Subgroups — #44525167

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	1	no	—
11	C₃×C₁₂₇⋊C₃	—	3	2	no	—
12	C₃×C₁₂₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₁₂₇⋊C₃	3₋¹⁺²	1	2	yes	—
14	#11765919	—	9	3	no	—
15	C₉×C₁₂₇	—	3	1	no	—
16	#11765917	—	3	2	no	—
17	C₃×C₁₂₇	—	3	1	no	—
18	C₃×C₁₂₇	C₃²⋊C₉	1	1	yes	characteristic
19	C₁₂₇⋊C₃	—	3	2	no	—
20	C₁₂₇⋊C₃	#732	1	1	yes	characteristic
21	C₁₂₇⋊C₃	#733	1	2	yes	—
22	#6868	—	127	1	no	maximal, Sylow
23	C₁₂₇	#6868	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₉	—	127	1	no	—
25	C₃²⋊C₉	—	127	3	no	—
26	C₃³	—	127	1	no	—
27	C₃×C₉	—	381	2	no	—
28	C₃×C₉	—	381	1	no	—
29	C₃×C₉	—	381	3	no	—
30	C₃×C₉	—	127	2	no	—
31	C₃×C₉	#11765919	1	1	yes	characteristic, complemented
32	C₃²	—	381	1	no	—
33	C₃²	—	381	2	no	—
34	C₃²	—	127	2	no	—
35	C₃²	—	127	1	no	—
36	C₃²	C₃×#11765919	1	1	yes	characteristic
37	C₉	—	3	1	no	—
38	C₉	—	1143	3	no	—
39	C₉	—	381	2	no	—
40	C₃	—	3	1	no	—
41	C₃	—	381	2	no	—
42	C₃	—	127	1	no	—
43	C₃	—	127	2	no	—
44	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.