Subgroups — C₇⋊D₁₁₉₇ #30660633

Order 16758.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₁₃₃)	—	3	1	no	maximal
3	C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
4	D₁₁₉₇	—	7	8	no	maximal
5	C₇⋊D₁₃₃	—	9	1	no	Hall
6	C₇×C₉×C₁₉	D₇	1	8	yes	complemented
7	C₇²×C₁₉	D₉	1	1	yes	characteristic, complemented, Hall
8	C₇⋊D₆₃	—	19	1	no	maximal, Hall
9	D₃₉₉	—	21	8	no	—
10	C₇²×C₉	D₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	D₂₁	1	8	yes	—
12	D₁₇₁	—	49	1	no	Hall
13	C₃⋊(C₇⋊D₇)	—	57	1	no	—
14	D₁₃₃	—	63	8	no	—
15	C₉×C₁₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇²	D₅₇	1	1	yes	characteristic
17	C₇×C₁₉	D₆₃	1	8	yes	complemented
18	D₆₃	—	133	8	no	—
19	D₅₇	—	147	1	no	—
20	C₇⋊D₇	—	171	1	no	Hall
21	C₇×C₉	D₁₃₃	1	8	yes	complemented
22	C₃×C₁₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
23	C₇²	D₁₇₁	1	1	yes	characteristic, complemented, Sylow
24	D₂₁	—	399	8	no	—
25	D₁₉	—	441	1	no	Hall
26	C₃×C₇	D₃₉₉	1	8	yes	—
27	C₁₉	C₇⋊D₆₃	1	1	yes	characteristic, complemented, Sylow
28	D₉	—	931	1	no	Hall
29	D₇	—	1197	8	no	—
30	C₉	C₇⋊D₁₃₃	1	1	yes	characteristic, complemented, Sylow
31	C₇	D₁₁₉₇	1	8	yes	complemented
32	D₃	—	2793	1	no	—
33	C₃	C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic
34	C₂	—	8379	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇²×C₉×C₁₉	C₂
Frattini	C₃	C₃⋊(C₇⋊D₁₃₃)
socle	C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₇²×C₉×C₁₉
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.