Subgroups — #44524948

Order 30861.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779840	C₃	1	3	yes	maximal, complemented
2	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	#16812178	—	3	3	no	—
4	C₃³×C₁₂₇	C₉	1	1	yes	characteristic
5	C₃×C₉×C₁₂₇	—	3	1	no	—
6	C₃×C₉×C₁₂₇	—	3	2	no	—
7	C₃×C₉×C₁₂₇	C₉	1	2	yes	—
8	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
9	C₃²×C₁₂₇	—	3	3	no	—
10	C₃²×C₁₂₇	—	3	1	no	—
11	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
12	C₉×C₁₂₇	—	3	2	no	—
13	C₉×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
14	C₉×C₁₂₇	3₋¹⁺²	1	2	yes	—
15	C₃×C₁₂₇	—	3	3	no	—
16	C₃×C₁₂₇	—	3	1	no	—
17	C₃×C₁₂₇	C₃²⋊C₉	1	1	yes	characteristic
18	#6869	—	127	1	no	maximal, Sylow
19	C₁₂₇	#6869	1	1	yes	characteristic, complemented, Sylow
20	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
21	C₂₇⋊C₃	—	127	3	no	—
22	C₃³	#11765917	1	1	yes	characteristic
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	—	3	2	no	—
25	C₃×C₉	#11765917	1	2	yes	—
26	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
27	C₂₇	—	381	3	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	3	1	no	—
30	C₃²	C₃×#11765917	1	1	yes	characteristic
31	C₉	—	3	2	no	—
32	C₉	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
33	C₉	#16812184	1	2	yes	—
34	C₃	—	3	1	no	—
35	C₃	—	3	3	no	—
36	C₃	C₃²⋊#11765917	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #23779840	C₃	semidirect
19. C₁₂₇	#6869	semidirect

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