Subgroups — C₃⋊#16838420 #26039413

Order 11466.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14274255	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉₁₁	C₃	1	1	yes	maximal, characteristic, complemented
3	#16838420	—	3	1	no	maximal
4	C₃×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented
5	#14274255	—	2	1	no	—
6	#14274255	D₃	1	1	yes	characteristic, complemented
7	C₃⋊#10587723	—	7	1	no	maximal
8	D₆₃₇	—	3	1	no	Hall
9	C₃⋊(D₄₉⋊C₃)	—	13	1	no	maximal, Hall
10	C₃×#63271	—	7	1	no	—
11	C₁₃×C₄₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	D₂₇₃	—	7	1	no	—
13	#10587723	—	21	1	no	—
14	C₃×C₄₉⋊C₃	—	13	1	no	Hall
15	D₁₄₇	—	13	1	no	—
16	D₄₉⋊C₃	—	39	1	no	—
17	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
18	#63271	—	7	1	no	—
19	#63271	—	14	1	no	—
20	C₃⋊(D₁₃⋊C₃)	—	49	1	no	Hall
21	D₉₁	—	21	1	no	—
22	C₃×C₄₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₄₉⋊C₃	—	13	1	no	—
24	C₄₉⋊C₃	—	26	1	no	—
25	C₃⋊AGL(1,𝔽₇)	—	91	1	no	—
26	C₃×C₁₃⋊C₃	—	49	1	no	Hall
27	D₄₉	—	39	1	no	Hall
28	C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
29	D₃₉	—	49	1	no	—
30	D₁₃⋊C₃	—	147	1	no	—
31	C₃×ΓL(1,𝔽₈)	—	91	1	no	—
32	C₄₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	D₂₁	—	91	1	no	—
34	AGL(1,𝔽₇)	—	273	1	no	—
35	C₃×C₁₃	D₄₉⋊C₃	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	49	1	no	—
37	C₁₃⋊C₃	—	98	1	no	—
38	D₁₃	—	147	1	no	Hall
39	C₃×C₇	#10587723	1	1	yes	characteristic
40	ΓL(1,𝔽₈)	—	91	1	no	—
41	ΓL(1,𝔽₈)	—	182	1	no	—
42	C₃×D₃	—	637	1	no	Hall
43	D₇	—	273	1	no	—
44	C₁₃	C₃⋊(D₄₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	637	1	no	Sylow
46	C₇	C₃⋊#10587723	1	1	yes	characteristic
47	C₂×C₃	—	1911	1	no	—
48	D₃	—	637	1	no	—
49	C₃	—	637	1	no	—
50	C₃	—	1274	1	no	—
51	C₃	#16838420	1	1	yes	characteristic, complemented
52	C₂	—	1911	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₁₃×C₄₉	C₂×C₃
Frattini	C₇	C₃⋊#10587723
socle	C₃×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₃×C₁₃×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#14274255	C₂	semidirect
2. D₁₉₁₁	C₃	semidirect
4. C₃×C₁₃×C₄₉	C₂×C₃	semidirect
6. #14274255	D₃	semidirect
11. C₁₃×C₄₉	C₃×D₃	semidirect
22. C₃×C₄₉	D₁₃⋊C₃	semidirect
32. C₄₉	C₃⋊(D₁₃⋊C₃)	semidirect
35. C₃×C₁₃	D₄₉⋊C₃	semidirect
44. C₁₃	C₃⋊(D₄₉⋊C₃)	semidirect
51. C₃	#16838420	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14274255	2
D₁₉₁₁	3
#16838420	3
C₃⋊#10587723	7
C₃⋊(D₄₉⋊C₃)	13

Subgroups — C3⋊#16838420 #26039413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#16838420 #26039413