Finite Group Databasebeta

← #13124977

Subgroups — #13124977

Order 1664.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719329C211yesmaximal, characteristic, complemented
2C2×#88147C211yesmaximal, characteristic, complemented
3C13×#483C211yesmaximal, characteristic, complemented
4#11718707C211yesmaximal, characteristic, complemented
5#11718628C211yesmaximal, characteristic, complemented
6#11718532C212yesmaximal, complemented
7#11718530C212yesmaximal, complemented
8#11718480C212yesmaximal, complemented
9#11718478C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13—21no—
14C13×C22⋊Q8C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88201C2211yescharacteristic, complemented
17Q8×Dic13C2211yescharacteristic, complemented
18C2×#6106C2212yes—
19#88184C2211yescharacteristic
20C2×#6103—21no—
21C2×C4×Dic13C2211yescharacteristic
22C2×D104C2212yes—
23#88152—21no—
24#88147—21no—
25#88147—21no—
26#88147C2212yes—
27#88147C2212yes—
28#88147C2211yescharacteristic, complemented
29#88146—21no—
30#88144C2211yescharacteristic, complemented
31#88140—21no—
32#88135—21no—
33C13×#106C2212yescomplemented
34C13×#103C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88061C2212yes—
38#88055C2212yescomplemented
39#88054C2212yescomplemented
40#88049C2212yes—
41#88049C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13—21no—
44C2×Q8×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C22×Dic13D411yescharacteristic
49C22×Dic13D411yescharacteristic
50C2×D52—21no—
51C2×D52—24no—
52C2×D52C2311yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—44no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2312yes—
62C13×C4⋊C4C2311yescharacteristic
63C13×C22⋊C4—21no—
64#6106—24no—
65#6103—21no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69#6103—22no—
70#6103—22no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75C4×Dic13—21no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81D104—24no—
82#3114—131nomaximal, Sylow
83C23×C13C2×D411yescharacteristic
84C22×D13—24no—
85C22×D13—22no—
86C22×D13—21no—
87C22×D13—42no—
88C22×D13—42no—
89Q8×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—42no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—42no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—41no—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—24no—
106D52—22no—
107D52—22no—
108D52#4114yes—
109C4×D13—42no—
110C4×D13—44no—
111C4×D13—44no—
112C8×C13—22no—
113#1055—22no—
114#529—131no—
115C2×C4×D4—131no—
116#483D1311yescharacteristic, complemented
117#480—131no—
118#478—132no—
119#463—132no—
120#450—131no—
121#447—131no—
122#442—132no—
123#440—132no—
124#432—131no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13AGL(1,ℤ/8)12yes—
128C22×C13C22×D411yescharacteristic
129C2×D13—24no—
130C2×D13—48no—
131C2×D13—42no—
132C2×D13—42no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—42no—
139C4×C13—41no—
140C4×C13C2×#4112yes—
141Dic13—21no—
142Dic13—21no—
143Dic13—21no—
144Dic13—21no—
145Dic13—41no—
146C22×D4—131no—
147C23×C4—261no—
148C2×SD16—132no—
149C2×D8—132no—
150#126—261no—
151#125—131no—
152#124—131no—
153#123—261no—
154C22⋊Q8C2×D1311yescharacteristic
155#121—131no—
156C4×Q8—131no—
157C4×D4—132no—
158C4×D4—132no—
159C4×D4—131no—
160C4×D4—261no—
161C4×D4—261no—
162C4×D4—261no—
163#117—261no—
164C2×C4⋊C4C2×D1311yescharacteristic
165C2×C22⋊C4—261no—
166C2×C42—131no—
167#107—132no—
168#106C2×D1312yescomplemented
169C4⋊C8—132no—
170#103C2×D1312yescomplemented
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—131no—
175C22⋊C8C2×D1311yescharacteristic
176#97—132no—
177C2×C13—22no—
178C2×C13#52511yescharacteristic
179C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C13#57511yescharacteristic
181D13—44no—
182D13—81no—
183C24—261no—
184C2×Q8C22×D1311yescharacteristic
185C2×D4—132no—
186C2×D4—131no—
187C2×D4—264no—
188C2×D4—261no—
189C2×D4—261no—
190C22×C4—21no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—261no—
194C22×C4—262no—
195C22×C4—262no—
196C22×C4—524no—
197C22×C4C22×D1311yescharacteristic
198SD16—264no—
199D8—264no—
200C2×C8—132no—
201C2×C8C22×D1312yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—131no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4C22×D1311yescharacteristic
209C4⋊C4C22×D1312yes—
210C22⋊C4—21no—
211C22⋊C4—262no—
212C22⋊C4—262no—
213C22⋊C4—261no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C22⋊C4—261no—
217C42—131no—
218C42—131no—
219C42—131no—
220C42—131no—
221C42—261no—
222C13#311411yescharacteristic, complemented, Sylow
223C23—264no—
224C23—262no—
225C23—261no—
226C23—522no—
227C23—522no—
228C23D4×D1311yescharacteristic
229Q8—22no—
230D4—134no—
231D4—264no—
232D4—262no—
233D4—262no—
234D4—522no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—262no—
245C2×C4—261no—
246C2×C4—522no—
247C2×C4—524no—
248C2×C4—524no—
249C2×C4—521no—
250C2×C4D4×D1311yescharacteristic
251C2×C4C23×D1311yescharacteristic
252C8—22no—
253C8—262no—
254C22—21no—
255C22—21no—
256C22—264no—
257C22—528no—
258C22—522no—
259C22—522no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8816812yes—
264C22C2×D4×D1311yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—41no—
269C4—261no—
270C4—261no—
271C4—261no—
272C4—261no—
273C4—521no—
274C4#41×D1312yes—
275C2—22no—
276C2—524no—
277C2—1041no—
278C2#1171936111yescharacteristic
279C2C2×#8816811yescharacteristic
280C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radical#11718393C2
hypercenter#483D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #11719329C2semidirect
2. C2×#88147C2semidirect
3. C13×#483C2semidirect
4. #11718707C2semidirect
5. #11718628C2semidirect
6. #11718532C2semidirect
7. #11718530C2semidirect
8. #11718480C2semidirect
9. #11718478C2semidirect
11. #11718380C2semidirect
16. #88201C22semidirect
17. Q8×Dic13C22semidirect
28. #88147C22semidirect
30. #88144C22semidirect
33. C13×#106C22semidirect
34. C13×#103C22semidirect
38. #88055C22semidirect
39. #88054C22semidirect
41. #88049C22semidirect
42. #88047C22semidirect
116. #483D13semidirect
168. #106C2×D13semidirect
170. #103C2×D13semidirect
222. C13#3114semidirect

Maximal subgroups

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

subgroupindex
#117193292
C2×#881472
C13×#4832
#117187072
#117186282
#117185322
#117185302
#117184802
#117184782
#117183932
#117183802
#311413