Subgroups — #23782758

Order 10449.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812513	C₃	1	2	yes	maximal, complemented
2	#16812500	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
5	C₃×C₄₃⋊C₉	—	3	1	no	—
6	3₋¹⁺²×C₄₃	—	3	1	no	—
7	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₄₃⋊C₃	—	9	2	no	—
10	C₉×C₄₃	—	3	1	no	—
11	C₉×C₄₃	—	9	1	no	—
12	C₄₃⋊C₉	—	9	1	no	—
13	#6881	—	43	1	no	maximal, Sylow
14	C₃×C₄₃	—	3	1	no	—
15	C₃×C₄₃	#732	1	1	yes	characteristic
16	C₄₃⋊C₃	—	27	2	no	—
17	#733	C₄₃⋊C₃	1	1	yes	characteristic, complemented
18	#732	—	43	2	no	—
19	C₉⋊C₉	—	43	1	no	—
20	C₄₃	#6881	1	1	yes	characteristic, complemented, Sylow
21	3₋¹⁺²	—	3	1	no	—
22	H(3,𝔽₃)	—	129	2	no	—
23	C₃×C₉	—	129	1	no	—
24	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
25	C₃²	—	387	2	no	—
26	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	387	1	no	—
30	C₃	—	3	1	no	—
31	C₃	—	1161	2	no	—
32	C₃	#16812512	1	1	yes	characteristic

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