Subgroups — #15750798

Order 3328.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁₆	C₂	1	1	yes	maximal, characteristic
2	#13113036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₀₈	—	2	1	no	—
5	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
6	#11718096	—	2	1	no	—
7	D₄₁₆	—	2	1	no	—
8	D₄₁₆	C₄	1	2	yes	complemented
9	C₁₃×C₆₄	—	2	1	no	—
10	C₂×D₁₀₄	—	4	1	no	—
11	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
12	#88058	—	4	1	no	—
13	D₂₀₈	—	2	2	no	—
14	D₂₀₈	—	4	1	no	—
15	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₃₂	D₄	1	1	yes	characteristic
17	#7537	—	13	1	no	maximal, Sylow
18	C₂×D₅₂	—	8	1	no	—
19	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	8	1	no	—
21	D₁₀₄	—	4	2	no	—
22	D₁₀₄	—	8	1	no	—
23	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×D₃₂	—	13	1	no	—
26	C₂×C₆₄	D₁₃	1	1	yes	characteristic, complemented
27	#1423	—	13	1	no	—
28	C₂²×D₁₃	—	16	1	no	—
29	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
30	C₂×Dic₁₃	—	16	1	no	—
31	D₅₂	—	8	2	no	—
32	D₅₂	—	16	1	no	—
33	C₈×C₁₃	#102	1	1	yes	characteristic
34	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
35	C₂×D₁₆	—	26	1	no	—
36	D₃₂	—	13	2	no	—
37	D₃₂	—	26	1	no	—
38	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
39	#366	—	26	1	no	—
40	C₆₄	—	2	1	no	—
41	C₂²×C₁₃	D₃₂	1	1	yes	characteristic
42	C₂×D₁₃	—	16	2	no	—
43	C₂×D₁₃	—	32	1	no	—
44	C₂×D₁₃	—	32	1	no	—
45	C₄×C₁₃	#357	1	1	yes	characteristic
46	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
47	Dic₁₃	—	32	1	no	—
48	C₂×D₈	—	52	1	no	—
49	D₁₆	—	26	2	no	—
50	D₁₆	—	52	1	no	—
51	C₂×C₁₆	D₅₂	1	1	yes	characteristic
52	#107	—	52	1	no	—
53	C₃₂	C₄×D₁₃	1	1	yes	characteristic
54	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
55	C₂×C₁₃	#1415	1	1	yes	characteristic
56	C₂×C₁₃	D₆₄	1	1	yes	characteristic
57	C₂×C₁₃	SD₁₂₈	1	1	yes	characteristic
58	D₁₃	—	32	2	no	—
59	C₂×D₄	—	104	1	no	—
60	D₈	—	52	2	no	—
61	D₈	—	104	1	no	—
62	C₂×C₈	D₁₀₄	1	1	yes	characteristic
63	C₄⋊C₄	—	104	1	no	—
64	C₁₆	#6095	1	1	yes	characteristic
65	C₁₆	#6103	1	1	yes	characteristic
66	C₁₃	#7537	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	208	1	no	—
68	D₄	—	104	2	no	—
69	D₄	—	208	1	no	—
70	C₂×C₄	—	208	1	no	—
71	C₂×C₄	D₂₀₈	1	1	yes	characteristic
72	C₈	#88040	1	1	yes	characteristic
73	C₈	#88061	1	1	yes	characteristic
74	C₂²	—	416	1	no	—
75	C₂²	—	416	1	no	—
76	C₂²	—	208	2	no	—
77	C₂²	D₄₁₆	1	1	yes	characteristic
78	C₄	—	416	1	no	—
79	C₄	#11718041	1	1	yes	characteristic
80	C₄	#11718101	1	1	yes	characteristic
81	C₂	—	416	2	no	—
82	C₂	#13113015	1	1	yes	characteristic
83	C₂	D₈₃₂	1	1	yes	characteristic
84	C₂	#13113052	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₁₆
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₂×C₁₃×C₆₄	C₂
socle	C₂²×C₁₃	D₃₂
prime radical	C₂×D₄₁₆	C₂
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₃
hypocenter	C₁₃	#7537
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. #13113036	C₂	semidirect
3. C₂×C₁₃×C₆₄	C₂	semidirect
8. D₄₁₆	C₄	semidirect
26. C₂×C₆₄	D₁₃	semidirect
66. C₁₃	#7537	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₁₆	2
#13113036	2
C₂×C₁₃×C₆₄	2
#7537	13