Subgroups — #44525077

Order 30861.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812182	C₃	1	4	yes	maximal
2	#23779835	C₃	1	8	yes	maximal, complemented
3	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
5	#16812182	—	3	12	no	—
6	C₃×#11765917	C₃²	1	8	yes	—
7	C₃×C₉×C₁₂₇	C₃²	1	4	yes	—
8	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
9	C₃×C₁₂₇⋊C₃	—	3	4	no	—
10	C₉×C₁₂₇	3₋¹⁺²	1	12	yes	complemented
11	#11765917	—	3	8	no	—
12	C₃×C₁₂₇	C₃×3₋¹⁺²	1	4	yes	—
13	C₁₂₇⋊C₃	—	9	1	no	—
14	#6900	—	127	1	no	maximal, Sylow
15	C₁₂₇	#6900	1	1	yes	characteristic, complemented, Sylow
16	C₃×3₋¹⁺²	—	127	4	no	—
17	C₉⋊C₉	—	127	8	no	—
18	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
19	C₃³	—	127	1	no	—
20	3₋¹⁺²	—	381	12	no	—
21	C₃×C₉	—	127	8	no	—
22	C₃×C₉	C₃×C₁₂₇⋊C₃	1	4	yes	—
23	C₃²	—	381	4	no	—
24	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
25	C₉	—	381	8	no	—
26	C₉	#16812182	1	12	yes	complemented
27	C₃	—	1143	1	no	—
28	C₃	C₃×#16812182	1	4	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.