Subgroups — #23782750

Order 10449.

48 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	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#732	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
5	C₃×C₄₃⋊C₉	—	3	1	no	—
6	H(3,𝔽₃)×C₄₃	—	3	1	no	—
7	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₃²×C₄₃	—	9	1	no	—
9	C₃²×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₄₃⋊C₃	—	9	2	no	—
11	C₉×C₄₃	—	3	1	no	—
12	C₄₃⋊C₉	—	3	3	no	—
13	#6879	—	43	1	no	maximal, Sylow
14	C₃×C₄₃	—	3	1	no	—
15	C₃×C₄₃	—	27	1	no	—
16	C₃×C₄₃	#732	1	1	yes	characteristic
17	C₄₃⋊C₃	—	27	2	no	—
18	#732	—	43	2	no	—
19	#732	C₄₃⋊C₃	1	1	yes	characteristic, complemented
20	C₉²	—	43	1	no	—
21	C₄₃	#6879	1	1	yes	characteristic, complemented, Sylow
22	H(3,𝔽₃)	—	3	1	no	—
23	H(3,𝔽₃)	—	129	2	no	—
24	C₃×C₉	—	129	1	no	—
25	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
26	C₃²	—	9	1	no	—
27	C₃²	—	387	2	no	—
28	C₃²	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
29	C₉	—	3	1	no	—
30	C₉	—	129	3	no	—
31	C₃	—	3	1	no	—
32	C₃	—	27	1	no	—
33	C₃	—	1161	2	no	—
34	C₃	#16812512	1	1	yes	characteristic

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