Finite Group Databasebeta

← #16779575

Subgroups — #16779575

Order 3328.

602 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 162 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
1D13⋊#432C212yesmaximal
2#13129701C214yesmaximal, complemented
3C2×D13×C4⋊C8C211yesmaximal, characteristic
4C22×C8×D13C412yes—
5C2×C42×D13C2211yescharacteristic
6#11719130C2214yes—
7#11719128—22no—
8D13⋊(C22⋊C8)—22no—
9#11719055C414yes—
10#11719054—22no—
11D13⋊(C4⋊C8)—22no—
12#11719047C414yes—
13C2×C13×C4⋊C8C411yescharacteristic
14C2×#88054C2212yes—
15C2×C4⋊#1055C411yescharacteristic
16D13×C4⋊C8—22no—
17D13×C4⋊C8—22no—
18C22×C4×D13C2×C411yescharacteristic
19C22×C4×D13D411yescharacteristic
20C22×C4×D13Q811yescharacteristic
21C2×D13⋊C8—24no—
22C22×C8×C13C2×C412yes—
23C2×C42×C13C2×C411yescharacteristic
24C2×C4×Dic13D411yescharacteristic
25C2×C4×Dic13Q811yescharacteristic
26C2×C4×Dic13C2311yescharacteristic
27C22×#1055C2×C412yes—
28C2×C8×D13—22no—
29C2×C8×D13—22no—
30C2×C8×D13—44no—
31C42×D13C2×C412yes—
32C42×D13C2×C412yes—
33C42×D13D412yes—
34C42×D13D412yes—
35C22⋊#1057—24no—
36#88112—24no—
37#88111—24no—
38#88110—24no—
39#88110C2×C418yes—
40C4⋊#1057—24no—
41C13×C4⋊C8—22no—
42#88054—24no—
43C4⋊#1055—22no—
44C2×#1290—131nomaximal, Sylow
45C23×D13C4⋊C411yescharacteristic
46C22×C4×C13C4⋊C411yescharacteristic
47C22×C4×C13C4⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C4⋊C411yescharacteristic
50C22×Dic13C2×D411yescharacteristic
51C22×Dic13C2×Q811yescharacteristic
52C2×C4×D13—24no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—42no—
56C2×C4×D13C4211yescharacteristic
57C2×C4×D13C4211yescharacteristic
58C2×C4×D13C22⋊C411yescharacteristic
59C2×C4×D13C22⋊C412yes—
60C2×C4×D13C22⋊C412yes—
61C2×C4×D13C22⋊C411yescharacteristic
62C2×C4×D13C4⋊C412yes—
63C2×C4×D13C4⋊C412yes—
64C2×#1057—28no—
65D13⋊C8—48no—
66C2×C8×C13—22no—
67C2×C8×C13—42no—
68C42×C13C4212yes—
69C42×C13C22⋊C412yes—
70C4×Dic13C22⋊C412yes—
71C4×Dic13C22⋊C412yes—
72C4×Dic13C4⋊C412yes—
73C4×Dic13C4⋊C412yes—
74C4×Dic13C22×C412yes—
75C4×Dic13C2×D412yes—
76C2×#1055—22no—
77C2×#1055—42no—
78C8×D13—44no—
79C8×D13—44no—
80C2×#432—132no—
81C22×C4⋊C8—131no—
82#1290—134no—
83C23×C13C2×C4⋊C411yescharacteristic
84C22×D13—22no—
85C22×D13—22no—
86C22×D13#9511yescharacteristic
87C22×D13#9511yescharacteristic
88C22×D13#10814yes—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13#9512yes—
94C2×C4×C13#9512yes—
95C2×C4×C13C2×C4211yescharacteristic
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—41no—
100C2×Dic13#9511yescharacteristic
101C2×Dic13#9511yescharacteristic
102C2×Dic13C2×C22⋊C412yes—
103C2×Dic13C2×C4⋊C412yes—
104C4×D13—24no—
105C4×D13—24no—
106C4×D13—24no—
107C4×D13—22no—
108C4×D13—21no—
109C4×D13—21no—
110C4×D13—22no—
111C4×D13—42no—
112C4×D13#10012yes—
113C4×D13#10112yes—
114#1057—48no—
115C8×C13—42no—
116#1055—42no—
117C23×C8—132no—
118C22×C42—131no—
119#432—134no—
120#432—134no—
121#432—262no—
122#432—262no—
123C2×C4⋊C8—132no—
124C2×C4⋊C8—131no—
125C2×C4⋊C8—262no—
126C2×C4⋊C8—262no—
127C2×C4⋊C8—262no—
128C2×C4⋊C8#26111yescharacteristic
129C2×C22⋊C8—262no—
