Subgroups — C₂×D₁₄₂₇₁ #72292166

Order 57084.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₂₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₆₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₇₅₇	—	3	1	no	maximal, Hall
4	C₃×C₆₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₆₇×C₇₁	D₃	1	1	yes	characteristic, complemented
6	D₄₇₅₇	—	3	2	no	—
7	C₆₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₁₃	—	67	1	no	maximal, Hall
9	C₂×D₂₀₁	—	71	1	no	maximal, Hall
10	C₂×C₃×C₇₁	D₆₇	1	1	yes	characteristic, complemented
11	D₂₁₃	—	67	2	no	—
12	C₂×C₃×C₆₇	D₇₁	1	1	yes	characteristic, complemented
13	D₂₀₁	—	71	2	no	—
14	C₂×D₇₁	—	201	1	no	Hall
15	C₂×D₆₇	—	213	1	no	Hall
16	C₃×C₇₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₆₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇₁	D₂₀₁	1	1	yes	characteristic, complemented
19	D₇₁	—	201	2	no	—
20	C₂×C₆₇	D₂₁₃	1	1	yes	characteristic, complemented
21	D₆₇	—	213	2	no	—
22	C₇₁	C₂×D₂₀₁	1	1	yes	characteristic, complemented, Sylow
23	C₆₇	C₂×D₂₁₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	4757	1	no	Hall
25	C₂×C₃	D₄₇₅₇	1	1	yes	characteristic, complemented
26	D₃	—	4757	2	no	—
27	C₂²	—	14271	1	no	Sylow
28	C₃	C₂×D₄₇₅₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	14271	2	no	—
30	C₂	D₁₄₂₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₄₂₇₁
commutator, cosocle, hypocenter	C₃×C₆₇×C₇₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₆₇×C₇₁	C₂
LCS	G ▷ C₃×C₆₇×C₇₁
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.