Finite Group Databasebeta

← #15760551

Subgroups — #15760551

Order 3328.

456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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#13125239C211yesmaximal, characteristic
2#13117942C211yesmaximal, characteristic, complemented
3#13113345C212yesmaximal
4#13112728C212yesmaximal, complemented
5C13×#1534C211yesmaximal, characteristic, complemented
6C2×C13×#125C2211yescharacteristic
7#11719182C2211yescharacteristic
8C13×#432C2212yes—
9#11718730C412yescomplemented
10#11718729—22no—
11#11718728C412yescomplemented
12#11718642—22no—
13#11718642—22no—
14C4⋊C4×Dic13—22no—
15#11718627—22no—
16#11718593C2212yes—
17C4×#6099C2211yescharacteristic
18C13×#330—22no—
19#11718062—22no—
20#11718062—22no—
21C2×#6127—21no—
22C13×#125—22no—
23C13×#125C2×C412yes—
24C13×#125D412yes—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D412yes—
27C2×C42×C13C2311yescharacteristic
28#88184—22no—
29C2×C4⋊Dic13—22no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13—22no—
32C2×#6099—21no—
33#88129—21no—
34#88128C2×C411yescharacteristic
35C4×D52—22no—
36#88123C2×C411yescharacteristic
37C13×C4⋊C8—22no—
38C13×C22⋊C8—22no—
39C13×#97—22no—
40#88071—22no—
41#88071—22no—
42#88071—22no—
43#88071D412yes—
44#88071D412yes—
45#88050—24no—
46#88049—24no—
47#88043C2×C412yes—
48C4×#1055—21no—
49#9442—131nomaximal, Sylow
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C2×C22⋊D13—41no—
54C22×Dic13—22no—
55C22×Dic13—22no—
56#6127—44no—
57C2×D52—21no—
58C2×D52—22no—
59C2×C4×D13—41no—
60C2×Dic26—21no—
61C2×C8×C13—42no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4C22⋊C414yes—
66C42×C13C22×C411yescharacteristic
67C42×C13C2×D411yescharacteristic
68C42×C13#4112yes—
69#6103—42no—
70C4⋊Dic13—22no—
71C4⋊Dic13—44no—
72C4×Dic13—44no—
73C4×Dic13—44no—
74#6099—42no—
75C2×#1055—22no—
76#3142—131no—
77#2371—131no—
78#1534D1311yescharacteristic, complemented
79#1505—132no—
80#1300—132no—
81C23×C13#12011yescharacteristic
82C22×D13—41no—
83C2×C4×C13—22no—
84C2×C4×C13—24no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13C4×D412yes—
90C2×C4×C13#12112yes—
91C2×C4×C13#12311yescharacteristic
92C22⋊D13—82no—
93C2×Dic13—24no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—41no—
99C2×Dic13—42no—
100D52—42no—
101D52—82no—
102C4×D13—82no—
103Dic26—42no—
104C8×C13—82no—
105#1055—42no—
106#532—131no—
107C2×#125C2×D1311yescharacteristic
108#491—132no—
109#490—132no—
110#488—262no—
111#432C2×D1312yes—
112#417—262no—
113C4×M16—131no—
114#387—262no—
115#387—262no—
116C4×C4⋊C4—262no—
117#376—132no—
118#330—22no—
119#327—262no—
120#327—262no—
121C22×C13—22no—
122C22×C13#38611yescharacteristic
123C22×C13#45412yes—
124C2×D13—81no—
125C2×D13—82no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—22no—
129C4×C13—22no—
130C4×C13—44no—
131Dic13—44no—
132Dic13—82no—
133Dic13—81no—
134C2×#41—261no—
135C2×M16—261no—
136C4⋊Q8—131no—
137#127—131no—
138#125—22no—
139#125C4×D1312yes—
140#125C22⋊D1312yes—
141#124—261no—
142#121—262no—
143C4×D4—262no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4D5212yes—
147C2×C42—262no—
148C2×C42—262no—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—22no—
151#103—264no—
152#102—264no—
153C22⋊C8—22no—
154#97—22no—
155#97—132no—
156C4×C8—261no—
157#95—132no—
158#95—132no—
159#95—262no—
160#95—262no—
161#95—262no—
162C2×C13—22no—
163C2×C13#188811yescharacteristic
164C2×C13#190612yes—
165D13—161no—
166#41—524no—
167C2×Q8—261no—
168C2×D4—262no—
169C2×D4—261no—
170C2×D4—521no—
171C22×C4—22no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—521no—
175C22×C4C2×D5211yescharacteristic
176C22×C4D4×D1312yes—
177M16—522no—
178C2×C8—42no—
179C2×C8—262no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—262no—
184C4⋊C4—524no—
185C4⋊C4#610314yes—
186C22⋊C4—522no—
187C42—524no—
188C42—524no—
189C42C2×C4×D1311yescharacteristic
190C42#612912yes—
191C42C2×C22⋊D1311yescharacteristic
192C13#944211yescharacteristic, complemented, Sylow
193C23—521no—
194C23#8813611yescharacteristic
195Q8—522no—
196D4—522no—
197D4—1042no—
198D4—1042no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—264no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—521no—
211C2×C4—1042no—
212C2×C4#8813512yes—
213C2×C4#8814011yescharacteristic
214C2×C4C2×#610311yescharacteristic
215C2×C4#8819312yes—
216C8—82no—
217C8—522no—
218C22—22no—
219C22—1041no—
220C22—1042no—
221C22#1171841412yes—
222C22#1171861911yescharacteristic
223C4—21no—
224C4—21no—
225C4—22no—
226C4—22no—
227C4—44no—
228C4—524no—
229C4—1042no—
230C4—1041no—
231C2—22no—
232C2—2081no—
233C2#1311523711yescharacteristic
234C2#1311533512yes—
subgroupG/H
centerC22#11718619
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1534C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#1534D13
hypocenterC13#9442
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #13117942C2semidirect
4. #13112728C2semidirect
5. C13×#1534C2semidirect
9. #11718730C4semidirect
11. #11718728C4semidirect
78. #1534D13semidirect
192. C13#9442semidirect

Maximal subgroups

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

subgroupindex
#131252392
#131179422
#131133452
#131127282
C13×#15342
#944213