Finite Group Databasebeta

← #15760601

Subgroups — #15760601

Order 3328.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#13123921C211yesmaximal, characteristic
2#13119821C211yesmaximal, characteristic
3#13113561C212yesmaximal
4#13112691C212yesmaximal
5C13×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198C412yes—
8C2×#88123C2211yescharacteristic
9C13×#432C2212yes—
10#11718685—24no—
11#11718644—21no—
12#11718644—21no—
13#11718635C412yes—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718589—21no—
16#11718589—21no—
17#11718587—21no—
18#11718587C2212yes—
19#11718586—21no—
20C13×#324—21no—
21C13×#324—21no—
22#11718073—24no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26C2×C412yes—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33#88198—44no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×#6101—22no—
38C2×#6101—22no—
39C2×C4×Dic13C2×C412yes—
40#88123—22no—
41#88123—22no—
42C13×C4⋊C8—22no—
43C13×C22⋊C8—22no—
44C13×#97—22no—
45#88071—22no—
46#88071—22no—
47#88071—21no—
48C22⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055—22no—
51C4⋊#1055D414yes—
52#88043—22no—
53#88043—22no—
54C4×#1055—22no—
55#9452—131nomaximal, Sylow
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—41no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C2×Dic26—24no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×C8×C13—42no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13C2×D412yes—
80C42×C13#4112yes—
81C4⋊Dic13—24no—
82C4⋊Dic13—41no—
83C4⋊Dic13—42no—
84C4⋊Dic13—41no—
85#6101—44no—
86#6101—44no—
87C4×Dic13—42no—
88C2×#1055—24no—
89#2983—131no—
90#2546—131no—
91#1558—132no—
92#1467D1311yescharacteristic
93#1285—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95Q8×C13—44no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13#10012yes—
110C2×C4×C13C4×D412yes—
111C2×C4×C13#12011yescharacteristic
112C2×C4×C13#12112yes—
113C2×C4×C13#12311yescharacteristic
114C2×Dic13—24no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120Dic26—84no—
121C8×C13—82no—
122#1055—44no—
123C2×C4⋊Q8—132no—
124C2×C4⋊Q8—131no—
125C2×C4×Q8C2×D1311yescharacteristic
126#446—264no—
127#432—132no—
128#432—261no—
129#432C2×D1312yes—
130#431—261no—
131#398—261no—
132#398—261no—
133#391—132no—
134#389—261no—
135#389—261no—
136C4×C4⋊C4—131no—
137#333—264no—
138#324—21no—
139#324—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#38611yescharacteristic
143C22×C13C2×#10011yescharacteristic
144C22×C13#41311yescharacteristic
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13#45612yes—
153Dic13—44no—
154Dic13—82no—
155C22×Q8—132no—
156C22×Q8C4×D1311yescharacteristic
157C4⋊Q8—262no—
158C4⋊Q8—262no—
159C4⋊Q8—524no—
160C4×Q8—22no—
161C4×Q8—22no—
162C2×C4⋊C4—261no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—261no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4C4×D1311yescharacteristic
168C2×C4⋊C4C22⋊D1311yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C42—132no—
171C2×C42D5211yescharacteristic
172C2×C42D5211yescharacteristic
173C2×C42C22×D1311yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—134no—
176C4⋊C8—262no—
177C4⋊C8—262no—
178C22⋊C8—22no—
179C22⋊C8—262no—
180#97—22no—
181#97—262no—
182#97—262no—
183C4×C8—262no—
184#95—262no—
185#95—262no—
186#95—261no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13#188611yescharacteristic
190C2×C13#190011yescharacteristic
191C2×C13#190911yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—264no—
196C2×Q8—522no—
197C2×Q8—522no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4#610311yescharacteristic
201C22×C4#610311yescharacteristic
202C22×C4#610311yescharacteristic
203C22×C4#610311yescharacteristic
204C22×C4C2×C4×D1311yescharacteristic
205C22×C4C2×D5211yescharacteristic
206C22×C4C2×C22⋊D1311yescharacteristic
207C2×C8—42no—
208C2×C8—264no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—264no—
213C4⋊C4—524no—
214C4⋊C4—521no—
215C4⋊C4—521no—
216C4⋊C4—522no—
217C4⋊C4—524no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—522no—
223C42D4×D1312yes—
224C42#612912yes—
225C13#945211yescharacteristic, complemented, Sylow
226C23C2×#610311yescharacteristic
227Q8—44no—
228Q8—1044no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—264no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4#8806312yes—
249C2×C4#8813512yes—
250C2×C4#8813611yescharacteristic
251C2×C4#8814011yescharacteristic
252C2×C4#8819312yes—
253C8—82no—
254C8—524no—
255C22—21no—
256C22—21no—
257C22#1171861911yescharacteristic
258C22C2×#8806311yescharacteristic
259C22#1171879311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—524no—
268C4—1042no—
269C4#1171841312yes—
270C2—21no—
271C2—21no—
272C2#1311522711yescharacteristic
273C2#1311529711yescharacteristic
274C2#1311535611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1467C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1467D13
hypocenterC13#9452
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
225. C13#9452semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131198212
#131135612
#131126912
C13×#14672
#945213