Finite Group Databasebeta

Subgroups — #38733002

Order 24843.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#16813075	—	7	8	no	maximal
3	#14274262	—	13	14	no	maximal
4	C₇×C₁₃²	ΓL(1,𝔽₈)	1	8	yes	complemented
5	C₇²×C₁₃	C₁₃⋊C₃	1	14	yes	complemented
6	#92788	—	49	1	no	Hall
7	#63271	—	91	112	no	—
8	C₁₃²	#3861	1	1	yes	characteristic, complemented, Sylow
9	#3861	—	169	1	no	Hall
10	C₇×C₁₃	#63271	1	112	yes	complemented
11	C₇²	#92788	1	1	yes	characteristic, complemented, Sylow
12	C₁₃⋊C₃	—	637	14	no	—
13	ΓL(1,𝔽₈)	—	1183	8	no	—
14	C₁₃	#14274262	1	14	yes	complemented
15	C₇	#16813075	1	8	yes	complemented
16	C₃	—	8281	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₃²	C₃
LCS	G ▷ C₇²×C₁₃²
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇²×C₁₃²	C₃	semidirect
4. C₇×C₁₃²	ΓL(1,𝔽₈)	semidirect
5. C₇²×C₁₃	C₁₃⋊C₃	semidirect
8. C₁₃²	#3861	semidirect
10. C₇×C₁₃	#63271	semidirect
11. C₇²	#92788	semidirect
14. C₁₃	#14274262	semidirect
15. C₇	#16813075	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇²×C₁₃²	3
#16813075	7
#14274262	13