Finite Group Databasebeta

← #15772566

Subgroups — #15772566

Order 3328.

424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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#13113174C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112780C214yesmaximal, complemented
4C13×#2563C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#393—21no—
8C13×#393—21no—
9C13×#390C412yes—
10C13×#382C2212yes—
11C13×#380—21no—
12C13×#380—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718868—21no—
15C2×C22⋊#1055—21no—
16#11718120C2212yes—
17#11718120C2212yes—
18#11718117—21no—
19#11718117—21no—
20C22×Q8×C13—21no—
21C22×D4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13C2×C412yes—
37C2×C42×C13C2×C411yescharacteristic
38C2×#6099—41no—
39C22×#1055—41no—
40C13×#95—21no—
41C13×#95—22no—
42C13×#95—22no—
43C22⋊#1055—22no—
44C22⋊#1055—22no—
45C22⋊#1055—41no—
46C22⋊#1055—41no—
47#11569—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C24×C13C22⋊C411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—82no—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—82no—
76C13×C22⋊C4—82no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—24no—
80#6099—82no—
81C2×#1055—42no—
82C2×#1055—42no—
83C2×#1055—82no—
84#2563D1311yescharacteristic
85#1465—131no—
86#1459—131no—
87#1324—134no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13#10112yes—
98C23×C13C2×C22⋊C411yescharacteristic
99Q8×C13—84no—
100D4×C13—44no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#13112yes—
123#1055—82no—
124#1055—82no—
125C2×C4⋊Q8Dic1311yescharacteristic
126C2×C4×D4C2×D1311yescharacteristic
127#407—261no—
128C2×C22⋊C8—261no—
129#393—21no—
130#393—21no—
131#390Dic1312yes—
132#382C2×D1312yes—
133#380—21no—
134#380—21no—
135C4×C4⋊C4Dic1311yescharacteristic
136#324—132no—
137#324—132no—
138#323—261no—
139#323—261no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—81no—
151C22×C13—81no—
152C22×C13#40811yescharacteristic
153C22×C13C2×#9911yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C4×C13—21no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—82no—
161C4×C13—82no—
162C4×C13#35412yes—
163C22×Q8—21no—
164C22×D4C2×Dic1311yescharacteristic
165C23×C4C22⋊D1311yescharacteristic
166C23×C4C22⋊D1311yescharacteristic
167C2×M16—521no—
168C22×C8—521no—
169C4⋊Q8—41no—
170C4⋊Q8—41no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×Dic1312yes—
176C2×C4⋊C4C22×D1311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4C22⋊D1311yescharacteristic
180C2×C22⋊C4C22⋊D1311yescharacteristic
181C2×C42C2×Dic1312yes—
182C2×C42C2×Dic1311yescharacteristic
183C22⋊C8—262no—
184C22⋊C8—262no—
185C22⋊C8—521no—
186C22⋊C8—521no—
187#95—21no—
188#95—22no—
189#95—22no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13—81no—
194C2×C13#147211yescharacteristic
195C2×C13C2×#35411yescharacteristic
196C2×C13#213411yescharacteristic
197C24C22⋊Dic1311yescharacteristic
198C24C22⋊Dic1311yescharacteristic
199C2×Q8—42no—
200C2×Q8—82no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22×Dic1311yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217M16—1042no—
218C2×C8—522no—
219C2×C8—522no—
220C2×C8—1042no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C42—24no—
233C13#1156911yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23#8807612yes—
244C23C2×C22⋊Dic1311yescharacteristic
245Q8—84no—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4#8807411yescharacteristic
267C2×C4#8807411yescharacteristic
268C2×C4#8820212yes—
269C8—1042no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C2×#8807411yescharacteristic
284C22C2×#8807611yescharacteristic
285C22#1171889511yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4#1171813312yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1311320011yescharacteristic
299C2C2×#1171813311yescharacteristic
300C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2563C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2563D13
hypocenterC13#11569
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13112780C2semidirect
233. C13#11569semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131542
#131127802
C13×#25632
#1156913