Subgroups — C₇⋊D₁₈₂₇ #38784644

Order 25578.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₂₀₃)	—	3	1	no	maximal
3	C₃×C₇²×C₂₉	D₃	1	1	yes	characteristic
4	D₁₈₂₇	—	7	8	no	maximal
5	C₇⋊D₂₀₃	—	9	1	no	Hall
6	C₇×C₉×C₂₉	D₇	1	8	yes	complemented
7	C₇²×C₂₉	D₉	1	1	yes	characteristic, complemented, Hall
8	D₆₀₉	—	21	8	no	—
9	C₇⋊D₆₃	—	29	1	no	maximal, Hall
10	C₃×C₇×C₂₉	D₂₁	1	8	yes	—
11	D₂₆₁	—	49	1	no	Hall
12	C₇²×C₉	D₂₉	1	1	yes	characteristic, complemented, Hall
13	D₂₀₃	—	63	8	no	—
14	C₃⋊(C₇⋊D₇)	—	87	1	no	—
15	C₉×C₂₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	D₆₃	1	8	yes	complemented
17	D₈₇	—	147	1	no	—
18	C₃×C₇²	D₈₇	1	1	yes	characteristic
19	D₆₃	—	203	8	no	—
20	C₇⋊D₇	—	261	1	no	Hall
21	C₃×C₂₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
22	C₇×C₉	D₂₀₃	1	8	yes	complemented
23	D₂₉	—	441	1	no	Hall
24	C₇²	D₂₆₁	1	1	yes	characteristic, complemented, Sylow
25	D₂₁	—	609	8	no	—
26	C₂₉	C₇⋊D₆₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	D₆₀₉	1	8	yes	—
28	D₉	—	1421	1	no	Hall
29	D₇	—	1827	8	no	—
30	C₉	C₇⋊D₂₀₃	1	1	yes	characteristic, complemented, Sylow
31	C₇	D₁₈₂₇	1	8	yes	complemented
32	D₃	—	4263	1	no	—
33	C₃	C₃⋊(C₇⋊D₂₀₃)	1	1	yes	characteristic
34	C₂	—	12789	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇²×C₉×C₂₉	C₂
Frattini	C₃	C₃⋊(C₇⋊D₂₀₃)
socle	C₃×C₇²×C₂₉	D₃
LCS	G ▷ C₇²×C₉×C₂₉
UCS	C₁

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.