Finite Group Databasebeta

← #16779853

Subgroups — #16779853

Order 3328.

604 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 140 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#13131283C212yesmaximal
2#13129716C214yesmaximal
3#13123468C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5#11719136—22no—
6#11719135—22no—
7C4×C22⋊#261C2214yes—
8#11719061C414yescomplemented
9#11719060C414yescomplemented
10C4×C4⋊#261—22no—
11#11719057—22no—
12C13×#423C411yescharacteristic, complemented
13#11718787C2212yes—
14M16×Dic13C412yescomplemented
15#11718585C411yescharacteristic, complemented
16#11718496—22no—
17#11718494—22no—
18C22×C4×D13D412yes—
19C22×C4×D13C2311yescharacteristic
20C2×C22⋊#261—24no—
21C2×C4⋊#261—24no—
22C2×C4×#261—24no—
23C2×C13×M16C2×C412yes—
24C2×C42×C13C2×C411yescharacteristic
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13Q812yes—
27C2×#6099C2×C412yes—
28C42×D13C2×C412yes—
29C42×D13C2×C412yes—
30C42×D13D412yes—
31C42×D13D412yes—
32(C2×#261)⋊C4—24no—
33(C2×#261)⋊C4—24no—
34(C2×#261)⋊C4—24no—
35(C2×#261)⋊C4C2×C418yes—
36C13×C4⋊C8—22no—
37#88060—24no—
38#88055—22no—
39C8×Dic13—22no—
40C4⋊#1055—22no—
41#8050—131nomaximal, Sylow
42C23×D13C2×D411yescharacteristic
43C22×#261—28no—
44C22×C4×C13C4⋊C412yes—
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13C4⋊C412yes—
47C22×Dic13C2×Q811yescharacteristic
48C2×C4×D13—41no—
49C2×C4×D13—41no—
50C2×C4×D13—44no—
51C2×C4×D13C22⋊C412yes—
52C2×C4×D13C22⋊C412yes—
53C2×C4×D13C22⋊C412yes—
54C2×C4×D13C22⋊C412yes—
55C2×C4×D13C22×C412yes—
56C2×C4×D13C2×D412yes—
57C22⋊#261—48no—
58C4⋊#261—48no—
59C4×#261—44no—
60C4×#261—44no—
61C13×M16—42no—
62C2×C8×C13—22no—
63C42×C13C4211yescharacteristic
64C42×C13C4211yescharacteristic
65C42×C13C22⋊C412yes—
66C4×Dic13C4212yes—
67C4×Dic13C22⋊C411yescharacteristic
68C4×Dic13C22⋊C411yescharacteristic
69C4×Dic13C4⋊C412yes—
70C4×Dic13C4⋊C412yes—
71C4×Dic13C4⋊C412yes—
72C4×Dic13C4⋊C412yes—
73#6099—42no—
74C2×#1055—22no—
75#2920—131no—
76#2283—132no—
77#1297—134no—
78C23×C13C2×C4⋊C411yescharacteristic
79C22×D13—24no—
80C22×D13—41no—
81C22×D13C2×C22⋊C412yes—
82C2×#261—48no—
83C2×#261—48no—
84C2×#261—48no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—42no—
88C2×C4×C13#9512yes—
89C2×C4×C13#9512yes—
90C2×C4×C13C2×C4211yescharacteristic
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×Dic13—42no—
93C2×Dic13—41no—
94C2×Dic13#9512yes—
95C2×Dic13#9512yes—
96C2×Dic13C2×C4⋊C412yes—
97C4×D13—24no—
98C4×D13—24no—
99C4×D13—22no—
100C4×D13—22no—
101C4×D13—42no—
102C4×D13—42no—
103C4×D13—42no—
104C8×C13—42no—
105#1055—42no—
106C22×C42—131no—
107#432—262no—
108#431—262no—
109#423—131no—
110#423#26111yescharacteristic, complemented
111#407—132no—
112C4×M16—132no—
113#383—134no—
114#382—134no—
115#381—262no—
116#380—262no—
117C4×C4⋊C4—262no—
118C4×C22⋊C4—134no—
119#376—262no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13C2×#9511yescharacteristic
123C2×D13—22no—
124C2×D13—22no—
125C2×D13—44no—
126C2×D13#42114yes—
127#261—88no—
128C4×C13—22no—
129C4×C13—22no—
130C4×C13—21no—
131C4×C13#41011yescharacteristic
132C4×C13#41011yescharacteristic
133Dic13—22no—
134Dic13—22no—
135Dic13—22no—
136C23×C4—132no—
137C23×C4—131no—
138C2×M16—132no—
139C2×M16C2×#26112yes—
140C2×C4⋊C4—264no—
141C2×C22⋊C4—264no—
142C2×C42—132no—
143C2×C42—131no—
144C2×C42—132no—
145C2×C42—132no—
146C2×C42—132no—
147C2×C42—132no—
148C2×C42—264no—
149C2×C42C2×#26111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—262no—
152C22⋊C8—264no—
153#97—262no—
154C4×C8—262no—
155#95—138no—
156#95—264no—
157#95—264no—
158#95—264no—
159C2×C13—41no—
160C2×C13#173312yes—
161C2×C13#174011yescharacteristic
162D13—24no—
163C24—131no—
164C22×C4—132no—
165C22×C4—131no—
166C22×C4—132no—
167C22×C4—132no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—268no—
173C22×C4—521no—
174C22×C4—521no—
175C22×C4—524no—
176C22×C4C4⋊#26112yes—
177C22×C4C22×#26111yescharacteristic
178M16—42no—
179M16—522no—
180C2×C8—22no—
181C2×C8—262no—
182C4⋊C4—528no—
183C22⋊C4—528no—
184C42—132no—
185C42—132no—
186C42—132no—
187C42—132no—
188C42—132no—
189C42—131no—
190C42—131no—
191C42—524no—
192C42—524no—
193C42C4×#26111yescharacteristic
194C42C4×#26111yescharacteristic
195C42C22⋊#26112yes—
196C13#805011yescharacteristic, complemented, Sylow
197C23—132no—
198C23—264no—
199C23—521no—
200C23C2×C4⋊#26111yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—132no—
205C2×C4—132no—
206C2×C4—132no—
207C2×C4—264no—
208C2×C4—264no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—521no—
216C2×C4—528no—
217C2×C4—528no—
218C2×C4—528no—
219C2×C4(C2×#261)⋊C412yes—
220C2×C4(C2×#261)⋊C412yes—
221C2×C4C2×C4×#26111yescharacteristic
222C2×C4C2×C22⋊#26111yescharacteristic
223C8—42no—
224C8—522no—
225C22—22no—
226C22—21no—
227C22—134no—
228C22—262no—
229C22—262no—
230C22—524no—
231C22C2×(C2×#261)⋊C411yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—262no—
236C4—262no—
237C4—262no—
238C4—1048no—
239C4#1171914211yescharacteristic
240C4#1171915611yescharacteristic
241C2—41no—
242C2—264no—
243C2#1313051812yes—
244C2#1313053611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#423C4
socleC22×C13C2×#95
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#423#261
hypocenterC13#8050
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
8. #11719061C4semidirect
9. #11719060C4semidirect
12. C13×#423C4semidirect
14. M16×Dic13C4semidirect
15. #11718585C4semidirect
110. #423#261semidirect
196. C13#8050semidirect

Maximal subgroups

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

subgroupindex
#131312832
#131297162
#131234682
#805013