Subgroups — #23782733

Order 10449.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃⋊C₂₇	C₃	1	3	yes	maximal
2	C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₄₃⋊C₂₇	—	3	3	no	—
4	C₃×C₉×C₄₃	C₉	1	2	yes	—
5	C₃×C₉×C₄₃	C₉	1	1	yes	characteristic
6	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
7	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
8	C₉×C₄₃	—	3	2	no	—
9	C₉×C₄₃	C₂₇	1	3	yes	complemented
10	C₉×C₄₃	3₋¹⁺²	1	3	yes	—
11	C₉⋊C₂₇	—	43	1	no	maximal, Sylow
12	C₃×C₄₃	C₉⋊C₉	1	1	yes	characteristic
13	C₃×C₄₃	C₃×C₂₇	1	1	yes	characteristic
14	C₃×C₄₃	C₂₇⋊C₃	1	2	yes	—
15	C₃×C₂₇	—	43	3	no	—
16	C₉²	C₄₃⋊C₃	1	1	yes	characteristic
17	C₄₃	C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₉	C₄₃⋊C₉	1	2	yes	—
19	C₃×C₉	C₄₃⋊C₉	1	1	yes	characteristic
20	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
21	C₂₇	—	129	3	no	—
22	C₃²	C₃×C₄₃⋊C₉	1	1	yes	characteristic
23	C₉	—	3	2	no	—
24	C₉	C₄₃⋊C₂₇	1	3	yes	complemented
25	C₉	#11923957	1	3	yes	—
26	C₃	#16812499	1	1	yes	characteristic
27	C₃	C₃×C₄₃⋊C₂₇	1	1	yes	characteristic
28	C₃	#16812505	1	2	yes	—

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