Subgroups — #44524985

Order 30861.

42 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, complemented
3	#23779835	C₃	1	1	yes	maximal, characteristic, complemented
4	#732×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	H(3,𝔽₃)×C₁₂₇	—	3	1	no	—
9	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
10	C₃²×C₁₂₇	—	9	1	no	—
11	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₁₂₇⋊C₃	—	9	1	no	—
13	C₉×C₁₂₇	—	3	1	no	—
14	#11765917	—	9	1	no	—
15	#11765917	—	9	1	no	—
16	C₃×C₁₂₇	—	3	1	no	—
17	C₃×C₁₂₇	—	27	1	no	—
18	C₃×C₁₂₇	#732	1	1	yes	characteristic
19	C₁₂₇⋊C₃	—	27	1	no	—
20	#6881	—	127	1	no	maximal, Sylow
21	C₁₂₇	#6881	1	1	yes	characteristic, complemented, Sylow
22	#733	—	127	1	no	—
23	#732	—	127	1	no	—
24	#732	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
25	C₉⋊C₉	—	127	1	no	—
26	3₋¹⁺²	—	381	1	no	—
27	H(3,𝔽₃)	—	3	1	no	—
28	H(3,𝔽₃)	—	381	1	no	—
29	C₃×C₉	—	381	1	no	—
30	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
31	C₃²	—	9	1	no	—
32	C₃²	—	1143	1	no	—
33	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
34	C₉	—	3	1	no	—
35	C₉	—	1143	1	no	—
36	C₉	—	1143	1	no	—
37	C₃	—	3	1	no	—
38	C₃	—	27	1	no	—
39	C₃	—	3429	1	no	—
40	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.