Finite Group Databasebeta

← #15760733

Subgroups — #15760733

Order 3328.

610 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 111 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#13114936C212yesmaximal
3#13113166C211yesmaximal, characteristic
4#13112689C212yesmaximal
5C13×#2274C211yesmaximal, characteristic
6C2×C13×#117—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180C2211yescharacteristic
9C4×C13×C4⋊C4—24no—
10C4×C13×C22⋊C4—21no—
11C4×C13×C22⋊C4C2212yes—
12#11718872—21no—
13#11718872C2211yescharacteristic
14#11718871—21no—
15#11718868C2212yes—
16#11718647C412yescomplemented
17#11718644C412yescomplemented
18#11718639—22no—
19#11718120—22no—
20#11718115—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C13×#117—28no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C42×C13—22no—
33C2×C42×C13D414yes—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36#88180—22no—
37#88180—22no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—22no—
41C2×C4×Dic13—21no—
42C2×#6099—22no—
43C13×#95—22no—
44C13×#95—22no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071C2×C412yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9478—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—24no—
57C22×C4×C13—24no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13#4112yes—
68C22×Dic13—22no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C13×C4⋊C4—28no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C22⋊C4—28no—
75C42×C13—28no—
76C42×C13—44no—
77C42×C13—82no—
78C22⋊Dic13—42no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C4⋊Dic13—22no—
82C4⋊Dic13—22no—
83#6101—44no—
84C4×Dic13—42no—
85#6099—44no—
86C2×#1055—42no—
87#2484—131no—
88#2274D1311yescharacteristic
89#1826—132no—
90#1463—131no—
91#1284—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—41no—
95C23×C13C2×C22⋊C411yescharacteristic
96C23×C13#12011yescharacteristic
97C23×C13#12311yescharacteristic
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—24no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—24no—
104C2×C4×C13—28no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—44no—
110C2×C4×C13—44no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—81no—
114C2×C4×C13#10414yes—
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12112yes—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124#1055—82no—
125C2×#117—21no—
126C2×#117—131no—
127C22×C4⋊C4C2×D1311yescharacteristic
128#407—132no—
129#400—132no—
130#398—132no—
131#387—262no—
132#385—261no—
133#381—131no—
134#381—261no—
135C4×C4⋊C4—24no—
136C4×C22⋊C4—21no—
137C4×C22⋊C4C2×D1312yes—
138#339—264no—
139#324—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—44no—
148C22×C13#38611yescharacteristic
149C22×C13C2×#10412yes—
150C22×C13#45812yes—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—24no—
154C4×C13—48no—
155C4×C13—42no—
156Dic13—82no—
157Dic13—81no—
158Dic13—81no—
159C23×C4C22⋊D1311yescharacteristic
160C23×C4C22⋊D1311yescharacteristic
161C23×C4C22×D1311yescharacteristic
162C2×M16—262no—
163#117—28no—
164#117—262no—
165#117—262no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4C4×D1312yes—
173C2×C4⋊C4D5212yes—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—261no—
176C2×C22⋊C4—261no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—261no—
180C2×C42C22⋊D1314yes—
181C22⋊C8—262no—
182C22⋊C8—262no—
183#95—22no—
184#95—22no—
185#95—132no—
186#95—262no—
187#95—262no—
188#95—262no—
189#95—261no—
190C2×C13—22no—
191C2×C13—22no—
192C2×C13—41no—
193C2×C13#189011yescharacteristic
194C2×C13#189611yescharacteristic
195C2×C13#191211yescharacteristic
196C24C2×C22⋊D1311yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4#610312yes—
209C22×C4#610312yes—
210C22×C4C2×C4×D1311yescharacteristic
211C22×C4C2×D5211yescharacteristic
212C22×C4#612712yes—
213C22×C4C2×C22⋊D1312yes—
214M16—524no—
215C2×C8—522no—
216C4⋊C4—28no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—262no—
220C4⋊C4—262no—
221C4⋊C4—524no—
222C22⋊C4—28no—
223C22⋊C4—522no—
224C22⋊C4—521no—
225C22⋊C4—521no—
226C42—28no—
227C42—44no—
228C42—82no—
229C42—522no—
230C13#947811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×#610311yescharacteristic
235C23#8818311yescharacteristic
236C23#8820711yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—28no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—81no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4#8804514yes—
261C2×C4C4×C22⋊D1312yes—
262C2×C4#8818412yes—
263C8—1042no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22C2×#8804512yes—
273C22#1171887411yescharacteristic
274C22#1171890412yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—48no—
279C4—42no—
280C4—1042no—
281C4—1041no—
282C4—1041no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#1311524911yescharacteristic
287C2#1311527911yescharacteristic
288C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2274C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2274D13
hypocenterC13#9478
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
16. #11718647C4semidirect
17. #11718644C4semidirect
230. C13#9478semidirect

Maximal subgroups

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

subgroupindex
#131191232
#131149362
#131131662
#131126892
C13×#22742
#947813