Finite Group Databasebeta

← #15758927

Subgroups — #15758927

Order 3328.

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

normal subgroups only

This group has 458 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#13120657C211yesmaximal, characteristic
2#13113518C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112696C212yesmaximal, complemented
5C13×#2921C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#433—24no—
9C13×#423C2212yes—
10C13×#407—21no—
11C4×C13×M16—21no—
12#11718873—21no—
13#11718647—21no—
14#11718640C412yes—
15#11718610—21no—
16#11718608C412yes—
17#11718597C2211yescharacteristic
18#11718589—21no—
19#11718586C2212yes—
20#11718120—21no—
21#11718117—21no—
22#11718073—24no—
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C412yes—
25C2×C13×M16—22no—
26C13×#117—22no—
27C13×#117—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C22⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×#6101—22no—
39#88123—22no—
40#88123—22no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8D414yes—
43C13×C22⋊C8—24no—
44C13×#97—22no—
45C4×C8×C13—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071C2×C412yes—
50C22⋊#1055—22no—
51C4⋊#1055—22no—
52C4×#1055—22no—
53#9192—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C2×Dic26—24no—
68C2×Dic26—82no—
69C13×M16—42no—
70C13×M16—42no—
71C2×C8×C13—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C22⋊C4—22no—
75C13×C22⋊C4—22no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13C2×D412yes—
79C42×C13#4112yes—
80C22⋊Dic13—82no—
81C4⋊Dic13—41no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—42no—
85#6101—82no—
86C2×#1055—42no—
87#2921D1311yescharacteristic
88#2628—131no—
89#1548—132no—
90#1458—131no—
91#1286—132no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13C2×C22⋊C411yescharacteristic
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13C4×D412yes—
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13#12112yes—
112C2×C4×C13#12311yescharacteristic
113C2×C4×C13#13512yes—
114C2×C4×C13#13712yes—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121Dic26—84no—
122C8×C13—44no—
123#1055—82no—
124C2×C4⋊Q8—131no—
125C2×#117C2×D1311yescharacteristic
126#433—24no—
127#431—132no—
128#423C2×D1312yes—
129#407—21no—
130C4×M16—21no—
131#400—261no—
132#399—261no—
133#395—132no—
134#393—132no—
135#389—261no—
136#382—131no—
137#380—261no—
138#333—264no—
139#324—261no—
140#323—261no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—42no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—81no—
148C22×C13#38611yescharacteristic
149C22×C13#41611yescharacteristic
150C22×C13#41911yescharacteristic
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13#45212yes—
157C4×C13#48512yes—
158Dic13—82no—
159Dic13—82no—
160C22×Q8—132no—
161C23×C4C22⋊D1311yescharacteristic
162C2×M16—22no—
163C4⋊Q8—262no—
164C4⋊Q8—262no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—262no—
171C2×C4⋊C4C4×D1311yescharacteristic
172C2×C4⋊C4D5211yescharacteristic
173C2×C22⋊C4—262no—
174C2×C22⋊C4C4×D1311yescharacteristic
175C2×C22⋊C4D5211yescharacteristic
176C2×C42C22⋊D1311yescharacteristic
177C2×C42C22×D1311yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—262no—
180C4⋊C8C22⋊D1314yes—
181C22⋊C8—24no—
182C22⋊C8—262no—
183#97—22no—
184C4×C8—22no—
185C4×C8—262no—
186#95—132no—
187#95—262no—
188#95—262no—
189#95—261no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—81no—
193C2×C13#187311yescharacteristic
194C2×C13#190911yescharacteristic
195C2×C13#191411yescharacteristic
196C24#610311yescharacteristic
197C2×Q8—264no—
198C2×Q8—1042no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4#610311yescharacteristic
206C22×C4#610311yescharacteristic
207C22×C4#610311yescharacteristic
208C22×C4C2×C4×D1311yescharacteristic
209C22×C4C2×D5211yescharacteristic
210C22×C4C2×C22⋊D1311yescharacteristic
211M16—42no—
212M16—42no—
213C2×C8—24no—
214C2×C8—522no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—521no—
218C4⋊C4—522no—
219C4⋊C4—522no—
220C4⋊C4—521no—
221C4⋊C4—1042no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—1042no—
225C42—21no—
226C42—21no—
227C42#612712yes—
228C42C2×C22⋊D1312yes—
229C13#919211yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×#610311yescharacteristic
236Q8—1044no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4C4×C22⋊D1312yes—
255C2×C4#8818311yescharacteristic
256C2×C4#8818412yes—
257C2×C4#8820412yes—
258C2×C4#8820512yes—
259C2×C4#8820711yescharacteristic
260C8—44no—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1171866311yescharacteristic
270C22#1171866511yescharacteristic
271C22#1171887411yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1042no—
278C4—1042no—
279C4#1171865712yes—
280C4#1171890012yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1311514811yescharacteristic
285C2#1311535811yescharacteristic
286C2#1311538311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2921C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2921D13
hypocenterC13#9192
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #13113518C2semidirect
4. #13112696C2semidirect
229. C13#9192semidirect

Maximal subgroups

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

subgroupindex
#131206572
#131135182
#131131502
#131126962
C13×#29212
#919213