Subgroups — #64605

Order 312.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
4	Dic₂₆	—	3	1	no	maximal, Hall
5	C₂×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₄×C₁₃	—	3	1	no	—
7	Dic₁₃	—	3	1	no	—
8	Dic₁₃	D₃	1	1	yes	characteristic
9	C₃×C₁₃	Q₈	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	C₂×D₃	1	1	yes	characteristic
11	Dic₆	—	13	1	no	maximal, Hall
12	C₁₃	Dic₆	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₄	—	13	1	no	—
14	Dic₃	—	13	1	no	—
15	Dic₃	D₁₃	1	1	yes	characteristic
16	Q₈	—	39	1	no	Sylow
17	C₂×C₃	C₂×D₁₃	1	1	yes	characteristic
18	C₄	—	3	1	no	—
19	C₄	—	13	1	no	—
20	C₄	—	39	1	no	—
21	C₃	Dic₂₆	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₃
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	Q₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂

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.