Subgroups — #13117078

Order 1664.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718356	C₂	1	1	yes	maximal, characteristic
2	#11718344	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718101	C₂	1	4	yes	maximal, complemented
5	C₂×D₁₀₄	—	2	1	no	—
6	C₂×D₁₀₄	C₂²	1	2	yes	—
7	#88128	—	2	1	no	—
8	#88124	—	2	1	no	—
9	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	#88058	C₂²	1	2	yes	—
12	#88057	—	2	1	no	—
13	C₂×D₅₂	—	2	2	no	—
14	C₂×D₅₂	—	4	2	no	—
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₄²×C₁₃	D₄	1	1	yes	characteristic
18	C₄⋊Dic₁₃	—	2	2	no	—
19	#6101	—	4	2	no	—
20	D₁₀₄	—	2	4	no	—
21	D₁₀₄	—	4	2	no	—
22	C₁₃×C₁₆	—	2	2	no	—
23	#2244	—	13	1	no	maximal, Sylow
24	C₂²×D₁₃	—	4	2	no	—
25	C₂×C₄×C₁₃	D₈	1	2	yes	—
26	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₁₃	—	4	2	no	—
28	D₅₂	—	4	2	no	—
29	D₅₂	—	4	2	no	—
30	D₅₂	—	8	4	no	—
31	C₈×C₁₃	SD₁₆	1	2	yes	—
32	C₈×C₁₃	#41	1	2	yes	—
33	#499	—	13	1	no	—
34	#493	—	13	1	no	—
35	#357	—	13	4	no	—
36	#346	D₁₃	1	1	yes	characteristic, complemented
37	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
38	C₂×D₁₃	—	8	2	no	—
39	C₂×D₁₃	—	8	4	no	—
40	C₄×C₁₃	—	2	2	no	—
41	C₄×C₁₃	#124	1	1	yes	characteristic
42	C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
43	Dic₁₃	—	8	2	no	—
44	C₂×D₈	—	13	2	no	—
45	C₂×D₈	—	26	1	no	—
46	#127	—	26	1	no	—
47	#125	—	26	1	no	—
48	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
49	#107	—	13	2	no	—
50	#106	—	26	1	no	—
51	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	#486	1	1	yes	characteristic
53	C₂×C₁₃	#509	1	2	yes	—
54	D₁₃	—	16	2	no	—
55	C₂×D₄	—	26	2	no	—
56	C₂×D₄	—	52	2	no	—
57	D₈	—	26	4	no	—
58	D₈	—	52	2	no	—
59	C₂×C₈	D₅₂	1	1	yes	characteristic
60	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
61	C₄⋊C₄	—	26	2	no	—
62	C₄⋊C₄	—	52	2	no	—
63	C₄²	D₅₂	1	1	yes	characteristic
64	C₁₆	—	2	2	no	—
65	C₁₃	#2244	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	52	2	no	—
67	D₄	—	52	2	no	—
68	D₄	—	52	2	no	—
69	D₄	—	104	4	no	—
70	C₂×C₄	—	52	2	no	—
71	C₂×C₄	D₁₀₄	1	2	yes	—
72	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
73	C₈	#6095	1	2	yes	—
74	C₈	#6127	1	2	yes	—
75	C₂²	—	104	4	no	—
76	C₂²	—	104	2	no	—
77	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	104	2	no	—
80	C₄	#88129	1	1	yes	characteristic
81	C₄	C₂×#6095	1	1	yes	characteristic
82	C₂	—	208	2	no	—
83	C₂	#11718355	1	1	yes	characteristic
84	C₂	#11718569	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#346	C₂
socle	C₂²×C₁₃	C₂×D₈
prime radical	#11718356	C₂
hypercenter	#346	D₁₃
hypocenter	C₁₃	#2244
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #11718344	C₂	semidirect
3. C₁₃×#346	C₂	semidirect
4. #11718101	C₂	semidirect
36. #346	D₁₃	semidirect
65. C₁₃	#2244	semidirect

Maximal subgroups

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

subgroup	index
#11718356	2
#11718344	2
C₁₃×#346	2
#11718101	2
#2244	13