Subgroups — #44531936

Order 31347.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782734	C₃	1	3	yes	maximal
2	C₄₃×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃⋊C₂₇	—	3	3	no	—
4	C₃×C₂₇×C₄₃	C₉	1	2	yes	—
5	C₃×C₂₇×C₄₃	C₉	1	1	yes	characteristic
6	C₉²×C₄₃	C₃²	1	1	yes	characteristic
7	C₄₃⋊C₂₇	—	9	3	no	—
8	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
10	C₂₇×C₄₃	—	3	2	no	—
11	C₂₇×C₄₃	C₂₇	1	3	yes	complemented
12	#10624462	—	43	1	no	maximal, Sylow
13	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
14	C₉×C₄₃	—	3	3	no	—
15	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₄₃	C₂₇⋊C₃	1	2	yes	—
17	C₉⋊C₂₇	—	43	3	no	—
18	#6864	C₄₃⋊C₃	1	1	yes	characteristic
19	C₃×C₄₃	C₉⋊C₂₇	1	1	yes	characteristic
20	C₃×C₄₃	#6875	1	3	yes	—
21	C₃×C₂₇	—	129	3	no	—
22	C₃×C₂₇	C₄₃⋊C₉	1	2	yes	—
23	C₃×C₂₇	C₄₃⋊C₉	1	1	yes	characteristic
24	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
25	C₄₃	#10624462	1	1	yes	characteristic, complemented, Sylow
26	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
27	C₃×C₉	#11923956	1	3	yes	—
28	C₂₇	—	3	2	no	—
29	C₂₇	—	387	3	no	—
30	C₂₇	C₄₃⋊C₂₇	1	3	yes	complemented
31	C₃²	#16812500	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	C₃×C₄₃⋊C₂₇	1	1	yes	characteristic
34	C₉	#16812505	1	2	yes	—
35	C₃	#23782734	1	1	yes	characteristic
36	C₃	#23782737	1	3	yes	—

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.