Finite Group Databasebeta

← #15760370

Subgroups — #15760370

Order 3328.

644 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 115 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#13117193C211yesmaximal, characteristic, complemented
2#13113352C212yesmaximal
3#13113166C211yesmaximal, characteristic, complemented
4#13112722C212yesmaximal, complemented
5C13×#2591C211yesmaximal, characteristic
6C2×C13×#121C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180—21no—
9C13×#400C412yescomplemented
10C13×#394C412yescomplemented
11C13×#388—22no—
12C13×#386—21no—
13C13×#386—21no—
14C4×C13×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic13—21no—
16C4×C22⋊Dic13C2212yes—
17#11718868C2212yes—
18C4⋊C4×Dic13—24no—
19#11718129—24no—
20#11718120—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#121—22no—
27C13×#121—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13—21no—
38C2×C22⋊Dic13—22no—
39#88180—28no—
40C2×C4⋊Dic13—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—22no—
43C2×C4×Dic13—22no—
44C2×#6099—22no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95C2×C412yes—
48#88071—22no—
49#88071D414yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9410—131nomaximal, Sylow
53C24×C13—21no—
54C24×C13C2×D411yescharacteristic
55C2×D4×C13—22no—
56C2×D4×C13—44no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—81no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C22×Dic13—24no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—82no—
83C42×C13—81no—
84C22⋊Dic13—28no—
85C4⋊Dic13—28no—
86C4×Dic13—28no—
87C4×Dic13—82no—
88C4×Dic13—82no—
89#6099—82no—
90C2×#1055—42no—
91#2591D1311yescharacteristic
92#2274—131no—
93#1507—132no—
94#1463—131no—
95#1297—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#12011yescharacteristic
105C23×C13#12311yescharacteristic
106D4×C13—82no—
107D4×C13—82no—
108D4×C13—82no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13#10414yes—
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12112yes—
130C2×Dic13—28no—
131C2×Dic13—44no—
132C2×Dic13—44no—
133#1055—82no—
134C2×#121C2×D1311yescharacteristic
135C2×#117—261no—
136C22×C4⋊C4C2×D1311yescharacteristic
137#407—132no—
138#400Dic1312yescomplemented
139#394Dic1312yescomplemented
140#388—22no—
141#386—21no—
142#386—21no—
143C4×C4⋊C4—264no—
144C4×C22⋊C4—132no—
145C4×C22⋊C4—261no—
146C4×C22⋊C4C2×D1311yescharacteristic
147#327—264no—
148#324—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—44no—
157C22×C13—84no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13#38611yescharacteristic
162C22×C13C2×#10412yes—
163C22×C13#45412yes—
164C4×C13—24no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—42no—
168C4×C13—82no—
169C4×C13—81no—
170Dic13—48no—
171C22×D4—21no—
172C22×D4C2×Dic1311yescharacteristic
173C23×C4C22⋊D1311yescharacteristic
174C23×C4C22⋊D1311yescharacteristic
175C23×C4C22×D1311yescharacteristic
176C2×M16—262no—
177#121—22no—
178#121—22no—
179#117—268no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—262no—
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C2×Dic1312yes—
185C2×C4⋊C4C22⋊D1312yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—262no—
191C2×C42—21no—
192C2×C42—262no—
193C2×C42—262no—
194C2×C42—262no—
195C22⋊C8—262no—
196C22⋊C8—262no—
197#95—22no—
198#95—22no—
199#95—134no—
200#95—262no—
201#95C2×Dic1312yes—
202C2×C13—22no—
203C2×C13—22no—
204C2×C13—41no—
205C2×C13—161no—
206C2×C13#188811yescharacteristic
207C2×C13#189611yescharacteristic
208C2×C13#191311yescharacteristic
209C24—21no—
210C24C2×C22⋊D1311yescharacteristic
211C2×D4—22no—
212C2×D4—44no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—81no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—264no—
226C22×C4C22⋊Dic1312yes—
227C22×C4C22⋊Dic1312yes—
228C22×C4D4×D1312yes—
229C22×C4#612912yes—
230C22×C4C22×Dic1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—1042no—
233C2×C8—522no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—268no—
238C22⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—268no—
243C42—81no—
244C42—268no—
245C42—1042no—
246C42—1042no—
247C13#941011yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—41no—
251C23—42no—
252C23—42no—
253C23—41no—
254C23—42no—
255C23#8818911yescharacteristic
256C23#8819111yescharacteristic
257C23C2×C22⋊Dic1311yescharacteristic
258D4—82no—
259D4—82no—
260D4—82no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—268no—
280C2×C4—524no—
281C2×C4—524no—
282C2×C4#8807714yes—
283C2×C4D4×Dic1312yes—
284C2×C4#8819312yes—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—84no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1171872312yes—
299C22#1171888111yescharacteristic
300C22C2×#8807712yes—
301C4—24no—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—81no—
307C4—528no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—161no—
312C2#1311524011yescharacteristic
313C2#1311528011yescharacteristic
314C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2591C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2591D13
hypocenterC13#9410
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. #13117193C2semidirect
3. #13113166C2semidirect
4. #13112722C2semidirect
9. C13×#400C4semidirect
10. C13×#394C4semidirect
138. #400Dic13semidirect
139. #394Dic13semidirect
247. C13#9410semidirect

Maximal subgroups

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

subgroupindex
#131171932
#131133522
#131131662
#131127222
C13×#25912
#941013