Finite Group Databasebeta

← #15756456

Subgroups — #15756456

Order 3328.

394 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117439C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112743C212yesmaximal
4#13112741C212yesmaximal
5C13×#1463C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C13×#407C2212yes—
8#11718873C2211yescharacteristic
9#11718873C2211yescharacteristic
10#11718872C412yes—
11C4×C22⋊Dic13C412yes—
12#11718868C2212yes—
13#11718642—22no—
14#11718642—22no—
15C13×#324—22no—
16#11718120—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2311yescharacteristic
20C2×C13×M16—22no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D412yes—
24C2×C13×C4⋊C4D412yes—
25C2×C22⋊Dic13C2×C412yes—
26C2×C22⋊Dic13C2×C412yes—
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—21no—
29C2×C4×Dic13—22no—
30C2×#6099—22no—
31C13×C22⋊C8—22no—
32C13×C22⋊C8—22no—
33#88071—22no—
34#88071—24no—
35#88071—21no—
36#88071—21no—
37C22⋊#1055—22no—
38C22⋊#1055—22no—
39#8758—131nomaximal, Sylow
40C24×C13C22×C411yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13—81no—
48C22×C4×C13—81no—
49C22×C4×C13C22⋊C412yes—
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13#4112yes—
54C22×C4×C13#4112yes—
55C22×Dic13—22no—
56C22×Dic13—22no—
57C13×M16—82no—
58C2×C8×C13—42no—
59C13×C4⋊C4—24no—
60C13×C4⋊C4—24no—
61C22⋊Dic13—42no—
62C22⋊Dic13—42no—
63C4⋊Dic13—81no—
64C4⋊Dic13—81no—
65C4×Dic13—82no—
66#6099—82no—
67C2×#1055—42no—
68#2313—131no—
69#1463—131no—
70#1463D1311yescharacteristic
71#1305—132no—
72#1305—132no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—41no—
76C23×C13—41no—
77C23×C13C2×C22⋊C411yescharacteristic
78C23×C13#11711yescharacteristic
79C23×C13#11711yescharacteristic
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—81no—
92C2×C4×C13—81no—
93C2×C4×C13#12312yes—
94C2×C4×C13#12312yes—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C8×C13—82no—
102#1055—82no—
103C22×C4⋊C4C2×D1311yescharacteristic
104#407—132no—
105#407C2×D1312yes—
106#387—262no—
107#387—262no—
108#381—132no—
109#380—131no—
110#380—131no—
111C4×C22⋊C4—132no—
112#324—22no—
113#324—262no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13#38111yescharacteristic
125C22×C13#41311yescharacteristic
126C22×C13#41311yescharacteristic
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—42no—
130C4×C13—42no—
131Dic13—82no—
132Dic13—82no—
133C23×C4C4×D1311yescharacteristic
134C23×C4C4×D1311yescharacteristic
135C23×C4C22×D1311yescharacteristic
136C2×M16—22no—
137C2×M16—262no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—261no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4D5212yes—
143C2×C4⋊C4C22⋊D1312yes—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C42—262no—
147C22⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—262no—
150C22⋊C8—262no—
151#95—262no—
152#95—264no—
153#95—261no—
154#95—261no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13—41no—
158C2×C13—41no—
159C2×C13#182211yescharacteristic
160C2×C13#182811yescharacteristic
161C2×C13#183011yescharacteristic
162C24C2×C4×D1311yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4#610312yes—
174C22×C4#610312yes—
175C22×C4C2×D5211yescharacteristic
176C22×C4#612912yes—
177C22×C4#612912yes—
178C22×C4C2×C22⋊D1311yescharacteristic
179M16—82no—
180M16—1042no—
181C2×C8—42no—
182C2×C8—522no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C4⋊C4—1041no—
186C4⋊C4—1041no—
187C22⋊C4—522no—
188C22⋊C4—522no—
189C42—1042no—
190C13#875811yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23#8813111yescharacteristic
196C23#8813111yescharacteristic
197C23C2×#610311yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4—522no—
217C2×C4#8814012yes—
218C2×C4#8818912yes—
219C8—82no—
220C8—1042no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22#1171860411yescharacteristic
232C22#1171879311yescharacteristic
233C22#1171879311yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—1042no—
239C4—1042no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2#1311491711yescharacteristic
245C2#1311494211yescharacteristic
246C2#1311494811yescharacteristic
subgroupG/H
centerC22#11718604
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1463C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1463D13
hypocenterC13#8758
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
190. C13#8758semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131131662
#131127432
#131127412
C13×#14632
#875813