Finite Group Databasebeta

← #15760539

Subgroups — #15760539

Order 3328.

490 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117948C211yesmaximal, characteristic
2#13113460C211yesmaximal, characteristic
3#13113348C212yesmaximal, complemented
4#13112730C212yesmaximal, complemented
5C13×#3140C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×C13×#124C2211yescharacteristic
8C13×#489C414yescomplemented
9C13×#488—22no—
10C13×#419—21no—
11C13×#418—21no—
12C4×C13×M16C2211yescharacteristic
13#11718891—21no—
14#11718881—21no—
15#11718612—22no—
16C22⋊C4×Dic13—22no—
17#11718593C2212yes—
18#11718587C2212yes—
19#11718132—22no—
20#11718130—22no—
21#11718130—22no—
22C22×Q8×C13D411yescharacteristic
23C22×D4×C13D411yescharacteristic
24C23×Dic13—21no—
25C2×C13×M16—21no—
26C13×C4⋊Q8C2×C412yescomplemented
27C13×#125—21no—
28C13×#124—22no—
29C13×#124C2×C412yes—
30C13×#124D412yes—
31C13×C22⋊Q8—22no—
32C4×Q8×C13—22no—
33C13×#117—21no—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13—21no—
41C13×#103—24no—
42C13×#102—24no—
43C13×#97C2×C412yescomplemented
44C4×C8×C13—21no—
45#88071—22no—
46#88071—22no—
47#88071D412yes—
48#88071D412yes—
49C22⋊#1055—22no—
50C4⋊#1055—22no—
51#88043—22no—
52#9439—131nomaximal, Sylow
53C24×C13—21no—
54C2×Q8×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×Q8×C13C22⋊C412yes—
59C2×D4×C13—21no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13C22⋊C412yes—
63C22×C4×C13—21no—
64C22×C4×C13C2×D412yes—
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—44no—
69C22×Dic13—81no—
70C13×M16—41no—
71C13×M16—41no—
72C2×C8×C13—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—24no—
78C13×C22⋊C4—41no—
79C42×C13—41no—
80C42×C13C22×C411yescharacteristic
81C42×C13C2×D411yescharacteristic
82C42×C13#4112yes—
83C22⋊Dic13—44no—
84C22⋊Dic13—81no—
85C4⋊Dic13—81no—
86C4×Dic13—44no—
87C4×Dic13—81no—
88C2×#1055—42no—
89#3140D1311yescharacteristic
90#2372—131no—
91#1533—131no—
92#1506—132no—
93#1300—132no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#12011yescharacteristic
100Q8×C13—42no—
101Q8×C13—81no—
102Q8×C13—82no—
103D4×C13—42no—
104D4×C13—81no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13C4×D412yes—
114C2×C4×C13#12112yes—
115C2×C4×C13#12311yescharacteristic
116C2×Dic13—24no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—84no—
123C8×C13—42no—
124#1055—82no—
125#533C2×D1311yescharacteristic
126C2×#124C2×D1311yescharacteristic
127#489Dic1314yescomplemented
128#488—22no—
129#432—132no—
130#419—21no—
131#418—21no—
132C4×M16C2×D1311yescharacteristic
133#391—261no—
134#388—262no—
135#386—261no—
136C4×C22⋊C4—262no—
137#376—132no—
138#329—262no—
139#328—262no—
140#328—262no—
141C22×C13—22no—
142C22×C13—42no—
143C22×C13—44no—
144C22×C13—81no—
145C22×C13—81no—
146C22×C13—82no—
147C22×C13#38611yescharacteristic
148C22×C13#45511yescharacteristic
149C22×C13#45511yescharacteristic
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—22no—
153C4×C13—22no—
154C4×C13—42no—
155C4×C13—82no—
156Dic13—44no—
157Dic13—82no—
158C22×Q8C22⋊D1311yescharacteristic
159C22×D4C22⋊D1311yescharacteristic
160C23×C4—261no—
161C2×M16—21no—
162C4⋊Q8C2×Dic1312yescomplemented
163#125—21no—
164#124—22no—
165#124C2×Dic1312yes—
166#124C22⋊D1312yes—
167C22⋊Q8—22no—
168C4×Q8—22no—
169#117—21no—
170C2×C4⋊C4—261no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—262no—
173C2×C22⋊C4—261no—
174C2×C42—262no—
175C2×C42—261no—
176C2×C42C22×D1311yescharacteristic
177C4⋊C8—262no—
178#103—24no—
179#102—24no—
180C22⋊C8—262no—
181#97—262no—
182#97C2×Dic1312yescomplemented
183C4×C8—21no—
184#95—132no—
185#95—132no—
186#95—262no—
187#95—262no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—82no—
191C2×C13#188511yescharacteristic
192C2×C13#190612yes—
193C24—21no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8C22⋊Dic1312yes—
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C22⋊Dic1312yes—
203C22×C4—21no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—524no—
207C22×C4—1041no—
208C22×C4D4×D1312yes—
209C22×C4C2×C22⋊D1311yescharacteristic
210M16—41no—
211M16—41no—
212C2×C8—22no—
213C2×C8—522no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C4⋊C4—1041no—
218C22⋊C4—24no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—524no—
222C22⋊C4—1041no—
223C42—41no—
224C42—524no—
225C42—1041no—
226C42#612912yes—
227C42C22×Dic1311yescharacteristic
228C42C2×C22⋊D1311yescharacteristic
229C13#943911yescharacteristic, complemented, Sylow
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23#8819111yescharacteristic
236Q8—42no—
237Q8—81no—
238Q8—82no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—264no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—1044no—
255C2×C4D4×Dic1312yes—
256C2×C4#8818911yescharacteristic
257C2×C4#8819312yes—
258C2×C4C2×C22⋊Dic1311yescharacteristic
259C8—42no—
260C8—1042no—
261C22—22no—
262C22—42no—
263C22—44no—
264C22—81no—
265C22—81no—
266C22—82no—
267C22#1171872211yescharacteristic
268C22#1171872211yescharacteristic
269C22#1171888111yescharacteristic
270C4—21no—
271C4—21no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—82no—
276C4—524no—
277C4—1042no—
278C2—21no—
279C2—21no—
280C2—82no—
281C2#1311522511yescharacteristic
282C2#1311533912yes—
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3140C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#3140D13
hypocenterC13#9439
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
3. #13113348C2semidirect
4. #13112730C2semidirect
8. C13×#489C4semidirect
26. C13×C4⋊Q8C2×C4semidirect
43. C13×#97C2×C4semidirect
127. #489Dic13semidirect
162. C4⋊Q8C2×Dic13semidirect
182. #97C2×Dic13semidirect
229. C13#9439semidirect

Maximal subgroups

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

subgroupindex
#131179482
#131134602
#131133482
#131127302
C13×#31402
#943913