Subgroups — #36379693

Order 22599.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419258	C₃	1	3	yes	maximal
2	C₃₁×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃₁⋊C₈₁	C₉	1	9	yes	complemented
4	C₃×C₂₇×C₃₁	C₉	1	2	yes	—
5	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
6	C₉²×C₃₁	C₉	1	1	yes	characteristic
7	C₃×C₉×C₃₁	—	3	1	no	—
8	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
9	C₂₇×C₃₁	—	3	2	no	—
10	C₂₇×C₃₁	C₃×C₉	1	3	yes	—
11	#10624500	—	31	1	no	maximal, Sylow
12	C₃²×C₃₁	C₂₇⋊C₃	1	1	yes	characteristic
13	C₉×C₃₁	—	9	1	no	—
14	C₉×C₃₁	C₉²	1	1	yes	characteristic
15	C₉×C₃₁	C₂₇⋊C₃	1	2	yes	—
16	C₈₁⋊C₃	—	31	3	no	—
17	#6864	C₃₁⋊C₃	1	1	yes	characteristic
18	C₃×C₃₁	—	3	1	no	—
19	C₃×C₃₁	#6864	1	1	yes	characteristic
20	C₃×C₂₇	C₃₁⋊C₉	1	2	yes	—
21	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
22	C₉²	C₃₁⋊C₉	1	1	yes	characteristic
23	C₈₁	—	31	9	no	—
24	C₃₁	#10624500	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
27	C₂₇	—	3	2	no	—
28	C₂₇	C₉×C₃₁⋊C₃	1	3	yes	—
29	C₃²	#14578892	1	1	yes	characteristic
30	C₉	—	9	1	no	—
31	C₉	C₉×C₃₁⋊C₉	1	1	yes	characteristic
32	C₉	#14578892	1	2	yes	—
33	C₃	—	3	1	no	—
34	C₃	#21419222	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₃₁⋊C₈₁	C₉	semidirect
24. C₃₁	#10624500	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.