Subgroups — C₂×D₁₆₂₂₇ #72302183

Order 64908.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₂₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₇×C₆₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₄₀₉	—	3	1	no	maximal
4	C₂₇×C₆₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₄₀₉	—	3	2	no	—
6	C₂×C₉×C₆₀₁	D₃	1	1	yes	characteristic
7	C₂×D₁₈₀₃	—	9	1	no	—
8	C₉×C₆₀₁	C₂×D₃	1	1	yes	characteristic
9	C₂×C₃×C₆₀₁	D₉	1	1	yes	characteristic
10	D₁₈₀₃	—	9	2	no	—
11	C₂×D₆₀₁	—	27	1	no	Hall
12	C₃×C₆₀₁	C₂×D₉	1	1	yes	characteristic
13	C₂×C₆₀₁	D₂₇	1	1	yes	characteristic, complemented
14	D₆₀₁	—	27	2	no	—
15	C₆₀₁	C₂×D₂₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₂₇	—	601	1	no	maximal, Hall
17	C₂×C₂₇	D₆₀₁	1	1	yes	characteristic, complemented
18	D₂₇	—	601	2	no	—
19	C₂×D₉	—	1803	1	no	—
20	C₂₇	C₂×D₆₀₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₉	D₁₈₀₃	1	1	yes	characteristic
22	D₉	—	1803	2	no	—
23	C₂×D₃	—	5409	1	no	—
24	C₉	C₂×D₁₈₀₃	1	1	yes	characteristic
25	C₂×C₃	D₅₄₀₉	1	1	yes	characteristic
26	D₃	—	5409	2	no	—
27	C₂²	—	16227	1	no	Sylow
28	C₃	C₂×D₅₄₀₉	1	1	yes	characteristic
29	C₂	—	16227	2	no	—
30	C₂	D₁₆₂₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₆₂₂₇
commutator, cosocle, hypocenter	C₂₇×C₆₀₁	C₂²
Frattini	C₉	C₂×D₁₈₀₃
Fitting	C₂×C₂₇×C₆₀₁	C₂
socle	C₂×C₃×C₆₀₁	D₉
LCS	G ▷ C₂₇×C₆₀₁
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.