Subgroups — C₂×D₁₃⋊SL(2,𝔽₃) #11929160

Order 1248.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃⋊SL(2,𝔽₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×Q₈×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂²×D₁₃⋊C₃	—	4	1	no	maximal
5	Q₈⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic, complemented
6	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	Q₈×D₁₃	—	3	2	no	—
8	Q₈×D₁₃	C₂×C₃	1	2	yes	complemented
9	C₂×C₄×D₁₃	—	3	1	no	—
10	C₂×Dic₂₆	—	3	1	no	—
11	C₂²×C₁₃⋊C₃	—	4	1	no	—
12	C₂×D₁₃⋊C₃	—	4	4	no	—
13	C₂×D₁₃⋊C₃	—	4	2	no	—
14	C₂²×D₁₃	A₄	1	1	yes	characteristic
15	Q₈×C₁₃	—	3	1	no	—
16	Q₈×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₂×C₄×C₁₃	—	3	1	no	—
18	C₂×Dic₁₃	—	3	1	no	—
19	C₄×D₁₃	—	3	2	no	—
20	C₄×D₁₃	—	3	2	no	—
21	Dic₂₆	—	3	2	no	—
22	Dic₂₆	—	3	2	no	—
23	C₂²×SL(2,𝔽₃)	—	13	1	no	maximal, Hall
24	C₂×C₁₃⋊C₃	—	4	2	no	—
25	C₂×C₁₃⋊C₃	—	4	1	no	—
26	D₁₃⋊C₃	—	4	4	no	—
27	C₂²×C₁₃	C₂×A₄	1	1	yes	characteristic
28	C₂×D₁₃	SL(2,𝔽₃)	1	4	yes	complemented
29	C₂×D₁₃	C₂×A₄	1	2	yes	—
30	C₄×C₁₃	—	3	1	no	—
31	C₄×C₁₃	—	3	1	no	—
32	Dic₁₃	—	3	2	no	—
33	C₂×SL(2,𝔽₃)	—	13	2	no	—
34	C₂×SL(2,𝔽₃)	—	13	1	no	—
35	C₁₃⋊C₃	—	4	1	no	Hall
36	C₂²×Q₈	—	13	1	no	Sylow
37	C₂×C₁₃	C₂×SL(2,𝔽₃)	1	2	yes	complemented
38	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
39	D₁₃	C₂×SL(2,𝔽₃)	1	4	yes	complemented
40	C₂³×C₃	—	52	1	no	—
41	SL(2,𝔽₃)	—	13	1	no	—
42	C₂×Q₈	—	13	2	no	—
43	C₂×Q₈	—	39	1	no	—
44	C₂×Q₈	—	39	2	no	—
45	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic, complemented
46	C₂²×C₄	—	39	1	no	—
47	C₁₃	C₂²×SL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₃	—	52	4	no	—
49	C₂²×C₃	—	52	2	no	—
50	C₂²×C₃	—	52	1	no	—
51	C₂³	—	13	1	no	—
52	Q₈	—	3	1	no	—
53	Q₈	—	39	2	no	—
54	Q₈	—	39	2	no	—
55	Q₈	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
56	C₂×C₄	—	3	1	no	—
57	C₂×C₄	—	39	2	no	—
58	C₂×C₄	—	39	2	no	—
59	C₂×C₄	—	39	1	no	—
60	C₂×C₃	—	52	4	no	—
61	C₂×C₃	—	52	2	no	—
62	C₂×C₃	—	52	1	no	—
63	C₂²	—	13	4	no	—
64	C₂²	—	13	2	no	—
65	C₂²	D₁₃⋊A₄	1	1	yes	characteristic
66	C₄	—	3	1	no	—
67	C₄	—	3	1	no	—
68	C₄	—	39	2	no	—
69	C₃	—	52	1	no	Sylow
70	C₂	—	13	4	no	—
71	C₂	D₁₃⋊SL(2,𝔽₃)	1	2	yes	direct product factor
72	C₂	C₂×D₁₃⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₁₃⋊A₄
commutator, cosocle, hypocenter	Q₈×C₁₃	C₂²×C₃
Frattini	C₂	C₂×D₁₃⋊A₄
Fitting	C₂×Q₈×C₁₃	C₂×C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ Q₈×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈⋊(C₁₃⋊C₃)	C₂	semidirect
2. D₁₃⋊SL(2,𝔽₃)	C₂	direct (N × H)
3. C₂×Q₈×D₁₃	C₃	semidirect
5. Q₈⋊(C₁₃⋊C₃)	C₂²	semidirect
6. C₂×Q₈×C₁₃	C₂×C₃	semidirect
8. Q₈×D₁₃	C₂×C₃	semidirect
16. Q₈×C₁₃	C₂²×C₃	semidirect
28. C₂×D₁₃	SL(2,𝔽₃)	semidirect
37. C₂×C₁₃	C₂×SL(2,𝔽₃)	semidirect
39. D₁₃	C₂×SL(2,𝔽₃)	semidirect
45. C₂×Q₈	D₁₃⋊C₃	semidirect
47. C₁₃	C₂²×SL(2,𝔽₃)	semidirect
55. Q₈	C₂×D₁₃⋊C₃	semidirect
71. C₂	D₁₃⋊SL(2,𝔽₃)	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×Q₈⋊(C₁₃⋊C₃)	2
D₁₃⋊SL(2,𝔽₃)	2
C₂×Q₈×D₁₃	3
C₂²×D₁₃⋊C₃	4
C₂²×SL(2,𝔽₃)	13

Subgroups — C2×D13⋊SL(2,𝔽3) #11929160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊SL(2,𝔽₃) #11929160