Finite Group Databasebeta

← #13124482

Subgroups — #13124482

Order 1664.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D13C211yesmaximal, characteristic, complemented
2C2×#88161C211yesmaximal, characteristic, complemented
3#11719312C212yesmaximal, complemented
4C13×#469C211yesmaximal, characteristic, complemented
5#11718820C211yesmaximal, characteristic, complemented
6#11718796C211yesmaximal, characteristic, complemented
7#11718699C212yesmaximal, complemented
8#11718526C211yesmaximal, characteristic, complemented
9#11718521C211yesmaximal, characteristic, complemented
10#11718436C212yesmaximal, complemented
11#11718431C212yesmaximal, complemented
12C2×D4×D13C2212yes—
13C2×#6127C2211yescharacteristic
14C2×C13×D8C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic, complemented
16C13×#121C2212yescomplemented
17#88194—22no—
18#88192C2212yescomplemented
19#88191—22no—
20C2×#6104C2212yes—
21#88184C2212yescomplemented
22C22×#1055C2211yescharacteristic, complemented
23D8×D13—24no—
24#88161—24no—
25C2×D104C2211yescharacteristic
26C2×#6094C2211yescharacteristic
27C2×#6094C2211yescharacteristic, complemented
28C2×C8×D13C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic, complemented
30#88149C2212yescomplemented
31#88146C2212yes—
32#88139—22no—
33#88136—22no—
34C13×#106C2211yescharacteristic, complemented
35C13×#102C2212yescomplemented
36#88072C2212yescomplemented
37#88061C2212yescomplemented
38#88057C2211yescharacteristic, complemented
39#88049C2212yescomplemented
40#88047C2212yescomplemented
41C23×D13—22no—
42C2×D4×C13—22no—
43C2×D4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13D411yescharacteristic
49C2×C22⋊D13D411yescharacteristic
50D4×D13—24no—
51D4×D13—24no—
52#6127—22no—
53#6127—22no—
54C2×D52—22no—
55C2×D52D411yescharacteristic
56C2×D52C2312yes—
57C2×C4×D13C2311yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×Dic26D411yescharacteristic
60C13×D8—22no—
61C13×M16—22no—
62C2×C8×C13C2311yescharacteristic
63C2×C8×C13C2311yescharacteristic
64C13×C4⋊C4C2312yes—
65C13×C22⋊C4—22no—
66C22⋊Dic13—22no—
67#6104—24no—
68#6103—22no—
69#6103—22no—
70#6103—22no—
71C4⋊Dic13C2312yes—
72C4×Dic13—22no—
73C2×#1055—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76D104—22no—
77#6094—22no—
78#6094—22no—
79C8×D13—22no—
80C8×D13D414yescomplemented
81#3058—131nomaximal, Sylow
82C23×C13—22no—
83C23×C13C2×D411yescharacteristic
84C22×D13—22no—
85C22×D13—44no—
86C22×D13—82no—
87C22×D13—82no—
88C22×D13C2×D411yescharacteristic
89C22×D13C2×D411yescharacteristic
90D4×C13—22no—
91D4×C13—22no—
92D4×C13—82no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—22no—
99C22⋊D13—22no—
100C22⋊D13—44no—
101C22⋊D13—82no—
102C22⋊D13—82no—
103C2×Dic13—22no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106D52—22no—
107D52—22no—
108D52—22no—
109D52—82no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13C2×D412yes—
113C4×D13#4112yes—
114Dic26—22no—
115C8×C13—21no—
116C8×C13C2×D412yes—
117#1055—21no—
118#1055C2×D412yes—
119C22×D8—131no—
120C2×#131—131no—
121#535—132no—
122#469—131no—
123#469—131no—
124#469—131no—
125#469D1311yescharacteristic, complemented
126#466—132no—
127#466—132no—
128#427—131no—
129#418—132no—
130C22×C13—21no—
131C22×C13—22no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13C22×D411yescharacteristic
136C2×D13—22no—
137C2×D13—21no—
138C2×D13—22no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13—42no—
142C2×D13—88no—
143C2×D13#12112yes—
144C4×C13—21no—
145C4×C13—42no—
146C4×C13C22×D411yescharacteristic
147C4×C13C2×#4111yescharacteristic
148Dic13—21no—
149Dic13—42no—
150Dic13#12112yes—
151C2×#41—131no—
