Finite Group Databasebeta

← #15755519

Subgroups — #15755519

Order 3328.

718 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114919C211yesmaximal, characteristic, complemented
2#13114907C211yesmaximal, characteristic, complemented
3#13113184C214yesmaximal, complemented
4C13×#3491C211yesmaximal, characteristic
5C13×#552—24no—
6C13×#551—24no—
7C13×#543C411yescharacteristic
8C13×#539—22no—
9C13×#534C411yescharacteristic
10C13×#529—22no—
11C2×C13×#123C2212yes—
12C13×#518C412yes—
13C2×C13×#117C2211yescharacteristic
14#11718868C2212yes—
15C2×C22⋊#1055C2212yes—
16#11718122—22no—
17#11718120—24no—
18#11718117—24no—
19#11718116—22no—
20C22×D4×C13C2×C412yes—
21C23×C4×C13C2311yescharacteristic
22C13×#126—24no—
23C13×#126—24no—
24C13×#125—22no—
25C13×#125—24no—
26C13×#124—22no—
27C13×#123—24no—
28C13×#123—22no—
29C13×#123—22no—
30C13×#123—22no—
31C13×#123—24no—
32C13×C22⋊Q8—24no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—24no—
35C13×#121—22no—
36C13×#120—22no—
37C4×Q8×C13—22no—
38C4×D4×C13—22no—
39C4×D4×C13—24no—
40C4×D4×C13—24no—
41C13×#117—24no—
42C13×#117—22no—
43C13×#117—24no—
44C2×C13×C4⋊C4D412yes—
45C2×C13×C4⋊C4D414yes—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4C2×C412yes—
50C2×C13×C22⋊C4D414yes—
51C2×C42×C13D412yes—
52C2×#6099—22no—
53C22×#1055—22no—
54C22⋊#1055—24no—
55C22⋊#1055—24no—
56#8540—131nomaximal, Sylow
57C24×C13C22⋊C412yes—
58C24×C13C22×C411yescharacteristic
59C2×Q8×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—44no—
64C22×C4×C13—24no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C414yes—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D414yes—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—24no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—24no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—24no—
87C13×C22⋊C4—24no—
88C42×C13—24no—
89C42×C13—22no—
90C42×C13—22no—
91#6099—44no—
92C2×#1055—44no—
93C2×#1055—42no—
94C2×#1055—42no—
95#3491D1311yescharacteristic
96#1822—131no—
97#1818—131no—
98#1468—134no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—44no—
104C23×C13C2×C22⋊C412yes—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—82no—
107D4×C13—44no—
108D4×C13—44no—
109D4×C13—82no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—24no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13—44no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—84no—
122C2×C4×C13#12012yes—
123C2×C4×C13#12012yes—
124#1055—82no—
125#1055—82no—
126#552—24no—
127#551—24no—
128#543Dic1311yescharacteristic
129#539—22no—
130#534Dic1311yescharacteristic
131#529—22no—
132C2×#123C2×D1312yes—
133#518Dic1312yes—
134C2×#117C2×D1311yescharacteristic
135#407—132no—
136C2×C22⋊C8—132no—
137#343—262no—
138#336—262no—
139#324—264no—
140#323—264no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—24no—
144C22×C13—42no—
145C22×C13—44no—
146C22×C13—82no—
147C22×C13—162no—
148C22×C13#37911yescharacteristic
149C22×C13#41012yes—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—44no—
155C4×C13—42no—
156C22×D4C2×Dic1312yes—
157C23×C4C22×D1311yescharacteristic
158C2×M16—262no—
159C22×C8—262no—
160#126—24no—
161#126—24no—
162#125—22no—
163#125—24no—
164#124—22no—
165#123—24no—
166#123—22no—
167#123—22no—
168#123—22no—
169#123—24no—
170C22⋊Q8—24no—
171C22⋊Q8—22no—
172C22⋊Q8—24no—
173#121—22no—
174#120—22no—
175C4×Q8—22no—
176C4×D4—22no—
177C4×D4—24no—
178C4×D4—24no—
179#117—24no—
180#117—22no—
181#117—24no—
182C2×C4⋊C4C22⋊D1312yes—
183C2×C4⋊C4C22⋊D1314yes—
184C2×C22⋊C4—22no—
185C2×C22⋊C4C2×Dic1311yescharacteristic
186C2×C22⋊C4C2×Dic1311yescharacteristic
187C2×C22⋊C4C2×Dic1312yes—
188C2×C22⋊C4C22⋊D1314yes—
189C2×C42C22⋊D1312yes—
190C22⋊C8—264no—
191C22⋊C8—264no—
192C2×C13—22no—
193C2×C13—42no—
194C2×C13—82no—
195C2×C13#178211yescharacteristic
196C2×C13#179112yes—
197C24C22⋊Dic1312yes—
198C24C22×Dic1311yescharacteristic
199C2×Q8—22no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—44no—
204C22×C4—24no—
205C22×C4—42no—
206C22×C4C22⋊Dic1312yes—
207C22×C4C22⋊Dic1312yes—
208C22×C4C22⋊Dic1314yes—
209C22×C4C22⋊Dic1312yes—
210C22×C4C2×C22⋊D1311yescharacteristic
211C22×C4C2×C22⋊D1311yescharacteristic
212C22×C4C2×C22⋊D1314yes—
213M16—524no—
214C2×C8—524no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C42—24no—
233C42—22no—
234C42—22no—
235C13#854011yescharacteristic, complemented, Sylow
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23—44no—
241C23C2×C22⋊Dic1312yes—
242C23C2×C22⋊Dic1311yescharacteristic
243Q8—82no—
244D4—44no—
245D4—44no—
246D4—82no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—84no—
259C2×C4#8820712yes—
260C2×C4#8820712yes—
261C8—1042no—
262C8—1042no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—42no—
267C22—44no—
268C22—82no—
269C22—162no—
270C22#1171890112yes—
271C22#1171890811yescharacteristic
272C4—22no—
273C4—22no—
274C4—42no—
275C4—42no—
276C4—44no—
277C4—42no—
278C2—22no—
279C2—42no—
280C2—82no—
281C2#1311475411yescharacteristic
282C2#1311478712yes—
subgroupG/H
centerC22#11718908
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3491C2
socleC22×C13#379
prime radicalC13×#534C4
cosocleC23×C4×C13C23
hypercenter#3491D13
hypocenterC13#8540
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #13114919C2semidirect
2. #13114907C2semidirect
3. #13113184C2semidirect
235. C13#8540semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131149072
#131131842
C13×#34912
#854013