Finite Group Databasebeta

← #13124974

Subgroups — #13124974

Order 1664.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D4×C13C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic, complemented
3#11718879C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic
5#11718679C212yesmaximal, complemented
6#11718677C212yesmaximal, complemented
7#11718675C212yesmaximal, complemented
8#11718670C212yesmaximal, complemented
9#11718632C211yesmaximal, characteristic, complemented
10#11718628C211yesmaximal, characteristic, complemented
11#11718587C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13—21no—
14C4×D4×C13—21no—
15C4×D4×C13—21no—
16C4×D4×C13C2212yes—
17C4×D4×C13C2212yes—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4—21no—
20C2×C42×C13C2211yescharacteristic
21C2×#6105C2212yes—
22C2×#6104C2212yes—
23#88184C2211yescharacteristic
24#88183—21no—
25C4×C22⋊D13—21no—
26#88178C2211yescharacteristic
27#88130—21no—
28#88129C2211yescharacteristic, complemented
29C4×D52C2211yescharacteristic, complemented
30#88126—21no—
31#88124C2211yescharacteristic, complemented
32C4×Dic26C2211yescharacteristic, complemented
33#88072C2212yes—
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88050C2212yescomplemented
38#88049C2212yescomplemented
39#88048C2212yescomplemented
40#88047C2212yescomplemented
41C4⋊#1055C2212yescomplemented
42#88043C2212yescomplemented
43C24×C13—21no—
44C2×D4×C13—24no—
45C2×D4×C13—21no—
46C2×D4×C13C2312yes—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—44no—
51C22×C4×C13D411yescharacteristic
52C22×C4×C13D411yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C2×C22⋊D13—21no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26C2311yescharacteristic
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2312yes—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C42×C13D411yescharacteristic
63C42×C13D411yescharacteristic
64C42×C13C2311yescharacteristic
65C42×C13C2311yescharacteristic
66C22⋊Dic13—21no—
67#6105—24no—
68#6104—24no—
69#6103—21no—
70#6103—21no—
71#6103—21no—
72#6103—21no—
73C4⋊Dic13C2311yescharacteristic
74C4⋊Dic13C2311yescharacteristic
75#6101—21no—
76#6101—21no—
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80C2×#1055C2312yes—
81C2×#1055C2312yes—
82#3114—131nomaximal, Sylow
83C23×C13—24no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89D4×C13—24no—
90D4×C13—22no—
91D4×C13#4114yes—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—44no—
97C2×C4×C13—44no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C22⋊D13—42no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109D52—22no—
110C4×D13—42no—
111Dic26—22no—
112#1055—22no—
113#1055—22no—
114#529—131no—
115C2×C4×D4D1311yescharacteristic, complemented
116#483—131no—
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×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—21no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—42no—
142C4×C13C2×#4112yes—
143Dic13—41no—
144Dic13—41no—
145Dic13—41no—
146C22×D4C2×D1311yescharacteristic
147C23×C4—21no—
148C2×SD16—132no—
149C2×D8—132no—
150#126—261no—
151#125—131no—
152#124—131no—
153#123—261no—
154C22⋊Q8—131no—
155#121—131no—
156C4×Q8—131no—
157C4×D4—21no—
158C4×D4—21no—
159C4×D4—131no—
160C4×D4—261no—
161C4×D4C2×D1312yes—
162C4×D4C2×D1312yes—
163#117—261no—
164C2×C4⋊C4C2×D1311yescharacteristic
165C2×C22⋊C4—21no—
166C2×C42C2×D1311yescharacteristic
167#107—132no—
168#106—132no—
169C4⋊C8—132no—
170#103—132no—
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—131no—
175C22⋊C8—131no—
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×Q8—131no—
185C2×D4—24no—
186C2×D4—21no—
187C2×D4—131no—
188C2×D4—261no—
189C2×D4C22×D1312yes—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—44no—
194C22×C4—261no—
195C22×C4C22⋊D1311yescharacteristic
196C22×C4C22⋊D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198SD16—264no—
199D8—264no—
200C2×C8—132no—
201C2×C8—132no—
202C4⋊C4—21no—
203C4⋊C4—131no—
204C4⋊C4—131no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C4⋊C4C22×D1312yes—
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C22⋊C4—261no—
217C42—261no—
218C42C22⋊D1311yescharacteristic
219C42C22⋊D1311yescharacteristic
220C42C22×D1311yescharacteristic
221C42C22×D1311yescharacteristic
222C13#311411yescharacteristic, complemented, Sylow
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—261no—
228C23C2×C22⋊D1311yescharacteristic
229Q8—262no—
230D4—24no—
231D4—22no—
232D4—262no—
233D4—522no—
234D4#612714yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—522no—
246C2×C4C2×C22⋊D1311yescharacteristic
247C2×C4C2×C22⋊D1311yescharacteristic
248C2×C4C2×C22⋊D1311yescharacteristic
249C2×C4C2×C22⋊D1311yescharacteristic
250C2×C4C2×C22⋊D1311yescharacteristic
251C2×C4C23×D1311yescharacteristic
252C8—262no—
253C8—262no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8818612yes—
264C22C22×C22⋊D1311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—521no—
272C4—521no—
273C4—521no—
274C4C2×#612712yes—
275C2—22no—
276C2—44no—
277C2—1041no—
278C2#1171949611yescharacteristic
279C2C2×#8818611yescharacteristic
280C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C4×D4×C13C2
socleC22×C13C22×D4
prime radical#11718878C2
hypercenterC2×C4×D4D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C13C2semidirect
2. #11719184C2semidirect
3. #11718879C2semidirect
5. #11718679C2semidirect
6. #11718677C2semidirect
7. #11718675C2semidirect
8. #11718670C2semidirect
9. #11718632C2semidirect
10. #11718628C2semidirect
11. #11718587C2semidirect
28. #88129C22semidirect
29. C4×D52C22semidirect
31. #88124C22semidirect
32. C4×Dic26C22semidirect
37. #88050C22semidirect
38. #88049C22semidirect
39. #88048C22semidirect
40. #88047C22semidirect
41. C4⋊#1055C22semidirect
42. #88043C22semidirect
115. C2×C4×D4D13semidirect
222. C13#3114semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
#117191842
#117188792
#117188782
#117186792
#117186772
#117186752
#117186702
#117186322
#117186282
#117185872
#311413