Finite Group Databasebeta

← #16781973

Subgroups — #16781973

Order 3328.

404 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130390C212yesmaximal, complemented
2#13130373C212yesmaximal
3#13129744C212yesmaximal, complemented
4#13123546C211yesmaximal, characteristic
5C2×C13×#131C411yescharacteristic
6#11719537C2211yescharacteristic
7C2×#88155C411yescharacteristic
8#11719129C2214yes—
9#11718895C411yescharacteristic
10#11718790C411yescharacteristic
11#11718789—22no—
12#11718779C2211yescharacteristic
13C8×C22⋊D13—22no—
14C2×C8×Dic13C2211yescharacteristic
15#11718303—22no—
16#11718297—22no—
17#11718255—22no—
18#11718253—22no—
19C2×C13×#41C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×#6122—24no—
22C13×#131—42no—
23C2×C13×M16—21no—
24C2×C13×M16C2×C411yescharacteristic
25C22×C8×C13—21no—
26C22×C8×C13C2×C411yescharacteristic
27#88201Q811yescharacteristic
28#88198D411yescharacteristic
29#88194D411yescharacteristic
30#88193—22no—
31#88190Q811yescharacteristic
32C4×C22⋊D13—22no—
33C2×C4×Dic13C2311yescharacteristic
34C2×#6099C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36#88155—42no—
37C2×#6094—21no—
38C2×C8×D13—21no—
39#88112—24no—
40C4⋊#1057—24no—
41C22⋊#1055—22no—
42#88060—22no—
43#88054—22no—
44C8×Dic13D412yes—
45C8×Dic13D412yes—
46#8636—131nomaximal, Sylow
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13C4⋊C411yescharacteristic
50C2×D4×C13—21no—
51C2×D4×C13C4⋊C411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—21no—
55C2×C22⋊D13—22no—
56C22×Dic13#4112yes—
57#6127—41no—
58#6127—41no—
59C2×D52C4⋊C411yescharacteristic
60C2×C4×D13—21no—
61C2×Dic26C4⋊C411yescharacteristic
62#6122—84no—
63C2×#1057—44no—
64C13×M16—42no—
65C13×M16—41no—
66C2×C8×C13—22no—
67C2×C8×C13—21no—
68C2×C8×C13—42no—
69C2×C8×C13C22⋊C411yescharacteristic
70C2×C8×C13C22⋊C411yescharacteristic
71C22⋊Dic13—22no—
72#6103—22no—
73#6101—22no—
74C4×Dic13C2×D411yescharacteristic
75C4×Dic13C2×D412yes—
76C4×Dic13C2×Q811yescharacteristic
77#6099—41no—
78C2×#1055—21no—
79C2×#1055—41no—
80C2×#1055C22⋊C412yes—
81#6094—42no—
82C8×D13—42no—
83#2931—131no—
84#1566—132no—
85#1560—132no—
86#1309—132no—
87C23×C13—21no—
88C23×C13#11711yescharacteristic
89C22×D13—21no—
90Q8×C13—41no—
91D4×C13—41no—
92D4×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C2×C4⋊C411yescharacteristic
100C22⋊D13—42no—
101C22⋊D13—44no—
102C2×Dic13—24no—
103C2×Dic13—21no—
104C2×Dic13#12112yes—
105C2×Dic13C22⋊Q812yes—
106D52—41no—
107C4×D13—41no—
108C4×D13—41no—
109Dic26—41no—
110#1057—84no—
111C8×C13—21no—
112C8×C13—41no—
113C8×C13#10012yes—
114#1055—22no—
115#1055—41no—
116C2×#131—131no—
117C2×#131#26111yescharacteristic
118#532—131no—
119#436—262no—
120C8×D4—262no—
121#423—131no—
122#423—134no—
123#408—131no—
124#408—131no—
125C2×C4×C8—131no—
126#334—262no—
127#334—262no—
128#333—262no—
129#331—262no—
130C22×C13—21no—
131C22×C13—22no—
132C22×C13—41no—
133C22×C13—42no—
134C22×C13#38011yescharacteristic
135C2×D13—41no—
136C2×D13—42no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13C2×#10011yescharacteristic
140C4×C13#41311yescharacteristic
141Dic13—22no—
142Dic13—41no—
143Dic13#47114yes—
144C2×#41—131no—
145C2×#41C2×#26111yescharacteristic
146#131—42no—
147#131—522no—
148C2×M16—21no—
149C2×M16—131no—
150C2×M16—261no—
151C2×M16—264no—
152C2×M16C2×#26111yescharacteristic
153C22×C8—21no—
154C22×C8—131no—
155C22×C8—261no—
156C22×C8C2×#26111yescharacteristic
157C4⋊Q8—131no—
158#127—131no—
159#124—131no—
160#124—131no—
161#121—262no—
162C4×D4—262no—
163C2×C42—131no—
164C4⋊C8—262no—
165C4⋊C8—264no—
166C4⋊C8—264no—
167C22⋊C8—262no—
168C22⋊C8—262no—
169C4×C8—132no—
170C4×C8—132no—
171C2×C13—41no—
172C2×C13—81no—
173C2×C13#180011yescharacteristic
174C2×C13#181512yes—
175D13—81no—
176#41—41no—
177#41—41no—
178#41—521no—
179#41—521no—
180C2×Q8—131no—
181C2×Q8C4⋊#26111yescharacteristic
182C2×D4—21no—
183C2×D4—131no—
184C2×D4—262no—
185C2×D4—261no—
186C2×D4C4⋊#26111yescharacteristic
187C22×C4—21no—
188C22×C4—132no—
189C22×C4—261no—
190C22×C4C22×#26111yescharacteristic
191M16—42no—
192M16—41no—
193M16—522no—
194M16—521no—
195M16—1044no—
196C2×C8—22no—
197C2×C8—21no—
198C2×C8—42no—
199C2×C8—132no—
200C2×C8—261no—
201C2×C8—521no—
202C2×C8—522no—
203C2×C8—524no—
204C2×C8C22⋊#26111yescharacteristic
205C2×C8C22⋊#26111yescharacteristic
206C4⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C42—131no—
210C42—131no—
211C42—132no—
212C13#863611yescharacteristic, complemented, Sylow
213C23—21no—
214C23—261no—
215C23#8823711yescharacteristic
216Q8—41no—
217Q8—521no—
218D4—41no—
219D4—42no—
220D4—521no—
221D4—524no—
222D4—522no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—264no—
231C2×C4—261no—
232C2×C4—521no—
233C2×C4—521no—
234C2×C4C2×C4⋊#26111yescharacteristic
235C2×C4C2×C22⋊#26111yescharacteristic
236C8—21no—
237C8—41no—
238C8—262no—
239C8—521no—
240C8—1044no—
241C8#8812112yes—
242C22—21no—
243C22—22no—
244C22—41no—
245C22—42no—
246C22—521no—
247C22—522no—
248C22#1171913611yescharacteristic
249C4—21no—
250C4—41no—
251C4—134no—
252C4—262no—
253C4—521no—
254C4#1171913211yescharacteristic
255C4C2×#8812111yescharacteristic
256C2—41no—
257C2—81no—
258C2—1041no—
259C2#1313070011yescharacteristic
260C2#1313072412yes—
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#131C4
socleC22×C13#380
prime radical#11719537C22
cosocleC2×C4×Dic13C23
hypercenterC2×#131#261
hypocenterC13#8636
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #13130390C2semidirect
3. #13129744C2semidirect
212. C13#8636semidirect

Maximal subgroups

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

subgroupindex
#131303902
#131303732
#131297442
#131235462
#863613