Finite Group Databasebeta

← #13130242

Subgroups — #13130242

Order 1664.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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
2#11719135C211yesmaximal, characteristic, complemented
3#11719127C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C2×D4×D13—21no—
7C2×D4×D13C411yescharacteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C2×C22⋊#261—21no—
10C2×#6118—21no—
11C13×#121C411yescharacteristic, complemented
12#88193—21no—
13#88192C2211yescharacteristic
14#88184C411yescharacteristic, complemented
15#88149C2211yescharacteristic
16C4⋊C4×D13C411yescharacteristic, complemented
17#88138—21no—
18C22⋊C4×D13—21no—
19C22⋊#1057—21no—
20(C2×#261)⋊C4—21no—
21(C2×#261)⋊C4C2212yescomplemented
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—42no—
44C2×#1057—22no—
45#6118—42no—
46C13×C4⋊C4C2×C411yescharacteristic
47C13×C22⋊C4—21no—
48C22⋊Dic13—21no—
49#6103—21no—
50#6103—21no—
51C4⋊Dic13C2×C411yescharacteristic
52#6101—21no—
53#1510—131nomaximal, Sylow
54C23×C13—21no—
55C23×C13C22⋊C411yescharacteristic
56C22×D13—22no—
57C22×D13—22no—
58C22×D13—21no—
59C22×D13—41no—
60C22×D13—42no—
61C22×D13—42no—
62C22×D13—42no—
63C22×D13C22⋊C411yescharacteristic
64C22×D13C2×D411yescharacteristic
65C2×#261—42no—
66C2×#261—42no—
67C2×#261—42no—
68D4×C13—41no—
69D4×C13—42no—
70C2×C4×C13—21no—
71C2×C4×C13—41no—
72C2×C4×C13C22⋊C411yescharacteristic
73C2×C4×C13C22×C411yescharacteristic
74C22⋊D13—42no—
75C22⋊D13—42no—
76C22⋊D13—42no—
77C2×Dic13—21no—
78C2×Dic13—41no—
79C2×Dic13C22⋊C411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—41no—
82D52—42no—
83C4×D13—22no—
84C4×D13—22no—
85C4×D13—41no—
86C4×D13—41no—
87C4×D13—42no—
88#1057—42no—
89C2×#121—131no—
90#407—131no—
91#381—131no—
92#327—132no—
93#327—132no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13—41no—
100C22×C13C2×C22⋊C411yescharacteristic
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—44no—
106C2×D13—41no—
107C2×D13—41no—
108C2×D13—41no—
109C2×D13—84no—
110C2×D13#9912yes—
111C2×D13AGL(1,ℤ/8)12yes—
112#261—82no—
113C4×C13—21no—
114C4×C13—21no—
115C4×C13—41no—
116Dic13—21no—
117Dic13—21no—
118Dic13—41no—
119C22×D4—131no—
120C22×D4—261no—
121C23×C4—131no—
122C2×M16—261no—
123#121—131no—
124#121—131no—
125#121—131no—
126#121—261no—
127#121—261no—
128#121#26111yescharacteristic, complemented
129C2×C4⋊C4—131no—
130C2×C22⋊C4—261no—
131C2×C22⋊C4—261no—
132C22⋊C8—132no—
133C22⋊C8—261no—
134#95—132no—
135#95—261no—
136C2×C13—41no—
137C2×C13—81no—
138C2×C13C2×#9911yescharacteristic
139C2×C13#41811yescharacteristic
140C2×C13#42111yescharacteristic
141D13—22no—
142D13—22no—
143D13—81no—
144C24—131no—
145C24—261no—
146C2×D4—21no—
147C2×D4—131no—
148C2×D4—261no—
149C2×D4—261no—
150C2×D4—261no—
151C2×D4—261no—
152C2×D4—522no—
153C2×D4—524no—
154C2×D4C2×#26111yescharacteristic
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—261no—
161C22×C4—262no—
162C22×C4—522no—
163C22×C4C2×#26111yescharacteristic
164M16—522no—
165C2×C8—262no—
166C4⋊C4—131no—
167C4⋊C4—261no—
168C4⋊C4C2×#26111yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C22⋊C4—261no—
173C22⋊C4—522no—
174C13#151011yescharacteristic, complemented, Sylow
175C23—21no—
176C23—131no—
177C23—131no—
178C23—262no—
179C23—262no—
180C23—261no—
181C23—521no—
182C23—522no—
183C23—522no—
184C23—522no—
185C23C22⋊#26111yescharacteristic
186D4—41no—
187D4—42no—
188D4—521no—
189D4—522no—
190D4—522no—
191D4—522no—
192D4—522no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—261no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4—522no—
203C2×C4—521no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4C22⋊#26111yescharacteristic
208C2×C4C22×#26111yescharacteristic
209C8—522no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—132no—
217C22—132no—
218C22—261no—
219C22—261no—
220C22—261no—
221C22—261no—
222C22—524no—
223C22—521no—
224C22—521no—
225C22—521no—
226C22—1044no—
227C22C2×C22⋊#26111yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—261no—
232C4—261no—
233C4—521no—
234C4—1042no—
235C2—41no—
236C2—81no—
237C2—262no—
238C2—262no—
239C2—1041no—
240C2#1171913811yescharacteristic
241C2D13⋊#9911yescharacteristic
242C2#1171916611yescharacteristic
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#1510
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. #11719135C2semidirect
3. #11719127C2semidirect
4. #11718292C2semidirect
5. #11718240C2semidirect
7. C2×D4×D13C4semidirect
11. C13×#121C4semidirect
14. #88184C4semidirect
16. C4⋊C4×D13C4semidirect
21. (C2×#261)⋊C4C22semidirect
22. #88111C22semidirect
128. #121#261semidirect
174. C13#1510semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
#117191352
#117191272
#117182922
#117182402
#151013