Subgroups — #13117145

Order 1664.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718565	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718041	C₂	1	2	yes	maximal, complemented
5	D₄₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#88158	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	Dic₁₀₄	C₂²	1	2	yes	—
9	#88040	—	2	2	no	—
10	D₂₀₈	C₂²	1	2	yes	—
11	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
13	#6127	—	4	2	no	—
14	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
15	Dic₅₂	—	2	2	no	—
16	D₁₀₄	—	2	2	no	—
17	#6095	—	4	2	no	—
18	C₁₃×C₁₆	D₄	1	1	yes	characteristic
19	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
20	#2262	—	13	1	no	maximal, Sylow
21	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
22	C₂²⋊D₁₃	—	8	2	no	—
23	D₅₂	—	4	2	no	—
24	C₄×D₁₃	—	8	2	no	—
25	Dic₂₆	—	4	2	no	—
26	C₈×C₁₃	D₈	1	1	yes	characteristic
27	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
28	#508	—	13	2	no	—
29	Q₆₄	—	13	1	no	—
30	SD₆₄	—	13	2	no	—
31	D₃₂	—	13	1	no	—
32	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
33	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
34	C₂×D₁₃	—	8	2	no	—
35	C₄×C₁₃	D₁₆	1	1	yes	characteristic
36	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
37	Dic₁₃	—	8	2	no	—
38	#135	—	26	2	no	—
39	Q₃₂	—	13	2	no	—
40	SD₃₂	—	26	2	no	—
41	D₁₆	—	13	2	no	—
42	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
43	C₃₂	C₂×D₁₃	1	1	yes	characteristic
44	C₃₂	C₂×D₁₃	1	1	yes	characteristic
45	C₂×C₁₃	—	2	1	no	—
46	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
47	D₁₃	—	16	2	no	—
48	#41	—	52	2	no	—
49	Q₁₆	—	26	2	no	—
50	SD₁₆	—	52	2	no	—
51	D₈	—	26	2	no	—
52	C₂×C₈	D₅₂	1	1	yes	characteristic
53	C₁₆	D₅₂	1	1	yes	characteristic
54	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
55	C₁₃	#2262	1	1	yes	characteristic, complemented, Sylow
56	Q₈	—	52	2	no	—
57	D₄	—	52	2	no	—
58	D₄	—	104	2	no	—
59	C₂×C₄	—	104	2	no	—
60	C₂×C₄	D₁₀₄	1	1	yes	characteristic
61	C₈	D₁₀₄	1	1	yes	characteristic
62	C₈	C₂×D₅₂	1	1	yes	characteristic
63	C₂²	—	104	2	no	—
64	C₂²	D₂₀₈	1	1	yes	characteristic
65	C₄	—	104	2	no	—
66	C₄	D₂₀₈	1	1	yes	characteristic
67	C₄	C₂×D₁₀₄	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	208	2	no	—
70	C₂	C₂×D₂₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₀₈
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×C₃₂	C₂
socle	C₂×C₁₃	C₂×D₁₆
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	#2262
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #11718565	C₂	semidirect
2. C₂×C₁₃×C₃₂	C₂	semidirect
3. Dic₂₀₈	C₂	semidirect
4. #11718041	C₂	semidirect
5. D₄₁₆	C₂	semidirect
32. C₂×C₃₂	D₁₃	semidirect
55. C₁₃	#2262	semidirect

Maximal subgroups

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

subgroup	index
#11718565	2
C₂×C₁₃×C₃₂	2
Dic₂₀₈	2
#11718041	2
D₄₁₆	2
#2262	13