Finite Group Databasebeta

← #13125219

Subgroups — #13125219

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#11719393C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic
3C13×#488C211yesmaximal, characteristic, complemented
4#11718729C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic, complemented
6#11718463C212yesmaximal, complemented
7#11718456C212yesmaximal, complemented
8#11718431C212yesmaximal
9#11718426C212yesmaximal, complemented
10#11718358C211yesmaximal, characteristic, complemented
11C4×#6094C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C13×#125C2211yescharacteristic, complemented
15C13×#124C2211yescharacteristic
16#88201C2211yescharacteristic
17#88190C2211yescharacteristic
18C2×#6094C2212yes—
19#88150—22no—
20#88146C2212yes—
21#88142C2212yescomplemented
22#88141—22no—
23#88139—22no—
24C22⋊C4×D13—22no—
25#88129C2211yescharacteristic
26C42×D13C2211yescharacteristic
27#88124C2211yescharacteristic, complemented
28C13×#103C2212yescomplemented
29C13×#102C2212yes—
30C4×C8×C13C2211yescharacteristic, complemented
31#88075C2212yescomplemented
32#88072C2212yes—
33#88061C2212yes—
34#88056C2212yescomplemented
35#88055C2212yescomplemented
36#88050C2212yescomplemented
37#88049C2212yes—
38C4×#1055C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×Q8×C13C2311yescharacteristic
41C2×D4×C13C2311yescharacteristic
42C2×C22⋊D13—21no—
43Q8×D13—24no—
44D4×D13—24no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×C4×D13D412yes—
48C2×C4×D13C2311yescharacteristic
49C2×Dic26—21no—
50C2×Dic26—22no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C13×C4⋊C4—22no—
54C13×C4⋊C4C2312yes—
55C13×C22⋊C4—22no—
56C42×C13C2311yescharacteristic
57C22⋊Dic13—22no—
58#6103—22no—
59#6103—22no—
60#6103—22no—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101—22no—
64C4×Dic13—22no—
65C4×Dic13D412yes—
66C4×Dic13C2311yescharacteristic
67C2×#1055C2312yes—
68#6094—24no—
69#3140—131nomaximal, Sylow
70C23×C13—21no—
71C22×D13—21no—
72C22×D13—44no—
73C22×D13—42no—
74C22×D13C2×D411yescharacteristic
75Q8×C13—22no—
76D4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—42no—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D411yescharacteristic
86D52—22no—
87C4×D13—42no—
88C4×D13—42no—
89C4×D13#4114yes—
90Dic26—22no—
91Dic26—44no—
92Dic26—42no—
93C8×C13—22no—
94#1055—22no—
95#533—131no—
96C2×#124—131no—
97#489—132no—
98#489—132no—
99#488—131no—
100#488—131no—
101#488—131no—
102#488D1311yescharacteristic, complemented
103#419—132no—
104#418—132no—
105C4×M16—131no—
106C22×C13—41no—
107C22×C13—42no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—41no—
111C2×D13—42no—
112C2×D13—84no—
113C2×D13#12412yes—
114C4×C13—22no—
115C4×C13—41no—
116C4×C13—42no—
117C4×C13C2×#4112yes—
118Dic13—22no—
119Dic13—41no—
120Dic13—42no—
121Dic13#12412yes—
122C22×Q8—131no—
123C22×D4—131no—
124C2×M16—132no—
125C4⋊Q8—132no—
126#125—131no—
127#125C2×D1311yescharacteristic, complemented
128#124—131no—
129#124—131no—
130#124—131no—
131#124—262no—
132#124C2×D1311yescharacteristic
133C22⋊Q8—262no—
134C4×Q8—262no—
135#117—132no—
136C2×C22⋊C4—262no—
137C2×C42—131no—
138#103—132no—
139#103—132no—
140#103—132no—
141#103C2×D1312yescomplemented
142#102—132no—
143#102—132no—
144#102—132no—
145#102C2×D1312yes—
146#97—132no—
147C4×C8—131no—
148C4×C8C2×D1311yescharacteristic, complemented
149C2×C13—81no—
150C2×C13C2×#12411yescharacteristic
151C2×C13#57512yes—
152D13—22no—
153D13—81no—
154C24—261no—
155C2×Q8—131no—
156C2×Q8—262no—
157C2×Q8—261no—
158C2×Q8—264no—
159C2×Q8C22×D1311yescharacteristic
160C2×D4—131no—
161C2×D4—264no—
162C2×D4—261no—
163C2×D4C22×D1311yescharacteristic
164C22×C4—131no—
165C22×C4—132no—
166C22×C4—261no—
167M16—264no—
168C2×C8—132no—
169C2×C8C22×D1312yes—
170C4⋊C4—22no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4C22×D1312yes—
175C22⋊C4—22no—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C22⋊C4—262no—
180C42—132no—
181C42—131no—
182C42—262no—
183C42C22×D1311yescharacteristic
184C13#314011yescharacteristic, complemented, Sylow
185C23—21no—
186C23—131no—
187C23—261no—
188C23—522no—
189C23—524no—
190Q8—22no—
191Q8—262no—
192Q8—522no—
193Q8—524no—
194D4—22no—
195D4—262no—
196D4—522no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—131no—
200C2×C4—134no—
201C2×C4—132no—
202C2×C4—262no—
203C2×C4—261no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4D4×D1312yes—
207C2×C4C23×D1311yescharacteristic
208C8—22no—
209C8—262no—
210C22—42no—
211C22—41no—
212C22—132no—
213C22—262no—
214C22—522no—
215C22—521no—
216C22—1044no—
217C22C2×D4×D1311yescharacteristic
218C4—22no—
219C4—42no—
220C4—41no—
221C4—132no—
222C4—262no—
223C4—522no—
224C4—521no—
225C4#41×D1312yes—
226C2—81no—
227C2—262no—
228C2—1041no—
229C2D13×#12411yescharacteristic
230C2#1171947312yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#488C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#488D13
hypocenterC13#3140
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11719393C2semidirect
3. C13×#488C2semidirect
4. #11718729C2semidirect
5. #11718717C2semidirect
6. #11718463C2semidirect
7. #11718456C2semidirect
9. #11718426C2semidirect
10. #11718358C2semidirect
11. C4×#6094C2semidirect
14. C13×#125C22semidirect
21. #88142C22semidirect
27. #88124C22semidirect
28. C13×#103C22semidirect
30. C4×C8×C13C22semidirect
31. #88075C22semidirect
34. #88056C22semidirect
35. #88055C22semidirect
36. #88050C22semidirect
38. C4×#1055C22semidirect
102. #488D13semidirect
127. #125C2×D13semidirect
141. #103C2×D13semidirect
148. C4×C8C2×D13semidirect
184. C13#3140semidirect

Maximal subgroups

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

subgroupindex
#117193932
D13×#1242
C13×#4882
#117187292
#117187172
#117184632
#117184562
#117184312
#117184262
#117183582
C4×#60942
#314013