Finite Group Databasebeta

← #15760751

Subgroups — #15760751

Order 3328.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 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#13119123C211yesmaximal, characteristic
2#13117439C211yesmaximal, characteristic
3#13114933C212yesmaximal
4#13112690C212yesmaximal
5C13×#1463C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180C2211yescharacteristic
8C13×#407C2212yes—
9#11718873—21no—
10#11718872—21no—
11#11718872—21no—
12#11718872C2211yescharacteristic
13#11718871—21no—
14C4×C22⋊Dic13C2212yes—
15#11718647C412yescomplemented
16#11718644C412yescomplemented
17#11718642—24no—
18#11718639—22no—
19C13×#324—22no—
20#11718147—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C2×C13×M16—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C22⋊Dic13—21no—
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—21no—
32#88180—22no—
33#88180—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—22no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13D414yes—
40C13×C22⋊C8—22no—
41C13×C22⋊C8—22no—
42#88071—24no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071C2×C412yes—
50#9482—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4112yes—
65C22×Dic13—22no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—24no—
69C13×M16—44no—
70C2×C8×C13—42no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—24no—
73C22⋊Dic13—44no—
74C22⋊Dic13—42no—
75C22⋊Dic13—41no—
76C22⋊Dic13—41no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—82no—
80#6101—44no—
81C4×Dic13—42no—
82C4×Dic13—44no—
83#2484—131no—
84#2313—131no—
85#1826—132no—
86#1463D1311yescharacteristic
87#1284—132no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—41no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13#12011yescharacteristic
93C23×C13#12311yescharacteristic
94C2×C4×C13—24no—
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×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—81no—
107C2×C4×C13C4×D412yes—
108C2×C4×C13#12112yes—
109C2×Dic13—42no—
110C2×Dic13—44no—
111C2×Dic13—42no—
112C2×Dic13—44no—
113C2×Dic13—42no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—44no—
119C8×C13—82no—
120C2×#117—131no—
121C22×C4⋊C4C2×D1311yescharacteristic
122#407C2×D1312yes—
123#400—132no—
124#398—132no—
125#387—264no—
126#387—262no—
127#385—261no—
128#381—131no—
129#381—261no—
130#381—261no—
131#380—261no—
132C4×C22⋊C4—132no—
133#339—264no—
134#324—22no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—44no—
143C22×C13#38611yescharacteristic
144C22×C13#42112yes—
145C22×C13#45812yes—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—42no—
149C4×C13—42no—
150Dic13—84no—
151Dic13—82no—
152Dic13—81no—
153Dic13—81no—
154C23×C4D5211yescharacteristic
155C23×C4D5211yescharacteristic
156C23×C4C22×D1311yescharacteristic
157C2×M16—22no—
158#117—262no—
159#117—262no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4C4×D1312yes—
167C2×C4⋊C4C22⋊D1312yes—
168C2×C22⋊C4—261no—
169C2×C22⋊C4—262no—
170C2×C22⋊C4—261no—
171C2×C42—134no—
172C2×C42—261no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—132no—
176#95—262no—
177#95—264no—
178#95—262no—
179#95—262no—
180#95—262no—
181#95—262no—
182#95—261no—
183C2×C13—22no—
184C2×C13—22no—
185C2×C13—41no—
186C2×C13#189011yescharacteristic
187C2×C13#189711yescharacteristic
188C2×C13#191211yescharacteristic
189C24C2×D5211yescharacteristic
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—264no—
198C22×C4—262no—
199C22×C4—261no—
200C22×C4—261no—
201C22×C4#610312yes—
202C22×C4#610312yes—
203C22×C4C2×C4×D1311yescharacteristic
204C22×C4D4×D1312yes—
205C22×C4#612912yes—
206C22×C4C2×C22⋊D1311yescharacteristic
207M16—44no—
208C2×C8—42no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—524no—
214C4⋊C4—1042no—
215C22⋊C4—522no—
216C22⋊C4—524no—
217C22⋊C4—521no—
218C22⋊C4—521no—
219C42—524no—
220C42—522no—
221C13#948211yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23—41no—
225C23#8813611yescharacteristic
226C23#8814011yescharacteristic
227C23C2×#610311yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—522no—
242C2×C4—524no—
243C2×C4—524no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—524no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4#8813512yes—
252C2×C4#8819312yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1171840312yes—
263C22#1171861911yescharacteristic
264C22#1171880012yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—1044no—
270C4—1042no—
271C4—1041no—
272C4—1041no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#1311524711yescharacteristic
277C2#1311528211yescharacteristic
278C2#1311537111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1463C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1463D13
hypocenterC13#9482
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
15. #11718647C4semidirect
16. #11718644C4semidirect
221. C13#9482semidirect

Maximal subgroups

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

subgroupindex
#131191232
#131174392
#131149332
#131126902
C13×#14632
#948213