Subgroups — C₁₅₁×#6872 #49144331

Order 36693.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#737×C₁₅₁	C₃	1	1	yes	maximal, characteristic
2	C₂₇⋊C₃×C₁₅₁	C₃	1	2	yes	maximal, complemented
3	C₃×C₂₇×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₁₅₁	—	3	2	no	—
5	3₋¹⁺²×C₁₅₁	C₉	1	2	yes	—
6	H(3,𝔽₃)×C₁₅₁	C₉	1	1	yes	characteristic
7	C₃×C₉×C₁₅₁	—	3	1	no	—
8	C₃×C₉×C₁₅₁	C₃²	1	1	yes	characteristic
9	C₂₇×C₁₅₁	—	3	1	no	—
10	C₂₇×C₁₅₁	—	3	2	no	—
11	C₃²×C₁₅₁	—	3	1	no	—
12	C₃²×C₁₅₁	C₃×C₉	1	1	yes	characteristic
13	C₉×C₁₅₁	—	3	2	no	—
14	C₉×C₁₅₁	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉×C₁₅₁	3₋¹⁺²	1	2	yes	—
16	C₃×C₁₅₁	—	3	1	no	—
17	C₃×C₁₅₁	—	9	1	no	—
18	C₃×C₁₅₁	C₃²⋊C₉	1	1	yes	characteristic
19	#6872	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₁₅₁	#6872	1	1	yes	characteristic, direct product factor, Sylow
21	#737	C₃×C₁₅₁	1	1	yes	characteristic
22	C₂₇⋊C₃	C₃×C₁₅₁	1	2	yes	complemented
23	C₃×C₂₇	C₃×C₁₅₁	1	1	yes	characteristic, complemented
24	3₋¹⁺²	—	3	2	no	—
25	3₋¹⁺²	C₉×C₁₅₁	1	2	yes	—
26	H(3,𝔽₃)	C₉×C₁₅₁	1	1	yes	characteristic
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	C₃²×C₁₅₁	1	1	yes	characteristic
29	C₂₇	—	3	1	no	—
30	C₂₇	—	3	2	no	—
31	C₃²	—	3	1	no	—
32	C₃²	C₃×C₉×C₁₅₁	1	1	yes	characteristic
33	C₉	—	3	2	no	—
34	C₉	H(3,𝔽₃)×C₁₅₁	1	1	yes	characteristic
35	C₉	3₋¹⁺²×C₁₅₁	1	2	yes	—
36	C₃	—	3	1	no	—
37	C₃	—	9	1	no	—
38	C₃	C₃²⋊C₉×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₁₅₁	H(3,𝔽₃)
commutator	C₃²	C₃×C₉×C₁₅₁
Frattini, cosocle	C₃×C₉	C₃²×C₁₅₁
socle	C₃×C₁₅₁	C₃²⋊C₉
prime radical	H(3,𝔽₃)×C₁₅₁	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₅₁ ◁ C₃×C₉×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₇⋊C₃×C₁₅₁	C₃	semidirect
3. C₃×C₂₇×C₁₅₁	C₃	semidirect
19. #6872	C₁₅₁	direct (N × H)
20. C₁₅₁	#6872	direct (N × H)
22. C₂₇⋊C₃	C₃×C₁₅₁	semidirect
23. C₃×C₂₇	C₃×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#737×C₁₅₁	3
C₂₇⋊C₃×C₁₅₁	3
C₃×C₂₇×C₁₅₁	3
#6872	151

Subgroups — C151×#6872 #49144331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#6872 #49144331