152C22×D4—132no—
153C2×D8—132no—
154C2×D8—131no—
155C2×D8—264no—
156C2×D8C2×D1311yescharacteristic
157#131—264no—
158C2×M16—131no—
159C2×M16—131no—
160C2×M16C2×D1311yescharacteristic, complemented
161C22×C8—131no—
162C22×C8—131no—
163C22×C8—131no—
164#127—262no—
165#124—262no—
166#121—132no—
167#121—132no—
168#121—132no—
169#121C2×D1312yescomplemented
170#120—262no—
171#120—262no—
172#117—132no—
173#107—132no—
174#106—131no—
175#106C2×D1311yescharacteristic, complemented
176#102—132no—
177#102—132no—
178#102—132no—
179#102C2×D1312yescomplemented
180C2×C13—41no—
181C2×C13—82no—
182C2×C13C2×#12111yescharacteristic
183C2×C13#57612yes—
184D13—22no—
185D13—41no—
186D13—82no—
187C24—262no—
188#41—262no—
189#41—262no—
190C2×Q8—131no—
191C2×D4—22no—
192C2×D4—131no—
193C2×D4—131no—
194C2×D4—131no—
195C2×D4—132no—
196C2×D4—262no—
197C2×D4—264no—
198C2×D4—264no—
199C2×D4—262no—
200C2×D4—262no—
201C2×D4—262no—
202C2×D4C22×D1312yes—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4C22×D1311yescharacteristic
206D8—22no—
207D8—264no—
208D8—262no—
209M16—22no—
210M16—262no—
211M16—262no—
212C2×C8—131no—
213C2×C8—134no—
214C2×C8—131no—
215C2×C8—262no—
216C2×C8—262no—
217C2×C8C22×D1311yescharacteristic
218C2×C8C22×D1311yescharacteristic
219C4⋊C4—132no—
220C4⋊C4C22×D1312yes—
221C22⋊C4—22no—
222C22⋊C4—262no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C42—262no—
227C13#305811yescharacteristic, complemented, Sylow
228C23—22no—
229C23—131no—
230C23—131no—
231C23—262no—
232C23—524no—
233C23—1042no—
234C23—1042no—
235C23D4×D1311yescharacteristic
236Q8—262no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—262no—
241D4—262no—
242D4—262no—
243D4—262no—
244D4—262no—
245D4—524no—
246D4—1042no—
247D4—1042no—
248D4—1042no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—131no—
253C2×C4—132no—
254C2×C4—132no—
255C2×C4—131no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—262no—
259C2×C4D4×D1311yescharacteristic
260C2×C4C23×D1311yescharacteristic
261C8—21no—
262C8—132no—
263C8—261no—
264C8D4×D1312yes—
265C22—22no—
266C22—21no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—132no—
271C22—262no—
272C22—262no—
273C22—261no—
274C22—522no—
275C22—522no—
276C22—522no—
277C22—1048no—
278C22C2×D4×D1311yescharacteristic
279C4—21no—
280C4—42no—
281C4—132no—
282C4—261no—
283C4—522no—
284C4C2×D4×D1311yescharacteristic
285C4#41×D1311yescharacteristic
286C2—41no—
287C2—82no—
288C2—262no—
289C2—521no—
290C2—1042no—
291C2D13×#12111yescharacteristic
292C2#1171947912yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3058
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D13C2semidirect
2. C2×#88161C2semidirect
3. #11719312C2semidirect
4. C13×#469C2semidirect
5. #11718820C2semidirect
6. #11718796C2semidirect
7. #11718699C2semidirect
8. #11718526C2semidirect
9. #11718521C2semidirect
10. #11718436C2semidirect
11. #11718431C2semidirect
15. C2×C13×M16C22semidirect
16. C13×#121C22semidirect
18. #88192C22semidirect
21. #88184C22semidirect
22. C22×#1055C22semidirect
27. C2×#6094C22semidirect
29. C2×C8×D13C22semidirect
30. #88149C22semidirect
34. C13×#106C22semidirect
35. C13×#102C22semidirect
36. #88072C22semidirect
37. #88061C22semidirect
38. #88057C22semidirect
39. #88049C22semidirect
40. #88047C22semidirect
80. C8×D13D4semidirect
125. #469D13semidirect
160. C2×M16C2×D13semidirect
169. #121C2×D13semidirect
175. #106C2×D13semidirect
179. #102C2×D13semidirect
227. C13#3058semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D132
C2×#881612
#117193122
C13×#4692
#117188202
#117187962
#117186992
#117185262
#117185212
#117184362
#117184312
#305813