Finite Group Databasebeta

← #15760389

Subgroups — #15760389

Order 3328.

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

normal subgroups only

This group has 552 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#13120316C211yesmaximal, characteristic
2#13113351C212yesmaximal
3#13113166C211yesmaximal, characteristic, complemented
4#13112722C212yesmaximal, complemented
5C13×#2313C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C13×#387—24no—
9C13×#381—21no—
10C13×#380—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
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C22⋊C4—22no—
32C2×C42×C13—22no—
33C2×C22⋊Dic13—21no—
34#88184—22no—
35#88184—22no—
36C2×#6103—22no—
37C2×#6103—21no—
38C2×#6103—22no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4×Dic13—21no—
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—24no—
44C13×#95D414yes—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50#9414—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C23×D13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—24no—
58C22×C4×C13—42no—
59C22×C4×C13—81no—
60C22×C4×C13—81no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4112yes—
67C2×C22⋊D13—44no—
68C2×C22⋊D13—41no—
69C2×C22⋊D13—41no—
70C22×Dic13—21no—
71C22×Dic13—22no—
72C2×D52—22no—
73C2×D52—81no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—82no—
77C13×C22⋊C4—44no—
78C42×C13—82no—
79C22⋊Dic13—42no—
80#6103—44no—
81#6103—42no—
82#6103—82no—
83C4⋊Dic13—22no—
84C4×Dic13—81no—
85#6099—82no—
86C2×#1055—42no—
87#2591—131no—
88#2313D1311yescharacteristic, complemented
89#1507—132no—
90#1463—131no—
91#1297—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—41no—
95C23×C13C2×C22⋊C411yescharacteristic
96C23×C13#12011yescharacteristic
97C23×C13#12311yescharacteristic
98C22×D13—42no—
99C22×D13—42no—
100C22×D13—41no—
101C22×D13—42no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—44no—
115C2×C4×C13—44no—
116C2×C4×C13—44no—
117C2×C4×C13—81no—
118C2×C4×C13C4×D412yes—
119C2×C4×C13#12112yes—
120C22⋊D13—82no—
121C22⋊D13—82no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127D52—82no—
128#1055—82no—
129C2×#121—131no—
130C22×C4⋊C4C2×D1311yescharacteristic
131#407—132no—
132#400—132no—
133#394—132no—
134#388—262no—
135#387—24no—
136#386—261no—
137#386—261no—
138#381—21no—
139#380—21no—
140C4×C22⋊C4—131no—
141C4×C22⋊C4C2×D1312yes—
142#327—264no—
143#324—262no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—44no—
152C22×C13#38611yescharacteristic
153C22×C13#42112yes—
154C22×C13#45412yes—
155C2×D13—84no—
156C2×D13—81no—
157C2×D13—81no—
158C2×D13—81no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—42no—
162C4×C13—42no—
163C4×C13—84no—
164Dic13—82no—
165Dic13—81no—
166C22×D4—131no—
167C22×D4—261no—
168C23×C4C22⋊D1311yescharacteristic
169C23×C4C22⋊D1311yescharacteristic
170C23×C4C22×D1311yescharacteristic
171C2×M16—262no—
172#121—262no—
173#121—262no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4C4×D1312yes—
179C2×C4⋊C4D5212yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—261no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—261no—
184C2×C22⋊C4—262no—
185C2×C42—22no—
186C2×C42—261no—
187C22⋊C8—262no—
188C22⋊C8—262no—
189#95—22no—
190#95—24no—
191#95—132no—
192#95—262no—
193#95—262no—
194#95C22⋊D1314yes—
195C2×C13—22no—
196C2×C13—22no—
197C2×C13—41no—
198C2×C13#188811yescharacteristic
199C2×C13#189711yescharacteristic
200C2×C13#191311yescharacteristic
201D13—161no—
202C24—261no—
203C24C2×C22⋊D1311yescharacteristic
204C2×D4—262no—
205C2×D4—524no—
206C2×D4—521no—
207C2×D4—521no—
208C2×D4—1041no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—24no—
214C22×C4—42no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—262no—
218C22×C4—261no—
219C22×C4#610312yes—
220C22×C4#610312yes—
221C22×C4C2×C4×D1311yescharacteristic
222C22×C4C2×D5211yescharacteristic
223C22×C4#612712yes—
224C22×C4C2×C22⋊D1312yes—
225M16—1042no—
226C2×C8—522no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—82no—
230C4⋊C4—262no—
231C22⋊C4—44no—
232C22⋊C4—524no—
233C22⋊C4—522no—
234C22⋊C4—522no—
235C22⋊C4—1042no—
236C42—82no—
237C42—1041no—
238C13#941411yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—41no—
242C23—522no—
243C23—522no—
244C23—522no—
245C23—521no—
246C23C2×#610311yescharacteristic
247C23#8818311yescharacteristic
248C23#8820711yescharacteristic
249D4—1042no—
250D4—1042no—
251D4—1042no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—521no—
273C2×C4C4×C22⋊D1312yes—
274C2×C4#8818412yes—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—1044no—
285C22—1041no—
286C22—1041no—
287C22—1041no—
288C22#1171866612yes—
289C22#1171887411yescharacteristic
290C22#1171890612yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—84no—
296C4—1042no—
297C4—1041no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—2081no—
302C2#1311523911yescharacteristic
303C2#1311528411yescharacteristic
304C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9414
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. #13113166C2semidirect
4. #13112722C2semidirect
5. C13×#2313C2semidirect
16. #11718652C4semidirect
18. #11718647C4semidirect
88. #2313D13semidirect
238. C13#9414semidirect

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×#23132
#941413