Group #16786585 — subgroups

Subgroups — #16786585

Order 3328.

330 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 176 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	C₄×#88098	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#13129748	C₂	1	2	yes	maximal, complemented
4	C₈×#6092	C₂	1	2	yes	maximal, complemented
5	#13113121	C₂	1	1	yes	maximal, characteristic
6	C₂×#88098	C₄	1	2	yes	—
7	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	—
8	#11718346	C₄	1	2	yes	—
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	#11718258	C₄	1	2	yes	—
11	#11718257	C₄	1	2	yes	—
12	C₄×#6092	C₂²	1	1	yes	characteristic
13	C₄×#6092	C₂²	1	2	yes	—
14	C₄×#6092	C₂²	1	1	yes	characteristic
15	C₁₃×#322	C₄	1	1	yes	characteristic
16	#11718047	C₄	1	1	yes	characteristic
17	C₈×#1055	C₂²	1	2	yes	—
18	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#6092	C₂×C₄	1	2	yes	—
22	C₂×#6092	C₂×C₄	1	2	yes	—
23	C₂×#6092	C₂×C₄	1	4	yes	—
24	#88098	C₈	1	8	yes	complemented
25	D₁₃⋊C₁₆	C₈	1	8	yes	complemented
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	#88060	C₈	1	4	yes	—
29	#88054	C₈	1	4	yes	—
30	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₄×#1055	C₂×C₄	1	2	yes	—
33	C₄×#1055	C₂³	1	1	yes	characteristic
34	#11399	—	13	1	no	maximal, Sylow
35	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
36	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
40	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
42	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
43	C₂×#1055	C₂×C₈	1	4	yes	—
44	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
45	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
46	C₈×D₁₃	C₂×C₈	1	4	yes	—
47	C₈×D₁₃	C₂×C₈	1	4	yes	—
48	#6092	C₂×C₈	1	4	yes	—
49	#6092	C₂×C₈	1	4	yes	—
50	#6092	C₂×C₈	1	8	yes	—
51	C₄×M₃₂	—	13	1	no	—
52	C₂×C₄×C₁₆	—	13	1	no	—
53	#1450	—	13	1	no	—
54	#1311	—	13	2	no	—
55	C₈×C₁₆	—	13	2	no	—
56	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
59	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
60	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
61	C₄×D₁₃	—	2	4	no	—
62	C₄×D₁₃	C₄×C₈	1	2	yes	—
63	C₄×D₁₃	C₄×C₈	1	2	yes	—
64	C₈×C₁₃	—	2	4	no	—
65	C₈×C₁₃	C₄×C₈	1	2	yes	—
66	C₈×C₁₃	C₄×C₈	1	2	yes	—
67	#1055	—	2	4	no	—
68	#1055	C₂²×C₈	1	2	yes	—
69	#1055	C₂²×C₈	1	2	yes	—
70	C₂×M₃₂	—	13	2	no	—
71	C₂²×C₁₆	—	13	2	no	—
72	#431	—	13	2	no	—
73	C₂×C₄×C₈	—	13	1	no	—
74	#346	—	13	2	no	—
75	C₄×C₁₆	—	13	1	no	—
76	C₄×C₁₆	—	13	2	no	—
77	C₄×C₁₆	—	13	1	no	—
78	C₄×C₁₆	—	13	2	no	—
79	#322	—	13	1	no	—
80	#322	#261	1	1	yes	characteristic
81	C₈²	—	13	2	no	—
82	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
83	C₂×D₁₃	—	2	2	no	—
84	C₂×D₁₃	C₈²	1	2	yes	—
85	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
86	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
87	C₄×C₁₃	#504	1	4	yes	—
88	Dic₁₃	—	2	2	no	—
89	Dic₁₃	C₈²	1	2	yes	—
90	C₂²×C₈	—	13	1	no	—
91	C₂²×C₈	—	13	1	no	—
92	C₂×C₄²	—	13	1	no	—
93	M₃₂	—	13	8	no	—
94	C₂×C₁₆	—	13	8	no	—
95	C₂×C₁₆	—	13	2	no	—
96	C₂×C₁₆	—	13	2	no	—
97	C₂×C₁₆	—	13	4	no	—
98	C₄⋊C₈	—	13	4	no	—
99	C₂²⋊C₈	—	13	4	no	—
100	C₄×C₈	—	13	1	no	—
101	C₄×C₈	—	13	1	no	—
102	C₄×C₈	—	13	1	no	—
103	C₄×C₈	—	13	2	no	—
104	C₄×C₈	C₂×#261	1	2	yes	—
105	C₄×C₈	C₂×#261	1	1	yes	characteristic
106	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
107	C₂×C₁₃	#2108	1	2	yes	—
108	D₁₃	—	2	2	no	—
109	C₂²×C₄	—	13	1	no	—
110	C₂²×C₄	—	13	2	no	—
111	C₂×C₈	—	13	1	no	—
112	C₂×C₈	—	13	1	no	—
113	C₂×C₈	—	13	4	no	—
114	C₂×C₈	—	13	4	no	—
115	C₂×C₈	—	13	4	no	—
116	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
117	C₂×C₈	C₄×#261	1	1	yes	characteristic
118	C₂×C₈	C₄×#261	1	1	yes	characteristic
119	C₄²	—	13	2	no	—
120	C₄²	—	13	1	no	—
121	C₄²	C₂²×#261	1	1	yes	characteristic
122	C₁₆	—	13	4	no	—
123	C₁₆	—	13	4	no	—
124	C₁₆	—	13	8	no	—
125	C₁₃	#11399	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	13	1	no	—
127	C₂×C₄	—	13	1	no	—
128	C₂×C₄	—	13	2	no	—
129	C₂×C₄	—	13	2	no	—
130	C₂×C₄	—	13	2	no	—
131	C₂×C₄	—	26	4	no	—
132	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
133	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
134	C₈	—	2	4	no	—
135	C₈	—	13	2	no	—
136	C₈	—	13	2	no	—
137	C₈	—	26	4	no	—
138	C₈	C₈×#261	1	2	yes	—
139	C₈	C₈×#261	1	2	yes	—
140	C₂²	—	13	2	no	—
141	C₂²	—	26	2	no	—
142	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
143	C₄	—	13	2	no	—
144	C₄	—	26	2	no	—
145	C₄	C₂×C₈×#261	1	1	yes	characteristic
146	C₄	C₂×C₈×#261	1	1	yes	characteristic
147	C₄	#11719096	1	4	yes	—
148	C₂	—	26	2	no	—
149	C₂	C₈×D₁₃⋊C₈	1	1	yes	characteristic
150	C₂	#13131046	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88098

