Subgroups — ΓL(1,𝔽₈)² #89207

Order 441.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3862	C₃	1	1	yes	maximal, characteristic, complemented
2	#3861	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×ΓL(1,𝔽₈)	C₃	1	2	yes	maximal, complemented
4	C₃×ΓL(1,𝔽₈)	—	7	2	no	maximal
5	C₇²	C₃²	1	1	yes	characteristic, complemented, Sylow
6	C₃×C₇	—	7	2	no	—
7	ΓL(1,𝔽₈)	—	7	2	no	—
8	ΓL(1,𝔽₈)	—	7	2	no	—
9	ΓL(1,𝔽₈)	—	21	2	no	—
10	ΓL(1,𝔽₈)	ΓL(1,𝔽₈)	1	2	yes	direct product factor
11	C₃²	—	49	1	no	Sylow
12	C₇	—	3	2	no	—
13	C₇	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
14	C₃	—	7	2	no	—
15	C₃	—	49	1	no	—
16	C₃	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²	C₃²
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.