Subgroups — #13117089

Order 1664.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₄	C₂	1	4	yes	maximal
2	#11718360	C₂	1	2	yes	maximal
3	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₂	—	2	2	no	—
5	C₂×Dic₅₂	C₂²	1	4	yes	—
6	#88123	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	Dic₁₀₄	—	2	8	no	—
10	C₂×Dic₂₆	—	2	4	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	—	4	4	no	—
15	Dic₅₂	—	2	8	no	—
16	Dic₅₂	—	4	4	no	—
17	C₁₃×C₁₆	D₄	1	4	yes	—
18	#2247	—	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	Dic₂₆	—	4	4	no	—
23	Dic₂₆	—	4	4	no	—
24	C₈×C₁₃	D₈	1	2	yes	—
25	C₈×C₁₃	C₂×D₄	1	2	yes	—
26	C₂×Q₃₂	—	13	4	no	—
27	#494	—	13	2	no	—
28	C₄×C₁₆	D₁₃	1	1	yes	characteristic
29	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
30	C₄×C₁₃	Q₃₂	1	4	yes	complemented
31	C₄×C₁₃	#127	1	1	yes	characteristic
32	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
33	Dic₁₃	—	8	4	no	—
34	C₂×Q₁₆	—	13	4	no	—
35	C₂×Q₁₆	—	26	2	no	—
36	C₄⋊Q₈	—	26	2	no	—
37	Q₃₂	—	26	8	no	—
38	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
39	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
40	C₂×C₁₃	#493	1	1	yes	characteristic
41	C₂×C₁₃	C₂×Q₃₂	1	2	yes	—
42	C₂×Q₈	—	26	4	no	—
43	Q₁₆	—	26	8	no	—
44	Q₁₆	—	52	4	no	—
45	C₂×C₈	D₅₂	1	1	yes	characteristic
46	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
47	C₄⋊C₄	—	52	4	no	—
48	C₄²	D₅₂	1	1	yes	characteristic
49	C₁₆	D₅₂	1	4	yes	—
50	C₁₃	#2247	1	1	yes	characteristic, complemented, Sylow
51	Q₈	—	52	4	no	—
52	Q₈	—	52	4	no	—
53	C₂×C₄	—	52	4	no	—
54	C₂×C₄	D₁₀₄	1	2	yes	—
55	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
56	C₈	D₁₀₄	1	2	yes	—
57	C₈	C₂×D₅₂	1	2	yes	—
58	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
59	C₄	—	104	4	no	—
60	C₄	Dic₁₀₄	1	4	yes	complemented
61	C₄	#88128	1	1	yes	characteristic
62	C₄	C₂×D₁₀₄	1	1	yes	characteristic
63	C₂	#11718356	1	1	yes	characteristic
64	C₂	C₂×Dic₁₀₄	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	#2247
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
30. C₄×C₁₃	Q₃₂	semidirect
50. C₁₃	#2247	semidirect
60. C₄	Dic₁₀₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₀₄	2
#11718360	2
C₄×C₁₃×C₁₆	2
#2247	13