Finite Group Databasebeta

← #15751166

Subgroups — #15751166

Order 3328.

590 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114530C212yesmaximal
2#13112659C214yesmaximal, complemented
3C13×#2296C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C42×C13C2211yescharacteristic
7C22×#6099—22no—
8C13×#389C412yes—
9C13×#389C2212yes—
10C13×#385—22no—
11C4×C13×C4⋊C4—22no—
12#11718116—22no—
13#11718116C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×C4×C13D412yes—
16C13×#117—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4C2×C412yes—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C22⋊C4—21no—
23C2×C13×C22⋊C4—21no—
24C2×C42×C13—21no—
25C2×C42×C13—21no—
26C2×C42×C13—42no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30C2×#6099—28no—
31C2×#6099—44no—
32C2×#6099—44no—
33C22×#1055—24no—
34C13×#95—22no—
35C13×#95—22no—
36#7632—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C22×C4×C13—24no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—24no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22⋊C412yes—
49C22×C4×C13C22×C411yescharacteristic
50C22×C4×C13C2×D412yes—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—44no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4M1614yescomplemented
57C13×C22⋊C4—24no—
58C13×C22⋊C4—42no—
59C42×C13—24no—
60C42×C13—41no—
61C42×C13—42no—
62C42×C13—41no—
63C42×C13—42no—
64#6099—416no—
65C2×#1055—28no—
66C2×#1055—44no—
67C2×#1055—44no—
68#2296D1311yescharacteristic
69#1728—132no—
70#1271—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13#9912yes—
76C23×C13C2×C22⋊C411yescharacteristic
77C2×C4×C13—28no—
78C2×C4×C13—28no—
79C2×C4×C13—28no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—24no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13#10112yes—
95C2×C4×C13#10414yes—
96C2×C4×C13C2×M1612yes—
97C2×C4×C13AGL(1,ℤ/8)12yes—
98C2×C4×C13#13712yes—
99#1055—48no—
100C22×M16—262no—
101C2×#117Dic1311yescharacteristic
102C2×#117Dic1311yescharacteristic
103C22×C42C2×D1311yescharacteristic
104#389Dic1312yes—
105#389C2×D1312yes—
106#385—22no—
107C4×C4⋊C4—22no—
108#336—134no—
109#336—262no—
110C22×C13—22no—
111C22×C13—24no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13—41no—
115C22×C13#40711yescharacteristic
116C22×C13C2×#9911yescharacteristic
117C22×C13C2×#10111yescharacteristic
118C22×C13#41712yes—
119C22×C13C2×#10412yes—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—24no—
124C4×C13—22no—
125C4×C13—44no—
126C4×C13—82no—
127C23×C4C2×Dic1311yescharacteristic
128C23×C4C22⋊D1312yes—
129C2×M16—268no—
130C2×M16—524no—
131C2×M16—524no—
132C22×C8—264no—
133#117—24no—
134#117—42no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C2×Dic1312yes—
138C2×C4⋊C4C2×Dic1312yes—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—21no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42—42no—
144C2×C42C2×Dic1311yescharacteristic
145C2×C42C22⋊D1312yes—
146C2×C42C22×D1311yescharacteristic
147#95—22no—
148#95—22no—
149C2×C13—42no—
150C2×C13#146311yescharacteristic
151C2×C13#148912yes—
152C2×C13#150412yes—
153C2×C13#152611yescharacteristic
154C2×C13#156111yescharacteristic
155C24C22⋊Dic1311yescharacteristic
156C22×C4—22no—
157C22×C4—24no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4C22⋊Dic1311yescharacteristic
166C22×C4C22⋊Dic1312yes—
167C22×C4C22×Dic1311yescharacteristic
168C22×C4C2×C22⋊D1312yes—
169M16—5216no—
170C2×C8—268no—
171C2×C8—524no—
172C2×C8—524no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—44no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4#609914yescomplemented
179C22⋊C4—24no—
180C22⋊C4—42no—
181C42—24no—
182C42—41no—
183C42—42no—
184C42—41no—
185C42—42no—
186C13#763211yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23#8807412yes—
192C23C2×C22⋊Dic1311yescharacteristic
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—28no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4#8807612yes—
211C2×C4#8807714yes—
212C2×C4C2×#609912yes—
213C2×C4#8820312yes—
214C2×C4#8820512yes—
215C8—528no—
216C22—22no—
217C22—24no—
218C22—41no—
219C22—42no—
220C22—41no—
221C22#1171886811yescharacteristic
222C22C2×#8807411yescharacteristic
223C22C2×#8807611yescharacteristic
224C22#1171889312yes—
225C22C2×#8807712yes—
226C4—22no—
227C4—22no—
228C4—22no—
229C4—24no—
230C4—22no—
231C4—44no—
232C4—82no—
233C2—42no—
234C2#1311316611yescharacteristic
235C2#1311327512yes—
236C2#1311334012yes—
237C2#1311343111yescharacteristic
238C2#1311357411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2296C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2296D13
hypocenterC13#7632
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #13112659C2semidirect
56. C13×C4⋊C4M16semidirect
178. C4⋊C4#6099semidirect
186. C13#7632semidirect

Maximal subgroups

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

subgroupindex
#131145302
#131126592
C13×#22962
#763213