C₂

yes

maximal, characteristic

C₄×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

#13129748

C₂

yes

maximal, complemented

C₈×#6092

C₂

yes

maximal, complemented

#13113121

C₂

yes

maximal, characteristic

C₂×#88098

C₄

yes

—

C₂×D₁₃⋊C₁₆

C₄

yes

—

#11718346

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718258

C₄

yes

—

#11718257

C₄

yes

—

C₄×#6092

C₂²

yes

characteristic

C₄×#6092

C₂²

yes

—

C₄×#6092

C₂²

yes

characteristic

C₁₃×#322

C₄

yes

characteristic

#11718047

C₄

yes

characteristic

C₈×#1055

C₂²

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×#6092

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

#88098

C₈

yes

complemented

D₁₃⋊C₁₆

C₈

yes

complemented

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

—

#88060

C₈

yes

—

#88054

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

characteristic

#11399

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

C₂²×C₄

yes

characteristic

C₈×D₁₃

C₂×C₈

yes

—

C₈×D₁₃

C₂×C₈

yes

—

#6092

C₂×C₈

yes

—

#6092

C₂×C₈

yes

—

#6092

C₂×C₈

yes

—

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

#1311

—

C₈×C₁₆

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₄×C₈

yes

—

C₄×D₁₃

C₄×C₈

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄×C₈

yes

—

C₈×C₁₃

C₄×C₈

yes

—

#1055

—

#1055

C₂²×C₈

yes

—

#1055

C₂²×C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

—

yes

C₈²

—

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₈²

yes

—

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

#504

yes

—

Dic₁₃

—

Dic₁₃

C₈²

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

C₂×#261

yes

—

105

C₄×C₈

C₂×#261

yes

characteristic

106

C₂×C₁₃

C₂×C₈²

yes

characteristic

107

C₂×C₁₃

#2108

yes

—

108

D₁₃

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

D₁₃⋊C₈

yes

—

117

C₂×C₈

C₄×#261

yes

characteristic

118

C₂×C₈

C₄×#261

yes

characteristic

119

C₄²

—

120

C₄²

—

121

C₄²

C₂²×#261

yes

characteristic

122

C₁₆

—

123

C₁₆

—

124

C₁₆

—

125

C₁₃

#11399

yes

characteristic, complemented, Sylow

126

C₂³

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

133

C₂×C₄

C₂×C₄×#261

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

C₈×#261

yes

—

139

C₈

C₈×#261

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₄×D₁₃⋊C₈

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

C₂×C₈×#261

yes

characteristic

146

C₄

C₂×C₈×#261

yes

characteristic

147

C₄

#11719096

yes

—

148

C₂

—

149

C₂

C₈×D₁₃⋊C₈

yes

characteristic

150

C₂

#13131046

yes

—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#261
commutator	C₂×C₁₃	C₂×C₈²
Fitting	C₁₃×#322	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×#1055	C₂³
hypercenter	#322	#261
hypocenter	C₁₃	#11399
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×#261

commutator

C₂×C₁₃

C₂×C₈²

Fitting

C₁₃×#322

C₄

socle

C₂²×C₁₃

C₂×C₄×C₈

prime radical

C₂²×D₁₃

C₄×C₈

C₂³

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
3. #13129748	C₂	semidirect
4. C₈×#6092	C₂	semidirect
24. #88098	C₈	semidirect
25. D₁₃⋊C₁₆	C₈	semidirect
125. C₁₃	#11399	semidirect

H ≅ G/N

type

3. #13129748

C₂

semidirect

4. C₈×#6092

C₂

semidirect

24. #88098

C₈

semidirect

25. D₁₃⋊C₁₆

C₈

semidirect

125. C₁₃

#11399

semidirect

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

subgroup	index
C₄×#88098	2
C₄×D₁₃⋊C₁₆	2
#13129748	2
C₈×#6092	2
#13113121	2
#11399	13

subgroup

index

C₄×D₁₃⋊C₁₆

Subgroups — #16786585

Conjugacy classes of subgroups

Complements

Maximal subgroups