Subgroups — C₇×(C₂²⋊C₉)⋊C₂ #92628

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#67	—	3	1	no	maximal
3	C₇×D₉	—	4	1	no	maximal
4	C₂²×C₃×C₇	D₃	1	1	yes	characteristic
5	C₂×D₃×C₇	—	3	1	no	—
6	C₇×Dic₃	—	3	1	no	—
7	(C₂²⋊C₉)⋊C₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₉	—	4	1	no	Hall
9	C₇×D₄	—	9	1	no	Hall
10	C₂×C₃×C₇	—	3	1	no	—
11	D₃×C₇	—	6	1	no	—
12	C₂²⋊C₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂²×C₇	—	9	1	no	—
14	C₂²×C₇	D₉	1	1	yes	characteristic, complemented
15	C₄×C₇	—	9	1	no	—
16	#67	—	3	1	no	—
17	C₃×C₇	S₄	1	1	yes	characteristic
18	D₉	—	4	1	no	—
19	C₂×C₇	—	3	1	no	—
20	C₂×C₇	—	18	1	no	—
21	C₂²×C₃	D₃×C₇	1	1	yes	characteristic
22	C₂×D₃	—	3	1	no	—
23	Dic₃	—	3	1	no	—
24	C₉	—	4	1	no	Sylow
25	D₄	—	9	1	no	Sylow
26	C₇	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	3	1	no	—
28	D₃	—	6	1	no	—
29	C₂²	—	9	1	no	—
30	C₂²	C₇×D₉	1	1	yes	characteristic, complemented
31	C₄	—	9	1	no	—
32	C₃	C₇×S₄	1	1	yes	characteristic
33	C₂	—	3	1	no	—
34	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₇	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₇
Frattini	C₃	C₇×S₄
Fitting, socle	C₂²×C₃×C₇	D₃
LCS	G ▷ C₂²⋊C₉
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.