Finite Group Databasebeta

← #15753840

Subgroups — #15753840

Order 3328.

528 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 129 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#13117375C211yesmaximal, characteristic
2#13114584C212yesmaximal, complemented
3C2×#11718056C212yesmaximal
4#13112717C211yesmaximal, characteristic, complemented
5C13×#1295C211yesmaximal, characteristic, complemented
6C2×#88147C411yescharacteristic
7C2×#88141C411yescharacteristic
8C2×#88129C2211yescharacteristic
9C2×C13×#97C2212yes—
10C13×#382C2211yescharacteristic
11#11718649C411yescharacteristic
12#11718635C411yescharacteristic
13C42×Dic13C2211yescharacteristic
14C2×#88043C2212yes—
15#11718330—22no—
16#11718327—22no—
17#11718142—22no—
18#11718142—22no—
19#11718056C418yescomplemented
20C22×D52C2×C411yescharacteristic
21C22×C4×D13—21no—
22C22×Dic26C2×C411yescharacteristic
23C22×C8×C13—22no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C42×C13C2311yescharacteristic
27C2×#6103—22no—
28C2×#6103—21no—
29C2×#6103—22no—
30C2×#6101—21no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C2×C4×Dic13D412yes—
36C22×#1055—22no—
37#88147—42no—
38#88141—42no—
39#88129—21no—
40#88129—21no—
41#88129C2×C414yes—
42C13×#97—22no—
43C13×#97C2×C414yescomplemented
44C13×#95—22no—
45#88071—22no—
46#88043—22no—
47#88043C2×C414yescomplemented
48#8224—131nomaximal, Sylow
49C23×D13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C22×C411yescharacteristic
53C22×C4×C13C2×D412yes—
54C22×Dic13—21no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C2×D52—21no—
59C2×D52—41no—
60C2×D52—41no—
61C2×D52C4212yes—
62C2×C4×D13—44no—
63C2×C4×D13—42no—
64C2×Dic26—21no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26C4212yes—
68C2×C8×C13—24no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C42×C13C22×C412yes—
74C42×C13#4111yescharacteristic
75C42×C13#4111yescharacteristic
76#6103—24no—
77#6103—24no—
78#6103—42no—
79#6103—44no—
80#6101—42no—
81C4×Dic13—22no—
82C4×Dic13—41no—
83C4×Dic13—42no—
84C4×Dic13—42no—
85C4×Dic13—42no—
86C2×#1055—24no—
87C2×#1055—42no—
88C2×#1055—42no—
89C4×#124—131no—
90#1745—132no—
91C2×#329—132no—
92#1295—131no—
93#1295D1311yescharacteristic, complemented
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—22no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13—42no—
99C22×D13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13C2×C4211yescharacteristic
109C2×C4×C13#11711yescharacteristic
110C2×C4×C13C4×D412yes—
111C2×C4×C13C4×D412yes—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—21no—
115C2×Dic13—22no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13#10012yes—
122D52—42no—
123D52—42no—
124C4×D13—84no—
125Dic26—42no—
126Dic26—42no—
127C8×C13—44no—
128#1055—44no—
129C2×#124—131no—
130C2×C4×Q8—131no—
131C2×C4×D4—131no—
132C2×#97—132no—
133C2×#97C2×D1312yes—
134#391—131no—
135#390—131no—
136#388—262no—
137#382C2×D1311yescharacteristic
138C4×C22⋊C4—262no—
139C43—131no—
140#336—262no—
141#336—262no—
142#329—138no—
143C22×C13C4×C22⋊C411yescharacteristic
144C22×C13C2×#10011yescharacteristic
145C22×C13#41311yescharacteristic
146C22×C13#42112yes—
147C22×C13#42112yes—
148C2×D13—42no—
149C2×D13—44no—
150C2×D13—81no—
151C2×D13—81no—
152C2×D13—82no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—81no—
158C4×C13—81no—
159Dic13—22no—
160Dic13—41no—
161Dic13—42no—
162Dic13—42no—
163C22×Q8—131no—
164C22×D4—131no—
165C23×C4—261no—
166C22×C8—22no—
167C22×C8—262no—
168#124—134no—
169#124—261no—
170#124—261no—
171C4×Q8—522no—
172C4×D4—522no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4C4×D1311yescharacteristic
175C2×C4⋊C4C4×D1311yescharacteristic
176C2×C22⋊C4—262no—
177C2×C22⋊C4—261no—
178C2×C22⋊C4—262no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42—132no—
182C2×C42—132no—
183C2×C42—261no—
184C2×C42C22×D1311yescharacteristic
185#97—22no—
186#97—134no—
187#97—262no—
188#97C4×D1314yescomplemented
189#95—22no—
190#95—262no—
191C2×C13#153311yescharacteristic
192C2×C13#153512yes—
193C2×C13#153611yescharacteristic
194C2×C13C4×#10011yescharacteristic
195C2×C13#175912yes—
196D13—82no—
197C24—261no—
198C2×Q8—132no—
199C2×Q8—261no—
200C2×Q8—521no—
201C2×Q8—521no—
202C2×D4—132no—
203C2×D4—261no—
204C2×D4—521no—
205C2×D4—521no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—131no—
209C22×C4—132no—
210C22×C4—131no—
211C22×C4—261no—
212C22×C4—522no—
213C22×C4—524no—
214C22×C4C2×C4×D1311yescharacteristic
215C22×C4D4×D1312yes—
216C2×C8—24no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—264no—
220C2×C8—522no—
221C2×C8—522no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—522no—
225C22⋊C4—264no—
226C22⋊C4—264no—
227C22⋊C4—522no—
228C22⋊C4—524no—
229C42—262no—
230C42—521no—
231C42—522no—
232C42—522no—
233C42—522no—
234C42C2×C4×D1312yes—
235C42#612911yescharacteristic
236C42#613111yescharacteristic
237C13#822411yescharacteristic, complemented, Sylow
238C23—262no—
239C23—521no—
240C23—521no—
241C23—522no—
242C23—522no—
243C23C22⋊C4×D1311yescharacteristic
244Q8—522no—
245Q8—522no—
246D4—522no—
247D4—522no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—132no—
257C2×C4—262no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—1044no—
267C2×C4C42×D1311yescharacteristic
268C2×C4#8813512yes—
269C2×C4#8814611yescharacteristic
270C2×C4#8814712yes—
271C8—44no—
272C8—524no—
273C22—522no—
274C22—524no—
275C22—1041no—
276C22—1042no—
277C22—1041no—
278C22#1171832711yescharacteristic
279C22D13×#10011yescharacteristic
280C22#1171841211yescharacteristic
281C22#1171848212yes—
282C22#1171848212yes—
283C4—21no—
284C4—21no—
285C4—22no—
286C4—22no—
287C4—81no—
288C4—81no—
289C4—262no—
290C4—522no—
291C4—522no—
292C4—521no—
293C2—1042no—
294C2#1311345811yescharacteristic
295C2#1311346612yes—
296C2#1311346911yescharacteristic
297C2#1311462711yescharacteristic
298C2#1311464512yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#8224
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #13114584C2semidirect
4. #13112717C2semidirect
5. C13×#1295C2semidirect
19. #11718056C4semidirect
43. C13×#97C2×C4semidirect
47. #88043C2×C4semidirect
93. #1295D13semidirect
188. #97C4×D13semidirect
237. C13#8224semidirect

Maximal subgroups

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

subgroupindex
#131173752
#131145842
C2×#117180562
#131127172
C13×#12952
#822413