Subgroups — C₂×C₃×C₄₇⋊D₄₇ #40997172

Order 26508.

500 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇⋊D₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇⋊D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₇²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄₇⋊D₄₇	C₂×C₃	1	2	yes	direct product factor
7	C₄₇²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×D₄₇	—	47	48	no	maximal
9	C₂×C₃×C₄₇	D₄₇	1	48	yes	complemented
10	C₃×D₄₇	—	47	96	no	—
11	C₂×D₄₇	—	47	48	no	—
12	C₃×C₄₇	C₂×D₄₇	1	48	yes	complemented
13	C₂×C₄₇	C₃×D₄₇	1	48	yes	complemented
14	D₄₇	—	47	96	no	—
15	C₄₇	C₂×C₃×D₄₇	1	48	yes	complemented
16	C₂²×C₃	—	2209	1	no	Hall
17	C₂×C₃	—	2209	2	no	—
18	C₂×C₃	C₄₇⋊D₄₇	1	1	yes	characteristic, direct product factor
19	C₂²	—	2209	1	no	Sylow
20	C₃	C₂×C₄₇⋊D₄₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	2209	2	no	—
22	C₂	C₃×C₄₇⋊D₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₄₇⋊D₄₇
commutator, cosocle, hypocenter	C₄₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₇²	C₂
LCS	G ▷ C₄₇²
UCS	C₁ ◁ C₂×C₃

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.