Subgroups — C₃⋊(C₃⋊(C₇⋊#1181)) #20300655

Order 7308.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#1181)	—	3	4	no	maximal
3	C₃²×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₂₉	D₃	1	4	yes	—
5	C₃⋊(C₃⋊#1181)	—	7	1	no	maximal, Hall
6	C₇⋊#1181	—	9	1	no	Hall
7	C₃×C₇×C₂₉	Dic₃	1	4	yes	complemented
8	C₃²×D₂₉	D₇	1	1	yes	characteristic
9	C₇×D₂₉	C₃⋊D₃	1	1	yes	characteristic
10	C₃⋊#1181	—	21	4	no	—
11	C₃²×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₃⋊Dic₂₁	—	29	1	no	maximal, Hall
13	C₇×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₂₉	D₂₁	1	4	yes	—
15	C₂×C₃²×C₇	—	29	1	no	—
16	#1181	—	63	1	no	Hall
17	C₃×C₂₉	Dic₂₁	1	4	yes	complemented
18	Dic₂₁	—	87	4	no	—
19	C₃²×C₇	#1181	1	1	yes	characteristic, complemented, Hall
20	D₂₉	C₃⋊D₂₁	1	1	yes	characteristic
21	C₂×C₃×C₇	—	29	4	no	—
22	C₃⋊Dic₃	—	203	1	no	Hall
23	C₂₉	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
24	Dic₇	—	261	1	no	Hall
25	C₃×C₇	C₃⋊#1181	1	4	yes	complemented
26	C₂×C₃²	—	29	1	no	—
27	C₂×C₇	—	29	1	no	—
28	Dic₃	—	609	4	no	—
29	C₃²	C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊(C₃⋊#1181)	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	29	4	no	—
32	C₄	—	1827	1	no	Sylow
33	C₃	C₃⋊(C₇⋊#1181)	1	4	yes	complemented
34	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₂₉	C₄
LCS	G ▷ C₃²×C₇×C₂₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.