Subgroups — C₃²×D₅₁₁ #22604151

Order 9198.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅₁₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₇₃	C₂×C₃	1	4	yes	complemented
4	C₃²×D₇₃	—	7	1	no	maximal, Hall
5	D₅₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₇₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₇₃	—	7	4	no	—
9	C₃×C₇₃	C₃×D₇	1	4	yes	complemented
10	D₇₃	—	7	1	no	Hall
11	C₃²×D₇	—	73	1	no	maximal, Hall
12	C₇₃	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₇	D₇₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₇	—	73	4	no	—
15	C₃×C₇	C₃×D₇₃	1	4	yes	complemented
16	C₂×C₃²	—	511	1	no	Hall
17	D₇	—	73	1	no	Hall
18	C₃²	D₅₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₃²×D₇₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	511	4	no	—
21	C₃	C₃×D₅₁₁	1	4	yes	direct product factor
22	C₂	—	511	1	no	Sylow

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