Finite Group Databasebeta

← #15772077

Subgroups — #15772077

Order 3328.

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

normal subgroups only

This group has 462 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#13112782C212yesmaximal, complemented
3#13112780C212yesmaximal, complemented
4C13×#2285C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C2211yescharacteristic
7C22×C42×C13C411yescharacteristic
8C13×#384C411yescharacteristic
9C13×#384C2211yescharacteristic
10C13×#382C411yescharacteristic
11C13×#382C2211yescharacteristic
12C13×#380—22no—
13C4×C13×C4⋊C4—22no—
14#11718586—22no—
15#11718120C2214yes—
16#11718117—22no—
17C23×C4×C13—21no—
18C23×C4×C13C2×C411yescharacteristic
19C13×#117—41no—
20C13×#117—41no—
21C13×#117—41no—
22C13×#117—41no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4D412yes—
31C2×C42×C13—21no—
32C2×C42×C13—22no—
33C2×C42×C13—21no—
34C2×C42×C13C814yescomplemented
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D412yes—
38C13×#95—22no—
39C13×#95—22no—
40C22⋊#1055—24no—
41C4⋊#1055—42no—
42C4×#1055—42no—
43#11447—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—24no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—42no—
54C22×C4×C13—42no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C2×C812yes—
58C22×C4×C13M1612yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—44no—
66C13×C4⋊C4—44no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—42no—
69C42×C13—24no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—41no—
75C42×C13—41no—
76C42×C13C2×C812yes—
77C42×C13C2×C812yes—
78C2×#1055—44no—
79#2285D1311yescharacteristic
80#1458—132no—
81#1325—132no—
82#1324—132no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13C22⋊C812yes—
88C23×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—48no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13C22⋊C812yes—
111C2×C4×C13#9911yescharacteristic
112C2×C4×C13#9911yescharacteristic
113C2×C4×C13#10112yes—
114C2×C4×C13C22×C811yescharacteristic
115C2×C4×C13C2×M1611yescharacteristic
116#1055—84no—
117C2×#117Dic1311yescharacteristic
118C2×#117C2×D1311yescharacteristic
119C22×C42Dic1311yescharacteristic
120#431—262no—
121#384Dic1311yescharacteristic
122#384C2×D1311yescharacteristic
123#382Dic1311yescharacteristic
124#382C2×D1311yescharacteristic
125#380—22no—
126C4×C4⋊C4—22no—
127#324—134no—
128#323—262no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—22no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13C2×C22⋊C811yescharacteristic
137C22×C13C2×#9911yescharacteristic
138C22×C13C2×#10111yescharacteristic
139C4×C13—24no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13—42no—
144C4×C13—42no—
145C4×C13—81no—
146C4×C13—81no—
147C4×C13#32412yes—
148C4×C13#32412yes—
149C23×C4—21no—
150C23×C4C2×Dic1311yescharacteristic
151#117—41no—
152#117—41no—
153#117—41no—
154#117—41no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4C2×Dic1311yescharacteristic
158C2×C4⋊C4C2×Dic1311yescharacteristic
159C2×C4⋊C4C2×Dic1311yescharacteristic
160C2×C4⋊C4C22×D1311yescharacteristic
161C2×C22⋊C4—21no—
162C2×C22⋊C4C22⋊D1312yes—
163C2×C42—22no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42#105514yescomplemented
167C2×C42C2×Dic1311yescharacteristic
168C2×C42C2×Dic1311yescharacteristic
169C2×C42C22⋊D1312yes—
170C4⋊C8—522no—
171C22⋊C8—264no—
172C4×C8—522no—
173#95—22no—
174#95—22no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—42no—
178C2×C13C2×#32411yescharacteristic
179C2×C13#212611yescharacteristic
180C2×C13#213211yescharacteristic
181C24C22⋊Dic1311yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4C2×#105512yes—
193C22×C4#609912yes—
194C22×C4C22⋊Dic1312yes—
195C22×C4C22⋊Dic1311yescharacteristic
196C22×C4C22×Dic1311yescharacteristic
197C22×C4C2×C22⋊D1312yes—
198C2×C8—524no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—44no—
204C4⋊C4—44no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C42—24no—
208C42—22no—
209C42—22no—
210C42—21no—
211C42—21no—
212C42—41no—
213C42—41no—
214C42C2×#105512yes—
215C42C2×#105512yes—
216C13#1144711yescharacteristic, complemented, Sylow
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23C22⋊#105512yes—
222C23C2×C22⋊Dic1311yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—48no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4C22⋊#105512yes—
245C2×C4#8807411yescharacteristic
246C2×C4#8807411yescharacteristic
247C2×C4#8807612yes—
248C2×C4C22×#105511yescharacteristic
249C2×C4C2×#609911yescharacteristic
250C8—1044no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×C22⋊#105511yescharacteristic
259C22C2×#8807411yescharacteristic
260C22C2×#8807611yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—42no—
267C4—81no—
268C4—81no—
269C4#1171812012yes—
270C4#1171812012yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#1171812011yescharacteristic
275C2#1311650111yescharacteristic
276C2#1311652111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2285C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2285D13
hypocenterC13#11447
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13112782C2semidirect
3. #13112780C2semidirect
34. C2×C42×C13C8semidirect
166. C2×C42#1055semidirect
216. C13#11447semidirect

Maximal subgroups

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

subgroupindex
#131131502
#131127822
#131127802
C13×#22852
#1144713