Subgroups — #34089151

Order 19698.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23754422	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₄₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#14584203	—	7	8	no	maximal
5	#13064105	—	7	8	no	—
6	D₄₆₉	—	7	8	no	—
7	C₇×C₆₇	AGL(1,𝔽₇)	1	8	yes	complemented
8	D₆₇⋊C₃	—	49	1	no	Hall
9	#64424	—	67	1	no	maximal, Hall
10	C₆₇⋊C₃	—	49	1	no	Hall
11	#3861	—	67	1	no	Hall
12	D₆₇	—	49	1	no	Hall
13	C₇⋊D₇	—	67	1	no	Hall
14	C₆₇	#64424	1	1	yes	characteristic, complemented, Sylow
15	C₇²	D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₇)	—	469	8	no	—
17	ΓL(1,𝔽₈)	—	469	8	no	—
18	D₇	—	469	8	no	—
19	C₇	#14584203	1	8	yes	complemented
20	C₂×C₃	—	3283	1	no	Hall
21	C₃	—	3283	1	no	Sylow
22	C₂	—	3283	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₆₇	C₂×C₃
LCS	G ▷ C₇²×C₆₇
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.