Finite Group Databasebeta

← #15758947

Subgroups — #15758947

Order 3328.

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

normal subgroups only

This group has 478 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#13120602C211yesmaximal, characteristic
2#13113509C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112696C212yesmaximal, complemented
5C13×#2921C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88178—21no—
8C2×#88123C2211yescharacteristic
9C13×#433—24no—
10C13×#423C2212yes—
11C13×#407—21no—
12C4×C13×M16—21no—
13#11718644—21no—
14#11718644C412yes—
15#11718614—21no—
16#11718614C412yes—
17#11718597C2211yescharacteristic
18#11718590—21no—
19#11718586C2212yes—
20#11718120—21no—
21#11718117—21no—
22#11718074—24no—
23C23×C4×C13D411yescharacteristic
24C22×Dic26—21no—
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⋊Dic13C2×C412yes—
38#88178—44no—
39C2×#6101—22no—
40#88123—22no—
41#88123—22no—
42C13×C4⋊C8—22no—
43C13×C4⋊C8D414yes—
44C13×C22⋊C8—24no—
45C13×#97—22no—
46C4×C8×C13—22no—
47#88071—22no—
48#88071—22no—
49#88071—21no—
50#88071C2×C412yes—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53C4×#1055—22no—
54#9196—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×Dic26—42no—
71C2×Dic26—42no—
72C13×M16—42no—
73C13×M16—42no—
74C2×C8×C13—24no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4—22no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13C2×D412yes—
82C42×C13#4112yes—
83C22⋊Dic13—44no—
84C4⋊Dic13—24no—
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87#6101—44no—
88C2×#1055—42no—
89#2921D1311yescharacteristic
90#2621—131no—
91#1546—132no—
92#1458—131no—
93#1286—132no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13C4×D412yes—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13#12112yes—
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13#13512yes—
116C2×C4×C13AGL(1,ℤ/8)12yes—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123Dic26—82no—
124Dic26—82no—
125C8×C13—44no—
126#1055—82no—
127C2×C4⋊Q8—131no—
128C2×C22⋊Q8—261no—
129C2×#117C2×D1311yescharacteristic
130#433—24no—
131#431—132no—
132#423C2×D1312yes—
133#407—21no—
134C4×M16—21no—
135#398—132no—
136#398—261no—
137#397—132no—
138#397—261no—
139#391—261no—
140#382—131no—
141#332—264no—
142#324—261no—
143#323—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—42no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—81no—
151C22×C13#38611yescharacteristic
152C22×C13#41611yescharacteristic
153C22×C13#41811yescharacteristic
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13#44912yes—
160C4×C13#48212yes—
161Dic13—82no—
162Dic13—82no—
163C22×Q8—261no—
164C23×C4C22⋊D1311yescharacteristic
165C2×M16—22no—
166C4⋊Q8—262no—
167C4⋊Q8—262no—
168C22⋊Q8—524no—
169#117—22no—
170#117—22no—
171C2×C4⋊C4—132no—
172C2×C4⋊C4—262no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4C4×D1311yescharacteristic
176C2×C4⋊C4D5211yescharacteristic
177C2×C22⋊C4—262no—
178C2×C22⋊C4C4×D1311yescharacteristic
179C2×C22⋊C4D5211yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C2×C42C22×D1311yescharacteristic
182C4⋊C8—22no—
183C4⋊C8—262no—
184C4⋊C8C22⋊D1314yes—
185C22⋊C8—24no—
186C22⋊C8—262no—
187#97—22no—
188C4×C8—22no—
189C4×C8—262no—
190#95—132no—
191#95—262no—
192#95—262no—
193#95—261no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—81no—
197C2×C13#187511yescharacteristic
198C2×C13#190911yescharacteristic
199C2×C13#191511yescharacteristic
200C24#610311yescharacteristic
201C2×Q8—521no—
202C2×Q8—522no—
203C2×Q8—522no—
204C2×Q8—521no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4C2×C4×D1311yescharacteristic
215C22×C4C2×D5211yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217M16—42no—
218M16—42no—
219C2×C8—24no—
220C2×C8—522no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—264no—
224C4⋊C4—524no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—524no—
230C42—21no—
231C42—21no—
232C42#612712yes—
233C42C2×C22⋊D1312yes—
234C13#919611yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×#610311yescharacteristic
241Q8—1042no—
242Q8—1042no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4C4×C22⋊D1312yes—
261C2×C4#8818311yescharacteristic
262C2×C4#8818412yes—
263C2×C4#8820312yes—
264C2×C4#8820412yes—
265C2×C4#8820711yescharacteristic
266C8—44no—
267C8—1042no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1171866211yescharacteristic
276C22#1171866311yescharacteristic
277C22#1171887411yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—1042no—
284C4—1042no—
285C4#1171866412yes—
286C4#1171889912yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1311515811yescharacteristic
291C2#1311535811yescharacteristic
292C2#1311538811yescharacteristic
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#9196
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. #13113509C2semidirect
4. #13112696C2semidirect
234. C13#9196semidirect

Maximal subgroups

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

subgroupindex
#131206022
#131135092
#131131502
#131126962
C13×#29212
#919613