Subgroups — C₂×C₃⋊#16864498 #39906804

Order 25956.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14524189	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#16864498	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₃₀₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864498	—	3	1	no	maximal
5	C₃×#14524189	C₂²	1	1	yes	characteristic, complemented, Hall
6	#16864498	—	3	2	no	—
7	C₇×D₃₀₉	C₂×C₃	1	2	yes	complemented
8	C₂×#14524189	—	2	1	no	—
9	C₂×#14524189	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃⋊(D₁₀₃⋊C₃)	—	7	1	no	maximal, Hall
12	C₂×C₇×D₁₀₃	—	3	1	no	Hall
13	C₃×C₇×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented
14	#14524189	—	2	1	no	—
15	#14524189	C₂×D₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₀₃⋊C₃	—	7	1	no	—
17	C₃⋊(D₁₀₃⋊C₃)	—	7	2	no	—
18	C₂×C₇×C₁₀₃	C₃×D₃	1	1	yes	characteristic, complemented
19	C₇×D₁₀₃	—	3	2	no	—
20	C₂×D₃₀₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₂×D₁₀₃⋊C₃	—	21	1	no	—
22	C₃×C₁₀₃⋊C₃	—	7	1	no	Hall
23	C₇×C₁₀₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₀₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
25	D₃₀₉	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
26	C₂×C₁₀₃⋊C₃	—	7	1	no	—
27	C₂×C₁₀₃⋊C₃	—	14	1	no	—
28	D₁₀₃⋊C₃	—	21	2	no	—
29	C₂×D₁₀₃	—	3	1	no	Hall
30	C₃×C₁₀₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
31	C₁₀₃⋊C₃	—	7	1	no	—
32	C₁₀₃⋊C₃	—	14	1	no	—
33	C₂×D₃×ΓL(1,𝔽₈)	—	103	1	no	maximal, Hall
34	C₂×C₁₀₃	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
35	D₁₀₃	—	3	2	no	—
36	C₂×C₃×ΓL(1,𝔽₈)	—	206	1	no	—
37	D₃×ΓL(1,𝔽₈)	—	103	2	no	—
38	C₁₀₃	C₂×D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃×C₇	—	103	1	no	—
40	C₂²×ΓL(1,𝔽₈)	—	309	1	no	—
41	C₃×ΓL(1,𝔽₈)	—	206	1	no	Hall
42	C₂×C₃×C₇	D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
43	D₃×C₇	—	103	2	no	—
44	C₂×ΓL(1,𝔽₈)	—	309	2	no	—
45	C₂×ΓL(1,𝔽₈)	—	206	1	no	—
46	C₂×ΓL(1,𝔽₈)	—	206	1	no	—
47	C₂×C₃×D₃	—	721	1	no	Hall
48	C₂²×C₇	—	309	1	no	Hall
49	C₃×C₇	C₂×D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
50	ΓL(1,𝔽₈)	—	206	1	no	—
51	ΓL(1,𝔽₈)	—	206	1	no	—
52	C₂×C₃²	—	1442	1	no	—
53	C₃×D₃	—	721	2	no	—
54	C₂×C₇	—	309	2	no	—
55	C₂×C₇	C₃⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic, complemented
56	C₂²×C₃	—	2163	1	no	—
57	C₂×D₃	—	103	1	no	—
58	C₃²	—	1442	1	no	Sylow
59	C₇	C₂×C₃⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2163	2	no	—
61	C₂×C₃	—	1442	1	no	—
62	C₂×C₃	—	1442	1	no	—
63	C₂×C₃	#16864498	1	1	yes	characteristic, complemented
64	D₃	—	103	2	no	—
65	C₂²	—	309	1	no	Sylow
66	C₃	—	1442	1	no	—
67	C₃	—	1442	1	no	—
68	C₃	C₂×#16864498	1	1	yes	characteristic, complemented
69	C₂	—	309	2	no	—
70	C₂	C₃⋊#16864498	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#16864498
commutator, cosocle, hypocenter	C₃×C₇×C₁₀₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₀₃	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₀₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#14524189	C₂	semidirect
2. C₃⋊#16864498	C₂	direct (N × H)
3. C₂×C₇×D₃₀₉	C₃	semidirect
5. C₃×#14524189	C₂²	semidirect
7. C₇×D₃₀₉	C₂×C₃	semidirect
9. C₂×#14524189	D₃	semidirect
10. C₂×C₃×C₇×C₁₀₃	C₂×C₃	semidirect
13. C₃×C₇×C₁₀₃	C₂²×C₃	semidirect
15. #14524189	C₂×D₃	semidirect
18. C₂×C₇×C₁₀₃	C₃×D₃	semidirect
20. C₂×D₃₀₉	ΓL(1,𝔽₈)	semidirect
23. C₇×C₁₀₃	C₂×C₃×D₃	semidirect
24. C₂×C₃×C₁₀₃	C₂×ΓL(1,𝔽₈)	semidirect
25. D₃₀₉	C₂×ΓL(1,𝔽₈)	semidirect
30. C₃×C₁₀₃	C₂²×ΓL(1,𝔽₈)	semidirect
34. C₂×C₁₀₃	D₃×ΓL(1,𝔽₈)	semidirect
38. C₁₀₃	C₂×D₃×ΓL(1,𝔽₈)	semidirect
42. C₂×C₃×C₇	D₁₀₃⋊C₃	semidirect
49. C₃×C₇	C₂×D₁₀₃⋊C₃	semidirect
55. C₂×C₇	C₃⋊(D₁₀₃⋊C₃)	semidirect
59. C₇	C₂×C₃⋊(D₁₀₃⋊C₃)	semidirect
63. C₂×C₃	#16864498	semidirect
68. C₃	C₂×#16864498	semidirect
70. C₂	C₃⋊#16864498	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#14524189	2
C₃⋊#16864498	2
C₂×C₇×D₃₀₉	3
C₂×#16864498	3
C₂×C₃⋊(D₁₀₃⋊C₃)	7
C₂×D₃×ΓL(1,𝔽₈)	103

Subgroups — C2×C3⋊#16864498 #39906804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#16864498 #39906804