Subgroups — #36379692

Order 22599.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419258	C₃	1	2	yes	maximal
2	#21419221	C₃	1	1	yes	maximal, characteristic
3	C₃₁×C₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×C₃₁⋊C₂₇	C₉	1	2	yes	—
5	C₉×C₃₁⋊C₉	C₉	1	1	yes	characteristic
6	C₃₁⋊C₈₁	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
8	C₃₁×C₈₁	C₉	1	3	yes	complemented
9	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
10	C₃×C₃₁⋊C₉	—	3	1	no	—
11	C₂₇×C₃₁	C₃×C₉	1	2	yes	—
12	C₂₇×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₃₁⋊C₂₇	—	3	2	no	—
14	#10624500	—	31	1	no	maximal, Sylow
15	C₃²×C₃₁	C₂₇⋊C₃	1	1	yes	characteristic
16	C₉×C₃₁	C₉²	1	1	yes	characteristic
17	C₉×C₃₁	C₂₇⋊C₃	1	2	yes	—
18	C₃₁⋊C₉	—	9	1	no	—
19	C₈₁⋊C₃	—	31	2	no	—
20	C₈₁⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic
21	#6864	—	31	1	no	—
22	C₃×C₃₁	—	3	1	no	—
23	C₃×C₃₁	#6864	1	1	yes	characteristic
24	C₃×C₂₇	—	31	2	no	—
25	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
26	C₉²	—	31	1	no	—
27	C₈₁	—	31	6	no	—
28	C₈₁	C₃₁⋊C₉	1	3	yes	complemented
29	C₃₁	#10624500	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₉	—	93	1	no	—
31	C₃×C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
32	C₂₇	—	93	2	no	—
33	C₂₇	C₉×C₃₁⋊C₃	1	2	yes	—
34	C₂₇	C₃×C₃₁⋊C₉	1	1	yes	characteristic
35	C₃²	#14578891	1	1	yes	characteristic
36	C₉	—	279	1	no	—
37	C₉	C₉×C₃₁⋊C₉	1	1	yes	characteristic
38	C₉	#14578891	1	2	yes	—
39	C₃	—	3	1	no	—
40	C₃	#21419221	1	1	yes	characteristic

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

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