Subgroups — #13113027

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718098	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₀₄	—	2	1	no	—
5	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	#88059	—	2	1	no	—
7	D₂₀₈	—	2	1	no	—
8	D₂₀₈	C₄	1	2	yes	—
9	C₁₃×C₃₂	—	2	1	no	—
10	C₂×D₅₂	—	4	1	no	—
11	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
12	#6099	—	4	1	no	—
13	D₁₀₄	—	2	2	no	—
14	D₁₀₄	—	4	1	no	—
15	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	#1419	—	13	1	no	maximal, Sylow
18	C₂²×D₁₃	—	8	1	no	—
19	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
20	D₅₂	—	4	2	no	—
21	D₅₂	—	8	1	no	—
22	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
24	#1055	—	8	1	no	—
25	C₂×D₁₆	—	13	1	no	—
26	M₆₄	D₁₃	1	1	yes	characteristic, complemented
27	#368	—	13	1	no	—
28	C₂²×C₁₃	SD₃₂	1	1	yes	characteristic
29	C₂×D₁₃	—	8	2	no	—
30	C₂×D₁₃	—	16	2	no	—
31	C₄×C₁₃	#102	1	1	yes	characteristic
32	C₄×C₁₃	D₁₆	1	1	yes	characteristic
33	C₂×D₈	—	26	1	no	—
34	D₁₆	—	13	2	no	—
35	D₁₆	—	26	1	no	—
36	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
37	#108	—	26	1	no	—
38	C₃₂	—	2	1	no	—
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	#357	1	1	yes	characteristic
41	D₁₃	—	16	2	no	—
42	C₂×D₄	—	52	1	no	—
43	D₈	—	26	2	no	—
44	D₈	—	52	1	no	—
45	M₁₆	—	52	1	no	—
46	C₂×C₈	D₅₂	1	1	yes	characteristic
47	C₁₆	C₄×D₁₃	1	1	yes	characteristic
48	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
49	C₁₃	#1419	1	1	yes	characteristic, complemented, Sylow
50	C₂³	—	104	1	no	—
51	D₄	—	52	2	no	—
52	D₄	—	104	1	no	—
53	C₂×C₄	D₁₀₄	1	1	yes	characteristic
54	C₈	—	104	1	no	—
55	C₈	#6095	1	1	yes	characteristic
56	C₈	#6103	1	1	yes	characteristic
57	C₂²	—	104	2	no	—
58	C₂²	—	208	2	no	—
59	C₂²	#88040	1	1	yes	characteristic
60	C₄	D₂₀₈	1	1	yes	characteristic
61	C₄	#88061	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	208	2	no	—
64	C₂	#11718101	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718101
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×M₆₄	C₂
socle	C₂×C₁₃	#357
prime radical	C₂×D₂₀₈	C₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	M₆₄	D₁₃
hypocenter	C₁₃	#1419
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. C₁₃×M₆₄	C₂	semidirect
3. #11718098	C₂	semidirect
26. M₆₄	D₁₃	semidirect
49. C₁₃	#1419	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₀₈	2
C₁₃×M₆₄	2
#11718098	2
#1419	13