Finite Group Databasebeta

← #16779815

Subgroups — #16779815

Order 3328.

726 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 176 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
1C2×#11719055C212yesmaximal
2#13129714C214yesmaximal, complemented
3D13×#384C211yesmaximal, characteristic
4C2×C4⋊C4×D13—22no—
5C2×C4⋊C4×D13C412yes—
6C2×C42×D13C2211yescharacteristic
7C2×#88112C2214yes—
8C2×#88111—22no—
9C2×#88110—22no—
10#11719055—24no—
11#11719055C418yescomplemented
12C13×#384C411yescharacteristic
13#11718637—22no—
14#11718637C2212yes—
15#11718596C411yescharacteristic
16C22×C4×D13—22no—
17C22×C4×D13C2×C411yescharacteristic
18C22×C4×D13D412yes—
19C22×#1057—24no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C42×C13C2×C411yescharacteristic
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13C2×C412yes—
25C2×#6101—22no—
26C2×#6101—24no—
27C2×C4×Dic13D412yes—
28C2×C4×Dic13C2311yescharacteristic
29C4⋊C4×D13—44no—
30C4⋊C4×D13—48no—
31C42×D13C2×C414yes—
32C42×D13D412yes—
33C42×D13Q812yes—
34#88112—24no—
35#88112C2×C418yescomplemented
36#88111—28no—
37#88110—28no—
38#8040—131nomaximal, Sylow
39C23×D13C22⋊C411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13C22⋊C412yes—
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13C22⋊C411yescharacteristic
45C22×Dic13C2×D412yes—
46C2×C4×D13—22no—
47C2×C4×D13—22no—
48C2×C4×D13—24no—
49C2×C4×D13—24no—
50C2×C4×D13—48no—
51C2×C4×D13—44no—
52C2×C4×D13C4212yes—
53C2×C4×D13C22⋊C414yes—
54C2×C4×D13C4⋊C412yes—
55C2×C4×D13C4⋊C414yes—
56C2×#1057—28no—
57C2×#1057—44no—
58C2×#1057—44no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—44no—
61C42×C13C4212yes—
62C42×C13C4⋊C412yes—
63C4⋊Dic13—44no—
64C4⋊Dic13—42no—
65#6101—44no—
66#6101—48no—
67C4×Dic13C22⋊C414yes—
68C4×Dic13C4⋊C414yes—
69C4×Dic13C22×C412yes—
70C4×Dic13C2×D411yescharacteristic
71C4×Dic13C2×Q811yescharacteristic
72C2×#432—132no—
73C2×#384—131no—
74#1296—134no—
75C23×C13C2×C22⋊C411yescharacteristic
76C22×D13—22no—
77C22×D13—22no—
78C22×D13#9512yes—
79C22×D13#10012yes—
80C22×D13#10112yes—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13—44no—
87C2×C4×C13#9514yes—
88C2×C4×C13C2×C4211yescharacteristic
89C2×C4×C13C2×C4⋊C411yescharacteristic
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—42no—
93C2×Dic13—44no—
94C2×Dic13#9512yes—
95C2×Dic13C2×C22⋊C412yes—
96C2×Dic13C2×C4⋊C412yes—
97C2×Dic13AGL(1,ℤ/8)14yes—
98C2×Dic13#13714yes—
99C4×D13—24no—
100C4×D13—24no—
101C4×D13—28no—
102C4×D13—28no—
103C4×D13—88no—
104#1057—48no—
105C22×C4⋊C4—132no—
106C22×C4⋊C4—262no—
107C22×C42—131no—
108#432—138no—
109#432—264no—
110C2×C4⋊C8—134no—
111C2×C22⋊C8—262no—
112C2×#97—262no—
113#384—132no—
114#384—131no—
115#384—262no—
116#384#26111yescharacteristic
117C22×C13C2×#9511yescharacteristic
118C22×C13C2×#10011yescharacteristic
119C22×C13C2×#10111yescharacteristic
120C22×C13#41812yes—
121C22×C13#41912yes—
122C2×D13—22no—
123C2×D13—24no—
124C2×D13—22no—
125C2×D13—24no—
126C2×D13#34314yes—
127C4×C13—24no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—82no—
131Dic13—22no—
132Dic13—82no—
133Dic13#41714yes—
134Dic13#42814yes—
135C23×C4—132no—
136C23×C4—131no—
137C23×C4—262no—
138C22×C8—264no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—262no—
142C2×C4⋊C4—264no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—524no—
145C2×C4⋊C4—528no—
146C2×C4⋊C4C2×#26112yes—
147C2×C42—132no—
148C2×C42—131no—
149C2×C42—134no—
150C2×C42—132no—
151C2×C42—132no—
152C2×C42C2×#26111yescharacteristic
153C4⋊C8—138no—
154C4⋊C8—264no—
155C22⋊C8—268no—
156#97—268no—
157C2×C13#155511yescharacteristic
158C2×C13#155612yes—
159C2×C13#155811yescharacteristic
160C2×C13#173612yes—
161C2×C13C2×#34311yescharacteristic
162D13—24no—
163C24—131no—
164C22×C4—22no—
165C22×C4—132no—
166C22×C4—131no—
167C22×C4—134no—
168C22×C4—134no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—264no—
172C22×C4—264no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4—524no—
177C22×C4—528no—
178C22×C4C22⋊#26112yes—
179C22×C4C22×#26111yescharacteristic
180C2×C8—268no—
181C2×C8—524no—
182C2×C8—524no—
183C4⋊C4—42no—
184C4⋊C4—44no—
185C4⋊C4—522no—
186C4⋊C4—524no—
187C4⋊C4—528no—
188C4⋊C4—524no—
189C42—134no—
190C42—134no—
191C42—132no—
192C42—131no—
193C42—131no—
194C42C4×#26112yes—
195C42C4⋊#26112yes—
196C13#804011yescharacteristic, complemented, Sylow
197C23—132no—
198C23—132no—
199C23—132no—
200C23—262no—
201C23—262no—
202C23C2×C22⋊#26111yescharacteristic
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—132no—
210C2×C4—132no—
211C2×C4—134no—
212C2×C4—134no—
213C2×C4—132no—
214C2×C4—268no—
215C2×C4—268no—
216C2×C4—264no—
217C2×C4—264no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—524no—
221C2×C4—522no—
222C2×C4—1048no—
223C2×C4(C2×#261)⋊C414yes—
224C2×C4C2×C4×#26111yescharacteristic
225C2×C4C2×C4⋊#26111yescharacteristic
226C8—528no—
227C22—134no—
228C22—264no—
229C22—262no—
230C22—264no—
231C22—262no—
232C22C2×(C2×#261)⋊C411yescharacteristic
233C22#1171913812yes—
234C22D13⋊#10011yescharacteristic
235C22#1171915312yes—
236C22D13⋊#10111yescharacteristic
237C4—24no—
238C4—21no—
239C4—21no—
240C4—82no—
241C4—134no—
242C4—134no—
243C4—262no—
244C4—1042no—
245C2—264no—
246C2#1313036411yescharacteristic
247C2#1313036612yes—
248C2#1313037011yescharacteristic
249C2#1313052312yes—
250C2#1313053911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#8040
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
11. #11719055C4semidirect
35. #88112C2×C4semidirect
196. C13#8040semidirect

Maximal subgroups

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

subgroupindex
C2×#117190552
#131297142
D13×#3842
#804013