Subgroups — #44524982

Order 30861.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779850	C₃	1	2	yes	maximal
2	C₉×#11765917	C₃	1	1	yes	maximal, characteristic
3	#733×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812184	—	3	2	no	—
5	C₃×#11765917	—	3	1	no	—
6	3₋¹⁺²×C₁₂₇	—	3	1	no	—
7	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
8	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₉×C₁₂₇	—	3	1	no	—
10	C₉×C₁₂₇	—	9	1	no	—
11	#11765917	—	3	3	no	—
12	#11765917	—	9	2	no	—
13	C₃×C₁₂₇	—	3	1	no	—
14	C₃×C₁₂₇	#732	1	1	yes	characteristic
15	#6880	—	127	1	no	maximal, Sylow
16	C₁₂₇	#6880	1	1	yes	characteristic, complemented, Sylow
17	#733	—	127	2	no	—
18	#733	C₁₂₇⋊C₃	1	1	yes	characteristic
19	C₉²	—	127	1	no	—
20	3₋¹⁺²	—	3	1	no	—
21	3₋¹⁺²	—	381	2	no	—
22	C₃×C₉	—	381	1	no	—
23	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
24	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	9	1	no	—
27	C₉	—	1143	2	no	—
28	C₉	—	381	3	no	—
29	C₃	—	3	1	no	—
30	C₃	#23779847	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
16. C₁₂₇	#6880	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.