Finite Group Databasebeta

← #13130659

Subgroups — #13130659

Order 1664.

852 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D13C211yesmaximal, characteristic
2C2×C22⋊#1057C212yesmaximal, complemented
3C2×#88111C214yesmaximal, complemented
4C24×D13C411yescharacteristic
5C23×C4×C13C411yescharacteristic
6C23×Dic13C2211yescharacteristic
7C22×C4×D13—24no—
8C22×C4×D13—28no—
9C22×C4×D13C412yes—
10C22×C4×D13C2212yes—
11C22×#1057C2214yescomplemented
12C22⋊#1057—24no—
13#88111—28no—
14C24×C13C2×C411yescharacteristic
15C23×D13—22no—
16C23×D13—22no—
17C23×D13—24no—
18C23×D13—24no—
19C23×D13C814yescomplemented
20C23×D13C2×C412yes—
21C22×C4×C13—22no—
22C22×C4×C13—24no—
23C22×C4×C13C2×C412yes—
24C22×Dic13—24no—
25C22×Dic13C2×C411yescharacteristic
26C22×Dic13D414yes—
27C22×Dic13C2311yescharacteristic
28C2×C4×D13—232no—
29C2×C4×D13—24no—
30C2×C4×D13—24no—
31C2×C4×D13—24no—
32C2×C4×D13—24no—
33C2×C4×D13—24no—
34C2×C4×D13D418yes—
35C2×#1057—28no—
36C2×#1057—24no—
37#1779—131nomaximal, Sylow
38C23×C13—22no—
39C23×C13—22no—
40C23×C13C22⋊C412yes—
41C23×C13C2×C812yes—
42C23×C13M1612yes—
43C23×C13C22×C411yescharacteristic
44C22×D13—28no—
45C22×D13—216no—
46C22×D13—28no—
47C22×D13—28no—
48C22×D13—22no—
49C22×D13—22no—
50C22×D13—22no—
51C22×D13—22no—
52C22×D13—216no—
53C22×D13C22⋊C414yes—
54C22×D13C2×C814yes—
55C22×D13M1614yes—
56C2×C4×C13—28no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13C22⋊C414yes—
60C2×Dic13—22no—
61C2×Dic13—28no—
62C2×Dic13C22⋊C412yes—
63C2×Dic13C2×D412yes—
64C2×Dic13C2×D414yes—
65C4×D13—216no—
66C4×D13—216no—
67#1057—44no—
68C24×C4—131no—
69C2×C22⋊C8—132no—
70C2×C22⋊C8—134no—
71C22×C13—22no—
72C22×C13—24no—
73C22×C13—22no—
74C22×C13—24no—
75C22×C13C22⋊C814yescomplemented
76C22×C13C2×C22⋊C412yes—
77C22×C13C2×C22⋊C411yescharacteristic
78C22×C13C22×C811yescharacteristic
79C22×C13C2×M1611yescharacteristic
80C22×C13C2×M1612yes—
81C2×D13—232no—
82C2×D13—24no—
83C2×D13—24no—
84C2×D13—24no—
85C2×D13—24no—
86C2×D13—24no—
87C2×D13—24no—
88C2×D13C22⋊C818yescomplemented
89C4×C13—24no—
90Dic13—22no—
91Dic13#12014yes—
92C25—131no—
93C23×C4—131no—
94C23×C4—132no—
95C23×C4—132no—
96C23×C4—264no—
97C23×C4—268no—
98C23×C4#26111yescharacteristic
99C22×C8—134no—
100C22⋊C8—268no—
101C22⋊C8—264no—
102C2×C13—24no—
103C2×C13#37911yescharacteristic
104C2×C13C2×C22⋊C811yescharacteristic
105C2×C13C2×C22⋊C812yes—
106C2×C13#40711yescharacteristic
107C2×C13#40712yes—
108D13—28no—
109C24—132no—
110C24—134no—
111C24—264no—
112C24—264no—
113C24—262no—
114C24—262no—
115C24C2×#26111yescharacteristic
116C22×C4—22no—
117C22×C4—24no—
118C22×C4—131no—
119C22×C4—134no—
120C22×C4—131no—
121C22×C4—138no—
122C22×C4—264no—
123C22×C4—264no—
124C22×C4—264no—
125C22×C4—264no—
126C22×C4—2632no—
127C22×C4—264no—
128C22×C4—264no—
129C22×C4C2×#26112yes—
130C2×C8—268no—
131C2×C8—264no—
132C13#177911yescharacteristic, complemented, Sylow
133C23—22no—
134C23—22no—
135C23—134no—
136C23—134no—
137C23—134no—
138C23—2616no—
139C23—268no—
140C23—268no—
141C23—2616no—
142C23—268no—
143C23—262no—
144C23—262no—
145C23—262no—
146C23—262no—
147C23D13⋊C812yes—
148C23#611812yes—
149C23C22⋊#26112yes—
150C23C22×#26111yescharacteristic
151C2×C4—28no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—132no—
155C2×C4—134no—
156C2×C4—132no—
157C2×C4—2616no—
158C2×C4—2616no—
159C2×C4—268no—
160C2×C4—262no—
161C2×C4C22⋊#26114yes—
162C8—524no—
163C22—22no—
164C22—24no—
165C22—22no—
166C22—24no—
167C22—138no—
168C22—2632no—
169C22—264no—
170C22—264no—
171C22—264no—
172C22—264no—
173C22—264no—
174C22—264no—
175C22#8811114yescomplemented
176C22C2×D13⋊C811yescharacteristic
177C22C2×#611811yescharacteristic
178C22D13⋊M1612yes—
179C22C2×C22⋊#26111yescharacteristic
180C22C2×C22⋊#26112yes—
181C4—24no—
182C4—134no—
183C4—262no—
184C2—24no—
185C2—268no—
186C2C2×#8811111yescharacteristic
187C2D13⋊(C22⋊C8)12yes—
188C2#1171912611yescharacteristic
189C2#1171912712yes—
190C2#1171917111yescharacteristic
subgroupG/H
center, FrattiniC23C22×#261
commutatorC22×C13C22×C8
FittingC23×C4×C13C4
socleC23×C13C22×C4
prime radicalC24×D13C4
cosocleC22×Dic13C23
hypercenterC23×C4#261
hypocenterC13#1779
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#1057C2semidirect
3. C2×#88111C2semidirect
11. C22×#1057C22semidirect
19. C23×D13C8semidirect
75. C22×C13C22⋊C8semidirect
88. C2×D13C22⋊C8semidirect
132. C13#1779semidirect
175. C22#88111semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D132
C2×C22⋊#10572
C2×#881112
#177913