Finite Group Databasebeta

← #15760302

Subgroups — #15760302

Order 3328.

730 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 131 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#13123860C211yesmaximal, characteristic, complemented
2#13119782C211yesmaximal, characteristic
3#13113505C212yesmaximal, complemented
4#13112737C212yesmaximal, complemented
5C13×#1800C211yesmaximal, characteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88194—21no—
8C2×#88184—22no—
9C2×#88128C2211yescharacteristic
10C13×#423C2212yes—
11C2×C13×#100—21no—
12C2×C22⋊#1055—22no—
13D4×#1055—24no—
14#11718649—21no—
15#11718621C414yes—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718586C2212yes—
18C13×#343—21no—
19#11718077—24no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D412yes—
22C22×C22⋊D13—24no—
23C22×D52—21no—
24C22×D52—21no—
25C22×D52C2×C412yes—
26C2×C13×M16—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C412yes—
31C2×C42×C13C2311yescharacteristic
32#88194—42no—
33#88194—42no—
34#88184—48no—
35C2×#6103—24no—
36C2×C4⋊Dic13—21no—
37C2×C4×Dic13—21no—
38C22×#1055—24no—
39#88128—22no—
40#88128—22no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#100—42no—
44#88071C2×C412yes—
45C22⋊#1055—24no—
46C22⋊#1055—22no—
47C4⋊#1055D414yescomplemented
48C4×#1055—22no—
49#9397—131nomaximal, Sylow
50C24×C13C22⋊C412yes—
51C23×D13—22no—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13D812yes—
55C2×D4×C13SD1612yes—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—44no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C2×C22⋊D13—48no—
64C2×C22⋊D13—48no—
65C2×C22⋊D13—84no—
66C22×Dic13—22no—
67C2×D52—24no—
68C2×D52—44no—
69C2×D52—41no—
70C2×D52—42no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—42no—
75C2×D52—82no—
76C13×M16—42no—
77C13×M16—42no—
78C2×C8×C13—42no—
79C13×C4⋊C4—22no—
80C13×C22⋊C4—24no—
81C42×C13C2×D412yes—
82C42×C13#4112yes—
83#6103—48no—
84C4⋊Dic13—24no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C2×#1055—24no—
88C2×#1055—84no—
89#2972—131no—
90#2541—131no—
91#1800D1311yescharacteristic, complemented
92#1545—132no—
93#1303—132no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13#10214yes—
99C23×C13C2×C22⋊C411yescharacteristic
100C22×D13—44no—
101C22×D13—44no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—42no—
105D4×C13—24no—
106D4×C13—24no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—44no—
111C2×C4×C13—42no—
112C2×C4×C13—82no—
113C2×C4×C13C4×D412yes—
114C2×C4×C13#12011yescharacteristic
115C2×C4×C13#12112yes—
116C2×C4×C13#12311yescharacteristic
117C2×C4×C13C2×D811yescharacteristic
118C2×C4×C13C2×SD1611yescharacteristic
119C2×C4×C13#13512yes—
120C22⋊D13—816no—
121C2×Dic13—24no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124D52—82no—
125D52—84no—
126D52—82no—
127D52—82no—
128D52—82no—
129C8×C13—82no—
130#1055—44no—
131C2×#127—131no—
132C2×#127—261no—
133C2×#121—262no—
134C2×C4×D4C2×D1311yescharacteristic
135C8×D4—264no—
136#431—132no—
137#423C2×D1312yes—
138C2×#100—21no—
139C2×C22⋊C8—262no—
140#392—134no—
141#390—261no—
142C4×C4⋊C4—131no—
143#343—21no—
144#331—264no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—24no—
148C22×C13—44no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—82no—
152C22×C13#38611yescharacteristic
153C22×C13C2×#10211yescharacteristic
