Subgroups — #13117111

Order 1664.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718343	C₂	1	2	yes	maximal
2	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#11718096	C₂	1	4	yes	maximal
4	#88123	—	2	2	no	—
5	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
6	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	#88058	—	2	2	no	—
8	#88058	C₂²	1	4	yes	—
9	C₂×Dic₂₆	—	4	2	no	—
10	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
12	C₄²×C₁₃	D₄	1	1	yes	characteristic
13	C₄⋊Dic₁₃	—	2	4	no	—
14	C₄⋊Dic₁₃	—	4	2	no	—
15	C₁₃×C₁₆	Q₈	1	4	yes	complemented
16	#2252	—	13	1	no	maximal, Sylow
17	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
20	C₂×Dic₁₃	—	4	4	no	—
21	Dic₂₆	—	8	4	no	—
22	C₈×C₁₃	Q₁₆	1	2	yes	—
23	C₈×C₁₃	C₂×Q₈	1	2	yes	—
24	#500	—	13	2	no	—
25	#366	—	13	4	no	—
26	C₄×C₁₆	D₁₃	1	1	yes	characteristic
27	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
28	C₄×C₁₃	D₁₆	1	2	yes	—
29	C₄×C₁₃	Q₃₂	1	2	yes	—
30	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
31	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
32	Dic₁₃	—	8	4	no	—
33	C₄⋊Q₈	—	26	2	no	—
34	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
35	#107	—	13	4	no	—
36	#107	—	26	2	no	—
37	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
38	C₂×C₁₃	#500	1	1	yes	characteristic
39	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
41	C₂×Q₈	—	52	2	no	—
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	2	no	—
46	C₄²	D₅₂	1	1	yes	characteristic
47	C₁₆	Dic₂₆	1	4	yes	complemented
48	C₁₃	#2252	1	1	yes	characteristic, complemented, Sylow
49	Q₈	—	104	4	no	—
50	C₂×C₄	—	52	4	no	—
51	C₂×C₄	D₁₀₄	1	1	yes	characteristic
52	C₂×C₄	D₁₀₄	1	1	yes	characteristic
53	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
54	C₈	Dic₅₂	1	2	yes	—
55	C₈	C₂×Dic₂₆	1	2	yes	—
56	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
57	C₄	—	104	4	no	—
58	C₄	D₂₀₈	1	2	yes	—
59	C₄	Dic₁₀₄	1	2	yes	—
60	C₄	#88123	1	1	yes	characteristic
61	C₄	C₂×Dic₅₂	1	1	yes	characteristic
62	C₂	#11718343	1	1	yes	characteristic
63	C₂	C₂×D₂₀₈	1	1	yes	characteristic
64	C₂	C₂×Dic₁₀₄	1	1	yes	characteristic

	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	#2252
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
15. C₁₃×C₁₆	Q₈	semidirect
47. C₁₆	Dic₂₆	semidirect
48. C₁₃	#2252	semidirect

Maximal subgroups

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

subgroup	index
#11718343	2
C₄×C₁₃×C₁₆	2
#11718096	2
#2252	13