Subgroups — #13131209

Order 1664.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718658	C₂	1	1	yes	maximal, characteristic
2	#11718284	C₂	1	2	yes	maximal
3	#11718233	C₂	1	2	yes	maximal, complemented
4	#11718232	C₂	1	2	yes	maximal, complemented
5	C₁₃×#117	C₄	1	1	yes	characteristic
6	C₂×#6099	C₂²	1	1	yes	characteristic
7	C₂²×#1055	C₄	1	1	yes	characteristic
8	#88106	C₂²	1	4	yes	—
9	#88043	C₄	1	1	yes	characteristic
10	#88043	C₂²	1	1	yes	characteristic
11	C₄×#1055	C₄	1	1	yes	characteristic
12	C₄×#1055	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₁₃×C₂²⋊C₄	—	2	1	no	—
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	#6099	—	2	2	no	—
19	C₂×#1055	—	2	2	no	—
20	C₂×#1055	C₂×C₄	1	1	yes	characteristic
21	C₂×#1055	C₂×C₄	1	1	yes	characteristic
22	C₂×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂×#1055	C₂³	1	1	yes	characteristic
24	#6092	—	2	4	no	—
25	#2166	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	—	2	1	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	#1055	—	2	1	no	—
34	#1055	—	2	1	no	—
35	#1055	M₁₆	1	2	yes	—
36	#1055	#41	1	2	yes	—
37	#405	—	13	1	no	—
38	#364	—	13	2	no	—
39	#349	—	13	2	no	—
40	#347	—	13	2	no	—
41	C₂²×C₁₃	—	2	1	no	—
42	C₂²×C₁₃	—	4	1	no	—
43	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₁₃	—	2	1	no	—
45	C₄×C₁₃	—	4	1	no	—
46	C₄×C₁₃	—	4	1	no	—
47	C₄×C₁₃	#117	1	1	yes	characteristic
48	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
49	C₂×M₁₆	—	13	1	no	—
50	C₂²×C₈	—	13	1	no	—
51	#117	#261	1	1	yes	characteristic
52	M₃₂	—	13	4	no	—
53	#97	—	13	1	no	—
54	#97	—	13	1	no	—
55	C₄×C₈	—	13	1	no	—
56	C₄×C₈	—	13	1	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	—	4	1	no	—
59	C₂×C₁₃	#432	1	1	yes	characteristic
60	C₂²×C₄	C₂×#261	1	1	yes	characteristic
61	M₁₆	—	26	2	no	—
62	C₂×C₈	—	13	1	no	—
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	—	13	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₂×C₈	—	26	2	no	—
67	C₄⋊C₄	—	2	1	no	—
68	C₂²⋊C₄	—	2	1	no	—
69	C₄²	C₂×#261	1	1	yes	characteristic
70	C₄²	C₂×#261	1	1	yes	characteristic
71	C₁₆	—	26	4	no	—
72	C₁₃	#2166	1	1	yes	characteristic, complemented, Sylow
73	C₂³	#6122	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	#6122	1	1	yes	characteristic
79	C₂×C₄	C₂²×#261	1	1	yes	characteristic
80	C₈	—	13	2	no	—
81	C₈	—	13	2	no	—
82	C₈	—	26	1	no	—
83	C₈	—	26	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂×#6122	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
91	C₄	#88237	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#11719128	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88237
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#117	C₄
socle	C₂×C₁₃	#432
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×#1055	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#2166
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₄² ◁ #117

Complements

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

N	H ≅ G/N	type
3. #11718233	C₂	semidirect
4. #11718232	C₂	semidirect
72. C₁₃	#2166	semidirect

Maximal subgroups

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

subgroup	index
#11718658	2
#11718284	2
#11718233	2
#11718232	2
#2166	13