Subgroups — ΓL(1,𝔽₈)×C₃₆₇⋊C₃ #37528834

Order 23121.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440474	C₃	1	1	yes	maximal, characteristic, complemented
2	#21440473	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×C₃₆₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₈)×C₃₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₃₆₇⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₃₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₃₆₇	—	7	1	no	—
8	C₃₆₇⋊C₃	—	7	1	no	—
9	C₃₆₇⋊C₃	—	7	1	no	—
10	C₃₆₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
11	C₃₆₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
12	C₃×ΓL(1,𝔽₈)	—	367	1	no	maximal, Hall
13	C₃×C₇	—	367	1	no	—
14	ΓL(1,𝔽₈)	—	367	1	no	—
15	ΓL(1,𝔽₈)	—	367	1	no	—
16	ΓL(1,𝔽₈)	C₃₆₇⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃²	—	2569	1	no	Sylow
18	C₇	C₃×C₃₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃	—	7	1	no	—
20	C₃	—	2569	1	no	—
21	C₃	—	2569	1	no	—
22	C₃	—	367	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₆₇	C₃²
LCS	G ▷ C₇×C₃₆₇
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.