Subgroups — C₇×C₃⋊(C₃⋊#1181) #20300653

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	C₇×C₃⋊#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)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#1181	—	9	1	no	Hall
7	C₃×C₇×C₂₉	Dic₃	1	4	yes	complemented
8	C₃²×D₂₉	C₂×C₇	1	1	yes	characteristic
9	C₇×D₂₉	C₃⋊D₃	1	1	yes	characteristic
10	C₃⋊#1181	—	3	4	no	—
11	C₃²×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₃⋊Dic₃	—	29	1	no	maximal, Hall
13	C₇×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₂₉	D₃×C₇	1	4	yes	—
15	C₂×C₃²×C₇	—	29	1	no	—
16	#1181	—	9	1	no	Hall
17	C₃×C₂₉	C₇×Dic₃	1	4	yes	complemented
18	C₇×Dic₃	—	87	4	no	—
19	C₃²×C₇	#1181	1	1	yes	characteristic, complemented, Hall
20	D₂₉	C₇×C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃×C₇	—	29	4	no	—
22	C₃⋊Dic₃	—	29	1	no	Hall
23	C₂₉	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
24	C₄×C₇	—	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	—	87	4	no	—
29	C₃²	C₇×#1181	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊(C₃⋊#1181)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	4	no	—
32	C₄	—	261	1	no	Sylow
33	C₃	C₇×C₃⋊#1181	1	4	yes	complemented
34	C₂	—	29	1	no	—

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