Finite Group Databasebeta

← #16786812

Subgroups — #16786812

Order 3328.

562 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 112 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×#11718305C212yesmaximal
2#13129780C214yesmaximal, complemented
3#13117450C211yesmaximal, characteristic
4C22×C13×C22⋊C4C411yescharacteristic
5C22×C22⋊Dic13C411yescharacteristic
6C22×C22⋊Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8#11718873—22no—
9#11718611—22no—
10#11718611C412yes—
11#11718611C2212yes—
12#11718305—22no—
13#11718305C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×Dic13C2×C412yes—
17C23×Dic13D412yes—
18C22×#1057—42no—
19C2×C13×C22⋊C4—21no—
20C2×C13×C22⋊C4—22no—
21C2×C13×C22⋊C4C814yescomplemented
22C2×C13×C22⋊C4C2×C412yes—
23C2×C22⋊Dic13—21no—
24C2×C22⋊Dic13—21no—
25C2×C22⋊Dic13—42no—
26C2×C22⋊Dic13—42no—
27C2×C22⋊Dic13C2×C411yescharacteristic
28C2×C22⋊Dic13D412yes—
29C2×C22⋊Dic13C2311yescharacteristic
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13—22no—
32C22⋊#1057—24no—
33C22⋊#1057—42no—
34#88071—22no—
35#88071—22no—
36#11453—131nomaximal, Sylow
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—82no—
40C24×C13C22⋊C411yescharacteristic
41C24×C13C22⋊C411yescharacteristic
42C24×C13C2×C812yes—
43C24×C13M1612yes—
44C24×C13C22×C411yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—24no—
47C22×C4×C13—82no—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—42no—
52C22×Dic13—82no—
53C22×Dic13—82no—
54C22×Dic13C22⋊C412yes—
55C22×Dic13C2×D412yes—
56C2×#1057—44no—
57C2×#1057—84no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4C2×C814yescomplemented
61C22⋊Dic13—41no—
62C22⋊Dic13—42no—
63C22⋊Dic13—41no—
64C22⋊Dic13—42no—
65C22⋊Dic13—42no—
66C4⋊Dic13—82no—
67C4⋊Dic13—82no—
68#2315—131no—
69C2×#323—132no—
70#1326—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—24no—
76C23×C13—24no—
77C23×C13—42no—
78C23×C13—42no—
79C23×C13—42no—
80C23×C13—82no—
81C23×C13—82no—
82C23×C13—84no—
83C23×C13—82no—
84C23×C13—82no—
85C23×C13C22⋊C812yes—
86C23×C13C22⋊C812yes—
87C23×C13#9912yes—
88C23×C13#10112yes—
89C23×C13C2×C22⋊C411yescharacteristic
90C23×C13C22×C811yescharacteristic
91C23×C13C2×M1611yescharacteristic
92C2×C4×C13—24no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—84no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—44no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—82no—
105C2×Dic13—84no—
106#1057—84no—
107C22×C22⋊C4—131no—
108C22×C22⋊C4—131no—
109C22×C22⋊C4#26111yescharacteristic
110C2×C22⋊C8—262no—
111#385—132no—
112#385—132no—
113#385—262no—
114#380—262no—
115#323—134no—
116#323—262no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—84no—
133C22×C13—84no—
134C22×C13#32414yes—
135C22×C13C2×C22⋊C811yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#10111yescharacteristic
138C4×C13—44no—
139Dic13—42no—
140Dic13—42no—
141Dic13—82no—
142C25C2×#26111yescharacteristic
143C23×C4—21no—
144C23×C4—132no—
145C23×C4—132no—
146C22×C8—522no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—262no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—132no—
152C2×C22⋊C4—131no—
153C2×C22⋊C4—131no—
154C2×C22⋊C4—261no—
155C2×C22⋊C4—261no—
156C2×C22⋊C4—522no—
157C2×C22⋊C4—522no—
158C2×C22⋊C4#105714yescomplemented
159C2×C22⋊C4C2×#26112yes—
160C22⋊C8—264no—
161C22⋊C8—522no—
162#95—262no—
163#95—262no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—24no—
167C2×C13—42no—
168C2×C13—41no—
169C2×C13—41no—
170C2×C13C2×#32411yescharacteristic
171C2×C13#212112yes—
172C24—22no—
173C24—22no—
174C24—82no—
175C24C2×#105712yes—
176C24#612212yes—
177C24C22⋊#26111yescharacteristic
178C24C22⋊#26111yescharacteristic
179C24C22×#26111yescharacteristic
180C22×C4—22no—
181C22×C4—24no—
182C22×C4—82no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—262no—
186C22×C4—262no—
187C22×C4—262no—
188C22×C4—522no—
189C22×C4—1042no—
190C22×C4—1042no—
191C2×C8—524no—
192C2×C8—1044no—
193C4⋊C4—1042no—
194C4⋊C4—1042no—
195C22⋊C4—24no—
196C22⋊C4—22no—
197C22⋊C4—521no—
198C22⋊C4—522no—
199C22⋊C4—521no—
200C22⋊C4—522no—
201C22⋊C4—522no—
202C22⋊C4C2×#105714yescomplemented
203C13#1145311yescharacteristic, complemented, Sylow
204C23—21no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—24no—
209C23—24no—
210C23—42no—
211C23—42no—
212C23—42no—
213C23—82no—
214C23—82no—
215C23—82no—
216C23—82no—
217C23—84no—
218C23#8810712yes—
219C23#8811312yes—
220C23C22⋊#105712yes—
221C23C22⋊#105712yes—
222C23C22×#105711yescharacteristic
223C23C2×#612211yescharacteristic
224C23C2×C22⋊#26111yescharacteristic
225C2×C4—24no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—1042no—
238C2×C4—1044no—
239C8—1044no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—84no—
257C22#1171828514yes—
258C22C2×#8810711yescharacteristic
259C22C2×#8811311yescharacteristic
260C22C2×C22⋊#105711yescharacteristic
261C4—44no—
262C4—522no—
263C4—522no—
264C4—1042no—
265C2—21no—
266C2—21no—
267C2—24no—
268C2—42no—
269C2—41no—
270C2—41no—
271C2C2×#1171828511yescharacteristic
272C2#1313109312yes—
subgroupG/H
centerC22C2×#88107
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C22⋊C4C4
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC22×C22⋊C4#261
hypocenterC13#11453
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129780C2semidirect
21. C2×C13×C22⋊C4C8semidirect
60. C13×C22⋊C4C2×C8semidirect
158. C2×C22⋊C4#1057semidirect
202. C22⋊C4C2×#1057semidirect
203. C13#11453semidirect

Maximal subgroups

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

subgroupindex
C2×#117183052
#131297802
#131174502
#1145313