Finite Group Databasebeta

← #13124975

Subgroups — #13124975

Order 1664.

450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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×D4×Dic13C211yesmaximal, characteristic, complemented
2#11719329C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic
5#11718826C212yesmaximal, complemented
6#11718825C212yesmaximal, complemented
7#11718704C211yesmaximal, characteristic, complemented
8#11718446C212yesmaximal, complemented
9#11718427C212yesmaximal, complemented
10#11718397C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×Dic13—21no—
14C2×C13×SD16C2212yes—
15C13×C22⋊Q8C2211yescharacteristic
16C2×C22⋊Dic13—21no—
17#88201C2211yescharacteristic, complemented
18Q8×Dic13C2211yescharacteristic, complemented
19D4×Dic13—21no—
20D4×Dic13—21no—
21D4×Dic13C2212yes—
22D4×Dic13C2212yes—
23C2×#6104C2212yes—
24#88184C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88152—21no—
28#88147C2211yescharacteristic, complemented
29#88146—21no—
30#88144C2211yescharacteristic, complemented
31#88140—21no—
32#88135—21no—
33C13×#102C2212yes—
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yescomplemented
36#88072C2212yes—
37C22⋊#1055C2211yescharacteristic
38#88061C2212yescomplemented
39#88058C2212yescomplemented
40#88055C2212yescomplemented
41#88054C2212yescomplemented
42#88048C2212yescomplemented
43C24×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—24no—
46C2×D4×C13—21no—
47C2×D4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—44no—
54C22×Dic13D411yescharacteristic
55C22×Dic13D411yescharacteristic
56C2×D52C2311yescharacteristic
57C2×C4×D13—21no—
58C13×SD16—24no—
59C2×C8×C13C2312yes—
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2311yescharacteristic
62C13×C22⋊C4—21no—
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65#6104—24no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69#6103—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2311yescharacteristic
74C4⋊Dic13C2312yes—
75#6101—21no—
76C4×Dic13—21no—
77C4×Dic13D411yescharacteristic
78C4×Dic13D411yescharacteristic
79C4×Dic13C2311yescharacteristic
80C4×Dic13C2311yescharacteristic
81C2×#1055C2312yes—
82#3114—131nomaximal, Sylow
83C23×C13—24no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89Q8×C13—22no—
90D4×C13—24no—
91D4×C13—22no—
92D4×C13#4114yes—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—42no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—44no—
104C2×Dic13—44no—
105C2×Dic13—42no—
106C2×Dic13C2×D411yescharacteristic
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110D52—22no—
111C4×D13—42no—
112C8×C13—22no—
113#1055—22no—
114#529—131no—
115C2×C4×D4—131no—
116#483—131no—
117#480—131no—
118#478—132no—
119#463—132no—
120#450D1311yescharacteristic, complemented
121#447—131no—
122#442—132no—
123#440—132no—
124#432—131no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—24no—
128C22×C13—48no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13AGL(1,ℤ/8)12yes—
132C22×C13C22×D411yescharacteristic
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13C2×#4112yes—
140Dic13—21no—
141Dic13—21no—
142Dic13—21no—
143Dic13—21no—
144Dic13—42no—
145Dic13—41no—
146C22×D4C2×D1311yescharacteristic
147C23×C4—261no—
148C2×SD16C2×D1312yes—
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⋊C4—131no—
165C2×C22⋊C4—261no—
166C2×C42—131no—
167#107—132no—
168#106—132no—
169C4⋊C8—132no—
170#103—132no—
171#102—132no—
172#102—132no—
173#102C2×D1312yes—
174C22⋊C8—131no—
175C22⋊C8C2×D1311yescharacteristic
176#97—132no—
177C2×C13—22no—
178C2×C13—44no—
179C2×C13#52511yescharacteristic
180C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C13#57511yescharacteristic
182D13—81no—
183C24—21no—
184C2×Q8C22×D1311yescharacteristic
185C2×D4—24no—
186C2×D4—21no—
187C2×D4—131no—
188C2×D4—261no—
189C2×D4C22×D1312yes—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—262no—
194C22×C4—262no—
195C22×C4—261no—
196C22×C4—524no—
197C22×C4C22×D1311yescharacteristic
198SD16—24no—
199D8—264no—
200C2×C8—132no—
201C2×C8C22×D1312yes—
202C4⋊C4—21no—
203C4⋊C4—131no—
204C4⋊C4—132no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C4⋊C4C22×D1311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C22⋊C4—262no—
215C22⋊C4—262no—
216C22⋊C4—261no—
217C42—131no—
218C42—131no—
219C42—131no—
220C42—131no—
221C42—261no—
222C13#311411yescharacteristic, complemented, Sylow
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—261no—
228C23D4×D1311yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232D4—262no—
233D4—522no—
234D4#612914yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—522no—
246C2×C4—521no—
247C2×C4—524no—
248C2×C4—524no—
249C2×C4—522no—
250C2×C4D4×D1311yescharacteristic
251C2×C4C23×D1311yescharacteristic
252C8—22no—
253C8—262no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8816812yes—
264C22C2×D4×D1311yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—261no—
269C4—261no—
270C4—261no—
271C4—261no—
272C4—522no—
273C4—521no—
274C4C2×#612912yes—
275C2—22no—
276C2—44no—
277C2—1041no—
278C2#1171929111yescharacteristic
279C2C2×#8816811yescharacteristic
280C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radical#11718878C2
hypercenter#450D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic13C2semidirect
2. #11719329C2semidirect
3. C13×#450C2semidirect
5. #11718826C2semidirect
6. #11718825C2semidirect
7. #11718704C2semidirect
8. #11718446C2semidirect
9. #11718427C2semidirect
10. #11718397C2semidirect
11. #11718380C2semidirect
17. #88201C22semidirect
18. Q8×Dic13C22semidirect
28. #88147C22semidirect
30. #88144C22semidirect
35. #88075C22semidirect
38. #88061C22semidirect
39. #88058C22semidirect
40. #88055C22semidirect
41. #88054C22semidirect
42. #88048C22semidirect
120. #450D13semidirect
222. C13#3114semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
#117193292
C13×#4502
#117188782
#117188262
#117188252
#117187042
#117184462
#117184272
#117183972
#117183802
#311413