130C2×#97—134no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13C2×#9511yescharacteristic
134C22×C13C2×#10812yes—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—28no—
138C2×D13H(3,ℤ/4)12yes—
139C2×D13#34112yes—
140C2×D13#34112yes—
141C2×D13#34312yes—
142C4×C13—22no—
143C4×C13—22no—
144C4×C13—21no—
145C4×C13C2×#10011yescharacteristic
146C4×C13C2×#10111yescharacteristic
147Dic13—22no—
148Dic13—22no—
149Dic13—21no—
150Dic13#34312yes—
151C23×C4—131no—
152C23×C4—131no—
153C23×C4—131no—
154C22×C8—132no—
155C22×C8—262no—
156C22×C8—262no—
157C22×C8—264no—
158C22×C8—524no—
159C22×C8C2×#26112yes—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—132no—
164C2×C42—132no—
165C2×C42—132no—
166C2×C42—132no—
167C2×C42C2×#26111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—264no—
170C4⋊C8—264no—
171C4⋊C8—264no—
172C4⋊C8—262no—
173C22⋊C8—264no—
174C22⋊C8—264no—
175#97—138no—
176#97—264no—
177C2×C13—22no—
178C2×C13C2×H(3,ℤ/4)11yescharacteristic
179C2×C13C2×#34111yescharacteristic
180C2×C13C2×#34311yescharacteristic
181D13—22no—
182D13#129014yescomplemented
183C24—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—132no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—132no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4—264no—
198C22×C4—522no—
199C22×C4C4⋊#26111yescharacteristic
200C22×C4C4⋊#26111yescharacteristic
201C22×C4C22×#26111yescharacteristic
202C2×C8—22no—
203C2×C8—42no—
204C2×C8—268no—
205C2×C8—262no—
206C2×C8—524no—
207C2×C8—524no—
208C2×C8—528no—
209C2×C8—522no—
210C42—132no—
211C42—132no—
212C42—132no—
213C42—132no—
214C42—132no—
215C42—132no—
216C42C4×#26112yes—
217C42C22⋊#26112yes—
218C13C2×#129011yescharacteristic, complemented, Sylow
219C23—131no—
220C23—134no—
221C23—131no—
222C23—262no—
223C23—262no—
224C23C2×C4⋊#26111yescharacteristic
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—131no—
230C2×C4—132no—
231C2×C4—132no—
232C2×C4—132no—
233C2×C4—131no—
234C2×C4—132no—
235C2×C4—262no—
236C2×C4—264no—
237C2×C4—264no—
238C2×C4—264no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—522no—
245C2×C4—521no—
246C2×C4(C2×#261)⋊C412yes—
247C2×C4(C2×#261)⋊C412yes—
248C2×C4C2×C4×#26111yescharacteristic
249C2×C4C2×C22⋊#26111yescharacteristic
250C8—42no—
251C8—528no—
252C8—522no—
253C22—21no—
254C22—21no—
255C22—132no—
256C22—132no—
257C22—132no—
258C22—132no—
259C22—268no—
260C22—261no—
261C22—261no—
262C22D13⋊#10812yes—
263C22C2×(C2×#261)⋊C411yescharacteristic
264C4—22no—
265C4—22no—
266C4—21no—
267C4—132no—
268C4—262no—
269C4—262no—
270C4—261no—
271C4D13⋊#10011yescharacteristic
272C4D13⋊#10111yescharacteristic
273C2—22no—
274C2—134no—
275C2—262no—
276C2#1313050811yescharacteristic
277C2#1313052811yescharacteristic
278C2#1313053911yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13C2×#95
prime radicalC23×D13C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊C8#261
hypocenterC13C2×#1290
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13129701C2semidirect
182. D13#1290semidirect
218. C13C2×#1290semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4322
#131297012
C2×D13×C4⋊C82
C2×#129013