Finite Group Databasebeta

← #16780686

Subgroups — #16780686

Order 3328.

528 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 116 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#13130553C212yesmaximal, complemented
2C2×#11718299C212yesmaximal
3#13129712C212yesmaximal, complemented
4#13117379C211yesmaximal, characteristic
5C2×#88201C2211yescharacteristic
6C2×Q8×Dic13C411yescharacteristic
7C2×#88147C411yescharacteristic
8C2×#88110C2214yes—
9C13×#391C411yescharacteristic
10#11718638C2211yescharacteristic
11#11718600C411yescharacteristic
12C42×Dic13C2211yescharacteristic
13#11718331—22no—
14#11718327—22no—
15#11718299C418yescomplemented
16#11718290—22no—
17#11718290—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D52C2×C411yescharacteristic
20C22×C4×D13—21no—
21C22×#1057—24no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24#88201—22no—
25#88201C2×C414yes—
26Q8×Dic13—42no—
27C2×#6103—22no—
28C2×#6103—22no—
29C2×#6103—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C2×C4×Dic13D412yes—
36C2×C4×Dic13C2311yescharacteristic
37#88147—42no—
38#88110—24no—
39#88110C2×C418yescomplemented
40C13×#95—22no—
41#88071—22no—
42#8224—131nomaximal, Sylow
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13C4212yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—21no—
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C22⋊C411yescharacteristic
55C22×Dic13C2×D412yes—
56C2×D52—21no—
57C2×D52—41no—
58C2×D52—41no—
59C2×D52C4212yes—
60C2×C4×D13—44no—
61C2×C4×D13—42no—
62C2×#1057—28no—
63C2×#1057—44no—
64C2×#1057—44no—
65C13×C4⋊C4—41no—
66C42×C13—41no—
67#6103—28no—
68#6103—42no—
69#6103—44no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4×Dic13—22no—
73C4×Dic13—42no—
74C4×Dic13—42no—
75C4×Dic13—42no—
76C4×Dic13C22×C412yes—
77C4×Dic13#4112yes—
78C4×#124—131no—
79#1745—132no—
80C2×#329—132no—
81#1295—132no—
82C23×C13C2×C22⋊C411yescharacteristic
83C22×D13—22no—
84C22×D13—41no—
85C22×D13—41no—
86C22×D13—42no—
87C22×D13—42no—
88Q8×C13—42no—
89Q8×C13—42no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13C2×C4211yescharacteristic
101C2×C4×C13#11711yescharacteristic
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—41no—
108C2×Dic13—42no—
109C2×Dic13#10012yes—
110C2×Dic13C4×D414yes—
111D52—42no—
112D52—42no—
113C4×D13—84no—
114#1057—48no—
115C2×#124—131no—
116C2×C4×Q8—131no—
117C2×C4×D4—131no—
118C2×#97—134no—
119#391#26111yescharacteristic
120#390—131no—
121#388—262no—
122#382—131no—
123C4×C22⋊C4—262no—
124C43—131no—
125#336—262no—
126#336—262no—
127#329—138no—
128C22×C13C4×C22⋊C411yescharacteristic
129C22×C13C2×#10011yescharacteristic
130C22×C13#41311yescharacteristic
131C22×C13#42112yes—
132C22×C13#42112yes—
133C2×D13—42no—
134C2×D13—44no—
135C2×D13—81no—
136C2×D13—81no—
137C2×D13—82no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—42no—
141C4×C13—42no—
142C4×C13—81no—
143Dic13—24no—
144Dic13—22no—
145Dic13—41no—
146Dic13—81no—
147C22×Q8C2×#26111yescharacteristic
148C22×D4—131no—
149C23×C4—261no—
150C22×C8—264no—
151#124—134no—
152#124—262no—
153C4×Q8—522no—
154C4×D4—522no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4C2×#26111yescharacteristic
158C2×C22⋊C4—262no—
159C2×C22⋊C4—261no—
160C2×C22⋊C4—262no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—132no—
164C2×C42—132no—
165C2×C42—261no—
166C2×C42C2×#26111yescharacteristic
167#97—138no—
168#97—264no—
169#95—22no—
170#95—262no—
171C2×C13#153311yescharacteristic
172C2×C13#153512yes—
173C2×C13#153611yescharacteristic
174C2×C13C4×#10011yescharacteristic
175C2×C13#175912yes—
176D13—82no—
177C24—261no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8C4×#26112yes—
182C2×D4—132no—
183C2×D4—261no—
184C2×D4—521no—
185C2×D4—521no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—132no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—261no—
192C22×C4—522no—
193C22×C4—524no—
194C22×C4C22⋊#26112yes—
195C22×C4C22×#26111yescharacteristic
196C2×C8—268no—
197C2×C8—524no—
198C2×C8—524no—
199C4⋊C4—41no—
200C4⋊C4—521no—
201C4⋊C4—522no—
202C22⋊C4—268no—
203C22⋊C4—524no—
204C22⋊C4—522no—
205C42—41no—
206C42—132no—
207C42—132no—
208C42—262no—
209C42—522no—
210C42—522no—
211C42—522no—
212C13#822411yescharacteristic, complemented, Sylow
213C23—262no—
214C23—521no—
215C23—521no—
216C23—522no—
217C23—522no—
218C23C2×C22⋊#26111yescharacteristic
219Q8—42no—
220Q8—42no—
221D4—522no—
222D4—522no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—134no—
234C2×C4—132no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—261no—
239C2×C4—262no—
240C2×C4—521no—
241C2×C4—522no—
242C2×C4—1044no—
243C2×C4C2×C4×#26111yescharacteristic
244C2×C4#8823711yescharacteristic
245C8—528no—
246C22—522no—
247C22—524no—
248C22—1041no—
249C22—1042no—
250C22—1041no—
251C22C4×C22⋊#26111yescharacteristic
252C22#1171914811yescharacteristic
253C22D13⋊#10011yescharacteristic
254C22#1171915512yes—
255C22#1171916612yes—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—42no—
260C4—81no—
261C4—262no—
262C4—264no—
263C4—521no—
264C4—1041no—
265C2—1042no—
266C2#1313031611yescharacteristic
267C2#1313032312yes—
268C2#1313032611yescharacteristic
269C2#1313058611yescharacteristic
270C2#1313060012yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#391C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenter#391#261
hypocenterC13#8224
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #13130553C2semidirect
3. #13129712C2semidirect
15. #11718299C4semidirect
39. #88110C2×C4semidirect
212. C13#8224semidirect

Maximal subgroups

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

subgroupindex
#131305532
C2×#117182992
#131297122
#131173792
#822413