Group #16791411 — subgroups

Subgroups — #16791411

Order 3328.

218 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718249	C₂	1	2	yes	maximal
2	#13129994	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₂²	1	1	yes	characteristic
7	#11718249	—	2	4	no	—
8	C₂×#88036	C₂²	1	4	yes	—
9	C₁₆×Dic₁₃	C₄	1	2	yes	—
10	C₁₆×Dic₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
13	C₂²×#1055	C₈	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	—	2	2	no	—
15	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
16	C₈×Dic₁₃	C₈	1	2	yes	—
17	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
18	C₂×#6090	C₂×C₄	1	1	yes	characteristic
19	C₂×#6090	D₄	1	2	yes	—
20	C₂×#6090	Q₈	1	2	yes	—
21	C₂×#6090	C₂³	1	1	yes	characteristic
22	#88036	—	2	4	no	—
23	#13627	—	13	1	no	maximal, Sylow
24	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₁₆	1	2	yes	—
26	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
29	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
31	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
32	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
33	C₂×#1055	—	2	2	no	—
34	C₂×#1055	C₂×C₈	1	2	yes	—
35	C₁₃×C₁₆	—	2	2	no	—
36	#6090	C₄⋊C₄	1	2	yes	—
37	#6090	C₂×D₄	1	1	yes	characteristic
38	#6090	C₂×Q₈	1	1	yes	characteristic
39	C₂×M₆₄	—	13	2	no	—
40	C₂×C₄×C₁₆	—	13	1	no	—
41	C₄⋊C₃₂	—	13	4	no	—
42	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
46	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
47	C₂×Dic₁₃	—	2	4	no	—
48	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
49	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
50	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
51	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
53	#1055	—	2	2	no	—
54	C₂²×C₁₆	—	13	1	no	—
55	C₂²×C₁₆	#261	1	1	yes	characteristic
56	C₂×C₄×C₈	—	13	1	no	—
57	M₆₄	—	26	4	no	—
58	C₂×C₃₂	—	13	4	no	—
59	C₄×C₁₆	—	13	2	no	—
60	C₄×C₁₆	—	13	2	no	—
61	C₂²×C₁₃	—	2	2	no	—
62	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
63	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
64	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
65	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
67	Dic₁₃	—	2	2	no	—
68	Dic₁₃	M₆₄	1	4	yes	complemented
69	C₂²×C₈	—	13	1	no	—
70	C₂²×C₈	C₂×#261	1	1	yes	characteristic
71	C₂×C₄²	—	13	1	no	—
72	C₂×C₁₆	—	2	2	no	—
73	C₂×C₁₆	—	13	2	no	—
74	C₂×C₁₆	—	13	2	no	—
75	C₂×C₁₆	—	13	1	no	—
76	C₂×C₁₆	—	13	1	no	—
77	C₂×C₁₆	C₂×#261	1	2	yes	—
78	C₄×C₈	—	13	2	no	—
79	C₄×C₈	—	13	2	no	—
80	C₃₂	—	26	4	no	—
81	C₂×C₁₃	—	2	2	no	—
82	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
83	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
84	C₂²×C₄	—	13	2	no	—
85	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	26	2	no	—
88	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
89	C₂×C₈	C₄⋊#261	1	2	yes	—
90	C₂×C₈	#6122	1	2	yes	—
91	C₂×C₈	C₂²×#261	1	1	yes	characteristic
92	C₄²	—	13	1	no	—
93	C₄²	—	13	1	no	—
94	C₄²	—	13	2	no	—
95	C₁₆	—	2	2	no	—
96	C₁₆	—	13	1	no	—
97	C₁₆	—	13	2	no	—
98	C₁₆	—	13	1	no	—
99	C₁₃	#13627	1	1	yes	characteristic, complemented, Sylow
100	C₂³	D₁₃⋊C₁₆	1	1	yes	characteristic
101	C₂×C₄	—	13	2	no	—
102	C₂×C₄	—	13	2	no	—
103	C₂×C₄	—	26	4	no	—
104	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
105	C₂×C₄	#88098	1	2	yes	—
106	C₂×C₄	#88112	1	2	yes	—
107	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
108	C₈	—	26	2	no	—
109	C₈	#88112	1	2	yes	—
110	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
111	C₈	C₂×#6122	1	1	yes	characteristic
112	C₂²	—	2	2	no	—
113	C₂²	#11718260	1	2	yes	—
114	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
115	C₄	—	13	4	no	—
116	C₄	—	26	2	no	—
117	C₄	#11718260	1	2	yes	—
118	C₄	C₂×#88098	1	1	yes	characteristic
119	C₄	C₂×#88112	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×#11718260	1	1	yes	characteristic
122	C₂	D₁₃⋊M₆₄	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718249

