Finite Group Databasebeta

← #16787231

Subgroups — #16787231

Order 3328.

394 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 74 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#13130098C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129766C214yesmaximal
4#13119825C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×#88198C412yes—
7C2×C4×Dic26C2211yescharacteristic
8#11719130—21no—
9#11719125—21no—
10#11718891C2212yes—
11#11718641—21no—
12#11718641—21no—
13#11718634—21no—
14#11718634—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718286—21no—
17#11718286—21no—
18#11718285C2212yes—
19#11718285C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×Dic26C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C42×C13C2×C411yescharacteristic
27#88198—44no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13C2311yescharacteristic
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101D411yescharacteristic
33C2×#6101D411yescharacteristic
34C2×C4×Dic13C2×C412yes—
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C4×Dic26—41no—
38C4×Dic26—41no—
39C22⋊#1057—22no—
40C22⋊#1057—22no—
41#88112—41no—
42#88110—41no—
43C4⋊#1057—41no—
44C4×#1057—41no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48#11568—131nomaximal, Sylow
49C2×Q8×C13—24no—
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C22×C4×C13—22no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×Dic26—22no—
62C2×Dic26—22no—
63C2×Dic26—41no—
64C2×#1057—42no—
65C2×#1057—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C42×C13—21no—
70C42×C13—21no—
71C4⋊Dic13—24no—
72C4⋊Dic13—41no—
73#6101—41no—
74#6101—41no—
75#6101—44no—
76#6101—44no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—42no—
82#2546—131no—
83#1467—131no—
84#1461—131no—
85#1319—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—84no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13#9911yescharacteristic
97C2×C4×C13#9911yescharacteristic
98C2×C4×C13#13112yes—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—24no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13#10012yes—
112Dic26—44no—
113#1057—82no—
114#1057—82no—
115C2×C4⋊Q8—132no—
116C2×C4⋊Q8#26111yescharacteristic
117C2×C4×Q8—131no—
118#432—261no—
119#431—261no—
120#398—261no—
121#398—261no—
122#391—132no—
123#389—261no—
124#389—261no—
125C4×C4⋊C4—131no—
126#324—132no—
127#324—132no—
128#324—261no—
129#324—261no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#40811yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13C2×#10011yescharacteristic
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—41no—
138C4×C13—82no—
139C4×C13#35612yes—
140Dic13—22no—
141Dic13—44no—
142Dic13—41no—
143Dic13—41no—
144Dic13—41no—
145C22×Q8—131no—
146C22×Q8C2×#26112yes—
147C4⋊Q8—41no—
148C4⋊Q8—41no—
149C4⋊Q8—524no—
150C4×Q8—521no—
151C4×Q8—521no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4—262no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—132no—
163C2×C42C2×#26111yescharacteristic
164C4⋊C8—521no—
165C4⋊C8—521no—
166C22⋊C8—262no—
167C22⋊C8—262no—
168#97—521no—
169C4×C8—521no—
170#95—262no—
171#95—262no—
172#95—261no—
173C2×C13—21no—
174C2×C13—21no—
175C2×C13#147111yescharacteristic
176C2×C13#212911yescharacteristic
177C2×C13C2×#35611yescharacteristic
178C2×Q8—24no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—262no—
182C2×Q8—262no—
183C2×Q8—521no—
184C22×C4—22no—
185C22×C4—131no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4C22⋊#26111yescharacteristic
191C22×C4C22⋊#26111yescharacteristic
192C22×C4C22×#26111yescharacteristic
193C2×C8—522no—
194C2×C8—522no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—264no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—521no—
202C4⋊C4—524no—
203C4⋊C4—524no—
204C42—21no—
205C42—21no—
206C42—261no—
207C42—261no—
208C42—261no—
209C42—261no—
210C42—522no—
211C13#1156811yescharacteristic, complemented, Sylow
212C23C2×C22⋊#26111yescharacteristic
213Q8—84no—
214Q8—524no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—132no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—264no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4#8811911yescharacteristic
237C2×C4#8811911yescharacteristic
238C2×C4#8823812yes—
239C8—1042no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22#1171914711yescharacteristic
244C22D13⋊#10011yescharacteristic
245C22C2×#8811911yescharacteristic
246C4—21no—
247C4—22no—
248C4—41no—
249C4—82no—
250C4—262no—
251C4—524no—
252C4—521no—
253C4—521no—
254C4—521no—
255C4#1171830112yes—
256C2—21no—
257C2—21no—
258C2#1313011111yescharacteristic
259C2#1313111811yescharacteristic
260C2C2×#1171830111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11568
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
211. C13#11568semidirect

Maximal subgroups

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

subgroupindex
#131300982
#131300782
#131297662
#131198252
#1156813