Subgroups — #44525024

Order 30861.

378 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	1	12	yes	maximal, complemented
2	C₃⁴×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₂₇⋊C₃	C₃²	1	9	yes	complemented
4	C₃²⋊(C₁₂₇⋊C₃)	—	3	36	no	—
5	C₃³×C₁₂₇	—	3	12	no	—
6	C₃³×C₁₂₇	C₃²	1	4	yes	—
7	C₃²×C₁₂₇	—	3	27	no	—
8	C₃²×C₁₂₇	—	3	12	no	—
9	C₃²×C₁₂₇	H(3,𝔽₃)	1	12	yes	complemented
10	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
11	C₃×C₁₂₇⋊C₃	—	3	36	no	—
12	C₃×C₁₂₇	—	3	12	no	—
13	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	4	yes	—
14	C₁₂₇⋊C₃	—	9	9	no	—
15	C₃²⋊H(3,𝔽₃)	—	127	1	no	maximal, Sylow
16	C₁₂₇	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
17	C₃⁴	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
18	C₃×H(3,𝔽₃)	—	127	12	no	—
19	C₃³	—	3	12	no	—
20	C₃³	—	127	9	no	—
21	C₃³	C₃×C₁₂₇⋊C₃	1	4	yes	—
22	H(3,𝔽₃)	—	381	36	no	—
23	C₃²	—	3	27	no	—
24	C₃²	—	3	12	no	—
25	C₃²	—	381	36	no	—
26	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	12	yes	complemented
27	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
28	C₃	—	3	12	no	—
29	C₃	—	1143	9	no	—
30	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)	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.