Subgroups — #44524996

Order 30861.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779850	C₃	1	1	yes	maximal, characteristic, complemented
2	#23779848	C₃	1	1	yes	maximal, characteristic
3	#23779834	C₃	1	1	yes	maximal, characteristic, complemented
4	#733×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	#16812184	—	3	1	no	—
6	C₃²⋊(C₁₂₇⋊C₃)	—	3	1	no	—
7	C₃×#11765917	—	3	1	no	—
8	3₋¹⁺²×C₁₂₇	—	3	1	no	—
9	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
10	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃×C₁₂₇⋊C₃	—	9	1	no	—
12	C₉×C₁₂₇	—	3	1	no	—
13	C₉×C₁₂₇	—	9	1	no	—
14	#11765917	—	9	1	no	—
15	#11765917	—	9	1	no	—
16	C₃×C₁₂₇	—	3	1	no	—
17	C₃×C₁₂₇	#732	1	1	yes	characteristic
18	C₁₂₇⋊C₃	—	27	1	no	—
19	#6883	—	127	1	no	maximal, Sylow
20	C₁₂₇	#6883	1	1	yes	characteristic, complemented, Sylow
21	#733	—	127	1	no	—
22	#733	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
23	#732	—	127	1	no	—
24	C₉⋊C₉	—	127	1	no	—
25	3₋¹⁺²	—	3	1	no	—
26	3₋¹⁺²	—	381	1	no	—
27	H(3,𝔽₃)	—	381	1	no	—
28	C₃×C₉	—	381	1	no	—
29	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
30	C₃²	—	1143	1	no	—
31	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
32	C₉	—	3	1	no	—
33	C₉	—	9	1	no	—
34	C₉	—	1143	1	no	—
35	C₉	—	1143	1	no	—
36	C₃	—	3	1	no	—
37	C₃	—	3429	1	no	—
38	C₃	#23779847	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.