Subgroups — #23782756

Order 10449.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812515	C₃	1	1	yes	maximal, characteristic, complemented
2	#16812513	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812499	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#732	C₃	1	1	yes	maximal, characteristic, complemented
5	#11923958	—	3	1	no	—
6	C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
7	C₃×C₄₃⋊C₉	—	3	1	no	—
8	H(3,𝔽₃)×C₄₃	—	3	1	no	—
9	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
10	C₃²×C₄₃	—	9	1	no	—
11	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₄₃⋊C₃	—	9	1	no	—
13	C₉×C₄₃	—	3	1	no	—
14	C₄₃⋊C₉	—	9	1	no	—
15	C₄₃⋊C₉	—	9	1	no	—
16	#6881	—	43	1	no	maximal, Sylow
17	C₃×C₄₃	—	3	1	no	—
18	C₃×C₄₃	—	27	1	no	—
19	C₃×C₄₃	#732	1	1	yes	characteristic
20	C₄₃⋊C₃	—	27	1	no	—
21	#733	—	43	1	no	—
22	#732	—	43	1	no	—
23	#732	C₄₃⋊C₃	1	1	yes	characteristic, complemented
24	C₉⋊C₉	—	43	1	no	—
25	C₄₃	#6881	1	1	yes	characteristic, complemented, Sylow
26	3₋¹⁺²	—	129	1	no	—
27	H(3,𝔽₃)	—	3	1	no	—
28	H(3,𝔽₃)	—	129	1	no	—
29	C₃×C₉	—	129	1	no	—
30	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
31	C₃²	—	9	1	no	—
32	C₃²	—	387	1	no	—
33	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
34	C₉	—	3	1	no	—
35	C₉	—	387	1	no	—
36	C₉	—	387	1	no	—
37	C₃	—	3	1	no	—
38	C₃	—	27	1	no	—
39	C₃	—	1161	1	no	—
40	C₃	#16812512	1	1	yes	characteristic

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