Group #16790259 — subgroups

Subgroups — #16790259

Order 3328.

278 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 104 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	#13131179	C₂	1	2	yes	maximal
2	#13131177	C₂	1	1	yes	maximal, characteristic
3	#13131173	C₂	1	1	yes	maximal, characteristic
4	#13131171	C₂	1	2	yes	maximal
5	#13114590	C₂	1	1	yes	maximal, characteristic
6	C₂×#88106	C₂²	1	2	yes	—
7	C₂×#88106	C₂²	1	1	yes	characteristic
8	C₂²×#6092	C₂²	1	1	yes	characteristic
9	#11718783	C₂²	1	1	yes	characteristic
10	#11718658	C₂²	1	2	yes	—
11	#11718261	—	2	2	no	—
12	#11718260	—	2	2	no	—
13	#11718233	—	2	4	no	—
14	C₄⋊#6092	—	2	4	no	—
15	C₁₃×H(3,ℤ/4)	C₄	1	1	yes	characteristic
16	#11718152	C₄	1	1	yes	characteristic
17	#11718123	C₄	1	2	yes	—
18	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
19	C₁₃×#117	C₂×C₄	1	2	yes	—
20	#88180	C₂×C₄	1	1	yes	characteristic
21	C₂×#6099	C₂×C₄	1	2	yes	—
22	C₂²×#1055	C₂³	1	1	yes	characteristic
23	#88106	—	2	2	no	—
24	#88106	—	2	2	no	—
25	#88106	—	2	2	no	—
26	C₂×#6092	—	2	2	no	—
27	C₂×#6092	—	2	2	no	—
28	C₂×#6092	—	2	1	no	—
29	C₂×#6092	—	2	1	no	—
30	#88055	Q₈	1	2	yes	—
31	C₈×Dic₁₃	D₄	1	2	yes	—
32	#88043	Q₈	1	4	yes	—
33	C₄×#1055	D₄	1	4	yes	—
34	#12902	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₁₃×M₁₆	—	2	2	no	—
37	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₁₃×C₂²⋊C₄	—	2	2	no	—
40	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
41	C₂²⋊Dic₁₃	—	2	1	no	—
42	C₄⋊Dic₁₃	—	2	1	no	—
43	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
44	#6099	—	2	2	no	—
45	#6099	—	2	2	no	—
46	C₂×#1055	C₄⋊C₄	1	4	yes	—
47	C₂×#1055	C₂×D₄	1	2	yes	—
48	C₂×#1055	C₂×D₄	1	1	yes	characteristic
49	C₂×#1055	C₂×Q₈	1	2	yes	—
50	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
51	#6092	—	4	1	no	—
52	#6092	—	4	2	no	—
53	#6092	—	4	1	no	—
54	#2153	—	13	1	no	—
55	#2153	—	13	2	no	—
56	#2151	—	13	2	no	—
57	#2151	—	13	1	no	—
58	#1747	—	13	1	no	—
59	C₂³×C₁₃	#131	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	4	no	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₃	#131	1	2	yes	—
64	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
65	C₂×Dic₁₃	—	2	2	no	—
66	C₈×C₁₃	—	2	2	no	—
67	#1055	—	2	4	no	—
68	#1055	#127	1	1	yes	characteristic
69	#1055	C₄⋊Q₈	1	2	yes	—
70	#1055	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×M₃₂	—	13	2	no	—
72	C₂×M₃₂	—	13	1	no	—
73	C₂²×C₁₆	—	13	1	no	—
74	#405	—	13	1	no	—
75	#405	—	13	2	no	—
76	#364	—	26	4	no	—
77	#364	—	26	2	no	—
78	C₄⋊C₁₆	—	26	4	no	—
79	C₄⋊C₁₆	—	26	2	no	—
80	#338	—	13	1	no	—
81	H(3,ℤ/4)	—	13	2	no	—
82	H(3,ℤ/4)	#261	1	1	yes	characteristic
83	C₂²×C₁₃	—	4	1	no	—
84	C₂²×C₁₃	#424	1	2	yes	—
85	C₂²×C₁₃	#424	1	1	yes	characteristic
86	C₄×C₁₃	—	4	4	no	—
87	C₄×C₁₃	#384	1	1	yes	characteristic
88	C₄×C₁₃	#424	1	1	yes	characteristic
89	C₄×C₁₃	#424	1	2	yes	—
90	Dic₁₃	—	4	2	no	—
91	C₂×M₁₆	—	13	2	no	—
92	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
93	C₂²×C₈	—	13	1	no	—
94	#117	—	13	1	no	—
95	#117	C₂×#261	1	2	yes	—
96	M₃₂	—	26	2	no	—
97	M₃₂	—	26	2	no	—
98	M₃₂	—	26	2	no	—
99	C₂×C₁₆	—	26	2	no	—
100	C₂×C₁₆	—	26	1	no	—
101	C₂×C₁₆	—	26	2	no	—
102	C₂×C₁₆	—	26	1	no	—
103	#97	—	13	2	no	—
104	#97	—	13	4	no	—
105	C₄×C₈	—	13	2	no	—
106	C₄×C₈	—	13	4	no	—
107	C₂×C₁₃	—	2	1	no	—
108	C₂×C₁₃	—	2	2	no	—
109	C₂×C₁₃	#1843	1	1	yes	characteristic
110	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
111	M₁₆	—	2	2	no	—
112	M₁₆	—	26	2	no	—
113	M₁₆	—	26	2	no	—
114	C₂×C₈	—	13	1	no	—
115	C₂×C₈	—	13	2	no	—
116	C₂×C₈	—	13	1	no	—
117	C₂×C₈	—	13	2	no	—
118	C₂×C₈	—	13	4	no	—
119	C₂×C₈	C₄⋊#261	1	2	yes	—
120	C₄⋊C₄	—	2	2	no	—
121	C₄⋊C₄	—	26	1	no	—
122	C₂²⋊C₄	—	2	2	no	—
123	C₂²⋊C₄	—	26	1	no	—
124	C₄²	—	13	2	no	—
125	C₄²	C₄⋊#261	1	4	yes	—
126	C₁₆	—	52	1	no	—
127	C₁₆	—	52	2	no	—
128	C₁₆	—	52	1	no	—
129	C₁₃	#12902	1	1	yes	characteristic, complemented, Sylow
130	C₂³	#88238	1	1	yes	characteristic
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	26	2	no	—
133	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
134	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
135	C₂×C₄	#88238	1	2	yes	—
136	C₂×C₄	#88240	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	13	1	no	—
139	C₈	—	13	2	no	—
140	C₈	—	13	1	no	—
141	C₈	—	26	4	no	—
142	C₂²	—	4	1	no	—
143	C₂²	#11719067	1	2	yes	—
144	C₂²	#11719079	1	1	yes	characteristic
145	C₄	—	4	4	no	—
146	C₄	—	52	2	no	—
147	C₄	#11719059	1	1	yes	characteristic
148	C₄	#11719067	1	1	yes	characteristic
149	C₄	#11719079	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	—	2	1	no	—
152	C₂	#13130770	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13131179

