Subgroups — C₃₁⋊C₃×C₂₄₃ #36379806

Order 22599.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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