Finite Group Databasebeta

← #15760359

Subgroups — #15760359

Order 3328.

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

normal subgroups only

This group has 618 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#13120216C211yesmaximal, characteristic
2#13113355C212yesmaximal
3#13113166C211yesmaximal, characteristic
4#13112722C212yesmaximal
5C13×#2274C211yesmaximal, characteristic
6C2×C13×#117—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88178C2211yescharacteristic
9C4×C13×C4⋊C4—24no—
10C4×C13×C22⋊C4—21no—
11C4×C13×C22⋊C4C2212yes—
12#11718871—21no—
13#11718871—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16#11718644C412yescomplemented
17#11718640C412yescomplemented
18#11718633—22no—
19#11718120—22no—
20#11718044—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—28no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C22⋊C4—22no—
32C2×C42×C13—22no—
33C2×C42×C13—22no—
34C2×C42×C13—22no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38#88178—22no—
39#88178—22no—
40C2×#6101—22no—
41C2×#6101—21no—
42C2×#6101—22no—
43C2×C4×Dic13—21no—
44C2×#6099—22no—
45C13×#95—22no—
46C13×#95D414yes—
47#88071—22no—
48#88071—22no—
49#88071C2×C412yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9408—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—24no—
57C22×C4×C13—21no—
58C22×C4×C13—24no—
59C22×C4×C13—21no—
60C22×C4×C13—81no—
61C22×C4×C13—81no—
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—
71C2×Dic26—22no—
72C2×Dic26—81no—
73C13×C4⋊C4—28no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C22⋊C4—28no—
77C42×C13—28no—
78C42×C13—82no—
79C42×C13—82no—
80C22⋊Dic13—24no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C4⋊Dic13—22no—
84#6101—44no—
85#6101—42no—
86#6101—82no—
87C4×Dic13—81no—
88#6099—82no—
89C2×#1055—42no—
90#2583—131no—
91#2274D1311yescharacteristic
92#1508—132no—
93#1463—131no—
94#1297—132no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#12011yescharacteristic
100C23×C13#12311yescharacteristic
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—24no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—28no—
107C2×C4×C13—22no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—44no—
113C2×C4×C13—42no—
114C2×C4×C13—44no—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13#10414yes—
118C2×C4×C13C4×D412yes—
119C2×C4×C13#12112yes—
120C2×Dic13—24no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127Dic26—82no—
128#1055—82no—
129C2×C22⋊Q8—131no—
130C2×#117—21no—
131C22×C4⋊C4C2×D1311yescharacteristic
132#407—132no—
133#398—132no—
134#395—132no—
135#389—262no—
136#385—261no—
137#385—261no—
138C4×C4⋊C4—24no—
139C4×C22⋊C4—21no—
140C4×C22⋊C4—131no—
141C4×C22⋊C4C2×D1312yes—
142#328—264no—
143#324—262no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—44no—
152C22×C13#38611yescharacteristic
153C22×C13C2×#10412yes—
154C22×C13#45612yes—
155C4×C13—24no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—48no—
159C4×C13—42no—
160Dic13—44no—
161Dic13—81no—
162Dic13—81no—
163C22×Q8—131no—
164C23×C4C22⋊D1311yescharacteristic
165C23×C4C22⋊D1311yescharacteristic
166C23×C4C22×D1311yescharacteristic
167C2×M16—262no—
168C22⋊Q8—262no—
169C22⋊Q8—262no—
170#117—28no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—262no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4C4×D1312yes—
179C2×C4⋊C4D5212yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—261no—
182C2×C22⋊C4—261no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—261no—
187C22⋊C8—262no—
188C22⋊C8—262no—
189#95—22no—
190#95—132no—
191#95—262no—
192#95—262no—
193#95C22⋊D1314yes—
194C2×C13—22no—
195C2×C13—22no—
196C2×C13—41no—
197C2×C13#188611yescharacteristic
198C2×C13#189611yescharacteristic
199C2×C13#191311yescharacteristic
200C24C2×C22⋊D1311yescharacteristic
201C2×Q8—262no—
202C2×Q8—1041no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—24no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—21no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4—262no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4#610312yes—
215C22×C4#610312yes—
216C22×C4C2×C4×D1311yescharacteristic
217C22×C4C2×D5211yescharacteristic
218C22×C4#612712yes—
219C22×C4C2×C22⋊D1312yes—
220M16—1042no—
221C2×C8—522no—
222C4⋊C4—28no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—262no—
226C4⋊C4—522no—
227C4⋊C4—524no—
228C4⋊C4—1042no—
229C22⋊C4—28no—
230C22⋊C4—264no—
231C22⋊C4—521no—
232C22⋊C4—521no—
233C42—28no—
234C42—82no—
235C42—82no—
236C42—1041no—
237C13#940811yescharacteristic, complemented, Sylow
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×#610311yescharacteristic
242C23#8818311yescharacteristic
243C23#8820711yescharacteristic
244Q8—1042no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—81no—
261C2×C4—264no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4#8804514yes—
269C2×C4C4×C22⋊D1312yes—
270C2×C4#8818412yes—
271C8—1042no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22C2×#8804512yes—
281C22#1171887411yescharacteristic
282C22#1171890712yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—48no—
287C4—42no—
288C4—524no—
289C4—1041no—
290C4—1041no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2#1311522911yescharacteristic
295C2#1311527911yescharacteristic
296C2#1311537811yescharacteristic
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#9408
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. #11718644C4semidirect
17. #11718640C4semidirect
237. C13#9408semidirect

Maximal subgroups

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

subgroupindex
#131202162
#131133552
#131131662
#131127222
C13×#22742
#940813