Finite Group Databasebeta

← #16778554

Subgroups — #16778554

Order 3328.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130764C212yesmaximal, complemented
2#13129657C212yesmaximal, complemented
3#13129653C212yesmaximal
4#13117375C211yesmaximal, characteristic
5C2×#88147C411yescharacteristic
6C2×#88141C411yescharacteristic
7C2×#88129C411yescharacteristic
8C13×#382C411yescharacteristic
9#11718649C2211yescharacteristic
10#11718635C2211yescharacteristic
11C42×Dic13C2211yescharacteristic
12#11718330—22no—
13#11718327—22no—
14#11718290—22no—
15#11718290—22no—
16#11718290C2214yes—
17C22×D52C2×C411yescharacteristic
18C22×C4×D13—21no—
19C22×Dic26C2×C411yescharacteristic
20C22×#1057—24no—
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×#6103—22no—
25C2×#6103—21no—
26C2×#6103—22no—
27C2×#6101—21no—
28C2×C4×Dic13—21no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13D412yes—
31C2×C4×Dic13D412yes—
32C2×C4×Dic13C2311yescharacteristic
33#88147—42no—
34#88141—42no—
35#88129—22no—
36#88129—22no—
37C13×#95—22no—
38#88071—22no—
39#7649—131nomaximal, Sylow
40C23×D13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13C22⋊C412yes—
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—21no—
46C22×Dic13C22⋊C411yescharacteristic
47C22×Dic13C22⋊C411yescharacteristic
48C22×Dic13C2×D412yes—
49C2×D52—21no—
50C2×D52—41no—
51C2×D52—41no—
52C2×D52M1612yes—
53C2×C4×D13—44no—
54C2×C4×D13—42no—
55C2×Dic26—21no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26M1612yes—
59C2×#1057—44no—
60C2×#1057—44no—
61C2×#1057—44no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C42×C13—21no—
65C42×C13—21no—
66#6103—28no—
67#6103—42no—
68#6103—44no—
69#6101—42no—
70C4×Dic13—22no—
71C4×Dic13—24no—
72C4×Dic13—42no—
73C4×Dic13—41no—
74C4×Dic13—42no—
75C4×#124—131no—
76#1839—132no—
77#1272—132no—
78#1270—132no—
79C23×C13C2×C22⋊C411yescharacteristic
80C22×D13—22no—
81C22×D13—41no—
82C22×D13—41no—
83C22×D13—42no—
84C22×D13—42no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13C2×M1611yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13#10012yes—
105C2×Dic13#13514yes—
106D52—42no—
107D52—42no—
108C4×D13—84no—
109Dic26—42no—
110Dic26—42no—
111#1057—84no—
112C2×#124—131no—
113C2×C4×Q8—131no—
114C2×C4×D4—131no—
115#391—131no—
116#390—131no—
117#388—262no—
118#382#26111yescharacteristic
119C4×C22⋊C4—262no—
120C43—131no—
121#336—134no—
122#336—262no—
123#336—262no—
124C22×C13#40711yescharacteristic
125C22×C13#41011yescharacteristic
126C22×C13C2×#10011yescharacteristic
127C22×C13#41612yes—
128C22×C13#42112yes—
129C2×D13—42no—
130C2×D13—44no—
131C2×D13—81no—
132C2×D13—82no—
133C2×D13—81no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—81no—
138C4×C13—81no—
139Dic13—24no—
140Dic13—22no—
141Dic13—41no—
142Dic13—42no—
143C22×Q8—131no—
144C22×D4—131no—
145C23×C4—261no—
146C22×C8—264no—
147#124—262no—
148#124—262no—
149C4×Q8—522no—
150C4×D4—522no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C2×#26111yescharacteristic
153C2×C4⋊C4C2×#26111yescharacteristic
154C2×C22⋊C4—262no—
155C2×C22⋊C4—261no—
156C2×C22⋊C4—262no—
157C2×C42—132no—
158C2×C42—131no—
159C2×C42—132no—
160C2×C42—131no—
161C2×C42—261no—
162C2×C42C2×#26111yescharacteristic
163#95—22no—
164#95—262no—
165C2×C13#146611yescharacteristic
166C2×C13#148812yes—
167C2×C13#152112yes—
168C2×C13#153311yescharacteristic
169C2×C13#154311yescharacteristic
170D13—82no—
171C24—261no—
172C2×Q8—132no—
173C2×Q8—261no—
174C2×Q8—521no—
175C2×Q8—521no—
176C2×D4—132no—
177C2×D4—261no—
178C2×D4—521no—
179C2×D4—521no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—132no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—261no—
186C22×C4—522no—
187C22×C4—524no—
188C22×C4C22⋊#26112yes—
189C22×C4C22×#26111yescharacteristic
190C2×C8—524no—
191C2×C8—524no—
192C2×C8—524no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—522no—
196C22⋊C4—268no—
197C22⋊C4—524no—
198C22⋊C4—522no—
199C42—21no—
200C42—21no—
201C42—262no—
202C42—264no—
203C42—521no—
204C42—522no—
205C42—522no—
206C13#764911yescharacteristic, complemented, Sylow
207C23—262no—
208C23—521no—
209C23—521no—
210C23—522no—
211C23—522no—
212C23C2×C22⋊#26111yescharacteristic
213Q8—522no—
214Q8—522no—
215D4—522no—
216D4—522no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—132no—
227C2×C4—134no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—1044no—
237C2×C4D13⋊M1611yescharacteristic
238C2×C4D13⋊M1611yescharacteristic
239C8—1044no—
240C22—522no—
241C22—524no—
242C22—1042no—
243C22—1041no—
244C22—1041no—
245C22#1171912611yescharacteristic
246C22D13⋊#10011yescharacteristic
247C22#1171915611yescharacteristic
248C22#1171916512yes—
249C22#1171916612yes—
250C4—21no—
251C4—21no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—264no—
256C4—262no—
257C4—521no—
258C4—522no—
259C2—1042no—
260C2#1313009711yescharacteristic
261C2#1313016912yes—
262C2#1313027912yes—
263C2#1313031611yescharacteristic
264C2#1313034011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#7649
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
1. #13130764C2semidirect
2. #13129657C2semidirect
206. C13#7649semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131296572
#131296532
#131173752
#764913