Subgroups — C₃×#23779859 #44525147

Order 30861.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779859	C₃	1	27	yes	maximal, direct product factor
2	C₃×#16812184	C₃	1	8	yes	maximal, complemented
3	C₃²×#11765917	C₃	1	4	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₁₂₇	C₃	1	1	yes	maximal, characteristic
5	#16812184	C₃²	1	72	yes	complemented
6	C₃×#11765917	C₃²	1	1	yes	characteristic
7	C₃×#11765917	C₃²	1	8	yes	—
8	C₃×#11765917	C₃²	1	36	yes	complemented
9	C₃³×C₁₂₇	C₃²	1	4	yes	—
10	H(3,𝔽₃)×C₁₂₇	C₃²	1	9	yes	—
11	C₃²×C₁₂₇	—	3	12	no	—
12	C₃²×C₁₂₇	C₃³	1	12	yes	—
13	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
14	#11765917	C₃³	1	3	yes	—
15	#11765917	C₃³	1	24	yes	—
16	C₃×C₁₂₇	—	3	12	no	—
17	C₃×C₁₂₇	#737	1	3	yes	complemented
18	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
19	C₃×#737	—	127	1	no	maximal, Sylow
20	C₁₂₇	C₃×#737	1	1	yes	characteristic, complemented, Sylow
21	#737	—	127	27	no	—
22	C₃×3₋¹⁺²	—	127	8	no	—
23	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃	1	1	yes	characteristic
24	C₃²×C₉	—	127	4	no	—
25	C₃³	C₃×C₁₂₇⋊C₃	1	4	yes	—
26	3₋¹⁺²	—	127	72	no	—
27	H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	1	9	yes	—
28	C₃×C₉	—	127	36	no	—
29	C₃×C₉	—	127	1	no	—
30	C₃×C₉	—	127	8	no	—
31	C₃²	—	3	12	no	—
32	C₃²	C₃²×C₁₂₇⋊C₃	1	12	yes	—
33	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
34	C₉	—	127	3	no	—
35	C₉	—	127	24	no	—
36	C₃	—	3	12	no	—
37	C₃	#23779859	1	3	yes	direct product factor
38	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.