Subgroups — #44525154

Order 30861.

460 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779859	C₃	1	27	yes	maximal, complemented
2	C₃×#16812184	C₃	1	12	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812184	C₃²	1	9	yes	—
5	#16812184	C₃²	1	72	yes	complemented
6	C₃×#11765917	C₃²	1	36	yes	complemented
7	C₃³×C₁₂₇	C₃²	1	4	yes	—
8	H(3,𝔽₃)×C₁₂₇	C₃²	1	9	yes	—
9	C₃²×C₁₂₇	—	9	4	no	—
10	C₃²×C₁₂₇	C₃³	1	12	yes	—
11	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
12	#11765917	C₃³	1	27	yes	—
13	C₃×C₁₂₇	—	3	1	no	—
14	C₃×C₁₂₇	—	3	12	no	—
15	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
16	3₋¹⁺⁴	—	127	1	no	maximal, Sylow
17	C₁₂₇	3₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
18	#737	—	127	27	no	—
19	C₃×3₋¹⁺²	—	127	12	no	—
20	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃	1	1	yes	characteristic
21	C₃³	C₃×C₁₂₇⋊C₃	1	4	yes	—
22	3₋¹⁺²	—	127	9	no	—
23	3₋¹⁺²	—	127	72	no	—
24	H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	1	9	yes	—
25	C₃×C₉	—	127	36	no	—
26	C₃²	—	9	4	no	—
27	C₃²	C₃²×C₁₂₇⋊C₃	1	12	yes	—
28	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
29	C₉	—	127	27	no	—
30	C₃	—	3	1	no	—
31	C₃	—	3	12	no	—
32	C₃	C₃³×C₁₂₇⋊C₃	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.