Subgroups — C₂×(C₁₆₃⋊C₃)⋊D₇ #28331920

Order 13692.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₆₃⋊C₃)⋊D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₆₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₁₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₆₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₆₃	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₁₄₁	C₂×C₃	1	2	yes	complemented
7	C₂×D₁₆₃⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₆₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₆₃⋊C₃	D₇	1	1	yes	characteristic, complemented
10	D₁₆₃⋊C₃	—	7	2	no	—
11	C₂×D₁₆₃	—	7	1	no	Hall
12	C₁₆₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₆₃	C₃×D₇	1	1	yes	characteristic, complemented
14	D₁₆₃	—	7	2	no	—
15	C₁₆₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₇	—	163	1	no	maximal, Hall
17	C₂×C₃×C₇	—	326	1	no	—
18	C₃×D₇	—	163	2	no	—
19	C₂×D₇	—	163	1	no	Hall
20	C₃×C₇	—	326	1	no	Hall
21	C₂×C₇	D₁₆₃⋊C₃	1	1	yes	characteristic, complemented
22	D₇	—	163	2	no	—
23	C₂²×C₃	—	1141	1	no	Hall
24	C₇	C₂×D₁₆₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	326	1	no	—
26	C₂×C₃	—	1141	2	no	—
27	C₂²	—	1141	1	no	Sylow
28	C₃	—	326	1	no	Sylow
29	C₂	—	1141	2	no	—
30	C₂	(C₁₆₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₆₃⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₁₆₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₆₃	C₂×C₃
LCS	G ▷ C₇×C₁₆₃
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.