Finite Group Databasebeta

← #13130224

Subgroups — #13130224

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#11719229C211yesmaximal, characteristic
2C2×(C2×#261)⋊C4C211yesmaximal, characteristic, complemented
3#11719126C211yesmaximal, characteristic, complemented
4#11718241C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C23×#261—21no—
7C2×#6127C411yescharacteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C2×#6122—21no—
10C13×#117C411yescharacteristic, complemented
11#88151C411yescharacteristic, complemented
12#88151C2211yescharacteristic
13#88149C411yescharacteristic, complemented
14#88149C2211yescharacteristic
15#88140—21no—
16#88136—21no—
17C4×D52—21no—
18C4×D52—21no—
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—
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—21no—
30C22×Dic13D411yescharacteristic
31#6127—42no—
32C2×D52—21no—
33C2×D52—21no—
34C2×D52C2×C411yescharacteristic, complemented
35C2×C4×D13—21no—
36C2×C4×D13—42no—
37C2×C4×D13C2×C411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13D411yescharacteristic
40C2×C4×D13C2311yescharacteristic
41C2×Dic26C2×C411yescharacteristic, complemented
42#6122—42no—
43C2×#1057—22no—
44C13×C4⋊C4C2×C411yescharacteristic, complemented
45C13×C4⋊C4C2×C411yescharacteristic, complemented
46C13×C22⋊C4—21no—
47C42×C13—21no—
48#6103—21no—
49#6103—21no—
50#6103—21no—
51#6103—21no—
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54#1504—131nomaximal, Sylow
55C23×C13C22⋊C411yescharacteristic
56C22×D13—22no—
57C22×D13—22no—
58C22×D13—21no—
59C22×D13—21no—
60C22×D13—21no—
61C22×D13C22⋊C411yescharacteristic
62C22×D13C2×D411yescharacteristic
63C2×#261—24no—
64C2×#261—48no—
65C2×#261—42no—
66C2×#261—42no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13C22⋊C411yescharacteristic
71C2×C4×C13C22×C411yescharacteristic
72C22⋊D13—42no—
73C2×Dic13—22no—
74C2×Dic13—21no—
75C2×Dic13C22⋊C411yescharacteristic
76C2×Dic13C2×D411yescharacteristic
77D52—41no—
78D52—42no—
79D52—41no—
80D52—41no—
81C4×D13—41no—
82C4×D13—41no—
83C4×D13—41no—
84C4×D13—41no—
85C4×D13—42no—
86Dic26—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#9912yes—
96C22×C13C2×C22⋊C411yescharacteristic
97C2×D13—24no—
98C2×D13—24no—
99C2×D13—21no—
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—41no—
106C2×D13#10412yes—
107C2×D13AGL(1,ℤ/8)11yescharacteristic
108C2×D13#13711yescharacteristic
109#261—44no—
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—41no—
113C4×C13—41no—
114Dic13—21no—
115Dic13—21no—
116Dic13—41no—
117C2×#41—131no—
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#26111yescharacteristic, complemented
130C22⋊C8—132no—
131C22⋊C8—261no—
132#95—132no—
133#95—261no—
134C2×C13—22no—
135C2×C13C2×#9911yescharacteristic
136C2×C13#41711yescharacteristic
137C2×C13C2×#10411yescharacteristic
138D13—21no—
139D13—22no—
140D13—21no—
141D13—81no—
142C24—131no—
143#41—522no—
144C2×Q8—131no—
145C2×D4—131no—
146C2×D4—261no—
147C2×D4—261no—
148C2×D4—261no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—262no—
155C22×C4—264no—
156C22×C4—261no—
157C22×C4—522no—
158C22×C4—522no—
159C22×C4—522no—
160C22×C4C2×#26111yescharacteristic
161M16—522no—
162C2×C8—262no—
163C4⋊C4—261no—
164C4⋊C4—261no—
165C4⋊C4C2×#26111yescharacteristic, complemented
166C4⋊C4C2×#26111yescharacteristic, complemented
167C22⋊C4—21no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C42—21no—
173C13#150411yescharacteristic, complemented, Sylow
174C23—131no—
175C23—131no—
176C23—262no—
177C23—261no—
178C23—261no—
179C23—262no—
180C23—261no—
181C23C22⋊#26111yescharacteristic
182Q8—521no—
183D4—521no—
184D4—522no—
185D4—521no—
186D4—521no—
187D4—522no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—262no—
194C2×C4—264no—
195C2×C4—261no—
196C2×C4—521no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4—521no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4—528no—
203C2×C4—522no—
204C2×C4C22⋊#26111yescharacteristic
205C2×C4C22×#26111yescharacteristic
206C8—522no—
207C22—21no—
208C22—21no—
209C22—132no—
210C22—131no—
211C22—131no—
212C22—264no—
213C22—264no—
214C22—261no—
215C22—261no—
216C22—261no—
217C22—261no—
218C22—521no—
219C22—521no—
220C22—521no—
221C22#8810712yes—
222C22C2×C22⋊#26111yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—41no—
227C4—261no—
228C4—261no—
229C4—524no—
230C4—521no—
231C2—22no—
232C2—261no—
233C2—262no—
234C2—261no—
235C2—1041no—
236C2C2×#8810711yescharacteristic
237C2D13⋊#10411yescharacteristic
238C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC22×C13C2×C22⋊C4
prime radical#11719229C2
cosocleC2×C4×D13C23
hypercenter#117#261
hypocenterC13#1504
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×(C2×#261)⋊C4C2semidirect
3. #11719126C2semidirect
4. #11718241C2semidirect
5. #11718240C2semidirect
7. C2×#6127C4semidirect
10. C13×#117C4semidirect
11. #88151C4semidirect
13. #88149C4semidirect
34. C2×D52C2×C4semidirect
41. C2×Dic26C2×C4semidirect
44. C13×C4⋊C4C2×C4semidirect
45. C13×C4⋊C4C2×C4semidirect
129. #117#261semidirect
165. C4⋊C4C2×#261semidirect
166. C4⋊C4C2×#261semidirect
173. C13#1504semidirect

Maximal subgroups

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

subgroupindex
#117192292
C2×(C2×#261)⋊C42
#117191262
#117182412
#117182402
#150413