Subgroups — C₃²×#16812184 #44525145

Order 30861.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	36	yes	maximal, direct product factor
2	C₃²×#11765917	C₃	1	3	yes	maximal, complemented
3	C₃⁴×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812184	C₃²	1	81	yes	direct product factor
5	C₃×#11765917	C₃²	1	36	yes	complemented
6	C₃³×C₁₂₇	—	3	9	no	—
7	C₃³×C₁₂₇	C₃²	1	12	yes	—
8	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
9	C₃²×C₁₂₇	—	3	36	no	—
10	C₃²×C₁₂₇	3₋¹⁺²	1	9	yes	complemented
11	C₃²×C₁₂₇	C₃³	1	9	yes	—
12	C₃²×C₁₂₇	C₃³	1	4	yes	—
13	#11765917	C₃³	1	27	yes	complemented
14	C₃×C₁₂₇	—	3	9	no	—
15	C₃×C₁₂₇	C₃×3₋¹⁺²	1	12	yes	complemented
16	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
17	C₃²×3₋¹⁺²	—	127	1	no	maximal, Sylow
18	C₁₂₇	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
19	C₃⁴	C₁₂₇⋊C₃	1	1	yes	characteristic
20	C₃×3₋¹⁺²	—	127	36	no	—
21	C₃²×C₉	—	127	3	no	—
22	C₃³	—	3	9	no	—
23	C₃³	C₃×C₁₂₇⋊C₃	1	12	yes	—
24	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
25	3₋¹⁺²	—	127	81	no	—
26	C₃×C₉	—	127	36	no	—
27	C₃²	—	3	36	no	—
28	C₃²	#16812184	1	9	yes	direct product factor
29	C₃²	C₃²×C₁₂₇⋊C₃	1	9	yes	—
30	C₃²	C₃²×C₁₂₇⋊C₃	1	4	yes	—
31	C₉	—	127	27	no	—
32	C₃	—	3	9	no	—
33	C₃	C₃×#16812184	1	12	yes	direct product factor
34	C₃	C₃³×C₁₂₇⋊C₃	1	1	yes	characteristic

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.