Finite Group Databasebeta

← #16782198

Subgroups — #16782198

Order 3328.

514 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130693C212yesmaximal
2#13129714C212yesmaximal, complemented
3#13129714C212yesmaximal, complemented
4#13117242C211yesmaximal, characteristic
5C2×#88146C411yescharacteristic
6C2×#88146C411yescharacteristic
7C2×C42×D13C2211yescharacteristic
8C2×#88112C2214yes—
9C2×#88111—22no—
10C13×#382C411yescharacteristic
11#11718637C2211yescharacteristic
12#11718637C2211yescharacteristic
13#11718597C411yescharacteristic
14#11718328—22no—
15#11718310—22no—
16#11718290—22no—
17C22×C4×D13C2×C411yescharacteristic
18C22×C4×D13D412yes—
19C22×#1057—24no—
20C2×C13×C4⋊C4C2×C411yescharacteristic
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—21no—
24C2×#6103—21no—
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13C2×C411yescharacteristic
27C2×#6101—22no—
28C2×#6101—22no—
29C2×C4×Dic13—21no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13D412yes—
32C2×C4×Dic13C2311yescharacteristic
33#88146—42no—
34#88146—42no—
35C42×D13—24no—
36#88112—28no—
37#88111—44no—
38C13×#95—22no—
39#88071—22no—
40#8728—131nomaximal, Sylow
41C23×D13C22⋊C411yescharacteristic
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13C22⋊C412yes—
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C22×Dic13C22⋊C411yescharacteristic
49C22×Dic13C2×D412yes—
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—24no—
54C2×C4×D13—24no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×#1057—44no—
58C2×#1057—44no—
59C2×#1057—44no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C42×C13—22no—
63#6103—42no—
64#6103—42no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67#6101—44no—
68#6101—42no—
69#6101—42no—
70C4×Dic13—24no—
71C4×Dic13—42no—
72C4×Dic13—42no—
73C4×Dic13#4114yes—
74#2285—131no—
75#1797—132no—
76#1296—132no—
77#1296—132no—
78C23×C13C2×C22⋊C411yescharacteristic
79C22×D13—21no—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13#10112yes—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13#11712yes—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—41no—
97C2×Dic13—41no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13#10012yes—
101C2×Dic13#12314yes—
102C2×Dic13#13514yes—
103C2×Dic13AGL(1,ℤ/8)12yes—
104C2×Dic13#13712yes—
105C4×D13—28no—
106C4×D13—44no—
107C4×D13—44no—
108#1057—84no—
109C2×#117—131no—
110C2×#117—131no—
111C22×C42—131no—
112C2×C4⋊C8—134no—
113C2×C22⋊C8—262no—
114#384—131no—
115#384—131no—
116#382—131no—
117#382#26111yescharacteristic
118#380—262no—
119C4×C4⋊C4—262no—
120#336—262no—
121C22×C13#38111yescharacteristic
122C22×C13C2×#10011yescharacteristic
123C22×C13C2×#10111yescharacteristic
124C22×C13#41612yes—
125C22×C13#41712yes—
126C2×D13—24no—
127C2×D13—22no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—42no—
131C4×C13—22no—
132C4×C13—42no—
133C4×C13—81no—
134C4×C13—81no—
135Dic13—22no—
136Dic13—81no—
137Dic13—81no—
138Dic13#48214yes—
139Dic13#48514yes—
140C23×C4—132no—
141C23×C4—131no—
142C22×C8—264no—
143#117—522no—
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—261no—
152C2×C22⋊C4—261no—
153C2×C42—131no—
154C2×C42—132no—
155C2×C42—264no—
156C2×C42—261no—
157C2×C42—261no—
158C2×C42C2×#26111yescharacteristic
159C4⋊C8—268no—
160C22⋊C8—524no—
161#95—22no—
162#95—262no—
163C2×C13#154311yescharacteristic
164C2×C13#155212yes—
165C2×C13#156011yescharacteristic
166C2×C13#182111yescharacteristic
167C2×C13#182512yes—
168D13—42no—
169C24—131no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—132no—
173C22×C4—131no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4—264no—
177C22×C4—262no—
178C22×C4—264no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4—261no—
182C22×C4—261no—
183C22×C4C22⋊#26112yes—
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—522no—
196C22⋊C4—522no—
197C42—22no—
198C42—134no—
199C42—264no—
200C42—522no—
201C42—522no—
202C13#872811yescharacteristic, complemented, Sylow
203C23—132no—
204C23—261no—
205C23—261no—
206C23—262no—
207C23—262no—
208C23C2×C22⋊#26111yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
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—132no—
223C2×C4—268no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—524no—
227C2×C4—524no—
228C2×C4—521no—
229C2×C4—521no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4#8823712yes—
233C8—1044no—
234C22—264no—
235C22—262no—
236C22—521no—
237C22—521no—
238C22—522no—
239C22#1171913511yescharacteristic
240C22D13⋊#10011yescharacteristic
241C22D13⋊#10111yescharacteristic
242C22#1171916412yes—
243C22#1171916512yes—
244C4—22no—
245C4—42no—
246C4—81no—
247C4—81no—
248C4—134no—
249C4—134no—
250C4—262no—
251C4—1041no—
252C4—1041no—
253C2—522no—
254C2#1313034011yescharacteristic
255C2#1313035812yes—
256C2#1313037411yescharacteristic
257C2#1313073611yescharacteristic
258C2#1313074112yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#8728
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

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
#131306932
#131297142
#131172422
#872813