Subgroups — #13131057

Order 1664.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88106	C₂	1	2	yes	maximal
2	#11718658	C₂	1	1	yes	maximal, characteristic
3	#11718232	C₂	1	4	yes	maximal, complemented
4	C₁₃×#117	C₄	1	1	yes	characteristic
5	C₂×#6099	C₄	1	1	yes	characteristic
6	C₂²×#1055	C₂²	1	1	yes	characteristic
7	#88106	C₄	1	4	yes	complemented
8	#88106	C₂²	1	4	yes	—
9	C₂×#6092	C₄	1	4	yes	complemented
10	#88043	C₂²	1	2	yes	—
11	C₄×#1055	C₄	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₁₃×C₂²⋊C₄	—	2	1	no	—
15	C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	#6099	—	2	2	no	—
17	C₂×#1055	C₂×C₄	1	2	yes	—
18	C₂×#1055	C₂×C₄	1	1	yes	characteristic
19	C₂×#1055	C₂×C₄	1	2	yes	—
20	C₂×#1055	C₂×C₄	1	2	yes	—
21	C₂×#1055	C₂³	1	1	yes	characteristic
22	#6092	C₂×C₄	1	8	yes	—
23	#2110	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	2	no	—
26	C₂×C₄×C₁₃	C₄²	1	2	yes	—
27	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	#1055	—	2	2	no	—
31	#1055	C₄²	1	1	yes	characteristic
32	#1055	C₄²	1	1	yes	characteristic
33	#1055	C₂²×C₄	1	2	yes	—
34	C₂×M₃₂	—	13	2	no	—
35	#405	—	13	1	no	—
36	#347	—	13	4	no	—
37	C₂²×C₁₃	—	4	1	no	—
38	C₂²×C₁₃	#97	1	2	yes	—
39	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₁₃	—	4	2	no	—
41	C₄×C₁₃	#97	1	2	yes	—
42	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₁₆	—	13	1	no	—
45	C₂²×C₈	—	13	1	no	—
46	#117	#261	1	1	yes	characteristic
47	M₃₂	—	13	4	no	—
48	M₃₂	—	13	4	no	—
49	C₂×C₁₆	—	13	4	no	—
50	#97	—	13	2	no	—
51	C₄×C₈	—	13	2	no	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	2	2	no	—
54	C₂×C₁₃	C₂×#97	1	1	yes	characteristic
55	C₂²×C₄	C₂×#261	1	1	yes	characteristic
56	M₁₆	—	26	2	no	—
57	C₂×C₈	—	13	2	no	—
58	C₂×C₈	—	13	2	no	—
59	C₂×C₈	—	13	1	no	—
60	C₂×C₈	—	13	1	no	—
61	C₂×C₈	—	13	2	no	—
62	C₄⋊C₄	—	2	1	no	—
63	C₂²⋊C₄	—	2	1	no	—
64	C₄²	C₂×#261	1	2	yes	—
65	C₁₆	—	13	8	no	—
66	C₁₃	#2110	1	1	yes	characteristic, complemented, Sylow
67	C₂³	#6122	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#6118	1	2	yes	—
70	C₂×C₄	C₄×#261	1	2	yes	—
71	C₂×C₄	#6122	1	1	yes	characteristic
72	C₂×C₄	C₂²×#261	1	1	yes	characteristic
73	C₈	—	13	2	no	—
74	C₈	—	13	1	no	—
75	C₈	—	13	1	no	—
76	C₈	—	26	2	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#88110	1	2	yes	—
79	C₂²	C₂×#6122	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#88110	1	2	yes	—
82	C₄	C₂×#6118	1	1	yes	characteristic
83	C₄	C₂×C₄×#261	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#88110	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#261
commutator	C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#117	C₄
socle	C₂×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×#1055	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#2110
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #11718232	C₂	semidirect
7. #88106	C₄	semidirect
9. C₂×#6092	C₄	semidirect
66. C₁₃	#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88106	2
#11718658	2
#11718232	2
#2110	13