Subgroups — H(3,𝔽₃)×C₄₃⋊C₉ #23782785

Order 10449.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₉	C₃	1	4	yes	maximal, complemented
2	C₃²⋊(C₄₃⋊C₉)	C₃	1	8	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₉	—	3	12	no	—
5	C₃×C₄₃⋊C₉	C₃²	1	8	yes	—
6	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
7	C₃³×C₄₃	C₃²	1	4	yes	—
8	H(3,𝔽₃)×C₄₃	C₉	1	9	yes	complemented
9	C₃²×C₄₃	—	3	4	no	—
10	C₃²×C₄₃	—	3	8	no	—
11	C₃²×C₄₃	C₃×C₉	1	12	yes	complemented
12	C₃²×C₄₃	C₃³	1	1	yes	characteristic
13	C₄₃⋊C₉	—	3	8	no	—
14	C₄₃⋊C₉	H(3,𝔽₃)	1	3	yes	direct product factor
15	C₉×H(3,𝔽₃)	—	43	1	no	maximal, Sylow
16	C₃×C₄₃	—	3	12	no	—
17	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
18	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₄₃	#737	1	2	yes	—
20	C₃×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic
21	C₃²×C₉	—	43	4	no	—
22	C₃²⋊C₉	—	43	8	no	—
23	C₄₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
24	C₃³	C₃×C₄₃⋊C₃	1	4	yes	—
25	H(3,𝔽₃)	C₄₃⋊C₉	1	9	yes	direct product factor
26	C₃×C₉	—	43	1	no	—
27	C₃×C₉	—	43	8	no	—
28	C₃×C₉	—	129	12	no	—
29	C₃²	—	3	4	no	—
30	C₃²	—	3	8	no	—
31	C₃²	C₃×C₄₃⋊C₉	1	12	yes	complemented
32	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
33	C₉	—	43	3	no	—
34	C₉	—	129	8	no	—
35	C₃	—	3	12	no	—
36	C₃	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
37	C₃	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
38	C₃	#16812524	1	2	yes	—

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