Subgroups — #21419251

Order 7533.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578892	C₃	1	2	yes	maximal
2	#14578887	C₃	1	1	yes	maximal, characteristic
3	C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
5	C₃×C₃₁⋊C₉	—	3	1	no	—
6	C₂₇×C₃₁	C₉	1	3	yes	complemented
7	C₃₁⋊C₂₇	—	3	2	no	—
8	C₃²×C₃₁	3₋¹⁺²	1	1	yes	characteristic
9	C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
10	C₉×C₃₁	3₋¹⁺²	1	2	yes	—
11	C₃₁⋊C₉	—	9	1	no	—
12	#6875	—	31	1	no	maximal, Sylow
13	C₃×C₃₁	—	3	1	no	—
14	C₃×C₃₁	C₉⋊C₉	1	1	yes	characteristic
15	C₂₇⋊C₃	—	31	2	no	—
16	C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic
17	C₉⋊C₉	—	31	1	no	—
18	C₃₁	#6875	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₉	—	93	1	no	—
20	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
21	C₂₇	—	93	2	no	—
22	C₂₇	C₃₁⋊C₉	1	3	yes	complemented
23	C₃²	#11719687	1	1	yes	characteristic
24	C₉	—	279	1	no	—
25	C₉	#11719687	1	2	yes	—
26	C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
27	C₃	—	3	1	no	—
28	C₃	#14578887	1	1	yes	characteristic

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