C₂

yes

maximal

#13129994

C₂

yes

maximal, complemented

C₂×C₁₆×Dic₁₃

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₄

yes

characteristic

C₂×C₈×Dic₁₃

C₄

yes

characteristic

C₂²×#6090

C₂²

yes

characteristic

#11718249

—

C₂×#88036

C₂²

yes

—

C₁₆×Dic₁₃

C₄

yes

—

C₁₆×Dic₁₃

C₂²

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₈

yes

characteristic

C₂²×#1055

C₈

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₈×Dic₁₃

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

D₄

yes

—

C₂×#6090

Q₈

yes

—

C₂×#6090

C₂³

yes

—

—

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×Dic₁₃

C₁₆

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₁₆

yes

characteristic

C₄×Dic₁₃

C₁₆

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

—

C₂×#1055

C₂×C₈

yes

—

C₁₃×C₁₆

—

#6090

C₄⋊C₄

yes

—

#6090

C₂×D₄

yes

characteristic

#6090

C₂×Q₈

yes

characteristic

C₂×M₆₄

—

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₈×C₁₃

C₄⋊C₈

yes

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

C₂²×C₁₆

—

C₂²×C₁₆

#261

yes

characteristic

C₂×C₄×C₈

—

M₆₄

—

C₂×C₃₂

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₄⋊C₁₆

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₄×C₁₃

C₄⋊C₁₆

yes

—

C₄×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

Dic₁₃

M₆₄

yes

complemented

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#261

yes

—

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₁₃

C₂×M₆₄

yes

—

C₂²×C₄

—

C₂²×C₄

D₁₃⋊C₈

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₃⋊C₈

yes

characteristic

C₂×C₈

C₄⋊#261

yes

—

C₂×C₈

#6122

yes

—

C₂×C₈

C₂²×#261

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₃

#13627

yes

characteristic, complemented, Sylow

100

C₂³

D₁₃⋊C₁₆

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

D₁₃⋊C₁₆

yes

characteristic

105

C₂×C₄

#88098

yes

—

106

C₂×C₄

#88112

yes

—

107

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

108

C₈

—

109

C₈

#88112

yes

—

110

C₈

C₂×C₄⋊#261

yes

characteristic

111

C₈

C₂×#6122

yes

characteristic

112

C₂²

—

113

C₂²

#11718260

yes

—

114

C₂²

C₂×D₁₃⋊C₁₆

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#11718260

yes

—

118

C₄

C₂×#88098

yes

characteristic

119

C₄

C₂×#88112

yes

characteristic

120

C₂

—

121

C₂

C₂×#11718260

yes

characteristic

122

C₂

D₁₃⋊M₆₄

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂²×C₁₃×C₁₆	C₄
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×#6090	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	#13627
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂²×C₁₆

Fitting

C₂²×C₁₃×C₁₆

C₄

prime radical

C₂³×C₁₃

C₂×C₁₆

C₂³

C₂²×C₁₆

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. #13129994	C₂	semidirect
68. Dic₁₃	M₆₄	semidirect
99. C₁₃	#13627	semidirect

H ≅ G/N

type

2. #13129994

C₂

semidirect

68. Dic₁₃

M₆₄

semidirect

99. C₁₃

#13627

semidirect

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

subgroup	index
C₂×#11718249	2
#13129994	2
C₂×C₁₆×Dic₁₃	2
#13627	13

subgroup

index

C₂×#11718249

#13129994

C₂×C₁₆×Dic₁₃

#13627

Subgroups — #16791411

Conjugacy classes of subgroups

Complements

Maximal subgroups