Finite Group Databasebeta

← #15760349

Subgroups — #15760349

Order 3328.

554 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 119 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#13119835C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic, complemented
3#13113503C212yesmaximal
4#13112738C212yesmaximal, complemented
5C13×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201—21no—
8C2×#88128C2211yescharacteristic
9C13×#446—24no—
10C13×#432—22no—
11C13×#431C2212yes—
12C2×#88076—21no—
13#11718652C414yes—
14#11718649—21no—
15#11718600—22no—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718585C2212yes—
18#11718122—21no—
19#11718077—24no—
20C22×Q8×C13D411yescharacteristic
21C22×D52—21no—
22C22×D52—21no—
23C22×D52C2×C412yes—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30#88201—44no—
31C2×#6103—24no—
32C2×#6103—24no—
33C2×C4⋊Dic13—21no—
34C2×C4×Dic13—21no—
35C2×#6099—22no—
36#88128—22no—
37#88128—22no—
38C13×C4⋊C8—24no—
39C13×C4⋊C8D414yes—
40C13×C22⋊C8—22no—
41C13×#97—24no—
42C4×C8×C13—22no—
43#88076—42no—
44#88071C2×C412yes—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47#9406—131nomaximal, Sylow
48C23×D13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—21no—
51C2×Q8×C13—22no—
52C2×Q8×C13—21no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×Dic13—22no—
59C2×D52—24no—
60C2×D52—44no—
61C2×D52—41no—
62C2×D52—42no—
63C2×D52—41no—
64C2×D52—42no—
65C2×D52—41no—
66C2×D52—41no—
67C2×D52—82no—
68C2×C8×C13—24no—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—22no—
71C42×C13—22no—
72C42×C13—22no—
73C42×C13C2×D412yes—
74C42×C13#4112yes—
75#6103—48no—
76#6103—84no—
77C4⋊Dic13—42no—
78C4×Dic13—42no—
79#6099—42no—
80#6099—42no—
81C2×#1055—42no—
82#2983D1311yescharacteristic, complemented
83#2548—131no—
84#1801—131no—
85#1545—132no—
86#1303—132no—
87C23×C13C2×C22⋊C411yescharacteristic
88C22×D13—44no—
89C22×D13—44no—
90C22×D13—42no—
91C22×D13—42no—
92C22×D13—42no—
93Q8×C13—42no—
94Q8×C13—42no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13C4×D412yes—
103C2×C4×C13#12011yescharacteristic
104C2×C4×C13#12112yes—
105C2×C4×C13#12311yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)12yes—
107C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C13#13711yescharacteristic
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112D52—82no—
113D52—84no—
114D52—82no—
115D52—82no—
116D52—82no—
117C8×C13—44no—
118#1055—82no—
119C2×#127—131no—
120C2×#124—261no—
121C2×C4×Q8C2×D1311yescharacteristic
122#446—24no—
123#432—22no—
124#431C2×D1312yes—
125#423—132no—
126C2×#101—261no—
127#394—134no—
128#390—261no—
129#390—262no—
130C4×C4⋊C4—131no—
131#343—261no—
132#331—264no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#38611yescharacteristic
136C22×C13#41711yescharacteristic
137C22×C13#41811yescharacteristic
138C2×D13—84no—
139C2×D13—84no—
140C2×D13—82no—
141C2×D13—82no—
142C2×D13—82no—
143C4×C13—21no—
144C4×C13—22no—
145C4×C13—42no—
146C4×C13—42no—
147C4×C13#45412yes—
148C4×C13#46812yes—
149C4×C13#46912yes—
150Dic13—82no—
151C22×Q8D5211yescharacteristic
152C22×D4—132no—
153C22×D4—261no—
154C22×D4—261no—
155C2×M16—262no—
156#127—262no—
157#127—262no—
158#124—524no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—261no—
162C2×C4⋊C4C4×D1312yes—
163C2×C4⋊C4D5211yescharacteristic
164C2×C22⋊C4—264no—
165C2×C22⋊C4—264no—
166C2×C42—261no—
167C2×C42C22⋊D1312yes—
168C2×C42C22×D1311yescharacteristic
169C4⋊C8—24no—
170C4⋊C8—262no—
171C4⋊C8—262no—
172C4⋊C8C22⋊D1314yes—
173#101—522no—
174C22⋊C8—22no—
175#97—24no—
176C4×C8—22no—
177#95—132no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#188811yescharacteristic
181C2×C13#189511yescharacteristic
182C2×C13#191411yescharacteristic
183D13—162no—
184C24—262no—
185C2×Q8—21no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×D4—264no—
190C2×D4—524no—
191C2×D4—522no—
192C2×D4—521no—
193C2×D4—521no—
194C2×D4—521no—
195C2×D4—522no—
196C2×D4—521no—
197C2×D4—1042no—
198C22×C4—262no—
199C22×C4#610312yes—
200C22×C4#610312yes—
201C22×C4C2×C4×D1311yescharacteristic
202C22×C4C2×D5211yescharacteristic
203C22×C4C2×C22⋊D1311yescharacteristic
204M16—522no—
205M16—522no—
206C2×C8—24no—
207C2×C8—522no—
208C4⋊C4—24no—
209C4⋊C4—22no—
210C4⋊C4—522no—
211C22⋊C4—528no—
212C22⋊C4—1044no—
213C42—22no—
214C42—22no—
215C42—522no—
216C42#612712yes—
217C42C2×C22⋊D1312yes—
218C13#940611yescharacteristic, complemented, Sylow
219C23—524no—
220C23—524no—
221C23—522no—
222C23—522no—
223C23—522no—
224C23C2×#610311yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—1044no—
228D4—1042no—
229D4—1042no—
230D4—1042no—
231D4—1042no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4#8816212yes—
243C2×C4#8816211yescharacteristic
244C2×C4#8816311yescharacteristic
245C2×C4C4×C22⋊D1312yes—
246C2×C4#8818311yescharacteristic
247C2×C4#8818412yes—
248C2×C4#8820711yescharacteristic
249C8—44no—
250C8—1042no—
251C22—21no—
252C22—21no—
253C22—1044no—
254C22—1044no—
255C22—1042no—
256C22—1042no—
257C22—1042no—
258C22#1171879211yescharacteristic
259C22#1171879411yescharacteristic
260C22#1171887411yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—1042no—
266C4#1171879512yes—
267C4#1171879612yes—
268C4#1171890612yes—
269C2—21no—
270C2—21no—
271C2—2082no—
272C2#1311523911yescharacteristic
273C2#1311527411yescharacteristic
274C2#1311538311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9406
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #13114832C2semidirect
4. #13112738C2semidirect
5. C13×#2983C2semidirect
82. #2983D13semidirect
218. C13#9406semidirect

Maximal subgroups

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

subgroupindex
#131198352
#131148322
#131135032
#131127382
C13×#29832
#940613