Finite Group Databasebeta

← #15760369

Subgroups — #15760369

Order 3328.

644 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 111 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#13120316C211yesmaximal, characteristic
2#13113351C212yesmaximal
3#13113166C211yesmaximal, characteristic, complemented
4#13112722C212yesmaximal, complemented
5C13×#2274C211yesmaximal, characteristic, complemented
6C2×C13×#117—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88184C2211yescharacteristic
9C4×C13×C4⋊C4—24no—
10C4×C13×C22⋊C4—21no—
11C4×C13×C22⋊C4C2212yes—
12#11718874—21no—
13#11718874—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16#11718652C412yescomplemented
17#11718651—22no—
18#11718647C412yescomplemented
19#11718120—22no—
20#11718043—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C13×#117—28no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C22⋊C4—22no—
33C2×C42×C13—22no—
34C2×C42×C13—22no—
35C2×C42×C13—22no—
36C2×C22⋊Dic13—21no—
37#88184—22no—
38#88184—22no—
39C2×#6103—22no—
40C2×#6103—21no—
41C2×#6103—22no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4×Dic13—21no—
44C2×#6099—22no—
45C13×#95—22no—
46C13×#95D414yes—
47#88071—22no—
48#88071—22no—
49#88071C2×C412yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9410—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C23×D13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—24no—
58C22×C4×C13—21no—
59C22×C4×C13—24no—
60C22×C4×C13—21no—
61C22×C4×C13—81no—
62C22×C4×C13—81no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13#4112yes—
69C2×C22⋊D13—44no—
70C2×C22⋊D13—41no—
71C2×C22⋊D13—41no—
72C22×Dic13—21no—
73C22×Dic13—22no—
74C2×D52—22no—
75C2×D52—81no—
76C13×C4⋊C4—28no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C22⋊C4—28no—
80C42×C13—28no—
81C42×C13—82no—
82C42×C13—82no—
83C22⋊Dic13—42no—
84#6103—44no—
85#6103—42no—
86#6103—82no—
87C4⋊Dic13—22no—
88C4×Dic13—81no—
89#6099—82no—
90C2×#1055—42no—
91#2591—131no—
92#2274D1311yescharacteristic, complemented
93#1507—132no—
94#1463—131no—
95#1297—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#12011yescharacteristic
101C23×C13#12311yescharacteristic
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—41no—
105C22×D13—42no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—24no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—28no—
112C2×C4×C13—22no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—81no—
122C2×C4×C13#10414yes—
123C2×C4×C13C4×D412yes—
124C2×C4×C13#12112yes—
125C22⋊D13—82no—
126C22⋊D13—82no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13—42no—
132D52—82no—
133#1055—82no—
134C2×#121—131no—
135C2×#117—21no—
136C22×C4⋊C4C2×D1311yescharacteristic
137#407—132no—
138#400—132no—
139#394—132no—
140#388—262no—
141#386—261no—
142#386—261no—
143C4×C4⋊C4—24no—
144C4×C22⋊C4—21no—
145C4×C22⋊C4—131no—
146C4×C22⋊C4C2×D1312yes—
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#38611yescharacteristic
158C22×C13C2×#10412yes—
159C22×C13#45412yes—
160C2×D13—84no—
161C2×D13—81no—
162C2×D13—81no—
163C2×D13—81no—
164C4×C13—24no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—48no—
168C4×C13—42no—
169Dic13—82no—
170Dic13—81no—
171C22×D4—131no—
172C22×D4—261no—
173C23×C4C22⋊D1311yescharacteristic
174C23×C4C22⋊D1311yescharacteristic
175C23×C4C22×D1311yescharacteristic
176C2×M16—262no—
177#121—262no—
178#121—262no—
179#117—28no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4C4×D1312yes—
185C2×C4⋊C4D5212yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—261no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4—262no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—261no—
195C22⋊C8—262no—
196C22⋊C8—262no—
197#95—22no—
198#95—132no—
199#95—262no—
200#95—262no—
201#95C22⋊D1314yes—
202C2×C13—22no—
203C2×C13—22no—
204C2×C13—41no—
205C2×C13#188811yescharacteristic
206C2×C13#189611yescharacteristic
207C2×C13#191311yescharacteristic
208D13—161no—
209C24—261no—
210C24C2×C22⋊D1311yescharacteristic
211C2×D4—262no—
212C2×D4—524no—
213C2×D4—521no—
214C2×D4—521no—
215C2×D4—1041no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—262no—
225C22×C4—261no—
226C22×C4#610312yes—
227C22×C4#610312yes—
228C22×C4C2×C4×D1311yescharacteristic
229C22×C4C2×D5211yescharacteristic
230C22×C4#612712yes—
231C22×C4C2×C22⋊D1312yes—
232M16—1042no—
233C2×C8—522no—
234C4⋊C4—28no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—262no—
238C22⋊C4—28no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—524no—
242C22⋊C4—1042no—
243C42—28no—
244C42—82no—
245C42—82no—
246C42—1041no—
247C13#941011yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—41no—
251C23—522no—
252C23—522no—
253C23—522no—
254C23—521no—
255C23C2×#610311yescharacteristic
256C23#8818311yescharacteristic
257C23#8820711yescharacteristic
258D4—1042no—
259D4—1042no—
260D4—1042no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—521no—
282C2×C4#8804514yes—
283C2×C4C4×C22⋊D1312yes—
284C2×C4#8818412yes—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—1044no—
295C22—1041no—
296C22—1041no—
297C22—1041no—
298C22C2×#8804512yes—
299C22#1171887411yescharacteristic
300C22#1171890612yes—
301C4—24no—
302C4—22no—
303C4—22no—
304C4—48no—
305C4—42no—
306C4—1042no—
307C4—1041no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—2081no—
312C2#1311523911yescharacteristic
313C2#1311527911yescharacteristic
314C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2274C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#2274D13
hypocenterC13#9410
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13113166C2semidirect
4. #13112722C2semidirect
5. C13×#2274C2semidirect
16. #11718652C4semidirect
18. #11718647C4semidirect
92. #2274D13semidirect
247. C13#9410semidirect

Maximal subgroups

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

subgroupindex
#131203162
#131133512
#131131662
#131127222
C13×#22742
#941013