Finite Group Databasebeta

← #13123125

Subgroups — #13123125

Order 1664.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D13C211yesmaximal, characteristic, complemented
2C2×C13×#123C211yesmaximal, characteristic, complemented
3C2×#88191C211yesmaximal, characteristic
4C2×#88189C211yesmaximal, characteristic, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718650C214yesmaximal, complemented
7#11718617C214yesmaximal, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718604C211yesmaximal, characteristic, complemented
10C24×D13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C23×Dic13C2211yescharacteristic
15C22×C4×D13—24no—
16C22×C4×D13—24no—
17C22×C4×D13—24no—
18C22×C4×D13C2214yes—
19C13×#123—24no—
20C2×C13×C4⋊C4C2212yescomplemented
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2212yescomplemented
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2212yescomplemented
26#88191—24no—
27#88189—24no—
28C2×#6103C2212yes—
29C2×#6103C2214yes—
30C2×#6101C2212yescomplemented
31#88071C2214yescomplemented
32#88071C2214yescomplemented
33C24×C13C2311yescharacteristic
34C24×C13C2311yescharacteristic
35C23×D13—22no—
36C23×D13—22no—
37C23×D13—28no—
38C23×D13D414yes—
39C23×D13C2312yes—
40C2×D4×C13—22no—
41C2×D4×C13—22no—
42C2×D4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13D414yescomplemented
46C22×C4×C13C2312yes—
47C22×C4×C13C2311yescharacteristic
48C22×C4×C13C2312yes—
49C2×C22⋊D13—24no—
50C2×C22⋊D13—28no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13D414yescomplemented
54C22×Dic13C2312yes—
55C22×Dic13C2312yes—
56C22×Dic13C2312yes—
57C2×C4×D13—232no—
58C2×C4×D13—28no—
59C2×C4×D13—28no—
60C2×C4×D13—28no—
61C13×C4⋊C4—24no—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—24no—
64C22⋊Dic13—22no—
65C22⋊Dic13—22no—
66C22⋊Dic13—24no—
67#6103—24no—
68#6103—28no—
69#6101—24no—
70#2849—131nomaximal, Sylow
71C23×C13—24no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—24no—
76C23×C13C2×D412yes—
77C23×C13C2×D412yes—
78C23×C13C2×D412yes—
79C23×C13C2411yescharacteristic
80C22×D13—216no—
81C22×D13—216no—
82C22×D13—28no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—24no—
86C22×D13—216no—
87C22×D13C2×D414yes—
88C22×D13#4118yes—
89D4×C13—44no—
90C2×C4×C13—28no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—24no—
98C2×C4×C13C2×D414yes—
99C22⋊D13—48no—
100C2×Dic13—28no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—24no—
106C2×Dic13—24no—
107C2×Dic13C2×D414yes—
108C4×D13—232no—
109C24×C4—131no—
110C2×#123—131no—
111C2×#123D1311yescharacteristic, complemented
112C2×#120—131no—
113#386—134no—
114#385—134no—
115#381—131no—
116#381—131no—
117#379—131no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—24no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13#12014yes—
126C22×C13C22×D411yescharacteristic
127C22×C13C22×D411yescharacteristic
128C22×C13C22×D411yescharacteristic
129C22×C13C2×#4114yes—
130C2×D13—232no—
131C2×D13—24no—
132C2×D13—24no—
133C2×D13—28no—
134C2×D13—28no—
135C2×D13#12318yescomplemented
136C4×C13—24no—
137C4×C13—41no—
138C4×C13—42no—
139Dic13—24no—
140Dic13—42no—
141Dic13—42no—
142C25—131no—
143C22×D4—132no—
144C22×D4C2×D1311yescharacteristic
145C23×C4—131no—
146C23×C4—134no—
147C23×C4—264no—
148C23×C4—264no—
149C23×C4—264no—
150C23×C4C2×D1311yescharacteristic
151#123—24no—
152#123—264no—
153#120—264no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4C2×D1312yescomplemented
156C2×C22⋊C4—131no—
157C2×C22⋊C4—131no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—134no—
161C2×C22⋊C4C2×D1311yescharacteristic
162C2×C22⋊C4C2×D1312yescomplemented
163#95—134no—
164#95—134no—
165C2×C13—24no—
166C2×C13—81no—
167C2×C13C2×#12011yescharacteristic
168C2×C13C2×#12312yes—
169C2×C13#52512yes—
170C2×C13#52512yes—
171D13—28no—
172C24—132no—
173C24—134no—
174C24—268no—
175C24—262no—
176C24—262no—
177C24C22×D1311yescharacteristic
178C24C22×D1311yescharacteristic
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—264no—
183C2×D4—268no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—134no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—268no—
191C22×C4—268no—
192C22×C4—2632no—
193C22×C4—262no—
194C22×C4—262no—
195C22×C4—268no—
196C22×C4C22⋊D1314yescomplemented
197C22×C4C22×D1312yes—
198C22×C4C22×D1311yescharacteristic
199C22×C4C22×D1312yes—
200C4⋊C4—24no—
201C4⋊C4—264no—
202C22⋊C4—22no—
203C22⋊C4—24no—
204C22⋊C4—264no—
205C22⋊C4—268no—
206C22⋊C4—264no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C13#284911yescharacteristic, complemented, Sylow
210C23—24no—
211C23—21no—
212C23—21no—
213C23—24no—
214C23—21no—
215C23—134no—
216C23—138no—
217C23—2616no—
218C23—2616no—
219C23—2616no—
220C23—268no—
221C23—262no—
222C23—264no—
223C23—262no—
224C23D4×D1312yes—
225C23D4×D1312yes—
226C23C2×C22⋊D1312yes—
227C23C23×D1311yescharacteristic
228D4—44no—
229D4—528no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—134no—
239C2×C4—2632no—
240C2×C4—268no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—264no—
246C2×C4—264no—
247C2×C4C2×C22⋊D1314yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—138no—
256C22—2632no—
257C22—264no—
258C22—268no—
259C22—264no—
260C22—268no—
261C22#8819114yes—
262C22C2×D4×D1311yescharacteristic
263C22C2×D4×D1311yescharacteristic
264C22#41×D1314yes—
265C22C22×C22⋊D1311yescharacteristic
266C4—24no—
267C4—41no—
268C4—42no—
269C4—264no—
270C4—522no—
271C4—522no—
272C2—24no—
273C2—81no—
274C2—268no—
275C2D13×#12312yes—
276C2#1171936112yes—
277C2C2×#8819111yescharacteristic
278C2#1171953312yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#123C2
prime radicalC2×#88191C2
hypercenterC2×#123D13
hypocenterC13#2849
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C23×C4×D13C2semidirect
2. C2×C13×#123C2semidirect
4. C2×#88189C2semidirect
5. #11718872C2semidirect
6. #11718650C2semidirect
7. #11718617C2semidirect
8. #11718616C2semidirect
9. #11718604C2semidirect
20. C2×C13×C4⋊C4C22semidirect
22. C2×C13×C22⋊C4C22semidirect
25. C2×C22⋊Dic13C22semidirect
30. C2×#6101C22semidirect
31. #88071C22semidirect
32. #88071C22semidirect
45. C22×C4×C13D4semidirect
53. C22×Dic13D4semidirect
111. C2×#123D13semidirect
135. C2×D13#123semidirect
155. C2×C4⋊C4C2×D13semidirect
162. C2×C22⋊C4C2×D13semidirect
196. C22×C4C22⋊D13semidirect
209. C13#2849semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D132
C2×C13×#1232
C2×#881912
C2×#881892
#117188722
#117186502
#117186172
#117186162
#117186042
#284913