Subgroups — D₄×C₂₄₆₇ #34089433

Order 19736.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₄₆₇	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₄₆₇	—	2	2	no	—
4	C₂×C₂₄₆₇	C₂²	1	1	yes	characteristic
5	C₂₄₆₇	D₄	1	1	yes	characteristic, direct product factor, Sylow
6	D₄	C₂₄₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²	C₂×C₂₄₆₇	1	2	yes	complemented
8	C₄	C₂×C₂₄₆₇	1	1	yes	characteristic, complemented
9	C₂	—	2	2	no	—
10	C₂	C₂²×C₂₄₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₄₆₇	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₂₄₆₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₄₆₇ ◁ G

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.