Finite Group Databasebeta

← Sp(2,𝔽₁₃) #72209592

Subgroups — Sp(2,𝔽₁₃) #72209592

Order 2184.

21 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃⋊C₃	—	14	1	no	maximal
2	C₂×C₁₃⋊C₃	—	14	1	no	—
3	Dic₁₃	—	14	1	no	—
4	C₁₃⋊C₃	—	14	1	no	Hall
5	Dic₇	—	78	1	no	maximal
6	C₂×C₁₃	—	14	1	no	—
7	Dic₆	—	91	1	no	maximal, Hall
8	SL(2,𝔽₃)	—	91	1	no	maximal, Hall
9	C₂×C₇	—	78	1	no	—
10	C₁₃	—	14	1	no	Sylow
11	C₃×C₄	—	91	1	no	—
12	Dic₃	—	91	2	no	—
13	Q₈	—	91	1	no	Sylow
14	C₇	—	78	1	no	Sylow
15	C₂×C₃	—	91	1	no	—
16	C₄	—	91	1	no	—
17	C₃	—	91	1	no	Sylow
18	C₂	PSL(2,𝔽₁₃)	1	1	yes	maximal normal, characteristic

	subgroup	G/H
center, Frattini, Fitting, socle, cosocle, hypercenter	C₂	PSL(2,𝔽₁₃)
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁ ◁ C₂

Maximal subgroups

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

subgroup	index
Dic₁₃⋊C₃	14
Dic₇	78
Dic₆	91
SL(2,𝔽₃)	91