Finite Group Databasebeta

← #16782197

Subgroups — #16782197

Order 3328.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130692C212yesmaximal
2#13129714C212yesmaximal, complemented
3#13129714C212yesmaximal, complemented
4#13117239C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9C2×#88112C2214yes—
10#11718638C411yescharacteristic
11#11718638C411yescharacteristic
12#11718637C2211yescharacteristic
13#11718637C2211yescharacteristic
14#11718603—22no—
15C4×#6101—22no—
16#11718290—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13D412yes—
19C22×#1057—24no—
20C13×#117—42no—
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—21no—
24C2×C42×C13—21no—
25C2×C22⋊Dic13—21no—
26#88180—42no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×#6101—22no—
30C2×#6101—22no—
31C2×C4×Dic13—24no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C22⋊#1057—44no—
37#88112—28no—
38#88071—22no—
39#88071—22no—
40#8728—131nomaximal, Sylow
41C24×C13C22⋊C411yescharacteristic
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—24no—
50C22×Dic13—24no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57C2×#1057—44no—
58C2×#1057—44no—
59C2×#1057—44no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C22⋊C4—42no—
63C42×C13—42no—
64C22⋊Dic13—42no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67#6101—44no—
68#6101—42no—
69#6101—42no—
70C4×Dic13—22no—
71C4×Dic13—24no—
72C4×Dic13—42no—
73C4×Dic13#4114yes—
74#2285—131no—
75#1797—132no—
76#1296—132no—
77#1296—132no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13#10112yes—
83C23×C13C2×C22⋊C411yescharacteristic
84C2×C4×C13—28no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13#10012yes—
94C2×C4×C13#11712yes—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—44no—
99C2×Dic13—44no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13#12314yes—
105C2×Dic13#13514yes—
106C2×Dic13AGL(1,ℤ/8)12yes—
107C2×Dic13#13712yes—
108#1057—84no—
109C2×#117—131no—
110C2×#117#26111yescharacteristic
111C22×C42—131no—
112C2×C4⋊C8—134no—
113C2×C22⋊C8—262no—
114#384—131no—
115#384—131no—
116#382—131no—
117#382—131no—
118#380—262no—
119C4×C4⋊C4—262no—
120#336—262no—
121C22×C13—24no—
122C22×C13—22no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13#38111yescharacteristic
127C22×C13C2×#10011yescharacteristic
128C22×C13C2×#10111yescharacteristic
129C22×C13#41612yes—
130C22×C13#41712yes—
131C4×C13—22no—
132C4×C13—22no—
133C4×C13—81no—
134C4×C13—81no—
135Dic13—42no—
136Dic13—81no—
137Dic13—81no—
138Dic13#48214yes—
139Dic13#48514yes—
140C23×C4—132no—
141C23×C4C2×#26111yescharacteristic
142C22×C8—264no—
143#117—42no—
144#117—522no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4C2×#26111yescharacteristic
150C2×C4⋊C4C2×#26111yescharacteristic
151C2×C22⋊C4—21no—
152C2×C22⋊C4—261no—
153C2×C42—21no—
154C2×C42—131no—
155C2×C42—132no—
156C2×C42—131no—
157C2×C42—264no—
158C2×C42—261no—
159C4⋊C8—268no—
160C22⋊C8—524no—
161#95—262no—
162#95—262no—
163C2×C13—42no—
164C2×C13#154311yescharacteristic
165C2×C13#155212yes—
166C2×C13#156011yescharacteristic
167C2×C13#182111yescharacteristic
168C2×C13#182512yes—
169C24C22⋊#26111yescharacteristic
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—264no—
179C22×C4—262no—
180C22×C4—264no—
181C22×C4—261no—
182C22×C4—261no—
183C22×C4C22⋊#26111yescharacteristic
184C22×C4C22×#26111yescharacteristic
185C2×C8—524no—
186C2×C8—524no—
187C2×C8—524no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—521no—
191C4⋊C4—521no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C4⋊C4—524no—
195C22⋊C4—42no—
196C22⋊C4—522no—
197C42—42no—
198C42—134no—
199C42—264no—
200C42—262no—
201C42—522no—
202C13#872811yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—22no—
206C23—22no—
207C23#8811312yes—
208C23C2×C22⋊#26111yescharacteristic
209C2×C4—28no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—134no—
219C2×C4—132no—
220C2×C4—132no—
221C2×C4—134no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—524no—
226C2×C4—524no—
227C2×C4—521no—
228C2×C4—521no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4#8812112yes—
232C2×C4#8823712yes—
233C8—1044no—
234C22—24no—
235C22—22no—
236C22—41no—
237C22—41no—
238C22—42no—
239C22C2×#8811311yescharacteristic
240C22#1171913511yescharacteristic
241C22#1171916412yes—
242C22#1171916512yes—
243C22C2×#8812111yescharacteristic
244C4—22no—
245C4—22no—
246C4—81no—
247C4—81no—
248C4—134no—
249C4—134no—
250C4—522no—
251C4—1041no—
252C4—1041no—
253C2—42no—
254C2#1313033911yescharacteristic
255C2#1313035712yes—
256C2#1313037311yescharacteristic
257C2#1313073511yescharacteristic
258C2#1313074112yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8728
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
3. #13129714C2semidirect
202. C13#8728semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
#131172392
#872813