Finite Group Databasebeta

← #16786981

Subgroups — #16786981

Order 3328.

706 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130081C212yesmaximal
2#13129762C214yesmaximal, complemented
3C2×#11718872C211yesmaximal, characteristic
4C24×C4×C13C411yescharacteristic
5C22×C22⋊Dic13C411yescharacteristic
6C22×C22⋊Dic13C2211yescharacteristic
7#11719169—22no—
8#11718872—22no—
9#11718872C412yes—
10#11718872C2212yes—
11C2×#88071—22no—
12#11718305—22no—
13#11718305C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13—21no—
17C23×C4×C13—24no—
18C23×C4×C13—42no—
19C23×C4×C13—42no—
20C23×C4×C13C2×C412yes—
21C23×Dic13—21no—
22C23×Dic13D412yes—
23C2×#6122—42no—
24C2×C22⋊Dic13—21no—
25C2×C22⋊Dic13—42no—
26C2×C22⋊Dic13—42no—
27C2×C22⋊Dic13C2×C412yes—
28C2×C22⋊Dic13C2×C411yescharacteristic
29C2×C22⋊Dic13D412yes—
30C2×C22⋊Dic13C2311yescharacteristic
31C22⋊#1057—24no—
32C22⋊#1057—42no—
33#88071—24no—
34#88071—24no—
35#11500—131nomaximal, Sylow
36C24×C13—22no—
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—44no—
40C24×C13C22⋊C411yescharacteristic
41C24×C13C22⋊C411yescharacteristic
42C24×C13C22×C411yescharacteristic
43C22×C4×C13—24no—
44C22×C4×C13—24no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—416no—
48C22×C4×C13—42no—
49C22×C4×C13—42no—
50C22×C4×C13—42no—
51C22×C4×C13—42no—
52C22×C4×C13—42no—
53C22×C4×C13—42no—
54C22×C4×C13M1614yescomplemented
55C22×Dic13—22no—
56C22×Dic13—22no—
57C22×Dic13—22no—
58C22×Dic13—44no—
59C22×Dic13—42no—
60C22×Dic13—44no—
61C22×Dic13C22⋊C412yes—
62C22×Dic13C2×D412yes—
63#6122—84no—
64C2×#1057—44no—
65C22⋊Dic13—41no—
66C22⋊Dic13—42no—
67C22⋊Dic13—41no—
68C22⋊Dic13—42no—
69C22⋊Dic13—42no—
70C2×#381—131no—
71#1462—132no—
72#1317—134no—
73C23×C13—24no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—28no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—48no—
82C23×C13—48no—
83C23×C13—44no—
84C23×C13—42no—
85C23×C13—42no—
86C23×C13—44no—
87C23×C13#9912yes—
88C23×C13#10012yes—
89C23×C13C2×C22⋊C411yescharacteristic
90C23×C13C2×M1612yes—
91C2×C4×C13—24no—
92C2×C4×C13—48no—
93C2×C4×C13—48no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—44no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—44no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—44no—
104C2×Dic13—42no—
105C2×Dic13—82no—
106C2×Dic13—84no—
107#1057—84no—
108C24×C4#26111yescharacteristic
109C22×C22⋊C4—131no—
110C22×C22⋊C4—131no—
111#407—262no—
112#381—132no—
113#381—132no—
114#381—262no—
115C2×#95—262no—
116#323—134no—
117#323—262no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—416no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13#35214yes—
133C22×C13#40711yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13C2×#10011yescharacteristic
136C4×C13—44no—
137Dic13—42no—
138Dic13—42no—
139Dic13—82no—
140C25C2×#26111yescharacteristic
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—24no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—132no—
147C23×C4—261no—
148C23×C4C2×#26112yes—
149C2×M16—522no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—131no—
152C2×C22⋊C4—131no—
153C2×C22⋊C4—132no—
154C2×C22⋊C4—261no—
155C2×C22⋊C4—522no—
156C2×C22⋊C4—522no—
157C22⋊C8—264no—
158C22⋊C8—522no—
159#95—264no—
160#95—264no—
161C2×C13—21no—
162C2×C13—24no—
163C2×C13—21no—
164C2×C13—42no—
165C2×C13—42no—
166C2×C13#146211yescharacteristic
167C2×C13C2×#35212yes—
168C24—22no—
169C24—22no—
170C24—22no—
171C24—44no—
172C24C22⋊#26111yescharacteristic
173C24C22⋊#26111yescharacteristic
174C24C22×#26111yescharacteristic
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—416no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—132no—
187C22×C4—132no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—524no—
192C22×C4—522no—
193C22×C4—524no—
194C22×C4#612214yescomplemented
195M16—1044no—
196C2×C8—524no—
197C22⋊C4—521no—
198C22⋊C4—522no—
199C22⋊C4—521no—
200C22⋊C4—522no—
201C22⋊C4—522no—
202C13#1150011yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—24no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23#8811912yes—
218C23#8812112yes—
219C23C2×#612212yes—
220C23C2×C22⋊#26111yescharacteristic
221C2×C4—24no—
222C2×C4—48no—
223C2×C4—48no—
224C2×C4—44no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—524no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4—524no—
234C2×C4—522no—
235C2×C4—1042no—
236C2×C4—1044no—
237C8—1044no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—416no—
250C22—42no—
251C22—42no—
252C22#1171828814yes—
253C22C2×#8811911yescharacteristic
254C22#1171916911yescharacteristic
255C22C2×#8812111yescharacteristic
256C4—44no—
257C4—522no—
258C4—522no—
259C4—1042no—
260C2—21no—
261C2—21no—
262C2—24no—
263C2—42no—
264C2—42no—
265C2#1313008111yescharacteristic
266C2C2×#1171828812yes—
subgroupG/H
centerC22C2×#88119
commutatorC24×C13C22×C4
FrattiniC24C22×#261
FittingC24×C4×C13C4
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC24×C4#261
hypocenterC13#11500
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. #13129762C2semidirect
54. C22×C4×C13M16semidirect
194. C22×C4#6122semidirect
202. C13#11500semidirect

Maximal subgroups

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

subgroupindex
#131300812
#131297622
C2×#117188722
#1150013