Finite Group Databasebeta

← #15758948

Subgroups — #15758948

Order 3328.

478 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 119 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#13123474C211yesmaximal, characteristic
2#13113508C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112694C212yesmaximal, complemented
5C13×#2621C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×C22⋊Q8—21no—
8C2×C13×#117C2211yescharacteristic
9C13×#398—21no—
10C13×#398C412yes—
11C13×#397—21no—
12C13×#397C412yes—
13C13×#391—21no—
14C13×#382C2211yescharacteristic
15#11718868—21no—
16#11718661—24no—
17#11718586C2212yes—
18#11718585C2212yes—
19C4×#6099—21no—
20#11718139—24no—
21#11718120—21no—
22#11718117—21no—
23C22×Q8×C13—21no—
24C23×C4×C13D411yescharacteristic
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C13×C22⋊Q8—44no—
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—21no—
45C13×#95C2×C412yes—
46C22⋊#1055—24no—
47C22⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055D414yes—
51#88043—22no—
52C4×#1055—22no—
53C4×#1055—22no—
54#9196—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×Q8×C13—42no—
59C2×Q8×C13—42no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—44no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85#6099—42no—
86#6099—42no—
87C2×#1055—24no—
88C2×#1055—42no—
89#2921—131no—
90#2621D1311yescharacteristic
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
100Q8×C13—82no—
101Q8×C13—82no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13#12311yescharacteristic
123C2×C4×C13#13512yes—
124C2×C4×C13AGL(1,ℤ/8)12yes—
125#1055—44no—
126#1055—82no—
127C2×C4⋊Q8C2×D1311yescharacteristic
128C2×C22⋊Q8—21no—
129C2×#117C2×D1311yescharacteristic
130#433—264no—
131#431—132no—
132#423—132no—
133#407—261no—
134C4×M16—261no—
135#398—21no—
136#398Dic1312yes—
137#397—21no—
138#397Dic1312yes—
139#391—21no—
140#382C2×D1311yescharacteristic
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—82no—
160C4×C13—82no—
161C4×C13#44912yes—
162C4×C13#48212yes—
163C22×Q8—21no—
164C23×C4C22⋊D1311yescharacteristic
165C2×M16—262no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C22⋊Q8—44no—
169#117—22no—
170#117—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1312yes—
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C22⋊D1311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4C2×Dic1311yescharacteristic
179C2×C22⋊C4C22⋊D1311yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C2×C42C22×D1311yescharacteristic
182C4⋊C8—134no—
183C4⋊C8—262no—
184C4⋊C8—262no—
185C22⋊C8—264no—
186C22⋊C8—262no—
187#97—262no—
188C4×C8—262no—
189C4×C8—262no—
190#95—22no—
191#95—22no—
192#95—21no—
193#95C2×Dic1312yes—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—81no—
197C2×C13#187511yescharacteristic
198C2×C13#190911yescharacteristic
199C2×C13#191511yescharacteristic
200C24C22⋊Dic1311yescharacteristic
201C2×Q8—42no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22×Dic1311yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217M16—522no—
218M16—522no—
219C2×C8—264no—
220C2×C8—522no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—44no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—44no—
230C42—21no—
231C42—21no—
232C42D4×D1312yes—
233C42#612912yes—
234C13#919611yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×C22⋊Dic1311yescharacteristic
241Q8—82no—
242Q8—82no—
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—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4#8818612yes—
261C2×C4D4×Dic1312yes—
262C2×C4#8818911yescharacteristic
263C2×C4#8819111yescharacteristic
264C2×C4#8819312yes—
265C2×C4#8820412yes—
266C8—524no—
267C8—1042no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1171887611yescharacteristic
276C22#1171888111yescharacteristic
277C22#1171889411yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—82no—
284C4—82no—
285C4#1171869612yes—
286C4#1171869812yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1311515911yescharacteristic
291C2#1311535911yescharacteristic
292C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2621C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2621D13
hypocenterC13#9196
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. #13113508C2semidirect
4. #13112694C2semidirect
234. C13#9196semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131135082
#131131502
#131126942
C13×#26212
#919613