Subgroups — #13131240

Order 1664.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719103	C₂	1	2	yes	maximal, complemented
2	#11718573	C₂	1	1	yes	maximal, characteristic
3	#11718277	C₂	1	2	yes	maximal, complemented
4	#11718224	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718216	C₂	1	1	yes	maximal, characteristic, complemented
6	#88238	—	2	2	no	—
7	#88166	C₂²	1	2	yes	—
8	#88116	—	2	2	no	—
9	#88104	C₂²	1	2	yes	—
10	C₈×#261	C₂²	1	1	yes	characteristic
11	D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×D₁₆	C₄	1	1	yes	characteristic, complemented
13	#88067	C₄	1	2	yes	complemented
14	Dic₁₀₄	C₄	1	1	yes	characteristic, complemented
15	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
16	#6129	—	2	2	no	—
17	#6122	—	4	2	no	—
18	C₂×#1057	—	4	2	no	—
19	C₄×#261	D₄	1	1	yes	characteristic
20	#6118	—	2	2	no	—
21	D₁₃⋊C₈	D₄	1	1	yes	characteristic
22	C₁₃×D₈	C₂×C₄	1	2	yes	—
23	#6105	—	2	2	no	—
24	Dic₅₂	C₂×C₄	1	2	yes	—
25	C₈×D₁₃	C₂³	1	1	yes	characteristic
26	#6092	—	2	1	no	—
27	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
28	#6090	C₂×C₄	1	1	yes	characteristic
29	#2179	—	13	1	no	maximal, Sylow
30	C₂×#261	—	2	1	no	—
31	D₄×C₁₃	—	2	2	no	—
32	C₂²⋊D₁₃	—	4	2	no	—
33	C₂×Dic₁₃	—	4	2	no	—
34	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
35	Dic₂₆	—	2	2	no	—
36	#1057	—	4	2	no	—
37	#1057	D₈	1	2	yes	—
38	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	#1055	#41	1	1	yes	characteristic
40	#508	—	13	1	no	—
41	#443	—	13	2	no	—
42	#368	—	13	1	no	—
43	#359	—	13	2	no	—
44	#346	—	13	1	no	—
45	C₂²×C₁₃	—	4	2	no	—
46	C₂×D₁₃	#135	1	1	yes	characteristic
47	#261	—	4	1	no	—
48	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
49	Dic₁₃	—	4	2	no	—
50	Dic₁₃	C₂×D₈	1	1	yes	characteristic
51	#135	—	13	2	no	—
52	#131	—	26	2	no	—
53	Q₃₂	—	13	1	no	—
54	SD₃₂	—	13	2	no	—
55	D₁₆	#261	1	1	yes	characteristic, complemented
56	C₂×C₁₆	—	13	1	no	—
57	C₂×C₁₆	—	13	1	no	—
58	#108	—	13	2	no	—
59	#104	—	26	2	no	—
60	C₄×C₈	—	13	1	no	—
61	C₂×C₁₃	—	8	2	no	—
62	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
63	D₁₃	—	2	1	no	—
64	#41	—	26	2	no	—
65	Q₁₆	—	13	2	no	—
66	SD₁₆	—	26	2	no	—
67	D₈	C₂×#261	1	2	yes	—
68	M₁₆	—	26	2	no	—
69	M₁₆	—	52	2	no	—
70	C₂×C₈	—	13	1	no	—
71	C₂×C₈	—	13	1	no	—
72	C₂×C₈	—	52	2	no	—
73	C₄²	—	13	1	no	—
74	C₁₆	—	13	1	no	—
75	C₁₆	—	26	1	no	—
76	C₁₆	C₂×#261	1	1	yes	characteristic
77	C₁₃	#2179	1	1	yes	characteristic, complemented, Sylow
78	Q₈	—	26	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	52	2	no	—
81	C₂×C₄	—	13	1	no	—
82	C₂×C₄	—	26	1	no	—
83	C₂×C₄	—	52	2	no	—
84	C₈	—	13	2	no	—
85	C₈	—	13	1	no	—
86	C₈	—	52	2	no	—
87	C₈	C₂²×#261	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	—	13	1	no	—
90	C₄	—	13	1	no	—
91	C₄	—	52	1	no	—
92	C₄	—	52	2	no	—
93	C₄	D₄×#261	1	1	yes	characteristic
94	C₂	—	8	2	no	—
95	C₂	—	26	1	no	—
96	C₂	D₈×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#261
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₈	C₂²×#261
Fitting	C₁₃×D₁₆	C₄
socle	C₂×C₁₃	C₄×D₈
prime radical	#11718573	C₂
cosocle	C₈×D₁₃	C₂³
hypercenter	D₁₆	#261
hypocenter	C₁₃	#2179
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #11719103	C₂	semidirect
3. #11718277	C₂	semidirect
4. #11718224	C₂	semidirect
5. #11718216	C₂	semidirect
12. C₁₃×D₁₆	C₄	semidirect
13. #88067	C₄	semidirect
14. Dic₁₀₄	C₄	semidirect
55. D₁₆	#261	semidirect
77. C₁₃	#2179	semidirect

Maximal subgroups

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

subgroup	index
#11719103	2
#11718573	2
#11718277	2
#11718224	2
#11718216	2
#2179	13