Finite Group Databasebeta

Subgroups — #45689136

Order 33411.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#18012031	—	7	1	no	maximal, Hall
3	C₃₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
4	#11744748	—	37	1	no	maximal, Hall
5	#11715913	—	43	1	no	maximal, Hall
6	C₇×C₄₃	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
7	C₇×C₃₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
8	C₄₃⋊C₃	—	259	1	no	Hall
9	C₃₇⋊C₃	—	301	1	no	Hall
10	C₄₃	#11715913	1	1	yes	characteristic, complemented, Sylow
11	C₃₇	#11744748	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₈)	—	1591	1	no	Hall
13	C₇	#18012031	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	11137	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₇×C₄₃	C₃
LCS	G ▷ C₇×C₃₇×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₇×C₄₃	C₃	semidirect
3. C₃₇×C₄₃	ΓL(1,𝔽₈)	semidirect
6. C₇×C₄₃	C₃₇⋊C₃	semidirect
7. C₇×C₃₇	C₄₃⋊C₃	semidirect
10. C₄₃	#11715913	semidirect
11. C₃₇	#11744748	semidirect
13. C₇	#18012031	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₃₇×C₄₃	3
#18012031	7
#11744748	37
#11715913	43