Subgroups — #16864497⋊D₃ #39906752

Order 25956.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊#16864501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#16864505	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#16864497	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁×D₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
5	#16864497⋊C₂	—	3	1	no	maximal
6	C₃×#14524190	C₂²	1	1	yes	characteristic, complemented, Hall
7	#16864505	—	3	1	no	—
8	#16864501	—	3	1	no	—
9	#16864497	—	2	1	no	—
10	#16864497	D₃	1	1	yes	characteristic, complemented
11	D₂₁₆₃	C₂×C₃	1	1	yes	characteristic, complemented
12	D₂₁×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
14	D₃×D₁₀₃⋊C₃	—	7	1	no	maximal, Hall
15	D₇×D₁₀₃	—	3	1	no	Hall
16	C₃×C₇×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented
17	#14524190	—	2	1	no	—
18	#14524190	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊(D₁₀₃⋊C₃)	—	7	1	no	—
20	D₃×C₁₀₃⋊C₃	—	7	1	no	—
21	C₃×D₁₀₃⋊C₃	—	14	1	no	—
22	D₇₂₁	—	3	1	no	—
23	C₇×D₁₀₃	C₃×D₃	1	1	yes	characteristic, complemented
24	D₇×C₁₀₃	—	3	1	no	—
25	D₃×D₁₀₃	—	7	1	no	—
26	C₂×D₁₀₃⋊C₃	—	21	1	no	—
27	C₃×C₁₀₃⋊C₃	—	14	1	no	Hall
28	C₇×C₁₀₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	D₃₀₉	—	7	1	no	—
30	C₃×D₁₀₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
31	D₃×C₁₀₃	—	7	1	no	—
32	C₂×C₁₀₃⋊C₃	—	21	1	no	—
33	D₁₀₃⋊C₃	—	14	1	no	—
34	D₁₀₃⋊C₃	—	14	1	no	—
35	D₁₀₃⋊C₃	—	21	1	no	—
36	C₂×D₁₀₃	—	21	1	no	Hall
37	C₃×C₁₀₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
38	C₁₀₃⋊C₃	—	14	1	no	—
39	C₁₀₃⋊C₃	—	14	1	no	—
40	C₂×C₃⋊AGL(1,𝔽₇)	—	103	1	no	maximal, Hall
41	C₂×C₁₀₃	—	21	1	no	—
42	D₁₀₃	—	21	1	no	—
43	D₁₀₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
44	C₂×C₃×ΓL(1,𝔽₈)	—	103	1	no	—
45	C₃⋊AGL(1,𝔽₇)	—	103	1	no	—
46	C₃⋊AGL(1,𝔽₇)	—	206	1	no	—
47	C₁₀₃	C₂×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₂₁	—	103	1	no	—
49	C₂×AGL(1,𝔽₇)	—	309	1	no	—
50	C₃×ΓL(1,𝔽₈)	—	206	1	no	Hall
51	C₂×C₃×C₇	—	103	1	no	—
52	D₂₁	—	103	1	no	—
53	D₂₁	D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×ΓL(1,𝔽₈)	—	103	1	no	—
55	C₂×ΓL(1,𝔽₈)	—	206	1	no	—
56	AGL(1,𝔽₇)	—	309	1	no	—
57	AGL(1,𝔽₇)	—	618	1	no	—
58	C₂×C₃×D₃	—	721	1	no	Hall
59	C₂×D₇	—	309	1	no	Hall
60	C₃×C₇	C₂×D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
61	ΓL(1,𝔽₈)	—	412	1	no	—
62	ΓL(1,𝔽₈)	—	206	1	no	—
63	C₂×C₃²	—	1442	1	no	—
64	C₃×D₃	—	1442	1	no	—
65	C₃×D₃	—	721	1	no	—
66	C₂×C₇	—	103	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	309	1	no	—
69	C₂²×C₃	—	2163	1	no	—
70	C₂×D₃	—	721	1	no	—
71	C₃²	—	2884	1	no	Sylow
72	C₇	D₃×D₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	103	1	no	—
74	C₂×C₃	—	2163	1	no	—
75	C₂×C₃	—	1442	1	no	—
76	C₂×C₃	—	1442	1	no	—
77	C₂×C₃	—	4326	1	no	—
78	D₃	—	7	1	no	—
79	D₃	—	721	1	no	—
80	C₂²	—	2163	1	no	Sylow
81	C₃	—	2884	1	no	—
82	C₃	—	1442	1	no	—
83	C₃	#16864497⋊C₂	1	1	yes	characteristic, complemented
84	C₂	—	21	1	no	—
85	C₂	—	103	1	no	—
86	C₂	—	2163	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₀₃	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₀₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊#16864501	C₂	semidirect
2. C₃⋊#16864505	C₂	semidirect
3. C₃×#16864497	C₂	semidirect
4. D₂₁×D₁₀₃	C₃	semidirect
6. C₃×#14524190	C₂²	semidirect
10. #16864497	D₃	semidirect
11. D₂₁₆₃	C₂×C₃	semidirect
12. D₂₁×C₁₀₃	C₂×C₃	semidirect
13. C₃×C₇×D₁₀₃	C₂×C₃	semidirect
16. C₃×C₇×C₁₀₃	C₂²×C₃	semidirect
18. #14524190	C₂×D₃	semidirect
23. C₇×D₁₀₃	C₃×D₃	semidirect
28. C₇×C₁₀₃	C₂×C₃×D₃	semidirect
30. C₃×D₁₀₃	AGL(1,𝔽₇)	semidirect
37. C₃×C₁₀₃	C₂×AGL(1,𝔽₇)	semidirect
43. D₁₀₃	C₃⋊AGL(1,𝔽₇)	semidirect
47. C₁₀₃	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
53. D₂₁	D₁₀₃⋊C₃	semidirect
60. C₃×C₇	C₂×D₁₀₃⋊C₃	semidirect
72. C₇	D₃×D₁₀₃⋊C₃	semidirect
83. C₃	#16864497⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊#16864501	2
C₃⋊#16864505	2
C₃×#16864497	2
D₂₁×D₁₀₃	3
#16864497⋊C₂	3
D₃×D₁₀₃⋊C₃	7
C₂×C₃⋊AGL(1,𝔽₇)	103

Subgroups — #16864497⋊D3 #39906752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #16864497⋊D₃ #39906752