Finite Group Databasebeta

← #16787528

Subgroups — #16787528

Order 3328.

430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 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#13131194C211yesmaximal, characteristic, complemented
2#13130393C211yesmaximal, characteristic, complemented
3#13129791C214yesmaximal, complemented
4C2×#11718533C211yesmaximal, characteristic
5C22×D104C411yescharacteristic
6C2×#88147—21no—
7#11719129—21no—
8C2×C13×#107C411yescharacteristic
9C2×C8×Dic13C2211yescharacteristic
10C2×#88049—21no—
11#11718533—21no—
12#11718533—21no—
13#11718533C412yes—
14#11718533C2212yes—
15C22⋊#6092—21no—
16#11718260—21no—
17#11718257C2212yescomplemented
18#11718256—21no—
19#11718254C2212yescomplemented
20C22×D52—21no—
21C22×C4×D13—41no—
22C2×#6122—41no—
23C22×C8×C13C2×C411yescharacteristic
24C2×C13×C4⋊C4—21no—
25C2×#6103—41no—
26C2×C4×Dic13D411yescharacteristic
27C22×#1055D411yescharacteristic
28C2×D104—21no—
29C2×D104—24no—
30C2×D104C2×C412yes—
31#88147—22no—
32#88147—22no—
33#88147—41no—
34#88147—41no—
35#88112—41no—
36C4⋊#1057—22no—
37C2×#6092—22no—
38C13×#107—21no—
39C13×#107C2×C412yes—
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13D411yescharacteristic
42C8×Dic13D411yescharacteristic
43C8×Dic13C2311yescharacteristic
44#88049—22no—
45#88049—22no—
46#11657—131nomaximal, Sylow
47C23×D13—41no—
48C22×C4×C13—41no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×Dic13D811yescharacteristic
51C22×Dic13SD1611yescharacteristic
52C2×D52—24no—
53C2×D52—22no—
54C2×D52—42no—
55C2×D52—41no—
56C2×C4×D13—42no—
57C2×C4×D13—42no—
58C2×C4×D13—82no—
59C2×C4×D13—82no—
60#6122—82no—
61C2×#1057—42no—
62C2×C8×C13—22no—
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22×C411yescharacteristic
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67#6103—42no—
68#6103—42no—
69C4×Dic13C22⋊C411yescharacteristic
70C4×Dic13D811yescharacteristic
71C4×Dic13SD1611yescharacteristic
72C4×Dic13C2×D411yescharacteristic
73C2×#1055—41no—
74C2×#1055C22⋊C411yescharacteristic
75C2×#1055C2×D411yescharacteristic
76D104—24no—
77D104—22no—
78D104M1614yescomplemented
79#6092—42no—
80C2×C4×D8—131no—
81#2162—131no—
82#1567—131no—
83#1331—134no—
84C23×C13#10211yescharacteristic
85C22×D13—44no—
86C22×D13—42no—
87C22×D13—82no—
88C22×D13—82no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13—82no—
93C2×C4×C13#10211yescharacteristic
94C2×C4×C13C2×C22⋊C411yescharacteristic
95C2×Dic13—41no—
96C2×Dic13#10211yescharacteristic
97C2×Dic13#10211yescharacteristic
98C2×Dic13D1612yes—
99C2×Dic13SD3212yes—
100C2×Dic13C2×D811yescharacteristic
101C2×Dic13C2×SD1611yescharacteristic
102D52—24no—
103D52—44no—
104D52—42no—
105C4×D13—84no—
106C4×D13—82no—
107C4×D13—82no—
108#1057—82no—
109C8×C13—21no—
110C8×C13C2×M1612yes—
111#1055—21no—
112#1055—21no—
113C22×D8—131no—
114C2×C4×D4—261no—
115C4×D8—132no—
116C4×D8—132no—
117C4×D8—261no—
118C4×D8—261no—
119C2×#107#26111yescharacteristic
120#423—261no—
121C2×#102—261no—
122C2×C4×C8—131no—
123C4⋊C16—261no—
124C22⋊C16—261no—
125C4×C16—132no—
126#335—132no—
