Finite Group Databasebeta

← #15760649

Subgroups — #15760649

Order 3328.

528 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117439C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13113369C212yesmaximal
4#13112689C212yesmaximal
5C13×#2502C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#398—22no—
9C13×#391C412yescomplemented
10C13×#385—21no—
11C13×#385—21no—
12C13×#384C412yescomplemented
13C4×C13×C22⋊C4C2211yescharacteristic
14#11718873—21no—
15#11718872C2212yes—
16C4×C22⋊Dic13—21no—
17#11718868C2212yes—
18#11718642—24no—
19#11718130—24no—
20#11718122—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D412yes—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13C2×C412yes—
38C2×C22⋊Dic13—22no—
39C2×C4⋊Dic13—22no—
40C2×C4×Dic13—22no—
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—21no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071D414yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9461—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C2×Q8×C13—22no—
54C2×Q8×C13—42no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—81no—
64C22×C4×C13—81no—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D412yes—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4112yes—
71C22×Dic13—24no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—82no—
77C13×C4⋊C4—82no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C42×C13—42no—
82C22⋊Dic13—44no—
83C4⋊Dic13—82no—
84C4×Dic13—82no—
85#6099—44no—
86C2×#1055—42no—
87#2502D1311yescharacteristic
88#2313—131no—
89#1821—131no—
90#1511—132no—
91#1284—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—41no—
95C23×C13C2×C22⋊C411yescharacteristic
96C23×C13#12011yescharacteristic
97C23×C13#12311yescharacteristic
98Q8×C13—82no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—24no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13C4×D412yes—
119C2×C4×C13#12112yes—
120C2×Dic13—44no—
121C2×Dic13—44no—
122C2×Dic13—44no—
123#1055—82no—
124C2×C22⋊Q8C2×D1311yescharacteristic
125C22×C4⋊C4C2×D1311yescharacteristic
126#407—132no—
127#398—22no—
128#391Dic1312yescomplemented
129#387—264no—
130#385—21no—
131#385—21no—
132#384Dic1312yescomplemented
133#381—132no—
134#380—261no—
135C4×C22⋊C4—261no—
136C4×C22⋊C4C2×D1311yescharacteristic
137#343—262no—
138#328—264no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—44no—
147C22×C13#38611yescharacteristic
148C22×C13#41012yes—
149C22×C13#45612yes—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—44no—
153C4×C13—42no—
154C4×C13—42no—
155C4×C13—81no—
156C4×C13—81no—
157Dic13—84no—
158C22×Q8C2×Dic1311yescharacteristic
159C23×C4C22⋊D1311yescharacteristic
160C23×C4C22⋊D1311yescharacteristic
161C23×C4C22×D1311yescharacteristic
162C2×M16—262no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—262no—
171C2×C4⋊C4C2×Dic1311yescharacteristic
172C2×C4⋊C4C2×Dic1312yes—
173C2×C4⋊C4C22⋊D1312yes—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—262no—
177C2×C42—262no—
178C2×C42C2×Dic1312yes—
179C22⋊C8—262no—
180C22⋊C8—262no—
181#95—22no—
182#95—22no—
183#95—21no—
184#95—134no—
185#95—262no—
186#95—262no—
187#95—262no—
188C2×C13—22no—
189C2×C13—22no—
190C2×C13—41no—
191C2×C13#188611yescharacteristic
192C2×C13#189911yescharacteristic
193C2×C13#191111yescharacteristic
194C24C2×C22⋊D1311yescharacteristic
195C2×Q8—22no—
196C2×Q8—42no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—264no—
208C22×C4C22⋊Dic1312yes—
209C22×C4C22⋊Dic1312yes—
210C22×C4D4×D1312yes—
211C22×C4#612912yes—
212C22×C4C22×Dic1311yescharacteristic
213C22×C4C2×C22⋊D1311yescharacteristic
214M16—524no—
215C2×C8—522no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—22no—
219C4⋊C4—42no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C4⋊C4—1042no—
223C22⋊C4—24no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—524no—
227C42—42no—
228C42—1042no—
229C13#946111yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—41no—
233C23#8818911yescharacteristic
234C23#8819111yescharacteristic
235C23C2×C22⋊Dic1311yescharacteristic
236Q8—82no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—524no—
257C2×C4—524no—
258C2×C4—524no—
259C2×C4D4×Dic1312yes—
260C2×C4#8819312yes—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1171875612yes—
271C22#1171888111yescharacteristic
272C22#1171890112yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—81no—
279C4—81no—
280C4—1044no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#1311523011yescharacteristic
285C2#1311529511yescharacteristic
286C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2502C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2502D13
hypocenterC13#9461
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
9. C13×#391C4semidirect
12. C13×#384C4semidirect
128. #391Dic13semidirect
132. #384Dic13semidirect
229. C13#9461semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131149162
#131133692
#131126892
C13×#25022
#946113