Subgroups — C₃⋊#16838473 #26039677

Order 11466.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14274263	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₃₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#16838473	—	3	1	no	maximal
4	C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#14274263	—	2	1	no	—
6	#14274263	D₃	1	1	yes	characteristic, complemented
7	C₃⋊#10587716	—	7	8	no	maximal
8	C₇²×D₁₃	—	3	1	no	Hall
9	D₃×#3861	—	13	1	no	maximal, Hall
10	C₃×#63270	—	7	8	no	—
11	C₇²×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₇×D₃₉	ΓL(1,𝔽₈)	1	8	yes	complemented
13	#10587716	—	21	8	no	—
14	C₃×#3861	—	13	1	no	Hall
15	D₃×C₇²	—	13	1	no	—
16	C₂×#3861	—	39	1	no	—
17	C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
18	#63270	—	7	8	no	—
19	#63270	—	14	8	no	—
20	C₃⋊(D₁₃⋊C₃)	—	49	1	no	Hall
21	C₇×D₁₃	—	3	8	no	—
22	C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
23	#3861	—	13	1	no	—
24	#3861	—	26	1	no	—
25	D₃×ΓL(1,𝔽₈)	—	91	8	no	—
26	C₃×C₁₃⋊C₃	—	49	1	no	Hall
27	C₂×C₇²	—	39	1	no	Hall
28	C₇×C₁₃	D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
29	D₃₉	#3861	1	1	yes	characteristic, complemented
30	D₁₃⋊C₃	—	147	1	no	—
31	C₃×ΓL(1,𝔽₈)	—	91	8	no	—
32	C₇²	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	D₃×C₇	—	13	8	no	—
34	C₂×ΓL(1,𝔽₈)	—	273	8	no	—
35	C₃×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	49	1	no	—
37	C₁₃⋊C₃	—	98	1	no	—
38	D₁₃	—	3	1	no	Hall
39	C₃×C₇	#10587716	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	C₂×C₇	—	39	8	no	—
44	C₁₃	D₃×#3861	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	637	1	no	Sylow
46	C₇	C₃⋊#10587716	1	8	yes	complemented
47	C₂×C₃	—	1911	1	no	—
48	D₃	—	13	1	no	—
49	C₃	—	637	1	no	—
50	C₃	—	1274	1	no	—
51	C₃	#16838473	1	1	yes	characteristic, complemented
52	C₂	—	39	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×#14274263	C₂	semidirect
2. C₇²×D₃₉	C₃	semidirect
4. C₃×C₇²×C₁₃	C₂×C₃	semidirect
6. #14274263	D₃	semidirect
11. C₇²×C₁₃	C₃×D₃	semidirect
12. C₇×D₃₉	ΓL(1,𝔽₈)	semidirect
17. C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₃×C₇²	D₁₃⋊C₃	semidirect
28. C₇×C₁₃	D₃×ΓL(1,𝔽₈)	semidirect
29. D₃₉	#3861	semidirect
32. C₇²	C₃⋊(D₁₃⋊C₃)	semidirect
35. C₃×C₁₃	C₂×#3861	semidirect
39. C₃×C₇	#10587716	semidirect
44. C₁₃	D₃×#3861	semidirect
46. C₇	C₃⋊#10587716	semidirect
51. C₃	#16838473	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14274263	2
C₇²×D₃₉	3
#16838473	3
C₃⋊#10587716	7
D₃×#3861	13

Subgroups — C3⋊#16838473 #26039677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#16838473 #26039677