Finite Group Databasebeta

← #13127072

Subgroups — #13127072

Order 1664.

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

normal subgroups only

This group has 460 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
1C13×#555C211yesmaximal, characteristic, complemented
2D4×D52C211yesmaximal, characteristic, complemented
3#11718749C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718700C212yesmaximal, complemented
6#11718697C212yesmaximal, complemented
7#11718676C211yesmaximal, characteristic, complemented
8C4×#6104C211yesmaximal, characteristic, complemented
9#11718673C211yesmaximal, characteristic, complemented
10#11718664C212yesmaximal, complemented
11#11718662C212yesmaximal, complemented
12C2×D4×D13—21no—
13C22×D52C2212yes—
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C13×#124—22no—
16C13×#121—21no—
17C13×#121C2212yescomplemented
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic, complemented
20C13×#117—21no—
21C13×#117C2212yescomplemented
22C2×#6104C2211yescharacteristic
23C2×#6104C2212yescomplemented
24#88184C2212yes—
25C2×#6099C2212yescomplemented
26#88149—21no—
27#88136—22no—
28#88128C2211yescharacteristic
29C4×D52C2211yescharacteristic
30#88072C2211yescharacteristic, complemented
31C22⋊#1055C2212yescomplemented
32#88049C2211yescharacteristic
33#88049C2212yes—
34#88049C2212yescomplemented
35#88049C2212yescomplemented
36#88049C2212yescomplemented
37#88048C2212yescomplemented
38#88047C2211yescharacteristic, complemented
39C4⋊#1055C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13—21no—
43C2×D4×C13—22no—
44C2×D4×C13D411yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13C2312yes—
48C2×C22⋊D13—22no—
49D4×D13—44no—
50C2×D52—24no—
51C2×D52—21no—
52C2×D52—22no—
53C2×D52—21no—
54C2×D52—42no—
55C2×D52C2312yes—
56C2×D52C2311yescharacteristic
57C2×C4×D13—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4D411yescharacteristic
60C13×C4⋊C4C2311yescharacteristic
61C13×C4⋊C4C2312yes—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—21no—
65C13×C22⋊C4D412yes—
66C42×C13—22no—
67C42×C13C2311yescharacteristic
68#6104—22no—
69#6104—42no—
70#6103—21no—
71#6103—22no—
72C4⋊Dic13C2311yescharacteristic
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3325—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13C2×D412yes—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13—44no—
83C22×D13—44no—
84C22×D13—82no—
85Q8×C13—81no—
86D4×C13—22no—
87D4×C13—21no—
88D4×C13—21no—
89D4×C13—82no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—42no—
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—44no—
100C2×Dic13—21no—
101D52—22no—
102D52—21no—
103D52—22no—
104D52—44no—
105D52—42no—
106D52—81no—
107D52#4112yes—
108C4×D13—42no—
109#1055—21no—
110#1055—21no—
111#1055—22no—
112#555D1311yescharacteristic, complemented
113D42—131no—
114#486—131no—
115#482—132no—
116#476—131no—
117#469—132no—
118#459—131no—
119#447—132no—
120C4×D8—131no—
121#436—131no—
122#418—132no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13C22×D411yescharacteristic
130C2×D13—22no—
131C2×D13—41no—
132C2×D13—41no—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—88no—
137C4×C13—22no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13—42no—
141C4×C13AGL(1,ℤ/8)12yes—
142C4×C13C2×#4111yescharacteristic
143C4×C13H(5,𝔽2)11yescharacteristic
144Dic13—41no—
145C22×D4—132no—
146C22×D4—261no—
147C2×D8—131no—
148C2×D8—132no—
149C2×M16—132no—
150C4⋊Q8C2×D1311yescharacteristic, complemented
