Finite Group Databasebeta

← #13125221

Subgroups — #13125221

Order 1664.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719433C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718716C211yesmaximal, characteristic, complemented
6#11718463C212yesmaximal, complemented
7#11718461C212yesmaximal, complemented
8#11718431C212yesmaximal
9#11718429C212yesmaximal, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718368C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C13×#124C2211yescharacteristic
16#88201C2211yescharacteristic
17#88200—21no—
18Q8×Dic13—21no—
19#88190C2211yescharacteristic
20C2×#6094C2212yes—
21#88151—21no—
22#88146C2212yes—
23#88144C2212yescomplemented
24#88141—21no—
25#88139—21no—
26#88139—21no—
27C22⋊C4×D13—21no—
28C22⋊C4×D13—21no—
29#88129C2211yescharacteristic
30C42×D13C2211yescharacteristic
31#88123C2211yescharacteristic, complemented
32C13×#103C2212yescomplemented
33C13×#102C2212yes—
34C13×#97C2211yescharacteristic, complemented
35#88075C2212yescomplemented
36#88072C2212yes—
37#88061C2212yes—
38#88056C2212yescomplemented
39C8×Dic13C2212yescomplemented
40#88050C2212yescomplemented
41#88049C2212yes—
42#88043C2211yescharacteristic, complemented
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48Q8×D13—24no—
49D4×D13—24no—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13D411yescharacteristic
53C2×C4×D13D411yescharacteristic
54C2×C4×D13C2311yescharacteristic
55C2×Dic26—21no—
56C2×Dic26—21no—
57C2×Dic26C2311yescharacteristic
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2312yes—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65C22⋊Dic13—21no—
66#6103—22no—
67#6103—21no—
68#6103—21no—
69#6103—21no—
70#6103—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13—22no—
73C4⋊Dic13C2312yes—
74#6101—22no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#6094—24no—
81#3140—131nomaximal, Sylow
82C23×C13—21no—
83C22×D13—21no—
84C22×D13—42no—
85C22×D13—42no—
86C22×D13—42no—
87C22×D13C2×D411yescharacteristic
88Q8×C13—22no—
89Q8×C13—42no—
90D4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—42no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101C2×Dic13C2×D411yescharacteristic
102D52—22no—
103C4×D13—41no—
104C4×D13—41no—
105C4×D13—42no—
106C4×D13#4114yes—
107Dic26—22no—
108Dic26—42no—
109Dic26—42no—
110C8×C13—22no—
111#1055—22no—
112#533—131no—
113C2×#124—131no—
114#489—131no—
115#489—131no—
116#489—131no—
117#489D1311yescharacteristic, complemented
118#488—132no—
119#488—132no—
120#419—132no—
121#418—132no—
122C4×M16—131no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13C22×D411yescharacteristic
127C2×D13—21no—
128C2×D13—21no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—41no—
132C2×D13—84no—
133C2×D13#12412yes—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—41no—
137C4×C13—42no—
138C4×C13C2×#4112yes—
139Dic13—21no—
140Dic13—21no—
141Dic13—41no—
142Dic13—42no—
143Dic13#12412yes—
144C22×Q8—131no—
145C22×D4—131no—
146C2×M16—132no—
147C4⋊Q8—131no—
148C4⋊Q8C2×D1311yescharacteristic, complemented
149#125—132no—
150#124—131no—
151#124—131no—
152#124—131no—
153#124—261no—
154#124—261no—
155#124C2×D1311yescharacteristic
156C22⋊Q8—261no—
157C22⋊Q8—261no—
158C4×Q8—261no—
159C4×Q8—261no—
160#117—132no—
161C2×C22⋊C4—261no—
162C2×C22⋊C4—261no—
163C2×C42—131no—
164#103—132no—
165#103—132no—
166#103—132no—
167#103C2×D1312yescomplemented
168#102—132no—
169#102—132no—
170#102—132no—
171#102C2×D1312yes—
172#97—131no—
173#97C2×D1311yescharacteristic, complemented
174C4×C8—132no—
175C2×C13—81no—
176C2×C13C2×#12411yescharacteristic
177C2×C13#57511yescharacteristic
178C2×C13#57511yescharacteristic
179D13—22no—
180D13—81no—
181C24—261no—
182C2×Q8—21no—
183C2×Q8—131no—
184C2×Q8—261no—
185C2×Q8—264no—
186C2×Q8—261no—
187C2×Q8C22×D1311yescharacteristic
188C2×D4—131no—
189C2×D4—264no—
190C2×D4—261no—
191C2×D4C22×D1311yescharacteristic
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—261no—
196M16—264no—
197C2×C8—132no—
198C2×C8C22×D1312yes—
199C4⋊C4—21no—
200C4⋊C4—132no—
201C4⋊C4—262no—
202C4⋊C4—262no—
203C4⋊C4—261no—
204C4⋊C4C22×D1312yes—
205C22⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—261no—
208C22⋊C4—261no—
209C22⋊C4—262no—
210C22⋊C4—261no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—262no—
218C42C22×D1311yescharacteristic
219C13#314011yescharacteristic, complemented, Sylow
220C23—21no—
221C23—131no—
222C23—261no—
223C23—522no—
224C23—522no—
225C23—522no—
226Q8—22no—
227Q8—42no—
228Q8—262no—
229Q8—522no—
230Q8—522no—
231D4—22no—
232D4—262no—
233D4—522no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—131no—
237C2×C4—134no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—522no—
245C2×C4D4×D1311yescharacteristic
246C2×C4D4×D1311yescharacteristic
247C2×C4C23×D1311yescharacteristic
248C8—22no—
249C8—262no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—132no—
254C22—261no—
255C22—261no—
256C22—521no—
257C22—521no—
258C22—521no—
259C22—1044no—
260C22C2×D4×D1311yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—132no—
266C4—261no—
267C4—261no—
268C4—522no—
269C4—521no—
270C4#41×D1312yes—
271C2—81no—
272C2—262no—
273C2—1041no—
274C2D13×#12411yescharacteristic
275C2#1171947811yescharacteristic
276C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#489D13
hypocenterC13#3140
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#489C2semidirect
4. #11718750C2semidirect
5. #11718716C2semidirect
6. #11718463C2semidirect
7. #11718461C2semidirect
9. #11718429C2semidirect
10. #11718375C2semidirect
11. #11718368C2semidirect
14. C13×C4⋊Q8C22semidirect
23. #88144C22semidirect
31. #88123C22semidirect
32. C13×#103C22semidirect
34. C13×#97C22semidirect
35. #88075C22semidirect
38. #88056C22semidirect
39. C8×Dic13C22semidirect
40. #88050C22semidirect
42. #88043C22semidirect
117. #489D13semidirect
148. C4⋊Q8C2×D13semidirect
167. #103C2×D13semidirect
173. #97C2×D13semidirect
219. C13#3140semidirect

Maximal subgroups

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

subgroupindex
#117194332
D13×#1242
C13×#4892
#117187502
#117187162
#117184632
#117184612
#117184312
#117184292
#117183752
#117183682
#314013