Subgroups — #13117115

Order 1664.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718344	C₂	1	2	yes	maximal
2	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#11718097	C₂	1	2	yes	maximal
4	#11718096	C₂	1	2	yes	maximal
5	#88124	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	#88058	C₂²	1	4	yes	—
10	#88057	—	2	2	no	—
11	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
13	C₄²×C₁₃	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₃	—	2	4	no	—
15	#6101	—	4	4	no	—
16	C₁₃×C₁₆	Q₈	1	2	yes	—
17	C₁₃×C₁₆	Q₈	1	2	yes	—
18	#2253	—	13	1	no	maximal, Sylow
19	C₂×C₄×C₁₃	D₈	1	2	yes	—
20	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
21	C₂×Dic₁₃	—	4	4	no	—
22	C₈×C₁₃	Q₁₆	1	2	yes	—
23	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
24	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
25	#499	—	13	2	no	—
26	#367	—	13	2	no	—
27	#366	—	13	2	no	—
28	C₄×C₁₆	D₁₃	1	1	yes	characteristic
29	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
30	C₄×C₁₃	—	2	2	no	—
31	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
32	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
33	Dic₁₃	—	8	4	no	—
34	#125	—	26	2	no	—
35	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
36	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
37	#107	—	13	4	no	—
38	#106	—	26	2	no	—
39	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
40	C₂×C₁₃	#500	1	1	yes	characteristic
41	C₂×C₁₃	#508	1	2	yes	—
42	C₂×C₈	D₅₂	1	1	yes	characteristic
43	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
44	C₄⋊C₄	—	26	4	no	—
45	C₄⋊C₄	—	52	4	no	—
46	C₄²	D₅₂	1	1	yes	characteristic
47	C₁₆	Dic₂₆	1	2	yes	—
48	C₁₆	Dic₂₆	1	2	yes	—
49	C₁₃	#2253	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	52	4	no	—
51	C₂×C₄	D₁₀₄	1	2	yes	—
52	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
53	C₈	Dic₅₂	1	2	yes	—
54	C₈	C₂×Dic₂₆	1	1	yes	characteristic
55	C₈	C₂×Dic₂₆	1	1	yes	characteristic
56	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	104	4	no	—
59	C₄	#88123	1	1	yes	characteristic
60	C₄	C₂×Dic₅₂	1	1	yes	characteristic
61	C₂	#11718343	1	1	yes	characteristic
62	C₂	#11718565	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	#2253
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
49. C₁₃	#2253	semidirect

Maximal subgroups

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

subgroup	index
#11718344	2
C₄×C₁₃×C₁₆	2
#11718097	2
#11718096	2
#2253	13