Subgroups — #13129809

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718529	C₂	1	1	yes	maximal, characteristic
2	#11718267	C₂	1	1	yes	maximal, characteristic
3	#11718263	C₂	1	1	yes	maximal, characteristic
4	#88237	—	2	1	no	—
5	C₂×Dic₅₂	C₄	1	1	yes	characteristic, complemented
6	C₂×#6094	C₂²	1	1	yes	characteristic
7	#88151	—	2	1	no	—
8	#88106	—	2	1	no	—
9	C₁₃×#106	C₄	1	1	yes	characteristic, complemented
10	#88050	—	2	1	no	—
11	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
12	C₂×Dic₂₆	—	2	1	no	—
13	C₂²⋊#261	—	4	1	no	—
14	C₄⋊#261	—	4	1	no	—
15	C₄×#261	—	2	2	no	—
16	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₁₃×C₄⋊C₄	—	2	1	no	—
18	#6103	—	4	1	no	—
19	C₄⋊Dic₁₃	—	4	1	no	—
20	C₂×#1055	D₄	1	1	yes	characteristic
21	Dic₅₂	—	4	1	no	—
22	#6094	—	4	1	no	—
23	#6092	—	4	1	no	—
24	#1340	—	13	1	no	maximal, Sylow
25	C₂²×D₁₃	D₈	1	1	yes	characteristic
26	C₂×#261	—	4	2	no	—
27	C₂×C₄×C₁₃	—	4	1	no	—
28	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	1	no	—
30	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
31	C₄×D₁₃	—	2	1	no	—
32	C₄×D₁₃	—	2	1	no	—
33	Dic₂₆	—	4	1	no	—
34	Dic₂₆	—	4	1	no	—
35	C₈×C₁₃	—	2	1	no	—
36	#1055	—	2	1	no	—
37	#470	—	13	1	no	—
38	#349	—	13	1	no	—
39	H(3,ℤ/4)	—	13	1	no	—
40	C₂²×C₁₃	#102	1	1	yes	characteristic
41	C₂×D₁₃	—	2	1	no	—
42	C₂×D₁₃	—	4	1	no	—
43	#261	—	8	2	no	—
44	C₄×C₁₃	—	8	1	no	—
45	C₄×C₁₃	#99	1	1	yes	characteristic
46	C₄×C₁₃	#104	1	1	yes	characteristic
47	Dic₁₃	—	2	1	no	—
48	Dic₁₃	—	8	1	no	—
49	C₂×Q₁₆	—	13	1	no	—
50	C₂×M₁₆	—	13	1	no	—
51	C₂²⋊Q₈	—	26	1	no	—
52	#117	—	26	1	no	—
53	M₃₂	—	26	1	no	—
54	#106	#261	1	1	yes	characteristic, complemented
55	#103	—	26	1	no	—
56	C₂×C₁₃	—	2	1	no	—
57	C₂×C₁₃	#327	1	1	yes	characteristic
58	D₁₃	—	4	1	no	—
59	C₂×Q₈	—	26	1	no	—
60	C₂²×C₄	—	13	1	no	—
61	Q₁₆	—	52	1	no	—
62	M₁₆	—	52	1	no	—
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	C₂×#261	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	52	1	no	—
67	C₄⋊C₄	—	52	1	no	—
68	C₂²⋊C₄	—	52	1	no	—
69	C₂²⋊C₄	—	52	1	no	—
70	C₄²	—	26	2	no	—
71	C₁₆	—	52	1	no	—
72	C₁₃	#1340	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	13	1	no	—
74	Q₈	—	52	1	no	—
75	Q₈	—	52	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	13	1	no	—
78	C₂×C₄	—	26	1	no	—
79	C₂×C₄	—	26	1	no	—
80	C₂×C₄	—	52	2	no	—
81	C₂×C₄	—	52	1	no	—
82	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	26	1	no	—
85	C₂²	—	26	1	no	—
86	C₂²	—	52	1	no	—
87	C₂²	#88115	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	26	1	no	—
90	C₄	—	104	2	no	—
91	C₄	—	104	1	no	—
92	C₄	#88107	1	1	yes	characteristic
93	C₄	#88118	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	52	1	no	—
96	C₂	#11718240	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718240
commutator	C₂×C₈×C₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#106	C₄
socle	C₂×C₁₃	#327
prime radical	C₂²×D₁₃	D₈
cosocle	C₂×#6094	C₂²
hypercenter	#106	#261
hypocenter	C₁₃	#1340
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
5. C₂×Dic₅₂	C₄	semidirect
9. C₁₃×#106	C₄	semidirect
54. #106	#261	semidirect
72. C₁₃	#1340	semidirect

Maximal subgroups

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

subgroup	index
#11718529	2
#11718267	2
#11718263	2
#1340	13