Finite Group Databasebeta

← #13123179

Subgroups — #13123179

Order 1664.

924 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 201 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
1C2×C13×#121C211yesmaximal, characteristic, complemented
2C2×#88194C211yesmaximal, characteristic, complemented
3C2×#88193C214yesmaximal, complemented
4C2×#88184C211yesmaximal, characteristic, complemented
5C22×C4×Dic13C211yesmaximal, characteristic, complemented
6#11718882C211yesmaximal, characteristic, complemented
7#11718649C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718618C214yesmaximal, complemented
10C22×D4×C13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×C22⋊D13C2214yes—
15C23×Dic13C2212yes—
16C22×D52C2211yescharacteristic
17C13×#121—24no—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2214yes—
21#88194—24no—
22#88193—216no—
23#88184—24no—
24C2×#6103C2212yes—
25C2×#6103C2214yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2214yes—
28C2×C4×Dic13—24no—
29C2×C4×Dic13C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31C2×C4×Dic13C2211yescharacteristic
32C24×C13C2312yes—
33C24×C13C2311yescharacteristic
34C23×D13C2312yes—
35C2×D4×C13—28no—
36C2×D4×C13—24no—
37C2×D4×C13—22no—
38C2×D4×C13—22no—
39C2×D4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13D414yescomplemented
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—24no—
47C2×C22⋊D13—28no—
48C2×C22⋊D13—28no—
49C2×C22⋊D13—28no—
50C2×C22⋊D13—28no—
51C22×Dic13—24no—
52C22×Dic13—24no—
53C22×Dic13D418yescomplemented
54C22×Dic13C2312yes—
55C22×Dic13C2312yes—
56C22×Dic13C2312yes—
57C2×D52—22no—
58C2×D52—22no—
59C2×D52—22no—
60C13×C4⋊C4—22no—
61C13×C22⋊C4—24no—
62C22⋊Dic13—28no—
63#6103—24no—
64#6103—28no—
65C4⋊Dic13—22no—
66#6101—28no—
67C4×Dic13—22no—
68C4×Dic13—24no—
69C4×Dic13D414yescomplemented
70#2856—131nomaximal, Sylow
71C23×C13—21no—
72C23×C13—22no—
73C23×C13—21no—
74C23×C13—24no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—24no—
78C23×C13—22no—
79C23×C13C2×D414yes—
80C23×C13C2×D412yes—
81C23×C13C2411yescharacteristic
82C22×D13—22no—
83C22×D13—24no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—24no—
87D4×C13—48no—
88D4×C13—44no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—28no—
92C2×C4×C13—24no—
93C2×C4×C13—22no—
94C2×C4×C13C2×D412yes—
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2×D412yes—
97C2×C4×C13#4112yes—
98C22⋊D13—48no—
99C22⋊D13—416no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—216no—
103C2×Dic13—24no—
104C2×Dic13—22no—
105C2×Dic13C2×D414yes—
106C2×Dic13C2×D414yes—
107C2×Dic13C2×D414yes—
108C2×Dic13#4114yes—
109D52—44no—
110C2×#127—131no—
111C2×#121—134no—
112C2×#121—131no—
113C2×#121D1311yescharacteristic, complemented
114C22×C42—131no—
115#390—131no—
116#390—131no—
117#390—134no—
118#384—131no—
119C22×C13—24no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—24no—
123C22×C13—44no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—44no—
128C22×C13#12714yescomplemented
129C22×C13C22×D411yescharacteristic
130C22×C13C22×D412yes—
131C22×C13C22×D411yescharacteristic
132C22×C13C2×#4111yescharacteristic
133C22×C13C2×#4112yes—
134C2×D13—42no—
135C2×D13—44no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—44no—
139C4×C13—22no—
140C4×C13—42no—
141C4×C13#12114yescomplemented
142Dic13—24no—
143Dic13—42no—
144Dic13#12118yescomplemented
145C22×D4—132no—
146C22×D4—134no—
147C22×D4—131no—
148C22×D4C2×D1312yes—
