Subgroups — #24925949

Order 10878.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129588	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#13095535	—	7	8	no	maximal
5	#11715913	—	7	8	no	—
6	D₇×C₃₇	—	7	8	no	—
7	#64424	—	37	1	no	maximal, Hall
8	C₇×C₃₇	AGL(1,𝔽₇)	1	8	yes	complemented
9	C₂×C₃₇⋊C₃	—	49	1	no	Hall
10	#3861	—	37	1	no	Hall
11	C₃₇⋊C₃	—	49	1	no	Hall
12	C₇⋊D₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₇	—	49	1	no	Hall
14	C₇²	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	AGL(1,𝔽₇)	—	259	8	no	—
16	C₃₇	#64424	1	1	yes	characteristic, complemented, Sylow
17	ΓL(1,𝔽₈)	—	259	8	no	—
18	D₇	—	7	8	no	—
19	C₇	#13095535	1	8	yes	complemented
20	C₂×C₃	—	1813	1	no	Hall
21	C₃	—	1813	1	no	Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁

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.