	7	1	no	maximal, Hall
6	C₇×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	#11763961	—	13	14	no	maximal
8	C₂×#92788	—	7	1	no	—
9	C₄×C₁₃²	—	7	1	no	Hall
10	C₂×#63270	—	13	14	no	—
11	#92788	—	7	1	no	Hall
12	C₁₃×Dic₇	C₁₃⋊C₃	1	14	yes	complemented
13	C₂×C₁₃²	AGL(1,𝔽₇)	1	1	yes	characteristic
14	#63270	—	13	14	no	—
15	C₂×C₇×C₁₃	C₂×C₁₃⋊C₃	1	14	yes	—
16	C₁₃²	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₁₃⋊C₃	—	91	14	no	—
18	C₇×C₁₃	C₄×C₁₃⋊C₃	1	14	yes	complemented
19	ΓL(1,𝔽₈)⋊C₄	—	169	1	no	Hall
20	C₂×C₁₃⋊C₃	—	91	14	no	—
21	C₄×C₁₃	—	7	14	no	—
22	C₂×ΓL(1,𝔽₈)	—	169	1	no	—
23	C₁₃⋊C₃	—	91	14	no	—
24	Dic₇	#92788	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃	#10587720	1	14	yes	—
26	ΓL(1,𝔽₈)	—	169	1	no	Hall
27	C₂×C₇	C₂×#92788	1	1	yes	characteristic
28	C₁₃	#11763961	1	14	yes	complemented
29	C₃×C₄	—	1183	1	no	Hall
30	C₇	C₄×#92788	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	1183	1	no	—
32	C₄	—	7	1	no	Sylow
33	C₃	—	1183	1	no	Sylow
34	C₂	#20296910	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#20296910
commutator, hypocenter	C₇×C₁₃²	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₃²	C₂×C₃
prime radical	C₂×#16813074	C₂
LCS	G ▷ C₇×C₁₃²
UCS	C₁ ◁ C₂

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

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