Subgroups — #44525166

Order 30861.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#11765919	C₃	1	3	yes	maximal
2	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃×#11765919	—	3	3	no	—
4	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×#11765917	C₉	1	2	yes	complemented
6	C₉×C₁₂₇⋊C₃	—	3	1	no	—
7	C₉×C₁₂₇⋊C₃	—	3	2	no	—
8	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic, complemented
9	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
10	C₃×C₁₂₇⋊C₃	—	3	3	no	—
11	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₁₂₇⋊C₃	3₋¹⁺²	1	2	yes	—
13	#11765919	—	9	3	no	—
14	C₉×C₁₂₇	—	3	1	no	—
15	#11765917	—	3	2	no	—
16	C₃×C₁₂₇	—	3	1	no	—
17	C₃×C₁₂₇	C₃²⋊C₉	1	1	yes	characteristic
18	C₁₂₇⋊C₃	—	3	2	no	—
19	C₁₂₇⋊C₃	#731	1	3	yes	—
20	#6867	—	127	1	no	maximal, Sylow
21	C₁₂₇	#6867	1	1	yes	characteristic, complemented, Sylow
22	C₃²×C₉	—	127	1	no	—
23	C₃²⋊C₉	—	127	3	no	—
24	C₃³	—	127	1	no	—
25	C₃×C₉	—	381	2	no	—
26	C₃×C₉	—	381	1	no	—
27	C₃×C₉	—	381	3	no	—
28	C₃×C₉	—	127	2	no	—
29	C₃×C₉	#11765919	1	1	yes	characteristic, complemented
30	C₃²	—	381	3	no	—
31	C₃²	—	127	2	no	—
32	C₃²	—	127	1	no	—
33	C₃²	C₃×#11765919	1	1	yes	characteristic
34	C₉	—	3	1	no	—
35	C₉	—	1143	3	no	—
36	C₉	—	381	2	no	—
37	C₃	—	3	1	no	—
38	C₃	—	381	2	no	—
39	C₃	—	127	3	no	—
40	C₃	C₃²⋊#11765919	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.