151#127—131no—
152#124—22no—
153#121—21no—
154#121—132no—
155#121—261no—
156#121C2×D1312yescomplemented
157#120—262no—
158C4×D4—131no—
159C4×D4C2×D1311yescharacteristic
160C4×D4C2×D1311yescharacteristic, complemented
161#117—21no—
162#117C2×D1312yescomplemented
163#107—131no—
164#106—132no—
165C4⋊C8—131no—
166#102—131no—
167#102—131no—
168#102—132no—
169#102—132no—
170#102—132no—
171#102—132no—
172C22⋊C8—132no—
173C4×C8—131no—
174C2×C13—42no—
175C2×C13—81no—
176C2×C13#54611yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C13#57611yescharacteristic
179D13—42no—
180D13—82no—
181C24—262no—
182C2×Q8—21no—
183C2×D4—22no—
184C2×D4—131no—
185C2×D4—132no—
186C2×D4—264no—
187C2×D4—262no—
188C2×D4—262no—
189C2×D4—261no—
190C2×D4—261no—
191C2×D4—522no—
192C2×D4—524no—
193C2×D4C22⋊D1311yescharacteristic
194C2×D4C22×D1311yescharacteristic
195C22×C4—21no—
196C22×C4—261no—
197C22×C4C22×D1312yes—
198D8—262no—
199D8—522no—
200M16—522no—
201C2×C8—131no—
202C2×C8—131no—
203C2×C8—132no—
204C4⋊C4—21no—
205C4⋊C4—131no—
206C4⋊C4C22⋊D1311yescharacteristic
207C4⋊C4C22×D1312yes—
208C4⋊C4C22×D1311yescharacteristic
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4—21no—
212C22⋊C4—261no—
213C22⋊C4—262no—
214C22⋊C4C22⋊D1312yes—
215C42—22no—
216C42C22×D1311yescharacteristic
217C13#332511yescharacteristic, complemented, Sylow
218C23—21no—
219C23—261no—
220C23—262no—
221C23—524no—
222C23—524no—
223C23—1042no—
224C23C2×C22⋊D1312yes—
225Q8—81no—
226D4—22no—
227D4—21no—
228D4—21no—
229D4—82no—
230D4—132no—
231D4—262no—
232D4—261no—
233D4—262no—
234D4—524no—
235D4—524no—
236D4—522no—
237D4—1041no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—261no—
244C2×C4—522no—
245C2×C4C2×C22⋊D1312yes—
246C2×C4C2×C22⋊D1311yescharacteristic
247C2×C4C2×C22⋊D1311yescharacteristic
248C2×C4C23×D1311yescharacteristic
249C8—261no—
250C8—261no—
251C8—262no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—262no—
259C22—521no—
260C22—521no—
261C22—522no—
262C22—522no—
263C22—522no—
264C22—1048no—
265C22C22×C22⋊D1311yescharacteristic
266C4—22no—
267C4—21no—
268C4—41no—
269C4—42no—
270C4—521no—
271C4#8820312yes—
272C4#41×D1311yescharacteristic
273C4#8825611yescharacteristic
274C2—42no—
275C2—81no—
276C2—522no—
277C2—1042no—
278C2C2×#8820311yescharacteristic
279C2#1171953411yescharacteristic
280C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#555C2
socleC22×C13C22×D4
hypercenter#555D13
hypocenterC13#3325
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C13×#555C2semidirect
2. D4×D52C2semidirect
3. #11718749C2semidirect
4. #11718745C2semidirect
5. #11718700C2semidirect
6. #11718697C2semidirect
7. #11718676C2semidirect
8. C4×#6104C2semidirect
9. #11718673C2semidirect
10. #11718664C2semidirect
11. #11718662C2semidirect
14. C13×C4⋊Q8C22semidirect
17. C13×#121C22semidirect
19. C4×D4×C13C22semidirect
21. C13×#117C22semidirect
23. C2×#6104C22semidirect
25. C2×#6099C22semidirect
30. #88072C22semidirect
31. C22⋊#1055C22semidirect
34. #88049C22semidirect
35. #88049C22semidirect
36. #88049C22semidirect
37. #88048C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
112. #555D13semidirect
150. C4⋊Q8C2×D13semidirect
156. #121C2×D13semidirect
160. C4×D4C2×D13semidirect
162. #117C2×D13semidirect
217. C13#3325semidirect

Maximal subgroups

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

subgroupindex
C13×#5552
D4×D522
#117187492
#117187452
#117187002
#117186972
#117186762
C4×#61042
#117186732
#117186642
#117186622
#332513