Subgroups — #44525061

Order 30861.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779833	C₃	1	8	yes	maximal, complemented
2	#23779831	C₃	1	4	yes	maximal
3	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×#11765917	C₃²	1	8	yes	—
6	C₃×C₉×C₁₂₇	C₃²	1	4	yes	—
7	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
8	C₃×C₁₂₇⋊C₃	—	3	4	no	—
9	C₉×C₁₂₇	—	3	4	no	—
10	#11765917	—	3	8	no	—
11	C₃×C₁₂₇	#737	1	4	yes	—
12	C₁₂₇⋊C₃	—	9	1	no	—
13	#6897	—	127	1	no	maximal, Sylow
14	C₁₂₇	#6897	1	1	yes	characteristic, complemented, Sylow
15	C₉⋊C₉	—	127	8	no	—
16	C₃²⋊C₉	—	127	4	no	—
17	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
18	C₃³	—	127	1	no	—
19	C₃×C₉	—	127	8	no	—
20	C₃×C₉	C₃×C₁₂₇⋊C₃	1	4	yes	—
21	C₃²	—	381	4	no	—
22	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
23	C₉	—	3	4	no	—
24	C₉	—	381	8	no	—
25	C₃	—	1143	1	no	—
26	C₃	#23779860	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.