Finite Group Databasebeta

← #13124752

Subgroups — #13124752

Order 1664.

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

normal subgroups only

This group has 420 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
1#11719332C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic, complemented
3C13×#484C211yesmaximal, characteristic, complemented
4#11718704C211yesmaximal, characteristic, complemented
5#11718629C211yesmaximal, characteristic, complemented
6#11718546C212yesmaximal, complemented
7#11718541C212yesmaximal, complemented
8#11718475C212yesmaximal, complemented
9#11718465C212yesmaximal, complemented
10#11718397C211yesmaximal, characteristic, complemented
11D13×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C13×C22⋊Q8C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88200C2211yescharacteristic
17#88184C2211yescharacteristic
18C2×#6103—21no—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4×Dic13—21no—
21C2×C8×D13C2212yes—
22#88149C2211yescharacteristic
23#88148—21no—
24#88147—21no—
25#88146—21no—
26#88146—21no—
27#88146C2212yes—
28#88146C2212yes—
29#88146C2211yescharacteristic
30#88136—21no—
31#88135—21no—
32C13×#107C2212yescomplemented
33C13×#103C2212yescomplemented
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yescomplemented
36C22⋊#1055C2211yescharacteristic
37#88061C2212yescomplemented
38#88060C2212yes—
39#88058C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49C22×Dic13D411yescharacteristic
50#6131—24no—
51C2×D52—21no—
52C2×D52—21no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—24no—
55C2×C4×D13—21no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×C4×D13C2311yescharacteristic
60C2×C8×C13C2312yes—
61C13×C4⋊C4—21no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C13×C22⋊C4—21no—
66#6103—21no—
67#6103—21no—
68#6103—22no—
69#6103—22no—
70#6103—21no—
71#6103—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2312yes—
74C4⋊Dic13C2311yescharacteristic
75#6101—21no—
76C4×Dic13—21no—
77C4×Dic13—22no—
78C4×Dic13—22no—
79C2×#1055C2312yes—
80C8×D13—24no—
81#3091—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—21no—
86C22×D13—41no—
87C22×D13C2×D411yescharacteristic
88C22×D13C2×D411yescharacteristic
89Q8×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—42no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—42no—
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104D52—22no—
105D52—42no—
106D52—42no—
107C4×D13—22no—
108C4×D13—22no—
109C4×D13—22no—
110C4×D13—42no—
111C4×D13#4114yes—
112C8×C13—22no—
113#1055—22no—
114#525—131no—
115C2×#117—131no—
116#485—132no—
117#484D1311yescharacteristic, complemented
118#483—131no—
119#482—132no—
120#481—131no—
121#480—131no—
122#427—132no—
123#416—132no—
124C2×C22⋊C8—131no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#13512yes—
128C22×C13C22×D411yescharacteristic
129C2×D13—21no—
130C2×D13—21no—
131C2×D13—21no—
132C2×D13—21no—
133C2×D13—21no—
134C2×D13—44no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—41no—
138C2×D13#12312yes—
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13C2×#4112yes—
144Dic13—21no—
145Dic13—42no—
146Dic13—41no—
147Dic13#12312yes—
148C2×#41—131no—
149C23×C4—131no—
150C22×C8—132no—
151#123—261no—
152C22⋊Q8—131no—
153C22⋊Q8C2×D1311yescharacteristic
154#121—131no—
155#121—131no—
156#120—261no—
157C4×D4—261no—
158C4×D4—261no—
159#117—132no—
160#117—132no—
161#117—131no—
162#117—261no—
163#117—261no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4C2×D1311yescharacteristic
166C2×C22⋊C4—261no—
167C2×C42—261no—
168#107—132no—
169#107C2×D1312yescomplemented
170#106—132no—
171#106—132no—
172#103—132no—
173#103C2×D1312yescomplemented
174#102—132no—
175#102—132no—
176C22⋊C8—131no—
177C22⋊C8—132no—
178C22⋊C8C2×D1311yescharacteristic
179C2×C13—22no—
180C2×C13C2×#12311yescharacteristic
181C2×C13C2×#13511yescharacteristic
182C2×C13#57511yescharacteristic
183D13—22no—
184D13—41no—
185D13—81no—
186C24—131no—
187#41—264no—
188C2×Q8C22×D1311yescharacteristic
189C2×D4—131no—
190C2×D4—261no—
191C2×D4—261no—
192C2×D4—261no—
193C22×C4—21no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—264no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4C22×D1311yescharacteristic
203C2×C8—132no—
204C2×C8—264no—
205C2×C8C22×D1312yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—132no—
209C4⋊C4—131no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4C22×D1312yes—
213C4⋊C4C22×D1311yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—261no—
216C22⋊C4—262no—
217C22⋊C4—262no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C42—262no—
222C42—262no—
223C42—261no—
224C13#309111yescharacteristic, complemented, Sylow
225C23—131no—
226C23—131no—
227C23—262no—
228C23—262no—
229C23—261no—
230C23—521no—
231C23D4×D1311yescharacteristic
232Q8—22no—
233D4—262no—
234D4—522no—
235D4—522no—
236D4—522no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—131no—
243C2×C4—134no—
244C2×C4—131no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4D4×D1311yescharacteristic
254C2×C4C23×D1311yescharacteristic
255C8—22no—
256C8—262no—
257C22—21no—
258C22—21no—
259C22—132no—
260C22—261no—
261C22—261no—
262C22—261no—
263C22—261no—
264C22—261no—
265C22—524no—
266C22—521no—
267C22—521no—
268C22—521no—
269C22#8817312yes—
270C22C2×D4×D1311yescharacteristic
271C4—21no—
272C4—42no—
273C4—41no—
274C4—41no—
275C4—132no—
276C4—261no—
277C4—522no—
278C4—521no—
279C4#41×D1312yes—
280C2—22no—
281C2—262no—
282C2—521no—
283C2—1041no—
284C2D13×#12311yescharacteristic
285C2C2×#8817311yescharacteristic
286C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radical#11719332C2
hypercenter#484D13
hypocenterC13#3091
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#88146C2semidirect
3. C13×#484C2semidirect
4. #11718704C2semidirect
5. #11718629C2semidirect
6. #11718546C2semidirect
7. #11718541C2semidirect
8. #11718475C2semidirect
9. #11718465C2semidirect
10. #11718397C2semidirect
11. D13×C22⋊C8C2semidirect
32. C13×#107C22semidirect
33. C13×#103C22semidirect
35. #88075C22semidirect
37. #88061C22semidirect
39. #88058C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88048C22semidirect
117. #484D13semidirect
169. #107C2×D13semidirect
173. #103C2×D13semidirect
224. C13#3091semidirect

Maximal subgroups

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

subgroupindex
#117193322
C2×#881462
C13×#4842
#117187042
#117186292
#117185462
#117185412
#117184752
#117184652
#117183972
D13×C22⋊C82
#309113