Subgroups — C₃⋊#16838449 #26039652

Order 11466.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14274262	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₃⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented
3	#16838449	—	3	1	no	maximal
4	C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#14274262	—	2	1	no	—
6	#14274262	D₃	1	1	yes	characteristic, complemented
7	C₃⋊#10587721	—	7	8	no	maximal
8	C₁₃×C₇⋊D₇	—	3	1	no	Hall
9	C₃⋊#64424	—	13	1	no	maximal, Hall
10	C₃×#63271	—	7	8	no	—
11	C₇²×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×D₂₁	—	7	8	no	—
13	#10587721	—	21	8	no	—
14	C₃×#3861	—	13	1	no	Hall
15	C₃⋊(C₇⋊D₇)	C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	#64424	—	39	1	no	—
17	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	8	yes	complemented
18	#63271	—	7	8	no	—
19	#63271	—	14	8	no	—
20	D₃×C₁₃⋊C₃	—	49	1	no	Hall
21	C₁₃×D₇	—	21	8	no	—
22	C₃×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
23	#3861	—	13	1	no	—
24	#3861	—	26	1	no	—
25	C₃⋊AGL(1,𝔽₇)	—	91	8	no	—
26	C₃×C₁₃⋊C₃	—	49	1	no	Hall
27	C₇⋊D₇	—	3	1	no	Hall
28	C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	1	8	yes	complemented
29	D₃×C₁₃	—	49	1	no	—
30	C₂×C₁₃⋊C₃	—	147	1	no	—
31	C₃×ΓL(1,𝔽₈)	—	91	8	no	—
32	C₇²	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	D₂₁	—	7	8	no	—
34	AGL(1,𝔽₇)	—	273	8	no	—
35	C₃×C₁₃	#64424	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	49	1	no	—
37	C₁₃⋊C₃	—	98	1	no	—
38	C₂×C₁₃	—	147	1	no	Hall
39	C₃×C₇	#10587721	1	8	yes	complemented
40	ΓL(1,𝔽₈)	—	91	8	no	—
41	ΓL(1,𝔽₈)	—	182	8	no	—
42	C₃×D₃	—	637	1	no	Hall
43	D₇	—	21	8	no	—
44	C₁₃	C₃⋊#64424	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	637	1	no	Sylow
46	C₇	C₃⋊#10587721	1	8	yes	complemented
47	C₂×C₃	—	1911	1	no	—
48	D₃	—	49	1	no	—
49	C₃	—	637	1	no	—
50	C₃	—	1274	1	no	—
51	C₃	#16838449	1	1	yes	characteristic, complemented
52	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#14274262	C₂	semidirect
2. C₁₃×C₃⋊(C₇⋊D₇)	C₃	semidirect
4. C₃×C₇²×C₁₃	C₂×C₃	semidirect
6. #14274262	D₃	semidirect
11. C₇²×C₁₃	C₃×D₃	semidirect
15. C₃⋊(C₇⋊D₇)	C₁₃⋊C₃	semidirect
17. C₃×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
22. C₃×C₇²	C₂×C₁₃⋊C₃	semidirect
28. C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	semidirect
32. C₇²	D₃×C₁₃⋊C₃	semidirect
35. C₃×C₁₃	#64424	semidirect
39. C₃×C₇	#10587721	semidirect
44. C₁₃	C₃⋊#64424	semidirect
46. C₇	C₃⋊#10587721	semidirect
51. C₃	#16838449	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14274262	2
C₁₃×C₃⋊(C₇⋊D₇)	3
#16838449	3
C₃⋊#10587721	7
C₃⋊#64424	13

Subgroups — C3⋊#16838449 #26039652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#16838449 #26039652