Finite Group Databasebeta

← #15772558

Subgroups — #15772558

Order 3328.

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

normal subgroups only

This group has 462 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#13113180C211yesmaximal, characteristic, complemented
2#13113160C211yesmaximal, characteristic, complemented
3#13112768C214yesmaximal, complemented
4C13×#2548C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#124C412yes—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#394—21no—
9C13×#394—21no—
10C13×#390—21no—
11C13×#390—21no—
12C13×#390C2212yes—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718587—21no—
15#11718586—21no—
16#11718120—21no—
17#11718120—21no—
18#11718120C2212yes—
19#11718120C2212yes—
20C22×Q8×C13C2×C411yescharacteristic
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C13×#127—41no—
25C13×#127—41no—
26C13×#124—44no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C412yes—
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C13×#95—21no—
42C22⋊#1055—22no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45C4⋊#1055—41no—
46#88043—41no—
47C4×#1055—41no—
48#11567—131nomaximal, Sylow
49C24×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—41no—
53C2×D4×C13—24no—
54C2×D4×C13—42no—
55C2×D4×C13—42no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—82no—
62C22×C4×C13—22no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C13×C22⋊C4—44no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—82no—
77C13×C22⋊C4—82no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—42no—
85C2×#1055—42no—
86C2×#1055—42no—
87#2548D1311yescharacteristic
88#1467—131no—
89#1461—131no—
90#1318—134no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13C2×C22⋊C411yescharacteristic
99Q8×C13—44no—
100D4×C13—82no—
101D4×C13—84no—
102D4×C13—84no—
103D4×C13—82no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#10012yes—
124C2×C4×C13#13112yes—
125#1055—82no—
126#1055—82no—
127C2×#127Dic1311yescharacteristic
128C2×#124Dic1312yes—
129C2×C4×Q8C2×D1311yescharacteristic
130#432—261no—
131#431—261no—
132#394—21no—
133#394—21no—
134#390—21no—
135#390—21no—
136#390C2×D1312yes—
137C4×C4⋊C4Dic1311yescharacteristic
138#324—132no—
139#324—132no—
140#324—261no—
141#324—261no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—82no—
145C22×C13—82no—
146C22×C13—82no—
147C22×C13—82no—
148C22×C13—82no—
149C22×C13—82no—
150C22×C13—82no—
151C22×C13#40811yescharacteristic
152C22×C13C2×#9911yescharacteristic
153C22×C13C2×#10011yescharacteristic
154C4×C13—21no—
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—82no—
162C4×C13#35512yes—
163C22×Q8C2×Dic1311yescharacteristic
164C22×D4—21no—
165C22×D4—21no—
166C22×D4C2×Dic1312yes—
167#127—41no—
168#127—41no—
169#124—44no—
170C4×Q8—41no—
171C4×Q8—41no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C22⋊D1311yescharacteristic
174C2×C4⋊C4C22⋊D1311yescharacteristic
175C2×C4⋊C4C22×D1311yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C42C2×Dic1311yescharacteristic
181C2×C42C2×Dic1312yes—
182C2×C42C22⋊D1311yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C4⋊C8—521no—
185C4⋊C8—521no—
186C22⋊C8—262no—
187C22⋊C8—262no—
188#97—521no—
189C4×C8—521no—
190#95—21no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13—162no—
194C2×C13#147111yescharacteristic
195C2×C13#212811yescharacteristic
196C2×C13C2×#35511yescharacteristic
197C24—22no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C2×D4—24no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—82no—
210C22×C4—22no—
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22⋊Dic1311yescharacteristic
215C22×C4C22×Dic1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C22×C4C2×C22⋊D1311yescharacteristic
218C2×C8—522no—
219C2×C8—522no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C22⋊C4—44no—
225C22⋊C4—44no—
226C22⋊C4—82no—
227C22⋊C4—82no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—42no—
235C13#1156711yescharacteristic, complemented, Sylow
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23C2×C22⋊Dic1311yescharacteristic
244Q8—44no—
245D4—84no—
246D4—82no—
247D4—84no—
248D4—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#8807312yes—
267C2×C4#8807411yescharacteristic
268C2×C4#8807411yescharacteristic
269C2×C4#8820212yes—
270C8—1042no—
271C8—1042no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22C2×#8807311yescharacteristic
282C22C2×#8807411yescharacteristic
283C22#1171889511yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4#1171813412yes—
293C2—21no—
294C2—21no—
295C2—162no—
296C2#1311319611yescharacteristic
297C2#1311650811yescharacteristic
298C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2548C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2548D13
hypocenterC13#11567
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #13113180C2semidirect
2. #13113160C2semidirect
3. #13112768C2semidirect
235. C13#11567semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131131602
#131127682
C13×#25482
#1156713