Subgroups — #23782730

Order 10449.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812505	C₃	1	2	yes	maximal, complemented
2	C₃×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#737	C₃	1	1	yes	maximal, characteristic
4	C₄₃⋊C₂₇	—	3	1	no	—
5	C₄₃⋊C₂₇	—	3	2	no	—
6	3₋¹⁺²×C₄₃	—	3	2	no	—
7	3₋¹⁺²×C₄₃	C₉	1	2	yes	—
8	H(3,𝔽₃)×C₄₃	C₉	1	1	yes	characteristic
9	C₃×C₉×C₄₃	—	3	1	no	—
10	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₃²×C₄₃	—	3	1	no	—
12	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
13	C₉×C₄₃	—	3	2	no	—
14	C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉×C₄₃	3₋¹⁺²	1	2	yes	—
16	#6873	—	43	1	no	maximal, Sylow
17	C₃×C₄₃	—	3	1	no	—
18	C₃×C₄₃	—	9	1	no	—
19	C₃×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
20	#737	C₄₃⋊C₃	1	1	yes	characteristic
21	C₂₇⋊C₃	—	43	2	no	—
22	C₃×C₂₇	—	43	1	no	—
23	C₄₃	#6873	1	1	yes	characteristic, complemented, Sylow
24	3₋¹⁺²	—	3	2	no	—
25	3₋¹⁺²	C₄₃⋊C₉	1	2	yes	—
26	H(3,𝔽₃)	C₄₃⋊C₉	1	1	yes	characteristic
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
29	C₂₇	—	129	1	no	—
30	C₂₇	—	129	2	no	—
31	C₃²	—	3	1	no	—
32	C₃²	C₃×C₄₃⋊C₉	1	1	yes	characteristic
33	C₉	—	3	2	no	—
34	C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
35	C₉	#11923958	1	2	yes	—
36	C₃	—	3	1	no	—
37	C₃	—	9	1	no	—
38	C₃	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic

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