Finite Group Databasebeta

← #13130231

Subgroups — #13130231

Order 1664.

346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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
1D13×#121C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic, complemented
3#11719126C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C2×D4×D13—21no—
7C2×D4×D13C411yescharacteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C2×C22⋊#261—21no—
10C2×#6122—21no—
11C2×C4×#261—21no—
12C13×#121C411yescharacteristic, complemented
13#88193—21no—
14#88192C2211yescharacteristic
15#88184C411yescharacteristic, complemented
16#88149C2211yescharacteristic
17C4⋊C4×D13C411yescharacteristic, complemented
18#88138—21no—
19C22⋊C4×D13—21no—
20(C2×#261)⋊C4C2212yescomplemented
21#88111—21no—
22#88111C2212yescomplemented
23C23×D13—21no—
24C23×D13D411yescharacteristic
25C22×#261—22no—
26C2×D4×C13—21no—
27C2×D4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C22×Dic13D411yescharacteristic
33D4×D13—42no—
34D4×D13—44no—
35C2×D52—21no—
36C2×D52C2×C411yescharacteristic
37C2×C4×D13—21no—
38C2×C4×D13—42no—
39C2×C4×D13C2×C411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13C2311yescharacteristic
43C22⋊#261—24no—
44#6122—42no—
45C2×#1057—22no—
46C4×#261—42no—
47C13×C4⋊C4C2×C411yescharacteristic
48C13×C22⋊C4—21no—
49C22⋊Dic13—21no—
50#6103—21no—
51#6103—21no—
52C4⋊Dic13C2×C411yescharacteristic
53#6101—21no—
54#1507—131nomaximal, Sylow
55C23×C13—21no—
56C23×C13C22⋊C411yescharacteristic
57C22×D13—22no—
58C22×D13—22no—
59C22×D13—21no—
60C22×D13—41no—
61C22×D13—42no—
62C22×D13—42no—
63C22×D13—42no—
64C22×D13C22⋊C411yescharacteristic
65C22×D13C2×D411yescharacteristic
66C2×#261—24no—
67C2×#261—42no—
68C2×#261—42no—
69D4×C13—41no—
70D4×C13—42no—
71C2×C4×C13—21no—
72C2×C4×C13—41no—
73C2×C4×C13C22⋊C411yescharacteristic
74C2×C4×C13C22×C411yescharacteristic
75C22⋊D13—42no—
76C22⋊D13—42no—
77C22⋊D13—42no—
78C2×Dic13—22no—
79C2×Dic13—21no—
80C2×Dic13C22⋊C411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82D52—41no—
83D52—42no—
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—41no—
87C4×D13—41no—
88C4×D13—42no—
89#1057—42no—
90C2×#121—131no—
91#407—131no—
92C4×C22⋊C4—131no—
93#327—132no—
94#327—132no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13—41no—
99C22×C13—41no—
100C22×C13—41no—
101C22×C13C2×C22⋊C411yescharacteristic
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C2×D13—44no—
107C2×D13—41no—
108C2×D13—41no—
109C2×D13—41no—
110C2×D13—84no—
111C2×D13#10412yes—
112C2×D13AGL(1,ℤ/8)12yes—
113#261—44no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—41no—
117Dic13—21no—
118Dic13—41no—
119Dic13#9912yes—
120C22×D4—131no—
121C22×D4—261no—
122C23×C4—131no—
123C2×M16—261no—
124#121—131no—
125#121—131no—
126#121—131no—
127#121—261no—
128#121—261no—
129#121#26111yescharacteristic, complemented
130C2×C4⋊C4—131no—
131C2×C22⋊C4—261no—
132C2×C22⋊C4—261no—
133C2×C42—261no—
134C22⋊C8—132no—
135C22⋊C8—261no—
136#95—132no—
137C2×C13—41no—
138C2×C13—81no—
139C2×C13C2×#9911yescharacteristic
140C2×C13#41811yescharacteristic
141C2×C13C2×#10411yescharacteristic
142D13—22no—
143D13—22no—
144D13—81no—
145C24—131no—
146C24—261no—
147C2×D4—21no—
148C2×D4—131no—
149C2×D4—261no—
150C2×D4—261no—
151C2×D4—261no—
152C2×D4—261no—
153C2×D4—522no—
154C2×D4—524no—
155C2×D4C2×#26111yescharacteristic
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—261no—
162C22×C4—262no—
163C22×C4—522no—
164C22×C4C2×#26111yescharacteristic
165M16—522no—
166C2×C8—262no—
167C4⋊C4—131no—
168C4⋊C4—261no—
169C4⋊C4C2×#26111yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—261no—
172C22⋊C4—261no—
173C22⋊C4—264no—
174C22⋊C4—261no—
175C42—522no—
176C13#150711yescharacteristic, complemented, Sylow
177C23—21no—
178C23—131no—
179C23—131no—
180C23—262no—
181C23—262no—
182C23—261no—
183C23—521no—
184C23—522no—
185C23—522no—
186C23—522no—
187C23C22⋊#26111yescharacteristic
188D4—41no—
189D4—42no—
190D4—521no—
191D4—522no—
192D4—522no—
193D4—522no—
194D4—522no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—131no—
198C2×C4—131no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—264no—
203C2×C4—261no—
204C2×C4—521no—
205C2×C4—521no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—522no—
209C2×C4C22⋊#26111yescharacteristic
210C2×C4C22×#26111yescharacteristic
211C8—522no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—132no—
219C22—132no—
220C22—261no—
221C22—261no—
222C22—261no—
223C22—261no—
224C22—524no—
225C22—521no—
226C22—521no—
227C22—521no—
228C22—1044no—
229C22C2×C22⋊#26111yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—132no—
234C4—261no—
235C4—524no—
236C4—521no—
237C2—41no—
238C2—81no—
239C2—262no—
240C2—262no—
241C2—1041no—
242C2#1171913811yescharacteristic
243C2D13⋊#9911yescharacteristic
244C2D13⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radicalD13×#121C2
cosocleC2×C4×D13C23
hypercenter#121#261
hypocenterC13#1507
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#261C2semidirect
3. #11719126C2semidirect
4. #11718292C2semidirect
5. #11718240C2semidirect
7. C2×D4×D13C4semidirect
12. C13×#121C4semidirect
15. #88184C4semidirect
17. C4⋊C4×D13C4semidirect
20. (C2×#261)⋊C4C22semidirect
22. #88111C22semidirect
129. #121#261semidirect
176. C13#1507semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
C4×C22⋊#2612
#117191262
#117182922
#117182402
#150713