Subgroups — C₄₃×#10624462 #44531399

Order 31347.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₉⋊C₂₇	C₃	1	3	yes	maximal
2	C₄₃×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₇×C₄₃	—	3	3	no	—
4	C₃×C₂₇×C₄₃	C₉	1	2	yes	—
5	C₃×C₂₇×C₄₃	C₉	1	1	yes	characteristic
6	C₉²×C₄₃	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
8	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
9	C₂₇×C₄₃	—	3	2	no	—
10	C₂₇×C₄₃	—	9	3	no	—
11	C₂₇×C₄₃	C₂₇	1	3	yes	complemented
12	#10624462	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
14	C₉×C₄₃	—	3	3	no	—
15	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₄₃	C₂₇⋊C₃	1	2	yes	—
17	C₉⋊C₂₇	C₃×C₄₃	1	3	yes	—
18	#6864	C₃×C₄₃	1	1	yes	characteristic
19	C₃×C₄₃	C₉⋊C₂₇	1	1	yes	characteristic
20	C₃×C₄₃	#6875	1	3	yes	—
21	C₃×C₂₇	—	3	3	no	—
22	C₃×C₂₇	C₉×C₄₃	1	2	yes	—
23	C₃×C₂₇	C₉×C₄₃	1	1	yes	characteristic
24	C₉²	C₃²×C₄₃	1	1	yes	characteristic
25	C₄₃	#10624462	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₉	C₃×C₉×C₄₃	1	1	yes	characteristic
27	C₃×C₉	3₋¹⁺²×C₄₃	1	3	yes	—
28	C₂₇	—	3	2	no	—
29	C₂₇	—	9	3	no	—
30	C₂₇	C₂₇×C₄₃	1	3	yes	complemented
31	C₃²	C₄₃×C₉⋊C₉	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	C₃×C₂₇×C₄₃	1	1	yes	characteristic
34	C₉	C₄₃×C₂₇⋊C₃	1	2	yes	—
35	C₃	C₄₃×C₉⋊C₂₇	1	1	yes	characteristic
36	C₃	C₄₃×#6875	1	3	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.