Finite Group Databasebeta

← #16778504

Subgroups — #16778504

Order 3328.

520 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130621C212yesmaximal, complemented
2#13129656C212yesmaximal, complemented
3#13129652C212yesmaximal
4#124×Dic13C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×Q8×Dic13C411yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8C2×#88112—22no—
9C2×#88110—22no—
10#11718891C2211yescharacteristic
11#11718882C2211yescharacteristic
12#11718612—22no—
13C22⋊C4×Dic13—22no—
14#11718597C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718290C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×Dic13—21no—
20C22×#1057—24no—
21C13×#124—22no—
22C13×#124—22no—
23C2×C13×C22⋊C4—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—21no—
26C2×C22⋊Dic13—22no—
27Q8×Dic13—42no—
28D4×Dic13—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C2×C4×Dic13D412yes—
36C2×C4×Dic13C2311yescharacteristic
37#88112—28no—
38#88110—44no—
39#88071—22no—
40#88071—22no—
41#7635—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13M1612yes—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13M1612yes—
51C22×C4×C13—21no—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13—42no—
57C22×Dic13—44no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C2×D412yes—
61C2×#1057—28no—
62C2×#1057—44no—
63C2×#1057—44no—
64C13×C22⋊C4—28no—
65C42×C13—21no—
66C42×C13—21no—
67C22⋊Dic13—42no—
68C22⋊Dic13—42no—
69C22⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73C4×Dic13—22no—
74C4×Dic13—24no—
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
89Q8×C13—42no—
90Q8×C13—42no—
91D4×C13—42no—
92D4×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13C2×M1611yescharacteristic
102C2×C4×C13C2×M1611yescharacteristic
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—84no—
112C2×Dic13#10012yes—
113C2×Dic13#10414yes—
114C2×Dic13AGL(1,ℤ/8)12yes—
115C2×Dic13#13712yes—
116#1057—48no—
117C2×#124#26111yescharacteristic
118C2×C4×Q8—131no—
119C2×C4×D4—131no—
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—42no—
142C4×C13—42no—
143Dic13—22no—
144Dic13—22no—
145Dic13—41no—
146Dic13—81no—
147Dic13—81no—
148Dic13#32914yes—
149C22×Q8C2×#26111yescharacteristic
150C22×D4C2×#26111yescharacteristic
151C23×C4—261no—
152C22×C8—264no—
153#124—22no—
154#124—22no—
155C4×Q8—522no—
156C4×D4—522no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—261no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—261no—
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—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8#612212yes—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4#612212yes—
188C22×C4—21no—
189C22×C4—131no—
190C22×C4—132no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4—522no—
195C22×C4—524no—
196C22×C4C22⋊#26112yes—
197C22×C4C22×#26111yescharacteristic
198C2×C8—268no—
199C2×C8—524no—
200C2×C8—524no—
201C4⋊C4—521no—
202C4⋊C4—521no—
203C4⋊C4—522no—
204C22⋊C4—28no—
205C22⋊C4—522no—
206C22⋊C4—522no—
207C22⋊C4—522no—
208C42—21no—
209C42—21no—
210C42—262no—
211C42—264no—
212C42—262no—
213C42—262no—
214C42—521no—
215C42—522no—
216C13#763511yescharacteristic, complemented, Sylow
217C23—22no—
218C23—41no—
219C23—41no—
220C23—42no—
221C23—42no—
222C23C2×C22⋊#26111yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—132no—
236C2×C4—134no—
237C2×C4—132no—
238C2×C4—132no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—262no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—1044no—
248C2×C4C2×#612211yescharacteristic
249C2×C4C2×#612211yescharacteristic
250C8—528no—
251C22—42no—
252C22—44no—
253C22—81no—
254C22—81no—
255C22—82no—
256C22#1171914211yescharacteristic
257C22D13⋊#10011yescharacteristic
258C22D13⋊#10412yes—
259C22#1171916412yes—
260C22#1171916911yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—134no—
266C4—262no—
267C4—262no—
268C4—521no—
269C4—1041no—
270C4—1041no—
271C2—82no—
272C2#1313009611yescharacteristic
273C2#1313017112yes—
274C2#1313023712yes—
275C2D13⋊#32911yescharacteristic
276C2#1313037411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#124C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×#124#261
hypocenterC13#7635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #13130621C2semidirect
2. #13129656C2semidirect
216. C13#7635semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131296562
#131296522
#124×Dic132
#763513