Subgroups — C₂×D₆₇₂₇ #41002053

Order 26908.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₉₆₁	—	7	1	no	maximal, Hall
5	C₂×C₉₆₁	D₇	1	1	yes	characteristic, complemented
6	D₉₆₁	—	7	2	no	—
7	C₉₆₁	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₂₁₇	—	31	1	no	maximal
9	C₂×C₇×C₃₁	D₃₁	1	1	yes	characteristic
10	D₂₁₇	—	31	2	no	—
11	C₇×C₃₁	C₂×D₃₁	1	1	yes	characteristic
12	C₂×D₃₁	—	217	1	no	—
13	C₂×C₃₁	D₂₁₇	1	1	yes	characteristic
14	D₃₁	—	217	2	no	—
15	C₃₁	C₂×D₂₁₇	1	1	yes	characteristic
16	C₂×D₇	—	961	1	no	Hall
17	C₂×C₇	D₉₆₁	1	1	yes	characteristic, complemented
18	D₇	—	961	2	no	—
19	C₇	C₂×D₉₆₁	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	6727	1	no	Sylow
21	C₂	—	6727	2	no	—
22	C₂	D₆₇₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₇₂₇
commutator, cosocle, hypocenter	C₇×C₉₆₁	C₂²
Frattini	C₃₁	C₂×D₂₁₇
Fitting	C₂×C₇×C₉₆₁	C₂
socle	C₂×C₇×C₃₁	D₃₁
LCS	G ▷ C₇×C₉₆₁
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.