Finite Group Databasebeta

← #13123129

Subgroups — #13123129

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×#88183C211yesmaximal, characteristic, complemented
3C2×#88140C211yesmaximal, characteristic, complemented
4C2×#88136C211yesmaximal, characteristic
5C13×#381C211yesmaximal, characteristic, complemented
6#11718616C211yesmaximal, characteristic, complemented
7#11718604C211yesmaximal, characteristic, complemented
8#11718329C214yesmaximal, complemented
9#11718326C214yesmaximal, complemented
10C24×D13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C22×D52C2212yes—
15C22×C4×D13—24no—
16C22×C4×D13—24no—
17C22×C4×D13—24no—
18C22×C4×D13C2214yes—
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22#88183—24no—
23C2×#6103C2212yes—
24C2×#6103C2214yes—
25C2×#6103C2212yescomplemented
26C2×#6103C2212yescomplemented
27C2×C4⋊Dic13C2212yescomplemented
28C2×#6101C2212yescomplemented
29#88140—24no—
30#88136—24no—
31C13×#95C2214yescomplemented
32#88071C2214yescomplemented
33C24×C13C2311yescharacteristic
34C23×D13—22no—
35C23×D13—22no—
36C23×D13—28no—
37C23×D13D414yes—
38C23×D13C2311yescharacteristic
39C23×D13C2312yes—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13D414yescomplemented
43C22×C4×C13C2312yes—
44C22×C4×C13C2312yes—
45C22×C4×C13C2312yes—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13D414yescomplemented
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2312yes—
55C2×D52—24no—
56C2×D52—28no—
57C2×C4×D13—232no—
58C2×C4×D13—28no—
59C2×C4×D13—28no—
60C2×C4×D13—28no—
61C13×C22⋊C4—22no—
62C13×C22⋊C4—22no—
63C22⋊Dic13—22no—
64#6103—24no—
65#6103—28no—
66#6103—24no—
67#6103—24no—
68C4⋊Dic13—24no—
69#6101—24no—
70#2849—131nomaximal, Sylow
71C23×C13—24no—
72C23×C13C2×D412yes—
73C23×C13C2×D412yes—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76C22×D13—216no—
77C22×D13—216no—
78C22×D13—28no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—24no—
82C22×D13—216no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—21no—
86C22×D13—24no—
87C22×D13C2×D414yes—
88C22×D13#4118yes—
89C2×C4×C13—28no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—24no—
95C2×C4×C13—24no—
96C2×C4×C13C2×D414yes—
97C22⋊D13—44no—
98C2×Dic13—28no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—24no—
106C2×Dic13C2×D414yes—
107D52—48no—
108C4×D13—232no—
109C24×C4—131no—
110C2×#123—131no—
111C2×#123—131no—
112C2×#120—131no—
113#386—134no—
114#385—134no—
115#381—131no—
116#381D1311yescharacteristic, complemented
117#379—131no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—24no—
121C22×C13#12014yes—
122C22×C13C22×D411yescharacteristic
123C22×C13C22×D411yescharacteristic
124C22×C13C22×D411yescharacteristic
125C22×C13C2×#4114yes—
126C2×D13—232no—
127C2×D13—24no—
128C2×D13—24no—
129C2×D13—28no—
130C2×D13—28no—
131C2×D13—41no—
132C2×D13—42no—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13#12318yescomplemented
136C4×C13—24no—
137C4×C13—42no—
138C4×C13—42no—
139Dic13—24no—
140Dic13—41no—
141Dic13—42no—
142C25—131no—
143C22×D4—131no—
144C22×D4—132no—
145C23×C4—131no—
146C23×C4—134no—
147C23×C4—264no—
148C23×C4—264no—
149C23×C4—264no—
150C23×C4C2×D1311yescharacteristic
151#123—264no—
152#123—264no—
153#120—264no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—132no—
156C2×C22⋊C4—131no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—134no—
161C2×C22⋊C4C2×D1311yescharacteristic
162C2×C22⋊C4C2×D1311yescharacteristic
163#95—134no—
164#95C2×D1314yescomplemented
165C2×C13—24no—
166C2×C13C2×#12011yescharacteristic
167C2×C13C2×#12312yes—
168C2×C13#52512yes—
169C2×C13#52512yes—
170D13—28no—
171D13—81no—
172C24—132no—
173C24—134no—
174C24—131no—
175C24—268no—
176C24—262no—
177C24—262no—
178C24C22×D1311yescharacteristic
179C2×D4—264no—
180C2×D4—268no—
181C2×D4—262no—
182C2×D4—262no—
183C2×D4—262no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—134no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—131no—
190C22×C4—268no—
191C22×C4—268no—
192C22×C4—2632no—
193C22×C4—262no—
194C22×C4—262no—
195C22×C4—268no—
196C22×C4D5214yescomplemented
197C22×C4C22×D1312yes—
198C22×C4C22×D1312yes—
199C22×C4C22×D1312yes—
200C4⋊C4—264no—
201C4⋊C4—264no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C22⋊C4—264no—
205C22⋊C4—264no—
206C22⋊C4—268no—
207C22⋊C4—262no—
208C22⋊C4—264no—
209C13#284911yescharacteristic, complemented, Sylow
210C23—24no—
211C23—134no—
212C23—138no—
213C23—2616no—
214C23—2616no—
215C23—2616no—
216C23—268no—
217C23—262no—
218C23—262no—
219C23—264no—
220C23—261no—
221C23—261no—
222C23—261no—
223C23—264no—
224C23C2×D5212yes—
225C23D4×D1312yes—
226C23D4×D1312yes—
227C23C23×D1311yescharacteristic
228D4—528no—
229D4—524no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—134no—
238C2×C4—2632no—
239C2×C4—268no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—264no—
247C2×C4C2×D5214yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—138no—
252C22—2632no—
253C22—264no—
254C22—268no—
255C22—264no—
256C22—268no—
257C22—521no—
258C22—522no—
259C22—522no—
260C22—522no—
261C22#8813614yes—
262C22C22×D5211yescharacteristic
263C22C2×D4×D1311yescharacteristic
264C22C2×D4×D1311yescharacteristic
265C22#41×D1314yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—264no—
270C4—521no—
271C4—522no—
272C2—24no—
273C2—268no—
274C2—1041no—
275C2C2×#8813611yescharacteristic
276C2#1171922912yes—
277C2D13×#12312yes—
278C2#1171936112yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC2×#88136C2
hypercenter#381D13
hypocenterC13#2849
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D13C2semidirect
2. C2×#88183C2semidirect
3. C2×#88140C2semidirect
5. C13×#381C2semidirect
6. #11718616C2semidirect
7. #11718604C2semidirect
8. #11718329C2semidirect
9. #11718326C2semidirect
25. C2×#6103C22semidirect
26. C2×#6103C22semidirect
27. C2×C4⋊Dic13C22semidirect
28. C2×#6101C22semidirect
31. C13×#95C22semidirect
32. #88071C22semidirect
42. C22×C4×C13D4semidirect
51. C22×Dic13D4semidirect
116. #381D13semidirect
135. C2×D13#123semidirect
164. #95C2×D13semidirect
196. C22×C4D52semidirect
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×#881832
C2×#881402
C2×#881362
C13×#3812
#117186162
#117186042
#117183292
#117183262
#284913