Finite Group Databasebeta

← #16779782

Subgroups — #16779782

Order 3328.

610 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 160 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#13129712C214yesmaximal, complemented
3#13117241C211yesmaximal, characteristic
4C2×#88146C412yes—
5C2×C42×D13C2211yescharacteristic
6C2×#88112—22no—
7C2×#88111—22no—
8C2×#88110C2214yes—
9#11719055—24no—
10#11719055C418yescomplemented
11C13×#384C411yescharacteristic
12#11718648—22no—
13#11718638C2212yes—
14C4⋊C4×Dic13—22no—
15#11718596C411yescharacteristic
16C22×C4×D13C2×C411yescharacteristic
17C22×C4×D13D412yes—
18C22×#1057—24no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4C2×C412yes—
21C2×C42×C13C2×C411yescharacteristic
22C2×#6103—22no—
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13C2×C412yes—
25C2×C4×Dic13—22no—
26C2×C4×Dic13D412yes—
27C2×C4×Dic13C2311yescharacteristic
28#88146—44no—
29C42×D13C2×C414yes—
30C42×D13D412yes—
31C42×D13Q812yes—
32#88112—28no—
33#88111—28no—
34#88110—24no—
35#88110C2×C418yes—
36#88071—24no—
37#8031—131nomaximal, Sylow
38C23×D13C22⋊C411yescharacteristic
39C22×C4×C13—22no—
40C22×C4×C13C22⋊C412yes—
41C22×C4×C13C22×C411yescharacteristic
42C22×Dic13—22no—
43C22×Dic13C22⋊C411yescharacteristic
44C22×Dic13C2×D412yes—
45C2×C4×D13—22no—
46C2×C4×D13—22no—
47C2×C4×D13—42no—
48C2×C4×D13—42no—
49C2×C4×D13C4212yes—
50C2×C4×D13C22⋊C414yes—
51C2×C4×D13C4⋊C412yes—
52C2×C4×D13C4⋊C414yes—
53C2×#1057—28no—
54C2×#1057—44no—
55C2×#1057—44no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—44no—
58C42×C13C4212yes—
59C42×C13C4⋊C412yes—
60#6103—44no—
61C4⋊Dic13—44no—
62C4⋊Dic13—42no—
63C4×Dic13—44no—
64C4×Dic13C22⋊C414yes—
65C4×Dic13C4⋊C414yes—
66C4×Dic13C22×C412yes—
67C4×Dic13C2×D411yescharacteristic
68C4×Dic13C2×Q811yescharacteristic
69C2×#432—132no—
70#2285—131no—
71#1295—134no—
72C23×C13C2×C22⋊C411yescharacteristic
73C22×D13—21no—
74C22×D13—21no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13#9512yes—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—42no—
83C2×C4×C13—44no—
84C2×C4×C13#9514yes—
85C2×C4×C13C2×C4211yescharacteristic
86C2×C4×C13C2×C4⋊C411yescharacteristic
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—42no—
90C2×Dic13—44no—
91C2×Dic13#9512yes—
92C2×Dic13#10012yes—
93C2×Dic13#10112yes—
94C2×Dic13C2×C22⋊C412yes—
95C2×Dic13C2×C4⋊C412yes—
96C4×D13—24no—
97C4×D13—24no—
98C4×D13—44no—
99C4×D13—44no—
100#1057—48no—
101C2×#117—132no—
102C22×C42—131no—
103#432—138no—
104#432—264no—
105C2×C4⋊C8—262no—
106C2×C22⋊C8—262no—
107C2×#97—134no—
108#384—131no—
109#384#26111yescharacteristic
110#382—132no—
111#380—262no—
112C4×C4⋊C4—262no—
113C22×C13C2×#9511yescharacteristic
114C22×C13C2×#10011yescharacteristic
115C22×C13C2×#10111yescharacteristic
116C22×C13#42112yes—
117C22×C13#42112yes—
118C2×D13—24no—
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—42no—
123C4×C13—24no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—82no—
127Dic13—22no—
128Dic13—22no—
129Dic13—82no—
130Dic13#34314yes—
131C23×C4—131no—
132C23×C4—132no—
133C22×C8—264no—
134#117—524no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4C2×#26112yes—
139C2×C22⋊C4—262no—
140C2×C42—132no—
141C2×C42—131no—
142C2×C42—134no—
143C2×C42—132no—
144C2×C42—132no—
145C2×C42—262no—
146C2×C42C2×#26111yescharacteristic
147C4⋊C8—268no—
148C22⋊C8—268no—
149#97—138no—
150#97—264no—
151#95—264no—
152C2×C13#153611yescharacteristic
153C2×C13#153611yescharacteristic
154C2×C13#153712yes—
155C2×C13#173312yes—
156C2×C13C2×#34311yescharacteristic
157D13—42no—
158C24—131no—
159C22×C4—22no—
160C22×C4—131no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—134no—
165C22×C4—134no—
166C22×C4—262no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4—522no—
170C22×C4—522no—
171C22×C4C22⋊#26112yes—
172C22×C4C22×#26111yescharacteristic
173C2×C8—268no—
174C2×C8—524no—
175C2×C8—524no—
176C4⋊C4—42no—
177C4⋊C4—44no—
178C4⋊C4—522no—
179C4⋊C4—524no—
180C22⋊C4—524no—
181C42—134no—
182C42—134no—
183C42—132no—
184C42—131no—
185C42—131no—
186C42—524no—
187C42C4×#26112yes—
188C42C4⋊#26112yes—
189C13#803111yescharacteristic, complemented, Sylow
190C23—132no—
191C23—262no—
192C23—261no—
193C23—262no—
194C23—261no—
195C23C2×C22⋊#26111yescharacteristic
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—132no—
206C2×C4—132no—
207C2×C4—264no—
208C2×C4—264no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—524no—
212C2×C4—524no—
213C2×C4—522no—
214C2×C4—524no—
215C2×C4(C2×#261)⋊C414yes—
216C2×C4C2×C4×#26111yescharacteristic
217C2×C4C2×C4⋊#26111yescharacteristic
218C8—528no—
219C22—264no—
220C22—262no—
221C22—521no—
222C22—521no—
223C22—522no—
224C22C2×(C2×#261)⋊C411yescharacteristic
225C22#1171914012yes—
226C22D13⋊#10011yescharacteristic
227C22#1171915512yes—
228C22D13⋊#10111yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—82no—
233C4—134no—
234C4—262no—
235C4—262no—
236C4—1042no—
237C2—522no—
238C2#1313032511yescharacteristic
239C2#1313032611yescharacteristic
240C2#1313032812yes—
241C2#1313051512yes—
242C2#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#8031
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. #13129712C2semidirect
10. #11719055C4semidirect
189. C13#8031semidirect

Maximal subgroups

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

subgroupindex
C2×#117190552
#131297122
#131172412
#803113