Finite Group Databasebeta

← #16777238

Subgroups — #16777238

Order 3328.

314 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 70 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#13131064C211yesmaximal, characteristic
2#13130501C211yesmaximal, characteristic
3#13116445C211yesmaximal, characteristic
4C2×#88237C411yescharacteristic
5C2×D13⋊M16C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7C2×#88098—21no—
8C2×#88038—21no—
9C22⋊#6092C412yescomplemented
10(C2×#261)⋊C8—21no—
11(C2×#261)⋊C8—21no—
12#11718259—21no—
13C13×C22⋊C16C411yescharacteristic, complemented
14C22⋊#6090C411yescharacteristic, complemented
15#11718099—21no—
16C22×C4×D13C2×C411yescharacteristic
17C2×C22⋊#261C812yes—
18C2×#6122C812yes—
19#88237—41no—
20#88237—41no—
21C2×C4⋊#261—21no—
22C2×C4×#261—21no—
23D13⋊M16—41no—
24D13⋊M16—41no—
25C2×#6118—21no—
26C2×D13⋊C8—21no—
27C22×C8×C13C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C2×C8×D13—41no—
30C2×C8×D13—41no—
31C2×C8×D13D411yescharacteristic
32C2×C8×D13D411yescharacteristic
33C2×C8×D13D411yescharacteristic
34C2×C8×D13Q811yescharacteristic
35C2×#6092—22no—
36#88098—41no—
37#88098—41no—
38C2×C13×C16—21no—
39C2×#6090—21no—
40#88038—41no—
41#88038—41no—
42#7185—131nomaximal, Sylow
43C23×D13C2×C811yescharacteristic
44C22×#261—22no—
45C22×C4×C13C4211yescharacteristic
46C22×Dic13C2×C811yescharacteristic
47C2×C4×D13—21no—
48C2×C4×D13—21no—
49C2×C4×D13—21no—
50C2×C4×D13—21no—
51C2×C4×D13C22⋊C411yescharacteristic
52C2×C4×D13C4⋊C411yescharacteristic
53C2×C4×D13M1611yescharacteristic
54C2×C4×D13M1611yescharacteristic
55C22⋊#261—42no—
56#6122—42no—
57C2×#1057—22no—
58C4⋊#261—42no—
59C4×#261—41no—
60C4×#261—41no—
61#6118—42no—
62D13⋊C8—41no—
63D13⋊C8—41no—
64C2×C8×C13—41no—
65C2×C8×C13C22⋊C411yescharacteristic
66C2×C8×C13C4⋊C411yescharacteristic
67C2×#1055—41no—
68C2×#1055C22⋊C411yescharacteristic
69C2×#1055C4⋊C411yescharacteristic
70C8×D13—21no—
71C8×D13—21no—
72C8×D13—21no—
73C8×D13—21no—
74C8×D13—41no—
75C8×D13—41no—
76#6092—42no—
77C13×C16—41no—
78#6090—41no—
79#2112—131no—
80#2112—131no—
81#1729—131no—
82C23×C13C4×C811yescharacteristic
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—41no—
86C22×D13—41no—
87C22×D13C22⋊C811yescharacteristic
88C22×D13C4⋊C811yescharacteristic
89C2×#261—42no—
90C2×#261—42no—
91C2×#261—42no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13#9511yescharacteristic
95C2×C4×C13#9711yescharacteristic
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13C22⋊C811yescharacteristic
99C2×Dic13C4⋊C811yescharacteristic
100C4×D13—21no—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—21no—
104C4×D13—21no—
105C4×D13—21no—
106C4×D13#9911yescharacteristic
107C4×D13#9911yescharacteristic
108C4×D13#10011yescharacteristic
109C4×D13#10111yescharacteristic
110#1057—42no—
111C8×C13—21no—
112C8×C13—21no—
113#1055—21no—
114#1055—21no—
115C22×M16—131no—
116C23×C8—131no—
117C2×#117—131no—
118C2×M32—261no—
119C2×M32—261no—
120C22⋊C16—132no—
121C22⋊C16—131no—
122C22⋊C16—261no—
123C22⋊C16—261no—
124C22⋊C16#26111yescharacteristic, complemented
