Finite Group Databasebeta

← #16787548

Subgroups — #16787548

Order 3328.

426 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 86 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#13131198C211yesmaximal, characteristic, complemented
2#13130390C211yesmaximal, characteristic, complemented
3#13129795C214yesmaximal, 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#11718258C2212yescomplemented
18#11718255—21no—
19#11718253C2212yescomplemented
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#11663—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—84no—
59#6122—82no—
60C2×#1057—42no—
61C2×C8×C13—22no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22×C411yescharacteristic
64C13×C4⋊C4—22no—
65C13×C4⋊C4—41no—
66#6103—42no—
67#6103—42no—
68C4×Dic13C22⋊C411yescharacteristic
69C4×Dic13D811yescharacteristic
70C4×Dic13SD1611yescharacteristic
71C4×Dic13C2×D411yescharacteristic
72C2×#1055—41no—
73C2×#1055C22⋊C411yescharacteristic
74C2×#1055C2×D411yescharacteristic
75D104—24no—
76D104—22no—
77D104M1614yescomplemented
78#6092—42no—
79C2×C4×D8—131no—
80#2163—131no—
81#1566—131no—
82#1333—134no—
83C23×C13#10211yescharacteristic
84C22×D13—44no—
85C22×D13—42no—
86C22×D13—82no—
87C22×D13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—82no—
92C2×C4×C13#10211yescharacteristic
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13#10211yescharacteristic
97C2×Dic13#10211yescharacteristic
98C2×Dic13C2×D811yescharacteristic
99C2×Dic13C2×SD1611yescharacteristic
100D52—24no—
101D52—44no—
102D52—42no—
103C4×D13—84no—
104C4×D13—84no—
105#1057—82no—
106C8×C13—21no—
107C8×C13C2×M1612yes—
108#1055—21no—
109#1055—21no—
110C22×D8—131no—
111C2×C4×D4—261no—
112C4×D8—132no—
113C4×D8—132no—
114C4×D8—261no—
115C4×D8—261no—
116C2×#107#26111yescharacteristic
117#423—261no—
118C2×#102—261no—
119C2×C4×C8—131no—
120C4⋊C16—261no—
121C22⋊C16—261no—
122#346—132no—
123#334—132no—
124#334—261no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#36012yes—
128C22×C13C2×#10211yescharacteristic
129C2×D13—44no—
130C2×D13—88no—
131C2×D13—82no—
132C2×D13—82no—
133C4×C13—21no—
134C4×C13—82no—
135C4×C13#40711yescharacteristic
136C4×C13#42111yescharacteristic
137Dic13—21no—
138Dic13—21no—
139Dic13—21no—
140Dic13#36112yes—
141C22×D4—261no—
142C23×C4—521no—
143C2×D8—132no—
144C2×D8—264no—
145C2×D8—261no—
146C2×M16—521no—
147C22×C8—131no—
148C22×C8C2×#26111yescharacteristic
149C4×D4—262no—
150C4×D4—262no—
151C4×D4—521no—
152C4×D4—521no—
153C2×C4⋊C4—21no—
154C2×C22⋊C4—521no—
155C2×C42—131no—
156C2×C16—262no—
157#107—21no—
158#107C2×#26112yes—
159C4⋊C8—262no—
160C4⋊C8—521no—
161#102—262no—
162#102—262no—
163C4×C8—131no—
164C4×C8—131no—
165C4×C8—131no—
166C4×C8—131no—
167C2×C13—22no—
168C2×C13#148611yescharacteristic
169C2×C13C2×#36011yescharacteristic
170C2×C13C2×#36111yescharacteristic
171D13—84no—
172C24—521no—
173C2×D4—264no—
174C2×D4—262no—
175C2×D4—522no—
176C2×D4—521no—
177C22×C4—41no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—522no—
181C22×C4—522no—
182C22×C4—1044no—
183C22×C4C22⋊#26111yescharacteristic
184D8—134no—
185D8—264no—
186D8—262no—
187M16—1042no—
188C2×C8—22no—
189C2×C8—131no—
190C2×C8—131no—
191C2×C8—521no—
192C2×C8—522no—
193C2×C8C22⋊#26111yescharacteristic
194C2×C8C22×#26111yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—41no—
197C22⋊C4—522no—
198C22⋊C4—522no—
199C42—131no—
200C42—131no—
201C42—131no—
202C42—131no—
203C16—522no—
204C13#1166311yescharacteristic, complemented, Sylow
205C23—524no—
206C23—522no—
207C23—1042no—
208C23—1042no—
209C23#8811511yescharacteristic
210D4—264no—
211D4—524no—
212D4—522no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—131no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—131no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—1044no—
224C2×C4—1044no—
225C2×C4#8811511yescharacteristic
226C2×C4C2×C22⋊#26111yescharacteristic
227C8—21no—
228C8—261no—
229C8—261no—
230C8—1042no—
231C8D13⋊M1612yes—
232C22—21no—
233C22—21no—
234C22—524no—
235C22—1048no—
236C22—1042no—
237C22—1042no—
238C22#1171827912yes—
239C22C2×#8811511yescharacteristic
240C4—21no—
241C4—82no—
242C4—132no—
243C4—261no—
244C4—261no—
245C4—261no—
246C4#1171912611yescharacteristic
247C4#1171915511yescharacteristic
248C2—22no—
249C2—1044no—
250C2#1313016311yescharacteristic
251C2C2×#1171827911yescharacteristic
252C2D13⋊#36111yescharacteristic
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#11663
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. #13131198C2semidirect
2. #13130390C2semidirect
3. #13129795C2semidirect
17. #11718258C22semidirect
19. #11718253C22semidirect
77. D104M16semidirect
204. C13#11663semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131303902
#131297952
C2×#117185332
#1166313