Finite Group Databasebeta

← #13126659

Subgroups — #13126659

Order 1664.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719435C211yesmaximal, characteristic, complemented
2#11719422C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718736C211yesmaximal, characteristic, complemented
6#11718439C212yesmaximal, complemented
7#11718438C212yesmaximal, complemented
8#11718437C212yesmaximal, complemented
9D13×#102C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C2×D4×D13C2212yes—
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C13×#127C2211yescharacteristic
16#88200—22no—
17#88192—21no—
18#88192C2212yes—
19#88191—22no—
20C2×#6105C2212yescomplemented
21C2×#6095C2211yescharacteristic
22C2×C8×D13C2212yescomplemented
23#88151C2212yescomplemented
24#88147—21no—
25C4⋊C4×D13C2212yescomplemented
26#88144—21no—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×Dic26C2211yescharacteristic, complemented
30C13×#102C2212yescomplemented
31C13×#102C2212yescomplemented
32C4×C8×C13C2211yescharacteristic, complemented
33#88072C2212yescomplemented
34#88061C2211yescharacteristic
35#88060C2212yescomplemented
36#88057C2211yescharacteristic, complemented
37#88056C2211yescharacteristic, complemented
38#88049C2212yes—
39#88048C2212yescomplemented
40C4⋊#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48D4×D13—24no—
49D4×D13—42no—
50D4×D13—44no—
51C2×D52D411yescharacteristic
52C2×D52C2311yescharacteristic
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13C2312yes—
56C2×Dic26C2311yescharacteristic
57C2×C8×C13C2311yescharacteristic
58C2×C8×C13C2311yescharacteristic
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2312yes—
61C42×C13C2311yescharacteristic
62C22⋊Dic13—22no—
63#6105—42no—
64#6103—22no—
65#6103—21no—
66#6103D412yes—
67C4⋊Dic13—22no—
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—22no—
73C4×Dic13—21no—
74C2×#1055C2312yes—
75#6095—22no—
76C8×D13—42no—
77#3295—131nomaximal, Sylow
78C23×C13—22no—
79C22×D13—21no—
80C22×D13—44no—
81C22×D13—44no—
82C22×D13—82no—
83C22×D13C2×D412yes—
84Q8×C13—81no—
85D4×C13—22no—
86D4×C13—22no—
87D4×C13—42no—
88D4×C13—81no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—44no—
94C22⋊D13—44no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13C2×D412yes—
99D52—21no—
100D52SD1614yescomplemented
101D52#4112yes—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—42no—
105C4×D13—82no—
106Dic26—21no—
107Dic26—21no—
108C8×C13—21no—
109C8×C13—21no—
110#1055—22no—
111#554—131no—
112D42—131no—
113#486D1311yescharacteristic, complemented
114#481—132no—
115#476—131no—
116#465—132no—
117#460—131no—
118#450—132no—
119C4×SD16—131no—
120C8×D4—131no—
121C2×#102—132no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13C22×D411yescharacteristic
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—22no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—88no—
132C2×D13C2×SD1614yes—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13C2×SD1612yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—22no—
139Dic13—41no—
140Dic13—41no—
141Dic13—41no—
142C22×D4—132no—
143C22×D4—261no—
144C2×SD16—132no—
145C2×SD16—131no—
146C22×C8—132no—
147C4⋊Q8C2×D1311yescharacteristic, complemented
148#127C2×D1311yescharacteristic
149#125—261no—
150C22⋊Q8—132no—
151C22⋊Q8—262no—
152#121—132no—
153#121—261no—
154#120—262no—
155C4×Q8—131no—
156C4×D4—131no—
157C4×D4—131no—
158C4×D4—261no—
159C2×C4⋊C4—132no—
160#106—131no—
161#106—132no—
162C4⋊C8—131no—
163#103—131no—
164#102—132no—
165#102—131no—
166#102—132no—
167#102C2×D1312yescomplemented
168#102C2×D1312yescomplemented
169C22⋊C8—132no—
170C4×C8C2×D1311yescharacteristic, complemented
171C2×C13—82no—
172C2×C13#54611yescharacteristic
173C2×C13C22×SD1611yescharacteristic
174C2×C13#57611yescharacteristic
175D13—24no—
176D13—42no—
177C24—262no—
178C2×Q8—21no—
179C2×Q8—131no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—131no—
183C2×D4—131no—
184C2×D4—262no—
185C2×D4—264no—
186C2×D4—262no—
187C2×D4—522no—
188C2×D4—524no—
189C2×D4C22×D1312yes—
190C22×C4—132no—
191C22×C4—262no—
192C22×C4—261no—
193SD16—262no—
194SD16—522no—
195C2×C8—132no—
196C2×C8—522no—
197C2×C8C22×D1311yescharacteristic
198C2×C8C22×D1311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—131no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4—261no—
206C4⋊C4C22×D1312yes—
207C22⋊C4—132no—
208C22⋊C4—262no—
209C22⋊C4—262no—
210C22⋊C4—261no—
211C42—261no—
212C42C22×D1311yescharacteristic
213C13#329511yescharacteristic, complemented, Sylow
214C23—22no—
215C23—132no—
216C23—261no—
217C23—524no—
218C23—524no—
219C23—1042no—
220Q8—81no—
221Q8—261no—
222Q8—261no—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—81no—
227D4—134no—
228D4—132no—
229D4—261no—
230D4—524no—
231D4—524no—
232C2×C4—22no—
233C2×C4—132no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—522no—
240C2×C4—1042no—
241C2×C4D4×D1311yescharacteristic
242C2×C4D4×D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—21no—
245C8—21no—
246C8—262no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—134no—
251C22—262no—
252C22—262no—
253C22—262no—
254C22—521no—
255C22—521no—
256C22—1048no—
257C22C2×D4×D1311yescharacteristic
258C4—21no—
259C4—42no—
260C4—262no—
261C4—521no—
262C4—521no—
263C4—521no—
264C4SD16×D1312yes—
265C4#41×D1311yescharacteristic
266C4#8825611yescharacteristic
267C2—82no—
268C2—264no—
269C2—522no—
270C2#1171938111yescharacteristic
271C2#1171946211yescharacteristic
272C2C2×SD16×D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719422C2
hypercenter#486D13
hypocenterC13#3295
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#486C2semidirect
4. #11718745C2semidirect
5. #11718736C2semidirect
6. #11718439C2semidirect
7. #11718438C2semidirect
8. #11718437C2semidirect
9. D13×#102C2semidirect
10. C4×#6095C2semidirect
11. C8×D52C2semidirect
14. C13×C4⋊Q8C22semidirect
20. C2×#6105C22semidirect
22. C2×C8×D13C22semidirect
23. #88151C22semidirect
25. C4⋊C4×D13C22semidirect
29. C4×Dic26C22semidirect
30. C13×#102C22semidirect
31. C13×#102C22semidirect
32. C4×C8×C13C22semidirect
33. #88072C22semidirect
35. #88060C22semidirect
36. #88057C22semidirect
37. #88056C22semidirect
39. #88048C22semidirect
40. C4⋊#1055C22semidirect
100. D52SD16semidirect
113. #486D13semidirect
147. C4⋊Q8C2×D13semidirect
167. #102C2×D13semidirect
168. #102C2×D13semidirect
170. C4×C8C2×D13semidirect
213. C13#3295semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194222
C13×#4862
#117187452
#117187362
#117184392
#117184382
#117184372
D13×#1022
C4×#60952
C8×D522
#329513