Subgroups — C₇×C₃⋊D₂₆₇ #26014257

Order 11214.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₆₇	—	3	4	no	maximal
3	C₃×C₇×C₈₉	D₃	1	4	yes	complemented
4	C₃⋊D₂₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₈₉	—	9	1	no	Hall
6	C₃²×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₈₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
8	D₂₆₇	—	3	4	no	—
9	C₃×C₈₉	D₃×C₇	1	4	yes	complemented
10	D₈₉	—	9	1	no	Hall
11	C₇×C₃⋊D₃	—	89	1	no	maximal, Hall
12	C₈₉	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₇	D₈₉	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇	—	267	4	no	—
15	C₃×C₇	D₂₆₇	1	4	yes	complemented
16	C₃⋊D₃	—	89	1	no	Hall
17	C₂×C₇	—	801	1	no	Hall
18	C₃²	C₇×D₈₉	1	1	yes	characteristic, complemented, Sylow
19	C₇	C₃⋊D₂₆₇	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	—	267	4	no	—
21	C₃	C₇×D₂₆₇	1	4	yes	complemented
22	C₂	—	801	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₂₆₇
commutator, cosocle, hypocenter	C₃²×C₈₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₈₉	C₂
LCS	G ▷ C₃²×C₈₉
UCS	C₁ ◁ C₇

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.