Finite Group Databasebeta

← #15758978

Subgroups — #15758978

Order 3328.

516 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 119 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#13113408C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112703C212yesmaximal
5C13×#2627C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400C412yescomplemented
9C13×#398—22no—
10C13×#395C412yescomplemented
11C13×#385—21no—
12C13×#381—21no—
13C13×#380C2211yescharacteristic
14#11718873C2212yes—
15#11718872—21no—
16C4×C22⋊Dic13—21no—
17C2×C22⋊#1055C2212yes—
18#11718642—24no—
19#11718130—24no—
20#11718120—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—21no—
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×C22⋊Dic13—22no—
38C2×C4⋊Dic13—22no—
39C2×C4×Dic13—22no—
40C22×#1055—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95C2×C412yes—
45#88071—22no—
46#88071—24no—
47#88071D414yes—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50#9202—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—81no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
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—81no—
77C13×C4⋊C4—82no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—42no—
81C22⋊Dic13—42no—
82C22⋊Dic13—42no—
83C4⋊Dic13—82no—
84C4×Dic13—82no—
85C2×#1055—42no—
86C2×#1055—82no—
87#2627D1311yescharacteristic
88#2313—131no—
89#1520—132no—
90C2×#324—131no—
91#1289—132no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13#12011yescharacteristic
96C23×C13#12311yescharacteristic
97C23×C13#13512yes—
98C23×C13#13712yes—
99Q8×C13—82no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—81no—
120C2×C4×C13C4×D412yes—
121C2×C4×C13#12112yes—
122C2×Dic13—44no—
123C2×Dic13—44no—
124C2×Dic13—44no—
125#1055—82no—
126C2×C22⋊Q8C2×D1311yescharacteristic
127C22×C4⋊C4C2×D1311yescharacteristic
128C2×C22⋊C8—132no—
129#400Dic1312yescomplemented
130#398—22no—
131#395Dic1312yescomplemented
132#387—264no—
133#385—21no—
134#381—21no—
135#381—261no—
136#380—132no—
137#380C2×D1311yescharacteristic
138C4×C22⋊C4—261no—
139#328—264no—
140#324—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13#38611yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#45212yes—
153C22×C13#48512yes—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—42no—
157C4×C13—42no—
158C4×C13—82no—
159C4×C13—81no—
160C4×C13—81no—
161Dic13—84no—
162C22×Q8C2×Dic1311yescharacteristic
163C23×C4C22⋊D1311yescharacteristic
164C23×C4C22⋊D1311yescharacteristic
165C23×C4C22×D1311yescharacteristic
166C22×C8—262no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C2×Dic1312yes—
177C2×C4⋊C4C22⋊D1312yes—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—21no—
180C2×C22⋊C4—262no—
181C2×C42—262no—
182C22⋊C8—262no—
183C22⋊C8—262no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—134no—
188#95—262no—
189#95—264no—
190#95C2×Dic1312yes—
191C2×C13—22no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13—22no—
195C2×C13#187311yescharacteristic
196C2×C13#191211yescharacteristic
197C2×C13#191311yescharacteristic
198C24C2×C22⋊D1311yescharacteristic
199C2×Q8—22no—
200C2×Q8—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—81no—
211C22×C4—81no—
212C22×C4—264no—
213C22×C4C22⋊Dic1312yes—
214C22×C4C22⋊Dic1312yes—
215C22×C4D4×D1312yes—
216C22×C4#612912yes—
217C22×C4C22×Dic1311yescharacteristic
218C22×C4C2×C22⋊D1311yescharacteristic
219C2×C8—522no—
220C2×C8—1042no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—81no—
226C4⋊C4—82no—
227C4⋊C4—1042no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C22⋊C4—522no—
232C22⋊C4—522no—
233C42—1042no—
234C13#920211yescharacteristic, complemented, Sylow
235C23—41no—
236C23—41no—
237C23#8818911yescharacteristic
238C23#8819111yescharacteristic
239C23#8819612yes—
240C23#8820412yes—
241C23C2×C22⋊Dic1311yescharacteristic
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—524no—
264C2×C4—524no—
265C2×C4—524no—
266C2×C4D4×Dic1312yes—
267C2×C4#8819312yes—
268C8—1042no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1171870612yes—
278C22#1171870812yes—
279C22#1171888111yescharacteristic
280C22#1171888611yescharacteristic
281C22#1171889411yescharacteristic
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—82no—
287C4—81no—
288C4—81no—
289C4—1044no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2—21no—
294C2#1311514911yescharacteristic
295C2#1311537411yescharacteristic
296C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2627C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2627D13
hypocenterC13#9202
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
8. C13×#400C4semidirect
10. C13×#395C4semidirect
129. #400Dic13semidirect
131. #395Dic13semidirect
234. C13#9202semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131134082
C2×#117181202
#131127032
C13×#26272
#920213