Finite Group Databasebeta

← #15756260

Subgroups — #15756260

Order 3328.

830 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 147 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#13114746C212yesmaximal
2#13112679C214yesmaximal, complemented
3C2×C13×#380C211yesmaximal, characteristic
4C24×C4×C13C2211yescharacteristic
5C22×C13×C4⋊C4C412yes—
6C22×C13×C22⋊C4C412yes—
7C13×#380—22no—
8C13×#380—22no—
9C2×C13×#95C2212yes—
10C2×C22⋊#1055—22no—
11C2×C22⋊#1055—22no—
12C2×C22⋊#1055C2214yes—
13C25×C13C2×C411yescharacteristic
14C23×C4×C13—24no—
15C23×C4×C13—44no—
16C23×C4×C13C2×C411yescharacteristic
17C23×C4×C13C2×C414yes—
18C23×C4×C13D412yes—
19C23×C4×C13D412yes—
20C23×C4×C13C2311yescharacteristic
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—44no—
24C2×C13×C22⋊C4—22no—
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—44no—
27C22×#1055—24no—
28C13×#95—24no—
29C22⋊#1055—28no—
30C22⋊#1055—44no—
31C22⋊#1055—44no—
32#8704—131nomaximal, Sylow
33C24×C13—22no—
34C24×C13—22no—
35C24×C13—22no—
36C24×C13—24no—
37C24×C13—42no—
38C24×C13C22⋊C411yescharacteristic
39C24×C13C22⋊C411yescharacteristic
40C24×C13C22×C411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—24no—
43C22×C4×C13—24no—
44C22×C4×C13—24no—
45C22×C4×C13—24no—
46C22×C4×C13—24no—
47C22×C4×C13—24no—
48C22×C4×C13—28no—
49C22×C4×C13—42no—
50C22×C4×C13—42no—
51C22×C4×C13—42no—
52C22×C4×C13—416no—
53C22×C4×C13—44no—
54C22×C4×C13—44no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C2×D412yes—
57C22×C4×C13#4114yes—
58C13×C4⋊C4—44no—
59C13×C4⋊C4—44no—
60C13×C22⋊C4—44no—
61C13×C22⋊C4—44no—
62C2×#1055—44no—
63C2×#1055—44no—
64C2×#1055—44no—
65C2×#380D1311yescharacteristic
66#1779—132no—
67#1280—134no—
68C23×C13—22no—
69C23×C13—21no—
70C23×C13—21no—
71C23×C13—28no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—48no—
81C23×C13—48no—
82C23×C13—44no—
83C23×C13—44no—
84C23×C13#10012yes—
85C23×C13#10112yes—
86C23×C13C2×C22⋊C411yescharacteristic
87C23×C13#11712yes—
88C23×C13#13114yes—
89C2×C4×C13—28no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—44no—
95C2×C4×C13—48no—
96C2×C4×C13—48no—
97C2×C4×C13—44no—
98C2×C4×C13—44no—
99C2×C4×C13—44no—
100C2×C4×C13—88no—
101C2×C4×C13#9914yes—
102C2×C4×C13#12314yes—
103#1055—84no—
104C24×C4C2×D1311yescharacteristic
105C22×C4⋊C4Dic1312yes—
106C22×C22⋊C4Dic1312yes—
107C2×C22⋊C8—134no—
108C2×C22⋊C8—262no—
109C2×C22⋊C8—262no—
110#380—22no—
111#380—22no—
112C2×#95C2×D1312yes—
113C22×C13—22no—
114C22×C13—22no—
115C22×C13—24no—
116C22×C13—24no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—24no—
120C22×C13—24no—
121C22×C13—416no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13#38111yescharacteristic
129C22×C13#40812yes—
130C22×C13C2×#9912yes—
131C22×C13C2×#10011yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C22×C13#43314yes—
134C4×C13—24no—
135C4×C13—24no—
136C4×C13—84no—
137C25C2×Dic1311yescharacteristic
138C23×C4—24no—
139C23×C4—44no—
140C23×C4C2×Dic1311yescharacteristic
141C23×C4C2×Dic1314yes—
142C23×C4C22⋊D1312yes—
143C23×C4C22⋊D1312yes—
144C23×C4C22×D1311yescharacteristic
145C22×C8—264no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—44no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—44no—
152C22⋊C8—268no—
153C22⋊C8—524no—
154C22⋊C8—524no—
155#95—24no—
156C2×C13—24no—
157C2×C13—42no—
158C2×C13—42no—
159C2×C13#147112yes—
160C2×C13#147212yes—
161C2×C13#181811yescharacteristic
162C2×C13#181911yescharacteristic
163C2×C13#182111yescharacteristic
164C24—22no—
165C24—22no—
166C24—22no—
167C24—24no—
168C24—42no—
169C24C22⋊Dic1311yescharacteristic
170C24C22⋊Dic1311yescharacteristic
171C24C22×Dic1311yescharacteristic
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—28no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—416no—
184C22×C4—44no—
185C22×C4—44no—
186C22×C4C22⋊Dic1312yes—
187C22×C4#612714yes—
188C22×C4C2×C22⋊D1312yes—
189C2×C8—524no—
190C2×C8—524no—
191C2×C8—524no—
192C4⋊C4—44no—
193C4⋊C4—44no—
194C22⋊C4—44no—
195C22⋊C4—44no—
196C13#870411yescharacteristic, complemented, Sylow
197C23—21no—
198C23—22no—
199C23—21no—
200C23—28no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—22no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—22no—
209C23—48no—
210C23—48no—
211C23—44no—
212C23—44no—
213C23#8807312yes—
214C23#8807612yes—
215C23#8818012yes—
216C23#8820214yes—
217C23C2×C22⋊Dic1311yescharacteristic
218C2×C4—28no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—44no—
224C2×C4—48no—
225C2×C4—48no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—88no—
230C2×C4#8807414yes—
231C2×C4#8818314yes—
232C8—1044no—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—22no—
239C22—24no—
240C22—24no—
241C22—416no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22#1171866114yes—
249C22#1171887211yescharacteristic
250C22C2×#8807311yescharacteristic
251C22C2×#8807412yes—
252C22C2×#8807611yescharacteristic
253C22#1171889512yes—
254C4—24no—
255C4—24no—
256C4—84no—
257C2—24no—
258C2—42no—
259C2—42no—
260C2#1311319612yes—
261C2#1311320012yes—
262C2#1311490711yescharacteristic
263C2#1311491011yescharacteristic
264C2#1311491611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#380C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC2×#380D13
hypocenterC13#8704
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13112679C2semidirect
196. C13#8704semidirect

Maximal subgroups

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

subgroupindex
#131147462
#131126792
C2×C13×#3802
#870413