Finite Group Databasebeta

← #16778494

Subgroups — #16778494

Order 3328.

590 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130499C212yesmaximal
2#13129655C214yesmaximal, complemented
3#13117318C211yesmaximal, characteristic
4C22×#6122—22no—
5C2×C13×#117C411yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8#11718634C412yes—
9#11718634C2212yes—
10#11718607—22no—
11C4×#6101—22no—
12#11718290—22no—
13#11718290C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13D412yes—
16C2×#6122—28no—
17C2×#6122—44no—
18C2×#6122—44no—
19C22×#1057—24no—
20C13×#117—42no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C22⋊C4—21no—
23C2×C42×C13—21no—
24C2×C22⋊Dic13—21no—
25#88180—24no—
26C2×C4⋊Dic13C2×C412yes—
27C2×#6101—22no—
28C2×#6101—22no—
29C2×C4×Dic13—21no—
30C2×C4×Dic13—42no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D412yes—
33C2×C4×Dic13C2311yescharacteristic
34#88071—22no—
35#88071—22no—
36#7632—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13C22⋊C411yescharacteristic
43C22×C4×C13C22×C411yescharacteristic
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—22no—
47C22×Dic13—22no—
48C22×Dic13—22no—
49C22×Dic13C22⋊C412yes—
50C22×Dic13C2×D412yes—
51#6122—416no—
52C2×#1057—28no—
53C2×#1057—44no—
54C2×#1057—44no—
55C13×C4⋊C4—42no—
56C13×C22⋊C4—42no—
57C42×C13—42no—
58C22⋊Dic13—24no—
59C4⋊Dic13—22no—
60C4⋊Dic13M1614yescomplemented
61#6101—44no—
62#6101—42no—
63#6101—42no—
64C4×Dic13—24no—
65C4×Dic13—41no—
66C4×Dic13—42no—
67C4×Dic13—41no—
68#2296—131no—
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—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13#10112yes—
86C2×C4×C13C2×M1612yes—
87C2×Dic13—28no—
88C2×Dic13—28no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—24no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13#10414yes—
97C2×Dic13AGL(1,ℤ/8)12yes—
98C2×Dic13#13712yes—
99#1057—48no—
100C22×M16—262no—
101C2×#117—131no—
102C2×#117#26111yescharacteristic
103C22×C42—131no—
104#389—132no—
105#389—132no—
106#385—262no—
107C4×C4⋊C4—262no—
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—82no—
123Dic13—22no—
124Dic13—24no—
125Dic13—22no—
126Dic13—44no—
127C23×C4—132no—
128C23×C4C2×#26111yescharacteristic
129C2×M16—268no—
130C2×M16—524no—
131C2×M16—524no—
132C22×C8—264no—
133#117—42no—
134#117—264no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—262no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4C2×#26112yes—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—261no—
141C2×C42—21no—
142C2×C42—132no—
143C2×C42—131no—
144C2×C42—131no—
145C2×C42—261no—
146C2×C42—522no—
147#95—262no—
148#95—262no—
149C2×C13—42no—
150C2×C13#146311yescharacteristic
151C2×C13#148912yes—
152C2×C13#150412yes—
153C2×C13#152611yescharacteristic
154C2×C13#156111yescharacteristic
155C24C22⋊#26111yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—264no—
163C22×C4—262no—
164C22×C4—262no—
165C22×C4—264no—
166C22×C4—262no—
167C22×C4C22⋊#26111yescharacteristic
168C22×C4C22×#26111yescharacteristic
169M16—5216no—
170C2×C8—268no—
171C2×C8—524no—
172C2×C8—524no—
173C4⋊C4—42no—
174C4⋊C4—134no—
175C4⋊C4—262no—
176C4⋊C4—524no—
177C4⋊C4—522no—
178C4⋊C4—522no—
179C22⋊C4—42no—
180C22⋊C4—264no—
181C42—42no—
182C42—264no—
183C42—522no—
184C42—521no—
185C42—521no—
186C13#763211yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23#8811912yes—
192C23C2×C22⋊#26111yescharacteristic
193C2×C4—28no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—134no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—268no—
205C2×C4—268no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—264no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4#8811312yes—
214C2×C4D13⋊M1612yes—
215C8—528no—
216C22—22no—
217C22—24no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22#1171912611yescharacteristic
222C22C2×#8811311yescharacteristic
223C22D13⋊#10412yes—
224C22#1171916412yes—
225C22C2×#8811911yescharacteristic
226C4—22no—
227C4—22no—
228C4—82no—
229C4—262no—
230C4—264no—
231C4—262no—
232C4—524no—
233C2—42no—
234C2#1313008611yescharacteristic
235C2#1313017312yes—
236C2#1313022212yes—
237C2#1313029311yescharacteristic
238C2#1313037511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#7632
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129655C2semidirect
60. C4⋊Dic13M16semidirect
186. C13#7632semidirect

Maximal subgroups

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

subgroupindex
#131304992
#131296552
#131173182
#763213