Finite Group Databasebeta

← #16778503

Subgroups — #16778503

Order 3328.

520 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130622C212yesmaximal, complemented
2#13129657C212yesmaximal, complemented
3#13129652C212yesmaximal
4C4×#88190C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88190C411yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C2×#88110—22no—
9C2×C4⋊#1057—22no—
10#11718882C2211yescharacteristic
11C4×C22⋊Dic13—22no—
12#11718638C411yescharacteristic
13#11718635C2211yescharacteristic
14#11718606—22no—
15C42×Dic13C2211yescharacteristic
16#11718290C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×Dic26C2×C411yescharacteristic
20C22×#1057—24no—
21C4×D4×C13—42no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13—22no—
27#88190—22no—
28#88190—22no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×#6101—21no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4×Dic26—42no—
37#88110—44no—
38C4⋊#1057—28no—
39#88071—22no—
40#88071—22no—
41#7635—131nomaximal, Sylow
42C24×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13—41no—
45C2×D4×C13—41no—
46C2×D4×C13M1612yes—
47C22×C4×C13—21no—
48C22×C4×C13—42no—
49C22×C4×C13—44no—
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57C2×Dic26—21no—
58C2×Dic26—41no—
59C2×Dic26—41no—
60C2×Dic26M1612yes—
61C2×#1057—28no—
62C2×#1057—44no—
63C2×#1057—44no—
64C13×C4⋊C4—41no—
65C13×C22⋊C4—42no—
66C42×C13—22no—
67C22⋊Dic13—28no—
68C22⋊Dic13—42no—
69C22⋊Dic13—42no—
70C4⋊Dic13—41no—
71#6101—42no—
72C4×Dic13—24no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—41no—
78C4×Dic13—42no—
79C4×#124—131no—
80#1767—132no—
81#1272—132no—
82#1270—132no—
83C23×C13—22no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13C2×C22⋊C411yescharacteristic
89D4×C13—42no—
90D4×C13—42no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—84no—
98C2×C4×C13#10012yes—
99C2×C4×C13#10414yes—
100C2×C4×C13C2×M1611yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13AGL(1,ℤ/8)12yes—
113C2×Dic13#13712yes—
114Dic26—42no—
115Dic26—42no—
116#1057—48no—
117C2×#124—131no—
118C2×C4×Q8—131no—
119C2×C4×D4#26111yescharacteristic
120C2×C4⋊C8—262no—
121C2×#97—262no—
122#391—131no—
123#390—131no—
124#388—262no—
125#382—131no—
126C4×C22⋊C4—262no—
127C43—131no—
128#336—134no—
129C22×C13—42no—
130C22×C13—44no—
131C22×C13—81no—
132C22×C13—82no—
133C22×C13—81no—
134C22×C13#40711yescharacteristic
135C22×C13#41011yescharacteristic
136C22×C13C2×#10011yescharacteristic
137C22×C13#41712yes—
138C22×C13C2×#10412yes—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13—81no—
143C4×C13#32914yes—
144Dic13—22no—
145Dic13—22no—
146Dic13—42no—
147Dic13—42no—
148Dic13—81no—
149C22×Q8—131no—
150C22×D4C2×#26111yescharacteristic
151C23×C4—21no—
152C22×C8—264no—
153#124—262no—
154#124—262no—
155C4×Q8—522no—
156C4×D4—42no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4C2×#26111yescharacteristic
160C2×C22⋊C4—21no—
161C2×C22⋊C4—262no—
162C2×C22⋊C4—262no—
163C2×C42—132no—
164C2×C42—132no—
165C2×C42—131no—
166C2×C42—131no—
167C2×C42—261no—
168C2×C42C2×#26111yescharacteristic
169C4⋊C8—268no—
170#97—524no—
171#95—262no—
172#95—262no—
173C2×C13—82no—
174C2×C13#146611yescharacteristic
175C2×C13#148912yes—
176C2×C13#150912yes—
177C2×C13C2×#32911yescharacteristic
178C2×C13#156011yescharacteristic
179C24—21no—
180C2×Q8—132no—
181C2×Q8—261no—
182C2×Q8—521no—
183C2×Q8—521no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4#611812yes—
188C22×C4—21no—
189C22×C4—44no—
190C22×C4—42no—
191C22×C4—132no—
192C22×C4—132no—
193C22×C4—261no—
194C22×C4—261no—
195C22×C4C22⋊#26111yescharacteristic
196C22×C4C22⋊#26111yescharacteristic
197C22×C4C22×#26111yescharacteristic
198C2×C8—268no—
199C2×C8—524no—
200C2×C8—524no—
201C4⋊C4—41no—
202C4⋊C4—521no—
203C4⋊C4—522no—
204C22⋊C4—42no—
205C22⋊C4—268no—
206C22⋊C4—522no—
207C22⋊C4—522no—
208C42—22no—
209C42—262no—
210C42—262no—
211C42—264no—
212C42—261no—
213C42—261no—
214C42—521no—
215C42—522no—
216C13#763511yescharacteristic, complemented, Sylow
217C23—22no—
218C23—41no—
219C23—41no—
220C23—42no—
221C23—42no—
222C23C2×C22⋊#26111yescharacteristic
223Q8—522no—
224Q8—522no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—84no—
234C2×C4—132no—
235C2×C4—132no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—522no—
246C2×C4#8811614yes—
247C2×C4#8812112yes—
248C2×C4C2×#611811yescharacteristic
249C2×C4D13⋊M1611yescharacteristic
250C8—528no—
251C22—42no—
252C22—44no—
253C22—81no—
254C22—81no—
255C22—82no—
256C22#1171911611yescharacteristic
257C22#1171912711yescharacteristic
258C22C2×#8811612yes—
259C22#1171916412yes—
260C22C2×#8812111yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—81no—
265C4—262no—
266C4—262no—
267C4—522no—
268C4—522no—
269C4—1041no—
270C4#1171829314yes—
271C2—82no—
272C2#1313009511yescharacteristic
273C2#1313017212yes—
274C2#1313023812yes—
275C2C2×#1171829311yescharacteristic
276C2#1313037311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#7635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130622C2semidirect
2. #13129657C2semidirect
216. C13#7635semidirect

Maximal subgroups

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

subgroupindex
#131306222
#131296572
#131296522
C4×#881902
#763513