Subgroups — #64423⋊C₂ #10596889

Order 588.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64424	C₂	1	1	yes	maximal, characteristic, complemented
2	#64423	C₂	1	2	yes	maximal, complemented
3	D₇²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#3861	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₇	C₂×C₃	1	2	yes	complemented
7	C₂×AGL(1,𝔽₇)	—	7	2	no	maximal
8	C₇²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
9	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
10	AGL(1,𝔽₇)	—	7	2	no	—
11	AGL(1,𝔽₇)	—	7	2	no	—
12	AGL(1,𝔽₇)	—	14	3	no	—
13	C₂×D₇	—	7	2	no	—
14	ΓL(1,𝔽₈)	—	7	2	no	—
15	ΓL(1,𝔽₈)	—	14	3	no	—
16	C₂×C₇	—	7	2	no	—
17	D₇	—	7	2	no	—
18	D₇	—	14	3	no	—
19	D₇	AGL(1,𝔽₇)	1	2	yes	complemented
20	C₂²×C₃	—	49	1	no	Hall
21	C₇	—	2	3	no	—
22	C₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
23	C₂×C₃	—	49	2	no	—
24	C₂×C₃	—	49	1	no	—
25	C₂²	—	49	1	no	Sylow
26	C₃	—	49	1	no	Sylow
27	C₂	—	7	2	no	—
28	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²	C₂²×C₃
LCS	G ▷ C₇²
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.