Finite Group Databasebeta

← #15772097

Subgroups — #15772097

Order 3328.

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

normal subgroups only

This group has 562 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×#11718117C212yesmaximal
2#13112784C214yesmaximal, complemented
3C13×#2315C211yesmaximal, characteristic
4C22×C13×C22⋊C4C411yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#385—22no—
8C13×#385C412yes—
9C13×#385C2212yes—
10C13×#380—22no—
11C2×C22⋊#1055—22no—
12#11718117—22no—
13#11718117C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13C2×C412yes—
17C23×C4×C13D412yes—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C22⋊C4—21no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—21no—
23C2×C13×C22⋊C4—21no—
24C2×C13×C22⋊C4—42no—
25C2×C13×C22⋊C4—42no—
26C2×C13×C22⋊C4C814yescomplemented
27C2×C13×C22⋊C4C2×C412yes—
28C2×C13×C22⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4D412yes—
30C2×C13×C22⋊C4C2311yescharacteristic
31C22×#1055—42no—
32C13×#95—22no—
33C13×#95—22no—
34C22⋊#1055—24no—
35C22⋊#1055—42no—
36#11453—131nomaximal, Sylow
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—82no—
40C24×C13C22⋊C411yescharacteristic
41C24×C13C22⋊C411yescharacteristic
42C24×C13C2×C812yes—
43C24×C13M1612yes—
44C24×C13C22×C411yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—24no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—42no—
51C22×C4×C13—82no—
52C22×C4×C13—82no—
53C22×C4×C13—82no—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C2×D412yes—
56C13×C4⋊C4—82no—
57C13×C4⋊C4—82no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—41no—
61C13×C22⋊C4—42no—
62C13×C22⋊C4—41no—
63C13×C22⋊C4—42no—
64C13×C22⋊C4—42no—
65C13×C22⋊C4C2×C814yescomplemented
66C2×#1055—44no—
67C2×#1055—84no—
68#2315D1311yescharacteristic
69C2×#323—132no—
70#1326—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—24no—
76C23×C13—24no—
77C23×C13—42no—
78C23×C13—42no—
79C23×C13—42no—
80C23×C13—82no—
81C23×C13—82no—
82C23×C13—84no—
83C23×C13—82no—
84C23×C13—82no—
85C23×C13C22⋊C812yes—
86C23×C13C22⋊C812yes—
87C23×C13#9912yes—
88C23×C13#10112yes—
89C23×C13C2×C22⋊C411yescharacteristic
90C23×C13C22×C811yescharacteristic
91C23×C13C2×M1611yescharacteristic
92C2×C4×C13—24no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—44no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—82no—
104C2×C4×C13—84no—
105C2×C4×C13—84no—
106#1055—84no—
107C22×C22⋊C4Dic1311yescharacteristic
108C22×C22⋊C4Dic1311yescharacteristic
109C22×C22⋊C4C2×D1311yescharacteristic
110C2×C22⋊C8—262no—
111#385—22no—
112#385Dic1312yes—
113#385C2×D1312yes—
114#380—22no—
115#323—134no—
116#323—262no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—84no—
133C22×C13—84no—
134C22×C13#32414yes—
135C22×C13C2×C22⋊C811yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#10111yescharacteristic
138C4×C13—44no—
139C4×C13—42no—
140C4×C13—42no—
141C4×C13—82no—
142C25C2×Dic1311yescharacteristic
143C23×C4—21no—
144C23×C4C2×Dic1312yes—
145C23×C4C22⋊D1312yes—
146C22×C8—522no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—42no—
154C2×C22⋊C4—42no—
155C2×C22⋊C4#105514yescomplemented
156C2×C22⋊C4C2×Dic1312yes—
157C2×C22⋊C4C2×Dic1311yescharacteristic
158C2×C22⋊C4C22⋊D1312yes—
159C2×C22⋊C4C22×D1311yescharacteristic
160C22⋊C8—264no—
161C22⋊C8—522no—
162#95—22no—
163#95—22no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—24no—
167C2×C13—42no—
168C2×C13—41no—
169C2×C13—41no—
170C2×C13C2×#32411yescharacteristic
171C2×C13#212112yes—
172C24—22no—
173C24—22no—
174C24—82no—
175C24C2×#105512yes—
176C24#609912yes—
177C24C22⋊Dic1311yescharacteristic
178C24C22⋊Dic1311yescharacteristic
179C24C22×Dic1311yescharacteristic
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—24no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—82no—
187C22×C4—82no—
188C22×C4—82no—
189C22×C4C22⋊Dic1312yes—
190C22×C4C2×C22⋊D1312yes—
191C2×C8—524no—
192C2×C8—1044no—
193C4⋊C4—82no—
194C4⋊C4—82no—
195C22⋊C4—24no—
196C22⋊C4—22no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—41no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4C2×#105514yescomplemented
203C13#1145311yescharacteristic, complemented, Sylow
204C23—21no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—24no—
209C23—24no—
210C23—42no—
211C23—42no—
212C23—42no—
213C23—82no—
214C23—82no—
215C23—82no—
216C23—82no—
217C23—84no—
218C23C22⋊#105512yes—
219C23C22⋊#105512yes—
220C23#8807412yes—
221C23#8807612yes—
222C23C22×#105511yescharacteristic
223C23C2×#609911yescharacteristic
224C23C2×C22⋊Dic1311yescharacteristic
225C2×C4—24no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—84no—
238C2×C4—84no—
239C8—1044no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—84no—
257C22#1171812014yes—
258C22C2×C22⋊#105511yescharacteristic
259C22C2×#8807411yescharacteristic
260C22C2×#8807611yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—24no—
268C2—42no—
269C2—41no—
270C2—41no—
271C2C2×#1171812011yescharacteristic
272C2#1311648212yes—
subgroupG/H
centerC22C2×#88074
commutatorC23×C13C22×C8
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2315C2
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#2315D13
hypocenterC13#11453
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #13112784C2semidirect
26. C2×C13×C22⋊C4C8semidirect
65. C13×C22⋊C4C2×C8semidirect
155. C2×C22⋊C4#1055semidirect
202. C22⋊C4C2×#1055semidirect
203. C13#11453semidirect

Maximal subgroups

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

subgroupindex
C2×#117181172
#131127842
C13×#23152
#1145313