Finite Group Databasebeta

← #15772610

Subgroups — #15772610

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#13113157C211yesmaximal, characteristic
3#13112784C214yesmaximal, complemented
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#400—21no—
8C13×#399—21no—
9C13×#389—21no—
10C13×#386C412yes—
11C13×#385C2212yes—
12C13×#380—21no—
13C13×#380C411yescharacteristic
14#11718868—21no—
15#11718586—21no—
16#11718120—21no—
17#11718117—21no—
18#11718117C2212yes—
19#11718117C2212yes—
20C22×D4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13D411yescharacteristic
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2311yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—41no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C22⋊#1055—22no—
43C22⋊#1055—22no—
44C22⋊#1055—41no—
45C4⋊#1055—41no—
46C4×#1055—41no—
47#11579—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C24×C13C22×C411yescharacteristic
50C2×D4×C13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—41no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—82no—
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×C4⋊C4—82no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—82no—
78C42×C13—21no—
79C42×C13—21no—
80#6099—82no—
81C2×#1055—42no—
82C2×#1055—42no—
83#2487D1311yescharacteristic
84#1465—131no—
85#1460—131no—
86#1326—134no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13C2×C22⋊C411yescharacteristic
97C23×C13#13112yes—
98D4×C13—44no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—81no—
118C2×C4×C13—84no—
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#10112yes—
122#1055—82no—
123#1055—82no—
124C2×C4×D4C2×D1311yescharacteristic
125C22×C4⋊C4Dic1311yescharacteristic
126#431—261no—
127#407—261no—
128#400—21no—
129#399—21no—
130#389—21no—
131#386Dic1312yes—
132#385C2×D1312yes—
133#380—21no—
134#380Dic1311yescharacteristic
135#324—261no—
136#323—132no—
137#323—132no—
138#323—261no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—42no—
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#40811yescharacteristic
152C22×C13C2×#9911yescharacteristic
153C22×C13C2×#10111yescharacteristic
154C4×C13—21no—
155C4×C13—22no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—82no—
160C4×C13—82no—
161C4×C13#35212yes—
162C22×D4C2×Dic1311yescharacteristic
163C23×C4C2×Dic1311yescharacteristic
164C23×C4C2×Dic1312yes—
165C23×C4C22⋊D1311yescharacteristic
166C2×M16—521no—
167C4×D4—41no—
168C4×D4—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4C22⋊D1311yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4C2×Dic1312yes—
178C2×C22⋊C4C22⋊D1311yescharacteristic
179C2×C22⋊C4C22×D1311yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C4⋊C8—521no—
182C22⋊C8—262no—
183C22⋊C8—262no—
184C22⋊C8—521no—
185C4×C8—521no—
186#95—21no—
187#95—22no—
188#95—22no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13—42no—
192C2×C13—81no—
193C2×C13#147211yescharacteristic
194C2×C13C2×#35211yescharacteristic
195C2×C13#212211yescharacteristic
196C24C22⋊Dic1311yescharacteristic
197C24C22×Dic1311yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—82no—
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216M16—1042no—
217C2×C8—522no—
218C2×C8—522no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—82no—
225C22⋊C4—24no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C42—21no—
230C42—21no—
231C13#1157911yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23#8820212yes—
242C23C2×C22⋊Dic1311yescharacteristic
243D4—44no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4#8807411yescharacteristic
265C2×C4#8807411yescharacteristic
266C2×C4#8807612yes—
267C8—1042no—
268C8—1042no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C2×#8807411yescharacteristic
282C22C2×#8807611yescharacteristic
283C22#1171889511yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—82no—
290C4—82no—
291C4#1171813112yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—81no—
296C2#1311320011yescharacteristic
297C2C2×#1171813111yescharacteristic
298C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#2487D13
hypocenterC13#11579
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13112784C2semidirect
231. C13#11579semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131572
#131127842
C13×#24872
#1157913