154C22×C13#41611yescharacteristic
155C2×D13—84no—
156C2×D13—84no—
157C2×D13—82no—
158C2×D13—82no—
159C2×D13—82no—
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—42no—
163C4×C13#45312yes—
164C4×C13#46512yes—
165C4×C13#46612yes—
166Dic13—44no—
167C22×D4—132no—
168C22×D4—264no—
169C22×D4—261no—
170C22×D4—261no—
171C22×D4C22⋊D1311yescharacteristic
172C23×C4D5212yes—
173C2×M16—22no—
174C22×C8—264no—
175#127—262no—
176#127—262no—
177#127—522no—
178#127—522no—
179#121—528no—
180C4×D4—22no—
181C4×D4—22no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4C22⋊D1311yescharacteristic
184C2×C22⋊C4—264no—
185C2×C22⋊C4C4×D1312yes—
186C2×C42—261no—
187C2×C42C22×D1311yescharacteristic
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—134no—
191#100—42no—
192C22⋊C8—264no—
193C22⋊C8—262no—
194C4×C8—262no—
195#95—132no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—44no—
199C2×C13#188711yescharacteristic
200C2×C13#189311yescharacteristic
201C2×C13#191411yescharacteristic
202D13—162no—
203C24—262no—
204C24#610312yes—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—264no—
208C2×D4—524no—
209C2×D4—528no—
210C2×D4—528no—
211C2×D4—521no—
212C2×D4—521no—
213C2×D4—521no—
214C2×D4—522no—
215C2×D4—521no—
216C2×D4—522no—
217C2×D4—1042no—
218C2×D4—1044no—
219C2×D4#610412yes—
220C2×D4#610612yes—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—44no—
224C22×C4—262no—
225C22×C4#610312yes—
226C22×C4C2×C4×D1311yescharacteristic
227C22×C4C2×D5211yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—264no—
233C2×C8—1044no—
234C4⋊C4—22no—
235C4⋊C4—264no—
236C22⋊C4—24no—
237C22⋊C4—528no—
238C42—521no—
239C42—521no—
240C42D4×D1312yes—
241C42#612912yes—
242C13#939711yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—524no—
248C23—524no—
249C23—522no—
250C23—522no—
251C23—522no—
252C23#8804914yes—
253C23C2×#610311yescharacteristic
254D4—24no—
255D4—24no—
256D4—1044no—
257D4—1042no—
258D4—10416no—
259D4—1042no—
260D4—1042no—
261D4—1042no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—82no—
268C2×C4—264no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4#8813512yes—
272C2×C4#8813611yescharacteristic
273C2×C4#8814011yescharacteristic
274C2×C4C2×#610411yescharacteristic
275C2×C4#8819312yes—
276C2×C4C2×#610611yescharacteristic
277C2×C4#8820412yes—
278C8—82no—
279C8—524no—
280C22—21no—
281C22—21no—
282C22—24no—
283C22—44no—
284C22—42no—
285C22—42no—
286C22—82no—
287C22—1044no—
288C22—1044no—
289C22—1042no—
290C22—1042no—
291C22—1042no—
292C22#1171861911yescharacteristic
293C22C2×#8804911yescharacteristic
294C22#1171866311yescharacteristic
295C4—21no—
296C4—22no—
297C4—42no—
298C4—524no—
299C4#1171840812yes—
300C4#1171869912yes—
301C4#1171870912yes—
302C2—21no—
303C2—21no—
304C2—44no—
305C2—2082no—
306C2#1311523211yescharacteristic
307C2#1311526211yescharacteristic
308C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1800C2
socleC22×C13#386
prime radical#13119782C2
cosocleC2×C42×C13C23
hypercenter#1800D13
hypocenterC13#9397
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
3. #13113505C2semidirect
4. #13112737C2semidirect
5. C13×#1800C2semidirect
47. C4⋊#1055D4semidirect
91. #1800D13semidirect
242. C13#9397semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131197822
#131135052
#131127372
C13×#18002
#939713