127#335—261no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#35712yes—
131C22×C13C2×#10211yescharacteristic
132C2×D13—44no—
133C2×D13—88no—
134C2×D13—82no—
135C2×D13—82no—
136C4×C13—21no—
137C4×C13—82no—
138C4×C13#40711yescharacteristic
139C4×C13#42111yescharacteristic
140Dic13—21no—
141Dic13—21no—
142Dic13#35712yes—
143Dic13C2×D1611yescharacteristic
144Dic13C2×SD3211yescharacteristic
145C22×D4—261no—
146C23×C4—521no—
147C2×D8—132no—
148C2×D8—264no—
149C2×D8—261no—
150C2×M16—521no—
151C22×C8—131no—
152C22×C8C2×#26111yescharacteristic
153C4×D4—262no—
154C4×D4—262no—
155C4×D4—521no—
156C4×D4—521no—
157C2×C4⋊C4—21no—
158C2×C22⋊C4—521no—
159C2×C42—131no—
160C2×C16—262no—
161#107—21no—
162#107C2×#26112yes—
163C4⋊C8—262no—
164C4⋊C8—521no—
165#102—262no—
166#102—262no—
167C4×C8—131no—
168C4×C8—131no—
169C4×C8—131no—
170C4×C8—131no—
171C2×C13—22no—
172C2×C13#148611yescharacteristic
173C2×C13C2×#35711yescharacteristic
174C2×C13#214311yescharacteristic
175D13—84no—
176C24—521no—
177C2×D4—264no—
178C2×D4—262no—
179C2×D4—522no—
180C2×D4—521no—
181C22×C4—41no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—522no—
185C22×C4—522no—
186C22×C4—1042no—
187C22×C4—1042no—
188C22×C4C22⋊#26111yescharacteristic
189D8—134no—
190D8—264no—
191D8—262no—
192M16—1042no—
193C2×C8—22no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8—521no—
197C2×C8—522no—
198C2×C8C22⋊#26111yescharacteristic
199C2×C8C22×#26111yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—41no—
202C22⋊C4—522no—
203C22⋊C4—522no—
204C42—131no—
205C42—131no—
206C42—131no—
207C42—131no—
208C16—522no—
209C13#1165711yescharacteristic, complemented, Sylow
210C23—524no—
211C23—522no—
212C23—1042no—
213C23—1042no—
214C23#8811511yescharacteristic
215D4—264no—
216D4—524no—
217D4—522no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—132no—
223C2×C4—132no—
224C2×C4—131no—
225C2×C4—131no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—521no—
229C2×C4—1044no—
230C2×C4—1042no—
231C2×C4—1042no—
232C2×C4#8811511yescharacteristic
233C2×C4C2×C22⋊#26111yescharacteristic
234C8—21no—
235C8—261no—
236C8—261no—
237C8—1042no—
238C8D13⋊M1612yes—
239C22—21no—
240C22—21no—
241C22—524no—
242C22—1048no—
243C22—1042no—
244C22—1042no—
245C22#1171827612yes—
246C22C2×#8811511yescharacteristic
247C4—21no—
248C4—82no—
249C4—132no—
250C4—131no—
251C4—131no—
252C4—261no—
253C4—261no—
254C4#1171912611yescharacteristic
255C4#1171915511yescharacteristic
256C2—22no—
257C2—1044no—
258C2#1313016311yescharacteristic
259C2C2×#1171827611yescharacteristic
260C2#1313115211yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC22×C13C2×#102
prime radicalC22×D104C4
cosocleC8×Dic13C23
hypercenterC2×#107#261
hypocenterC13#11657
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #13131194C2semidirect
2. #13130393C2semidirect
3. #13129791C2semidirect
17. #11718257C22semidirect
19. #11718254C22semidirect
78. D104M16semidirect
209. C13#11657semidirect

Maximal subgroups

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

subgroupindex
#131311942
#131303932
#131297912
C2×#117185332
#1165713