Finite Group Databasebeta

← #16787020

Subgroups — #16787020

Order 3328.

490 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 84 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#13129777C214yesmaximal, complemented
3C2×#11718638C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7#11719169—22no—
8C2×#88071—22no—
9#11718638—22no—
10#11718638C412yes—
11#11718638C2212yes—
12#11718285—22no—
13#11718285C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C2×#6122—42no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—41no—
21C2×C13×C4⋊C4—41no—
22C2×C13×C4⋊C4C2×C412yes—
23C2×C4⋊Dic13—41no—
24C2×C4⋊Dic13—41no—
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13C2311yescharacteristic
28C2×C4×Dic13—21no—
29C2×C4×Dic13—24no—
30C2×C4×Dic13C2×C412yes—
31C22⋊#1057—24no—
32C22⋊#1057—42no—
33#88071—24no—
34#88071—24no—
35#11511—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—21no—
38C22×C4×C13—21no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—44no—
43C22×C4×C13—41no—
44C22×C4×C13—41no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—24no—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—42no—
52C22×Dic13—42no—
53C22×Dic13—44no—
54C22×Dic13C22⋊C412yes—
55C22×Dic13C2×D412yes—
56#6122—84no—
57C2×#1057—44no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—42no—
60C4⋊Dic13—41no—
61C4⋊Dic13—42no—
62C4⋊Dic13—41no—
63C4×Dic13—24no—
64C4×Dic13—22no—
65C4×Dic13M1614yescomplemented
66C2×#382—131no—
67#1463—132no—
68#1324—134no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13#9911yescharacteristic
74C23×C13#9911yescharacteristic
75C23×C13C2×C22⋊C411yescharacteristic
76C2×C4×C13—24no—
77C2×C4×C13—24no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—44no—
83C2×C4×C13—42no—
84C2×C4×C13—82no—
85C2×C4×C13—82no—
86C2×C4×C13#10112yes—
87C2×C4×C13C2×M1612yes—
88C2×Dic13—24no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—48no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—44no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—82no—
98#1057—84no—
99C22×C4⋊C4—131no—
100C22×C4⋊C4#26111yescharacteristic
101C22×C42—131no—
102#407—262no—
103#382—132no—
104#382—132no—
105#382—262no—
106C2×#95—262no—
107#324—134no—
108#324—262no—
109C22×C13—24no—
110C22×C13—24no—
111C22×C13—21no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#35412yes—
118C22×C13#35512yes—
119C22×C13#40711yescharacteristic
120C22×C13C2×#9911yescharacteristic
121C22×C13C2×#10111yescharacteristic
122C4×C13—22no—
123C4×C13—22no—
124C4×C13—82no—
125Dic13—44no—
126Dic13—42no—
127Dic13—42no—
128C23×C4—21no—
129C23×C4—132no—
130C23×C4—261no—
131C23×C4C2×#26111yescharacteristic
132C2×M16—522no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—521no—
140C2×C4⋊C4—521no—
141C2×C4⋊C4C2×#26112yes—
142C2×C42—132no—
143C2×C42—264no—
144C2×C42—261no—
145C22⋊C8—264no—
146C22⋊C8—522no—
147#95—264no—
148#95—264no—
149C2×C13—21no—
150C2×C13—22no—
151C2×C13—22no—
152C2×C13—21no—
153C2×C13#146311yescharacteristic
154C2×C13C2×#35411yescharacteristic
155C2×C13C2×#35511yescharacteristic
156C24C22⋊#26111yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—44no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—132no—
166C22×C4—132no—
167C22×C4—264no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4—262no—
171C22×C4—522no—
172C22×C4—522no—
173C22×C4—524no—
174C22×C4C22⋊#26111yescharacteristic
175C22×C4C22×#26111yescharacteristic
176M16—1044no—
177C2×C8—524no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—522no—
181C4⋊C4—521no—
182C4⋊C4—521no—
183C42—134no—
184C42—264no—
185C42—262no—
186C13#1151111yescharacteristic, complemented, Sylow
187C23—22no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23#8811911yescharacteristic
192C23#8811911yescharacteristic
193C23C2×C22⋊#26111yescharacteristic
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—528no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—524no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—1042no—
214C2×C4#8811312yes—
215C2×C4D13⋊M1612yes—
216C8—1044no—
217C22—24no—
218C22—24no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22#1171829512yes—
226C22#1171830012yes—
227C22#1171912611yescharacteristic
228C22C2×#8811311yescharacteristic
229C22C2×#8811911yescharacteristic
230C4—22no—
231C4—22no—
232C4—82no—
233C4—524no—
234C4—522no—
235C4—522no—
236C2—21no—
237C2—22no—
238C2—22no—
239C2—21no—
240C2#1313008611yescharacteristic
241C2C2×#1171830011yescharacteristic
242C2C2×#1171829511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11511
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129777C2semidirect
65. C4×Dic13M16semidirect
186. C13#11511semidirect

Maximal subgroups

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

subgroupindex
#131300842
#131297772
C2×#117186382
#1151113