149C22×D4C2×D1311yescharacteristic
150C23×C4—132no—
151C23×C4C2×D1311yescharacteristic
152#127—264no—
153#121—24no—
154#121—2616no—
155#121—264no—
156C2×C4⋊C4—134no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4C2×D1311yescharacteristic
159C2×C22⋊C4—134no—
160C2×C22⋊C4—134no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4C2×D1312yes—
163C2×C42—131no—
164C2×C42—132no—
165C2×C42—131no—
166C2×C42—264no—
167C2×C13—24no—
168C2×C13—82no—
169C2×C13C2×#12111yescharacteristic
170C2×C13C2×#12112yes—
171C2×C13C2×#12711yescharacteristic
172C2×C13#53211yescharacteristic
173C2×C13#53212yes—
174D13—82no—
175C24—132no—
176C24C22×D1312yes—
177C24C22×D1311yescharacteristic
178C2×D4—28no—
179C2×D4—24no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—268no—
184C2×D4—268no—
185C2×D4—268no—
186C2×D4—268no—
187C2×D4—264no—
188C2×D4—262no—
189C2×D4—262no—
190C2×D4—262no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—132no—
194C22×C4—138no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4—264no—
198C22×C4—264no—
199C22×C4C22⋊D1314yescomplemented
200C22×C4C22×D1312yes—
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1311yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—268no—
205C4⋊C4—262no—
206C22⋊C4—24no—
207C22⋊C4—268no—
208C22⋊C4—268no—
209C22⋊C4—264no—
210C42—134no—
211C42—264no—
212C42—262no—
213C13#285611yescharacteristic, complemented, Sylow
214C23—21no—
215C23—21no—
216C23—22no—
217C23—24no—
218C23—22no—
219C23—22no—
220C23—24no—
221C23—22no—
222C23—264no—
223C23—262no—
224C23—262no—
225C23—264no—
226C23—262no—
227C23D4×D1314yes—
228C23C2×C22⋊D1312yes—
229C23C23×D1311yescharacteristic
230D4—48no—
231D4—44no—
232D4—5216no—
233D4—528no—
234D4—524no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—28no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—134no—
241C2×C4—134no—
242C2×C4—134no—
243C2×C4—134no—
244C2×C4—2616no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—264no—
248C2×C4—262no—
249C2×C4D4×D1312yes—
250C2×C4#612912yes—
251C2×C4C2×C22⋊D1312yes—
252C2×C4C2×C22⋊D1312yes—
253C22—22no—
254C22—22no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—44no—
261C22—44no—
262C22—522no—
263C22—522no—
264C22—522no—
265C22—524no—
266C22—524no—
267C22#8819414yescomplemented
268C22C2×D4×D1311yescharacteristic
269C22C2×D4×D1312yes—
270C22C2×#612911yescharacteristic
271C22#41×D1312yes—
272C22C22×C22⋊D1311yescharacteristic
273C4—22no—
274C4—42no—
275C4—138no—
276C4—264no—
277C4—522no—
278C4#8819314yescomplemented
279C2—24no—
280C2—82no—
281C2—1042no—
282C2#1171930112yes—
283C2D13×#12112yes—
284C2C2×#8819311yescharacteristic
285C2C2×#8819411yescharacteristic
286C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2856
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C13×#121C2semidirect
2. C2×#88194C2semidirect
3. C2×#88193C2semidirect
4. C2×#88184C2semidirect
5. C22×C4×Dic13C2semidirect
6. #11718882C2semidirect
7. #11718649C2semidirect
8. #11718637C2semidirect
9. #11718618C2semidirect
42. C22×C4×C13D4semidirect
53. C22×Dic13D4semidirect
69. C4×Dic13D4semidirect
113. C2×#121D13semidirect
128. C22×C13#127semidirect
141. C4×C13#121semidirect
144. Dic13#121semidirect
199. C22×C4C22⋊D13semidirect
213. C13#2856semidirect
267. C22#88194semidirect
278. C4#88193semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881942
C2×#881932
C2×#881842
C22×C4×Dic132
#117188822
#117186492
#117186372
#117186182
#285613