Finite Group Databasebeta

← #16782182

Subgroups — #16782182

Order 3328.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130562C212yesmaximal
2#13129712C212yesmaximal, complemented
3#13129712C212yesmaximal, complemented
4#13117239C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9C2×#88110C2214yes—
10#11718638C2211yescharacteristic
11#11718638C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718637C411yescharacteristic
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—28no—
37#88110—28no—
38#88071—22no—
39#88071—22no—
40#8721—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—21no—
52C22×Dic13—21no—
53C22×Dic13—42no—
54C22×Dic13C22⋊C412yes—
55C22×Dic13C2×D412yes—
56C2×#1057—28no—
57C2×#1057—44no—
58C2×#1057—44no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C22⋊C4—42no—
62C42×C13—42no—
63C22⋊Dic13—42no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66#6101—44no—
67#6101—44no—
68C4×Dic13—22no—
69C4×Dic13—24no—
70C4×Dic13—42no—
71C4×Dic13#4114yes—
72#2285—131no—
73#1749—132no—
74#1295—132no—
75#1295—132no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13#10112yes—
81C23×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13—28no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13#10012yes—
92C2×C4×C13#11712yes—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—48no—
98C2×Dic13—41no—
99C2×Dic13—41no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13#10414yes—
103C2×Dic13#12314yes—
104#1057—48no—
105C2×#117—131no—
106C2×#117#26111yescharacteristic
107C22×C42—131no—
108C2×C22⋊C8—262no—
109C2×#97—134no—
110#384—131no—
111#384—131no—
112#382—131no—
113#382—131no—
114#380—262no—
115C4×C4⋊C4—262no—
116#336—262no—
117C22×C13—22no—
118C22×C13—24no—
119C22×C13—41no—
120C22×C13—42no—
121C22×C13—41no—
122C22×C13#38111yescharacteristic
123C22×C13C2×#10011yescharacteristic
124C22×C13C2×#10111yescharacteristic
125C22×C13C2×#10412yes—
126C22×C13#42112yes—
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—81no—
130C4×C13—81no—
131Dic13—24no—
132Dic13—24no—
133Dic13—81no—
134Dic13—81no—
135C23×C4—132no—
136C23×C4C2×#26111yescharacteristic
137C22×C8—264no—
138#117—42no—
139#117—522no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—262no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4C2×#26111yescharacteristic
145C2×C4⋊C4C2×#26111yescharacteristic
146C2×C22⋊C4—21no—
147C2×C22⋊C4—261no—
148C2×C42—21no—
149C2×C42—131no—
150C2×C42—132no—
151C2×C42—131no—
152C2×C42—264no—
153C2×C42—261no—
154C22⋊C8—268no—
155#97—268no—
156#95—262no—
157#95—262no—
158C2×C13—42no—
159C2×C13#152511yescharacteristic
160C2×C13#153112yes—
161C2×C13#153611yescharacteristic
162C2×C13#182111yescharacteristic
163C2×C13#182612yes—
164C24C22⋊#26111yescharacteristic
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—264no—
173C22×C4—264no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4—522no—
177C22×C4C22⋊#26111yescharacteristic
178C22×C4C22×#26111yescharacteristic
179C2×C8—268no—
180C2×C8—524no—
181C2×C8—524no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C4⋊C4—524no—
187C4⋊C4—524no—
188C22⋊C4—42no—
189C22⋊C4—522no—
190C42—42no—
191C42—134no—
192C42—264no—
193C42—262no—
194C42—522no—
195C13#872111yescharacteristic, complemented, Sylow
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23#8811312yes—
201C23C2×C22⋊#26111yescharacteristic
202C2×C4—28no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—134no—
212C2×C4—134no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—528no—
218C2×C4—521no—
219C2×C4—521no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4#8812112yes—
223C2×C4#8823712yes—
224C8—528no—
225C22—24no—
226C22—22no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C2×#8811311yescharacteristic
231C22#1171913511yescharacteristic
232C22D13⋊#10412yes—
233C22#1171916612yes—
234C22C2×#8812111yescharacteristic
235C4—22no—
236C4—22no—
237C4—81no—
238C4—81no—
239C4—264no—
240C4—264no—
241C4—1041no—
242C4—1041no—
243C2—42no—
244C2#1313029011yescharacteristic
245C2#1313030812yes—
246C2#1313032411yescharacteristic
247C2#1313073511yescharacteristic
248C2#1313074412yes—
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#8721
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. #13129712C2semidirect
3. #13129712C2semidirect
195. C13#8721semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131297122
#131172392
#872113