Finite Group Databasebeta

← #16787021

Subgroups — #16787021

Order 3328.

578 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130084C212yesmaximal
2#13129778C214yesmaximal, complemented
3C2×#11718596C211yesmaximal, characteristic
4C22×C42×C13C411yescharacteristic
5C22×C4⋊Dic13—22no—
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8#11719169—22no—
9#11718596—22no—
10#11718596C412yes—
11#11718596C2212yes—
12#11718285—22no—
13#11718285C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C2×#6122—42no—
19C2×C42×C13—21no—
20C2×C42×C13—24no—
21C2×C42×C13C2×C412yes—
22C2×C4⋊Dic13—21no—
23C2×C4⋊Dic13—24no—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13—41no—
26C2×C4⋊Dic13—41no—
27C2×C4⋊Dic13—48no—
28C2×C4⋊Dic13—41no—
29C2×C4⋊Dic13—41no—
30C2×C4⋊Dic13C2×C412yes—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13D412yes—
33C2×C4⋊Dic13C2311yescharacteristic
34C22⋊#1057—24no—
35C22⋊#1057—42no—
36#11512—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C22×C4×C13—24no—
39C22×C4×C13—24no—
40C22×C4×C13—24no—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—44no—
52C22×Dic13—44no—
53C22×Dic13—41no—
54C22×Dic13—41no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57#6122—84no—
58C2×#1057—44no—
59C42×C13—24no—
60C42×C13—22no—
61C42×C13M1614yescomplemented
62C4⋊Dic13—41no—
63C4⋊Dic13—42no—
64C4⋊Dic13—41no—
65C4⋊Dic13—48no—
66C4⋊Dic13—48no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69C2×#384—131no—
70#1463—132no—
71#1325—134no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13#9911yescharacteristic
77C23×C13#9911yescharacteristic
78C23×C13C2×C22⋊C411yescharacteristic
79C2×C4×C13—24no—
80C2×C4×C13—216no—
81C2×C4×C13—24no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—21no—
85C2×C4×C13—24no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13#10112yes—
90C2×C4×C13C2×M1612yes—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—44no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—44no—
97C2×Dic13—42no—
98C2×Dic13—82no—
99C2×Dic13—82no—
100C2×Dic13—82no—
101#1057—84no—
102C22×C4⋊C4—131no—
103C22×C4⋊C4—131no—
104C22×C4⋊C4—262no—
105C22×C42#26111yescharacteristic
106#407—262no—
107#384—132no—
108#384—132no—
109#384—262no—
110#324—134no—
111#324—262no—
112C22×C13—24no—
113C22×C13—24no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#35312yes—
121C22×C13#35612yes—
122C22×C13#40711yescharacteristic
123C22×C13C2×#9911yescharacteristic
124C22×C13C2×#10111yescharacteristic
125C4×C13—28no—
126C4×C13—22no—
127C4×C13—22no—
128Dic13—42no—
129Dic13—42no—
130Dic13—82no—
131C23×C4—21no—
132C23×C4—132no—
133C23×C4—261no—
134C23×C4C2×#26111yescharacteristic
135C2×M16—522no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—264no—
141C2×C4⋊C4—264no—
142C2×C4⋊C4—261no—
143C2×C4⋊C4—521no—
144C2×C4⋊C4—521no—
145C2×C4⋊C4—521no—
146C2×C4⋊C4—521no—
147C2×C4⋊C4—528no—
148C2×C42—21no—
149C2×C42—24no—
150C2×C42C2×#26112yes—
151C22⋊C8—264no—
152C22⋊C8—522no—
153C2×C13—21no—
154C2×C13—22no—
155C2×C13—22no—
156C2×C13—21no—
157C2×C13#146311yescharacteristic
158C2×C13C2×#35311yescharacteristic
159C2×C13C2×#35611yescharacteristic
160C24C22⋊#26111yescharacteristic
161C22×C4—24no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—524no—
175C22×C4—524no—
176C22×C4—521no—
177C22×C4—521no—
178C22×C4C22⋊#26111yescharacteristic
179C22×C4C22×#26111yescharacteristic
180M16—1044no—
181C2×C8—524no—
182C4⋊C4—522no—
183C4⋊C4—521no—
184C4⋊C4—521no—
185C4⋊C4—522no—
186C4⋊C4—528no—
187C4⋊C4—528no—
188C4⋊C4—522no—
189C42—24no—
190C42—22no—
191C42#612214yescomplemented
192C13#1151211yescharacteristic, complemented, Sylow
193C23—21no—
194C23—22no—
195C23—22no—
196C23—21no—
197C23#8810711yescharacteristic
198C23#8810711yescharacteristic
199C23C2×C22⋊#26111yescharacteristic
200C2×C4—24no—
201C2×C4—216no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—524no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—524no—
216C2×C4—522no—
217C2×C4—1042no—
218C2×C4—1042no—
219C2×C4—1042no—
220C2×C4#8811312yes—
221C2×C4C2×#612212yes—
222C8—1044no—
223C22—24no—
224C22—24no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22#1171822512yes—
232C22#1171822712yes—
233C22C2×#8810711yescharacteristic
234C22C2×#8811311yescharacteristic
235C22#1171916911yescharacteristic
236C4—28no—
237C4—22no—
238C4—22no—
239C4—522no—
240C4—522no—
241C4—1042no—
242C2—21no—
243C2—22no—
244C2—22no—
245C2—21no—
246C2#1313008411yescharacteristic
247C2C2×#1171822511yescharacteristic
248C2C2×#1171822711yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C42#261
hypocenterC13#11512
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #13129778C2semidirect
61. C42×C13M16semidirect
191. C42#6122semidirect
192. C13#11512semidirect

Maximal subgroups

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

subgroupindex
#131300842
#131297782
C2×#117185962
#1151213