C₂

yes

maximal

#13131177

C₂

yes

maximal, characteristic

#13131173

C₂

yes

maximal, characteristic

#13131171

C₂

yes

maximal

#13114590

C₂

yes

maximal, characteristic

C₂×#88106

C₂²

yes

—

C₂×#88106

C₂²

yes

characteristic

C₂²×#6092

C₂²

yes

characteristic

#11718783

C₂²

yes

characteristic

#11718658

C₂²

yes

—

—

—

—

—

C₁₃×H(3,ℤ/4)

C₄

yes

characteristic

#11718152

C₄

yes

characteristic

#11718123

C₄

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

characteristic

C₁₃×#117

C₂×C₄

yes

—

#88180

C₂×C₄

yes

characteristic

C₂×#6099

C₂×C₄

yes

—

C₂²×#1055

C₂³

yes

—

—

—

—

—

—

—

Q₈

yes

—

C₈×Dic₁₃

D₄

yes

—

#88043

Q₈

yes

—

C₄×#1055

D₄

yes

—

#12902

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₁₃×M₁₆

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

C₄⋊C₄

yes

—

#6099

—

#6099

—

C₂×#1055

C₄⋊C₄

yes

—

C₂×#1055

C₂×D₄

yes

—

C₂×#1055

C₂×D₄

yes

characteristic

C₂×#1055

C₂×Q₈

yes

—

C₂×#1055

C₂×Q₈

yes

—

—

—

—

—

—

—

—

C₂³×C₁₃

#131

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

#131

yes

characteristic

C₂×Dic₁₃

—

C₈×C₁₃

—

—

yes

C₄⋊Q₈

yes

—

#1055

C₄⋊Q₈

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

—

C₂²×C₁₆

—

—

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

—

—

yes

C₂²×C₁₃

—

C₂²×C₁₃

#424

yes

—

C₂²×C₁₃

#424

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

C₂×#261

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×#261

yes

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

#97

—

104

#97

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₂×C₁₃

—

108

C₂×C₁₃

—

109

C₂×C₁₃

#1843

yes

characteristic

110

C₂²×C₄

C₂²×#261

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₄⋊#261

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

C₄⋊#261

yes

—

126

C₁₆

—

127

C₁₆

—

128

C₁₆

—

129

C₁₃

#12902

yes

characteristic, complemented, Sylow

130

C₂³

#88238

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

134

C₂×C₄

C₂×C₄⋊#261

yes

—

135

C₂×C₄

#88238

yes

—

136

C₂×C₄

#88240

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₂²

—

143

C₂²

#11719067

yes

—

144

C₂²

#11719079

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

#11719059

yes

characteristic

148

C₄

#11719067

yes

characteristic

149

C₄

#11719079

yes

—

150

C₂

—

151

C₂

—

152

C₂

#13130770

yes

characteristic

	subgroup	G/H
center	C₄	#11719059
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×H(3,ℤ/4)	C₄
socle	C₂×C₁₃	#1843
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×#1055	C₂³
hypercenter	H(3,ℤ/4)	#261
hypocenter	C₁₃	#12902
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#11719059

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×#261

Fitting

C₁₃×H(3,ℤ/4)

C₄

C₂×C₁₃

C₂³×C₁₃

C₂²×#1055

C₂³

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
129. C₁₃	#12902	semidirect

H ≅ G/N

type

129. C₁₃

#12902

semidirect

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

subgroup	index
#13131179	2
#13131177	2
#13131173	2
#13131171	2
#13114590	2
#12902	13

subgroup

index

Subgroups — #16790259

Conjugacy classes of subgroups

Complements

Maximal subgroups