Subgroups — #36379810

Order 22599.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₂₄₃	C₃	1	3	yes	maximal, complemented
2	C₃×C₃₁×C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₇×C₃₁	C₉	1	1	yes	characteristic
4	C₃₁×C₈₁	C₉	1	2	yes	—
5	C₃₁×C₈₁	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₃₁	C₂₇	1	1	yes	characteristic
7	C₂₇×C₃₁	C₂₇	1	2	yes	—
8	C₂₇×C₃₁	C₃×C₉	1	1	yes	characteristic
9	C₂₄₃⋊C₃	—	31	1	no	maximal, Sylow
10	C₃²×C₃₁	C₈₁	1	1	yes	characteristic
11	C₉×C₃₁	C₈₁	1	2	yes	—
12	C₉×C₃₁	C₃×C₂₇	1	1	yes	characteristic
13	C₃×C₈₁	C₃₁⋊C₃	1	1	yes	characteristic
14	C₂₄₃	—	31	3	no	—
15	C₃×C₃₁	—	3	1	no	—
16	C₃×C₃₁	C₃×C₈₁	1	1	yes	characteristic
17	C₃×C₂₇	C₃₁⋊C₉	1	1	yes	characteristic
18	C₈₁	C₃₁⋊C₉	1	2	yes	—
19	C₈₁	C₃×C₃₁⋊C₃	1	1	yes	characteristic
20	C₃₁	C₂₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₉	C₃₁⋊C₂₇	1	1	yes	characteristic
22	C₂₇	C₃₁⋊C₂₇	1	2	yes	—
23	C₂₇	C₃×C₃₁⋊C₉	1	1	yes	characteristic
24	C₃²	C₃₁⋊C₈₁	1	1	yes	characteristic
25	C₉	C₃₁⋊C₈₁	1	2	yes	—
26	C₉	C₃×C₃₁⋊C₂₇	1	1	yes	characteristic
27	C₃	—	3	1	no	—
28	C₃	C₃×C₃₁⋊C₈₁	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₃₁⋊C₂₄₃	C₃	semidirect
20. C₃₁	C₂₄₃⋊C₃	semidirect

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