Finite Group Databasebeta

← #15772035

Subgroups — #15772035

Order 3328.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#13113150C212yesmaximal
2#13112770C214yesmaximal, complemented
3C13×#2310C211yesmaximal, characteristic
4C23×Q8×C13C411yescharacteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C2211yescharacteristic
7C13×#391—22no—
8C13×#391C412yes—
9C13×#391C2212yes—
10C13×#381—22no—
11#11718586—22no—
12#11718120C2214yes—
13#11718117—22no—
14C22×Q8×C13—21no—
15C22×Q8×C13—22no—
16C22×Q8×C13—42no—
17C22×Q8×C13—42no—
18C22×Q8×C13C814yescomplemented
19C22×Q8×C13C2×C412yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C13×#117—42no—
23C13×#117—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4D412yes—
29C2×C42×C13C2×C412yes—
30C2×C42×C13D412yes—
31C13×#95—24no—
32C13×#95—24no—
33C22⋊#1055—24no—
34C4⋊#1055—42no—
35C4×#1055—42no—
36#11434—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C2×Q8×C13—24no—
39C2×Q8×C13—22no—
40C2×Q8×C13—48no—
41C2×Q8×C13—48no—
42C2×Q8×C13—42no—
43C2×Q8×C13—42no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2×C814yes—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13—24no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—42no—
53C22×C4×C13—42no—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C2×C812yes—
57C22×C4×C13M1612yes—
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D412yes—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—42no—
64C13×C22⋊C4—42no—
65C42×C13—22no—
66C42×C13—22no—
67C42×C13—42no—
68C2×#1055—44no—
69#2310D1311yescharacteristic
70#1458—132no—
71#1319—134no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—41no—
75C23×C13—41no—
76C23×C13C22⋊C812yes—
77C23×C13C2×C22⋊C411yescharacteristic
78Q8×C13—44no—
79Q8×C13—44no—
80Q8×C13—48no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—24no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—48no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13C22⋊C812yes—
97C2×C4×C13#9912yes—
98C2×C4×C13#10012yes—
99C2×C4×C13C22×C811yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101#1055—84no—
102C23×Q8Dic1311yescharacteristic
103C2×#117Dic1311yescharacteristic
104C2×#117C2×D1311yescharacteristic
105#431—262no—
106#391—22no—
107#391Dic1312yes—
108#391C2×D1312yes—
109#381—22no—
110#324—134no—
111#323—262no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—22no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13C2×C22⋊C811yescharacteristic
120C22×C13C2×#9911yescharacteristic
121C22×C13C2×#10011yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13—44no—
127C4×C13—82no—
128C4×C13#32314yes—
129C22×Q8—22no—
130C22×Q8—21no—
131C22×Q8—42no—
132C22×Q8—42no—
133C22×Q8#105514yescomplemented
134C22×Q8C2×Dic1312yes—
135C23×C4—21no—
136C23×C4C2×Dic1311yescharacteristic
137#117—42no—
138#117—42no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4C2×Dic1311yescharacteristic
141C2×C4⋊C4C22×D1311yescharacteristic
142C2×C22⋊C4—21no—
143C2×C22⋊C4C22⋊D1312yes—
144C2×C42C2×Dic1312yes—
145C2×C42C22⋊D1312yes—
146C4⋊C8—522no—
147C22⋊C8—264no—
148C4×C8—522no—
149#95—24no—
150#95—24no—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13—42no—
154C2×C13C2×#32311yescharacteristic
155C2×C13#212911yescharacteristic
156C2×C13#213511yescharacteristic
157C24C22⋊Dic1311yescharacteristic
158C2×Q8—24no—
159C2×Q8—22no—
160C2×Q8—48no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8C2×#105514yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4C2×#105512yes—
175C22×C4#609912yes—
176C22×C4C22⋊Dic1312yes—
177C22×C4C22⋊Dic1311yescharacteristic
178C22×C4C22×Dic1311yescharacteristic
179C22×C4C2×C22⋊D1312yes—
180C2×C8—524no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C22⋊C4—42no—
185C22⋊C4—42no—
186C42—22no—
187C42—22no—
188C42—42no—
189C13#1143411yescharacteristic, complemented, Sylow
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23C22⋊#105512yes—
195C23C2×C22⋊Dic1311yescharacteristic
196Q8—44no—
197Q8—44no—
198Q8—48no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—48no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4C22⋊#105512yes—
215C2×C4#8807312yes—
216C2×C4#8807412yes—
217C2×C4C22×#105511yescharacteristic
218C2×C4C2×#609911yescharacteristic
219C8—1044no—
220C22—21no—
221C22—21no—
222C22—22no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22C2×C22⋊#105511yescharacteristic
228C22C2×#8807311yescharacteristic
229C22C2×#8807411yescharacteristic
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—42no—
235C4—82no—
236C4#1171811714yes—
237C2—21no—
238C2—21no—
239C2—42no—
240C2C2×#1171811711yescharacteristic
241C2#1311651111yescharacteristic
242C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2310C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2310D13
hypocenterC13#11434
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13112770C2semidirect
18. C22×Q8×C13C8semidirect
133. C22×Q8#1055semidirect
189. C13#11434semidirect

Maximal subgroups

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

subgroupindex
#131131502
#131127702
C13×#23102
#1143413