125#336—261no—
126#336—261no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#33611yescharacteristic
131C2×D13—21no—
132C2×D13—21no—
133C2×D13—21no—
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13#32311yescharacteristic
139C2×D13#32411yescharacteristic
140#261—82no—
141C4×C13—21no—
142C4×C13#34211yescharacteristic
143C4×C13#34311yescharacteristic
144Dic13—21no—
145Dic13#32311yescharacteristic
146Dic13#32411yescharacteristic
147C23×C4—131no—
148C2×M16—132no—
149C2×M16—261no—
150C2×M16—521no—
151C2×M16—521no—
152C22×C8—131no—
153C22×C8—131no—
154C22×C8—131no—
155C22×C8—131no—
156C22×C8—131no—
157C22×C8—261no—
158C22×C8—521no—
159C22×C8—521no—
160C22×C8C2×#26111yescharacteristic
161#117—521no—
162#117—521no—
163C2×C4⋊C4—261no—
164C2×C22⋊C4—132no—
165C2×C42—261no—
166M32—521no—
167M32—521no—
168M32—521no—
169M32—521no—
170C2×C16—21no—
171C2×C16—262no—
172C2×C16—261no—
173C2×C13—41no—
174C2×C13#128011yescharacteristic
175C2×C13#137811yescharacteristic
176C2×C13#137811yescharacteristic
177D13—21no—
178D13—21no—
179D13—41no—
180C24—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—261no—
187C22×C4—261no—
188C22×C4—261no—
189C22×C4—261no—
190C22×C4—262no—
191C22×C4C4×#26111yescharacteristic
192M16—522no—
193M16—522no—
194C2×C8—41no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—261no—
198C2×C8—261no—
199C2×C8—261no—
200C2×C8—261no—
201C2×C8—262no—
202C2×C8—521no—
203C2×C8—521no—
204C2×C8—521no—
205C2×C8—521no—
206C2×C8—521no—
207C2×C8C4⋊#26111yescharacteristic
208C2×C8C22⋊#26111yescharacteristic
209C4⋊C4—522no—
210C22⋊C4—522no—
211C42—521no—
212C42—521no—
213C16—41no—
214C16—521no—
215C16—522no—
216C13#718511yescharacteristic, complemented, Sylow
217C23—131no—
218C23—131no—
219C23—261no—
220C23—261no—
221C23—521no—
222C23—521no—
223C23C8×#26111yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—131no—
231C2×C4—131no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4#8810011yescharacteristic
244C2×C4(C2×#261)⋊C411yescharacteristic
245C8—21no—
246C8—21no—
247C8—261no—
248C8—261no—
249C8—522no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—131no—
254C22—131no—
255C22—261no—
256C22—261no—
257C22—261no—
258C22—261no—
259C22—261no—
260C22—522no—
261C22—522no—
262C22(C2×#261)⋊C811yescharacteristic
263C4—21no—
264C4—131no—
265C4—131no—
266C4—261no—
267C4—1042no—
268C4#1171823811yescharacteristic
269C4#1171827111yescharacteristic
270C2—41no—
271C2—261no—
272C2—261no—
273C2—521no—
274C2#1312967311yescharacteristic
275C2#1312988511yescharacteristic
276C2#1312988811yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutatorC23×C13C4×C8
FrattiniC22×C8C2×#261
FittingC13×C22⋊C16C4
socleC22×C13#336
prime radicalC23×D13C2×C8
cosocleC22×C8×D13C22
hypercenterC22⋊C16#261
hypocenterC13#7185
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
9. C22⋊#6092C4semidirect
13. C13×C22⋊C16C4semidirect
14. C22⋊#6090C4semidirect
124. C22⋊C16#261semidirect
216. C13#7185semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131305012
#131164452
#718513