Finite Group Databasebeta

← #15758928

Subgroups — #15758928

Order 3328.

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

normal subgroups only

This group has 458 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#13113517C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic
4#13112694C212yesmaximal, complemented
5C13×#2628C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#400—21no—
9C13×#399—21no—
10C13×#395C412yes—
11C13×#393C412yes—
12C13×#389—21no—
13C13×#382C2211yescharacteristic
14C13×#380—21no—
15#11718868—21no—
16#11718661—24no—
17#11718586C2212yes—
18#11718585C2212yes—
19C4×#6099—21no—
20#11718138—24no—
21#11718120—21no—
22#11718117—21no—
23C22×Q8×C13C2×C412yes—
24C23×C4×C13D411yescharacteristic
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C13×#117—22no—
28C13×#117—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13C2311yescharacteristic
40C2×#6099—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95—21no—
44C13×#95C2×C412yes—
45C22⋊#1055—24no—
46C22⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055D414yes—
50#88043—22no—
51C4×#1055—22no—
52C4×#1055—22no—
53#9192—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C2×Q8×C13—24no—
56C2×Q8×C13—82no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—82no—
76C13×C22⋊C4—22no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4—82no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13C2×D412yes—
82C42×C13#4112yes—
83#6099—42no—
84#6099—42no—
85C2×#1055—24no—
86C2×#1055—42no—
87#2921—131no—
88#2628D1311yescharacteristic
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
98Q8×C13—84no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13C4×D412yes—
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13#12112yes—
119C2×C4×C13#12311yescharacteristic
120C2×C4×C13#13512yes—
121C2×C4×C13#13712yes—
122#1055—44no—
123#1055—82no—
124C2×C4⋊Q8C2×D1311yescharacteristic
125C2×#117C2×D1311yescharacteristic
126#433—264no—
127#431—132no—
128#423—132no—
129#407—261no—
130C4×M16—261no—
131#400—21no—
132#399—21no—
133#395Dic1312yes—
134#393Dic1312yes—
135#389—21no—
136#382C2×D1311yescharacteristic
137#380—21no—
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—82no—
157C4×C13—82no—
158C4×C13#45212yes—
159C4×C13#48512yes—
160C22×Q8C2×Dic1312yes—
161C23×C4C22⋊D1311yescharacteristic
162C2×M16—262no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×Dic1311yescharacteristic
172C2×C4⋊C4C22⋊D1311yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4C2×Dic1311yescharacteristic
175C2×C22⋊C4C22⋊D1311yescharacteristic
176C2×C42C22⋊D1311yescharacteristic
177C2×C42C22×D1311yescharacteristic
178C4⋊C8—134no—
179C4⋊C8—262no—
180C4⋊C8—262no—
181C22⋊C8—264no—
182C22⋊C8—262no—
183#97—262no—
184C4×C8—262no—
185C4×C8—262no—
186#95—22no—
187#95—22no—
188#95—21no—
189#95C2×Dic1312yes—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—81no—
193C2×C13#187311yescharacteristic
194C2×C13#190911yescharacteristic
195C2×C13#191411yescharacteristic
196C24C22⋊Dic1311yescharacteristic
197C2×Q8—24no—
198C2×Q8—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4C22⋊Dic1311yescharacteristic
206C22×C4C22⋊Dic1311yescharacteristic
207C22×C4C22⋊Dic1311yescharacteristic
208C22×C4C22×Dic1311yescharacteristic
209C22×C4C2×C22⋊D1311yescharacteristic
210C22×C4C2×C22⋊D1311yescharacteristic
211M16—522no—
212M16—522no—
213C2×C8—264no—
214C2×C8—522no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—82no—
225C42—21no—
226C42—21no—
227C42D4×D1312yes—
228C42#612912yes—
229C13#919211yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊Dic1311yescharacteristic
236Q8—84no—
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—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4D4×Dic1312yes—
255C2×C4#8818911yescharacteristic
256C2×C4#8819111yescharacteristic
257C2×C4#8819312yes—
258C2×C4#8819612yes—
259C2×C4#8820412yes—
260C8—524no—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1171888111yescharacteristic
270C22#1171888611yescharacteristic
271C22#1171889411yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—82no—
278C4—82no—
279C4#1171870612yes—
280C4#1171870812yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1311514911yescharacteristic
285C2#1311535911yescharacteristic
286C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2628C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2628D13
hypocenterC13#9192
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #13113517C2semidirect
4. #13112694C2semidirect
229. C13#9192semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131135172
#131131502
#131126942
C13×#26282
#919213