Finite Group Databasebeta

← #15772081

Subgroups — #15772081

Order 3328.

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

normal subgroups only

This group has 454 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
1C2×#11718120C212yesmaximal
2#13112782C212yesmaximal, complemented
3#13112780C212yesmaximal, complemented
4C13×#2317C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#389—22no—
9C13×#385—22no—
10C13×#384C411yescharacteristic
11C13×#384C2211yescharacteristic
12C13×#382C411yescharacteristic
13C13×#382C2211yescharacteristic
14C2×C22⋊#1055—22no—
15#11718120—22no—
16#11718120C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13D412yes—
19C13×#117—22no—
20C13×#117—42no—
21C13×#117C814yescomplemented
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—42no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C42×C13—21no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C22×#1055—42no—
37C13×#95—22no—
38C13×#95—22no—
39C22⋊#1055—24no—
40C22⋊#1055—42no—
41#11448—131nomaximal, Sylow
42C24×C13C22⋊C411yescharacteristic
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—82no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C2×C812yes—
55C22×C4×C13M1612yes—
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D412yes—
58C13×C4⋊C4—24no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—82no—
65C13×C4⋊C4—82no—
66C13×C22⋊C4—24no—
67C13×C22⋊C4—42no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—42no—
71C42×C13C2×C812yescomplemented
72C42×C13C2×C812yescomplemented
73C2×#1055—44no—
74C2×#1055—84no—
75#2317D1311yescharacteristic
76C2×#324—132no—
77#1325—132no—
78#1324—132no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13C22⋊C812yes—
82C23×C13#9912yes—
83C23×C13#10112yes—
84C23×C13C2×C22⋊C411yescharacteristic
85C2×C4×C13—24no—
86C2×C4×C13—24no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—44no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—82no—
107C2×C4×C13C22⋊C812yes—
108C2×C4×C13C22×C811yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110#1055—84no—
111C2×#117Dic1311yescharacteristic
112C2×#117Dic1311yescharacteristic
113C22×C4⋊C4C2×D1311yescharacteristic
114C2×C22⋊C8—262no—
115#389—22no—
116#385—22no—
117#384Dic1311yescharacteristic
118#384C2×D1311yescharacteristic
119#382Dic1311yescharacteristic
120#382C2×D1311yescharacteristic
121#324—134no—
122#324—262no—
123C22×C13—21no—
124C22×C13—22no—
125C22×C13—21no—
126C22×C13—22no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13#32414yes—
130C22×C13C2×C22⋊C811yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C4×C13—22no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—81no—
141C4×C13—81no—
142C23×C4C2×Dic1311yescharacteristic
143C23×C4C22⋊D1312yes—
144C22×C8—522no—
145#117—22no—
146#117—42no—
147#117#105514yescomplemented
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4C2×Dic1311yescharacteristic
153C2×C4⋊C4C2×Dic1311yescharacteristic
154C2×C4⋊C4C2×Dic1311yescharacteristic
155C2×C4⋊C4C22⋊D1312yes—
156C2×C4⋊C4C22×D1311yescharacteristic
157C2×C22⋊C4—21no—
158C2×C22⋊C4—21no—
159C2×C42—21no—
160C2×C42C2×Dic1311yescharacteristic
161C2×C42C2×Dic1311yescharacteristic
162C22⋊C8—264no—
163C22⋊C8—522no—
164#95—22no—
165#95—22no—
166C2×C13—21no—
167C2×C13—24no—
168C2×C13—21no—
169C2×C13C2×#32411yescharacteristic
170C2×C13#212711yescharacteristic
171C2×C13#213311yescharacteristic
172C24C22⋊Dic1311yescharacteristic
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—82no—
182C22×C4C2×#105512yes—
183C22×C4#609912yes—
184C22×C4C22⋊Dic1311yescharacteristic
185C22×C4C22⋊Dic1312yes—
186C22×C4C22×Dic1311yescharacteristic
187C22×C4C2×C22⋊D1312yes—
188C2×C8—524no—
189C2×C8—1044no—
190C4⋊C4—24no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C22⋊C4—24no—
199C22⋊C4—42no—
200C42—21no—
201C42—21no—
202C42—42no—
203C42C2×#105512yescomplemented
204C42C2×#105512yescomplemented
205C13#1144811yescharacteristic, complemented, Sylow
206C23—41no—
207C23—41no—
208C23C22⋊#105512yes—
209C23#8807412yes—
210C23#8807612yes—
211C23C2×C22⋊Dic1311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4C22⋊#105512yes—
235C2×C4C22×#105511yescharacteristic
236C2×C4C2×#609911yescharacteristic
237C8—1044no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1171812014yes—
245C22C2×C22⋊#105511yescharacteristic
246C22C2×#8807411yescharacteristic
247C22C2×#8807611yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—24no—
260C2C2×#1171812011yescharacteristic
261C2#1311650511yescharacteristic
262C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2317C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2317D13
hypocenterC13#11448
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #13112782C2semidirect
3. #13112780C2semidirect
21. C13×#117C8semidirect
71. C42×C13C2×C8semidirect
72. C42×C13C2×C8semidirect
147. #117#1055semidirect
203. C42C2×#1055semidirect
204. C42C2×#1055semidirect
205. C13#11448semidirect

Maximal subgroups

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

subgroupindex
C2×#117181202
#131127822
#131127802
C13×#23172
#1144813