Subgroups — C₃²×C₃₁⋊C₂₇ #21419365

Order 7533.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁⋊C₂₇	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₃₁	C₉	1	1	yes	characteristic
4	C₃×C₉×C₃₁	C₉	1	8	yes	—
5	C₃×C₉×C₃₁	C₃²	1	4	yes	—
6	C₃₁⋊C₂₇	C₃²	1	9	yes	direct product factor
7	C₃²×C₃₁	C₂₇	1	9	yes	complemented
8	C₃²×C₃₁	C₃×C₉	1	4	yes	—
9	C₉×C₃₁	C₃×C₉	1	8	yes	—
10	C₉×C₃₁	C₃³	1	1	yes	characteristic
11	C₃²×C₂₇	—	31	1	no	maximal, Sylow
12	C₃×C₃₁	C₃×C₂₇	1	12	yes	complemented
13	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
14	C₃²×C₉	C₃₁⋊C₃	1	1	yes	characteristic
15	C₃×C₂₇	—	31	12	no	—
16	C₃₁	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
17	C₃³	C₃₁⋊C₉	1	1	yes	characteristic
18	C₃×C₉	C₃₁⋊C₉	1	8	yes	—
19	C₃×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
20	C₂₇	—	31	9	no	—
21	C₃²	C₃₁⋊C₂₇	1	9	yes	direct product factor
22	C₃²	C₃×C₃₁⋊C₉	1	4	yes	—
23	C₉	C₃×C₃₁⋊C₉	1	8	yes	—
24	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
25	C₃	C₃×C₃₁⋊C₂₇	1	12	yes	direct product factor
26	C₃	C₃²×C₃₁⋊C₉	1	1	yes	characteristic

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