Finite Group Databasebeta

← #13130222

Subgroups — #13130222

Order 1664.

334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719533C211yesmaximal, characteristic
2C2×(C2×#261)⋊C4C211yesmaximal, characteristic, complemented
3#11719126C211yesmaximal, characteristic, complemented
4#11718298C212yesmaximal, complemented
5#11718292C212yesmaximal, complemented
6C23×#261—21no—
7C2×C13×#41C411yescharacteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C2×#6122—21no—
10#88200C411yescharacteristic, complemented
11#88200C2211yescharacteristic
12#88192C411yescharacteristic, complemented
13#88192C2211yescharacteristic
14#88191—21no—
15#88189—21no—
16C4×C22⋊D13—21no—
17C4×C22⋊D13—21no—
18#88180C411yescharacteristic, complemented
19(C2×#261)⋊C4—21no—
20(C2×#261)⋊C4C2212yes—
21#88111—21no—
22#88111C2212yes—
23C23×D13D411yescharacteristic
24C22×#261—24no—
25C22×#261—22no—
26C22×#261—42no—
27C22×#261—42no—
28C13×#41—42no—
29C2×Q8×C13C2×C411yescharacteristic, complemented
30C2×D4×C13—21no—
31C2×D4×C13C2×C411yescharacteristic, complemented
32C22×C4×C13—21no—
33C22×C4×C13C2×C411yescharacteristic
34C2×C22⋊D13—21no—
35C2×C22⋊D13—21no—
36C22×Dic13D411yescharacteristic
37C2×C4×D13—42no—
38C2×C4×D13C2×C411yescharacteristic
39C2×C4×D13D411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13C2311yescharacteristic
42#6122—42no—
43C2×#1057—22no—
44C22⋊Dic13—21no—
45C22⋊Dic13—21no—
46C22⋊Dic13—21no—
47#6103—21no—
48#6103—21no—
49C4⋊Dic13C2×C411yescharacteristic, complemented
50C4⋊Dic13C2×C411yescharacteristic, complemented
51#6101—21no—
52#6101—21no—
53C4×Dic13—21no—
54#1504—131nomaximal, Sylow
55C23×C13—21no—
56C23×C13C22⋊C411yescharacteristic
57C22×D13—22no—
58C22×D13—22no—
59C22×D13—21no—
60C22×D13—21no—
61C22×D13C22⋊C411yescharacteristic
62C22×D13C2×D411yescharacteristic
63C2×#261—24no—
64C2×#261—48no—
65C2×#261—42no—
66C2×#261—42no—
67Q8×C13—41no—
68D4×C13—41no—
69D4×C13—42no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—42no—
73C2×C4×C13C22⋊C411yescharacteristic
74C2×C4×C13C22×C411yescharacteristic
75C22⋊D13—42no—
76C22⋊D13—41no—
77C22⋊D13—41no—
78C2×Dic13—22no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13C22⋊C411yescharacteristic
82C2×Dic13C2×D411yescharacteristic
83C4×D13—41no—
84C4×D13—41no—
85C4×D13—41no—
86C4×D13—41no—
87#1057—42no—
88#525—131no—
89#407—131no—
90C2×#95—131no—
91#328—132no—
92#327—132no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13—41no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13#9912yes—
99C22×C13C2×C22⋊C411yescharacteristic
100C2×D13—24no—
101C2×D13—24no—
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C2×D13#10412yes—
107C2×D13AGL(1,ℤ/8)11yescharacteristic
108C2×D13#13711yescharacteristic
109#261—44no—
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—41no—
113Dic13—21no—
114Dic13—21no—
115Dic13—41no—
116Dic13—41no—
117C2×#41#26111yescharacteristic, complemented
118C23×C4—131no—
119C23×C4—261no—
120C2×M16—261no—
121#123—261no—
122C22⋊Q8—131no—
123C22⋊Q8—131no—
124#121—131no—
125#121—131no—
126#120—261no—
127C4×D4—261no—
128C4×D4—261no—
129#117—131no—
130C22⋊C8—132no—
131C22⋊C8—261no—
132#95—132no—
133#95—261no—
134C2×C13—22no—
135C2×C13—81no—
136C2×C13C2×#9911yescharacteristic
137C2×C13#41711yescharacteristic
138C2×C13C2×#10411yescharacteristic
139D13—21no—
140D13—22no—
141D13—21no—
142C24—131no—
143#41—42no—
144C2×Q8C2×#26111yescharacteristic, complemented
145C2×D4—21no—
146C2×D4—261no—
147C2×D4—261no—
148C2×D4C2×#26111yescharacteristic, complemented
149C22×C4—21no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—262no—
156C22×C4—264no—
157C22×C4—522no—
158C22×C4—522no—
159C22×C4—522no—
160C22×C4C2×#26111yescharacteristic
161M16—522no—
162C2×C8—262no—
163C4⋊C4—131no—
164C4⋊C4—131no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C22⋊C4—261no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C42—261no—
173C13#150411yescharacteristic, complemented, Sylow
174C23—21no—
175C23—131no—
176C23—131no—
177C23—262no—
178C23—261no—
179C23—261no—
180C23—262no—
181C23C22⋊#26111yescharacteristic
182Q8—41no—
183D4—41no—
184D4—42no—
185D4—522no—
186D4—521no—
187D4—521no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—262no—
194C2×C4—264no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4—521no—
200C2×C4—521no—
201C2×C4—522no—
202C2×C4—528no—
203C2×C4—522no—
204C2×C4C22⋊#26111yescharacteristic
205C2×C4C22×#26111yescharacteristic
206C8—522no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—132no—
213C22—131no—
214C22—131no—
215C22—264no—
216C22—264no—
217C22—261no—
218C22—261no—
219C22—261no—
220C22—261no—
221C22#8811912yes—
222C22C2×C22⋊#26111yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—261no—
227C4—261no—
228C4—524no—
229C4—521no—
230C4—521no—
231C2—22no—
232C2—81no—
233C2—261no—
234C2—262no—
235C2—261no—
236C2D13⋊#10411yescharacteristic
237C2#1171916411yescharacteristic
238C2C2×#8811911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×#41C4
socleC22×C13C2×C22⋊C4
prime radical#11719533C2
cosocleC2×C4×D13C23
hypercenterC2×#41#261
hypocenterC13#1504
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×(C2×#261)⋊C4C2semidirect
3. #11719126C2semidirect
4. #11718298C2semidirect
5. #11718292C2semidirect
7. C2×C13×#41C4semidirect
10. #88200C4semidirect
12. #88192C4semidirect
18. #88180C4semidirect
29. C2×Q8×C13C2×C4semidirect
31. C2×D4×C13C2×C4semidirect
49. C4⋊Dic13C2×C4semidirect
50. C4⋊Dic13C2×C4semidirect
117. C2×#41#261semidirect
144. C2×Q8C2×#261semidirect
148. C2×D4C2×#261semidirect
173. C13#1504semidirect

Maximal subgroups

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

subgroupindex
#117195332
C2×(C2×#261)⋊C42
#117191262
#117182982
#117182922
#150413