Finite Group Databasebeta

← #15773134

Subgroups — #15773134

Order 3328.

452 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114575C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112842C214yesmaximal, complemented
4C13×#2621C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C22⋊Q8—21no—
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#398—21no—
10C13×#398C2212yes—
11C13×#397—21no—
12C13×#397C412yes—
13C13×#391—21no—
14C13×#382C411yescharacteristic
15#11718586—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×Q8×C13—21no—
21C23×C4×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×C22⋊Q8—42no—
25C13×C22⋊Q8—42no—
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×#6099—24no—
40C2×#6099—22no—
41C2×#6099—41no—
42C2×#6099—42no—
43C22×#1055—41no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95C2×C412yes—
48C22⋊#1055—22no—
49C4⋊#1055—41no—
50C4×#1055—41no—
51#11700—131nomaximal, Sylow
52C24×C13C22⋊C411yescharacteristic
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—42no—
56C2×Q8×C13—42no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13D812yes—
66C22×C4×C13SD1612yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—44no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84#6099—24no—
85#6099—44no—
86#6099—42no—
87C2×#1055—42no—
88C2×#1055—44no—
89C2×#1055—42no—
90#2621D1311yescharacteristic
91#1742—131no—
92#1458—131no—
93#1346—134no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13#10212yes—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—82no—
101Q8×C13—82no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#10212yes—
125C2×C4×C13#10412yes—
126C2×C4×C13C2×D811yescharacteristic
127C2×C4×C13C2×SD1611yescharacteristic
128#1055—44no—
129#1055—82no—
130C22×M16—261no—
131C2×C4⋊Q8Dic1311yescharacteristic
132C2×C22⋊Q8—21no—
133C2×#117C2×D1311yescharacteristic
134#431—261no—
135#398—21no—
136#398C2×D1312yes—
137#397—21no—
138#397Dic1312yes—
139#391—21no—
140#382Dic1311yescharacteristic
141#343—132no—
142#343—261no—
143#324—132no—
144#323—261no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
148C22×C13—42no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—81no—
152C22×C13C2×#9911yescharacteristic
153C22×C13C2×#10211yescharacteristic
154C22×C13C2×#10411yescharacteristic
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—82no—
162C4×C13—82no—
163C4×C13#32712yes—
164C4×C13#32712yes—
165C22×Q8—21no—
166C23×C4C22⋊D1311yescharacteristic
167C2×M16—264no—
168C2×M16—262no—
169C2×M16—521no—
170C2×M16—522no—
171C22×C8—521no—
172C4⋊Q8—41no—
173C4⋊Q8—41no—
174C22⋊Q8—42no—
175C22⋊Q8—42no—
176#117—41no—
177#117—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×Dic1312yes—
182C2×C4⋊C4C22⋊D1311yescharacteristic
183C2×C4⋊C4C22×D1311yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4C2×Dic1311yescharacteristic
186C2×C22⋊C4C22⋊D1311yescharacteristic
187C2×C42C2×Dic1311yescharacteristic
188C2×C42C22⋊D1311yescharacteristic
189C4⋊C8—521no—
190C22⋊C8—262no—
191C4×C8—521no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95C2×Dic1312yes—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—42no—
199C2×C13C2×#32711yescharacteristic
200C2×C13#212311yescharacteristic
201C2×C13#213511yescharacteristic
202C24C22⋊Dic1311yescharacteristic
203C2×Q8—42no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—42no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4#610412yes—
213C22×C4#610512yes—
214C22×C4C22⋊Dic1311yescharacteristic
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22×Dic1311yescharacteristic
218C22×C4C2×C22⋊D1311yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220M16—264no—
221M16—524no—
222M16—522no—
223C2×C8—522no—
224C2×C8—524no—
225C2×C8—522no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—44no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C13#1170011yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23#8807212yes—
246C23C2×C22⋊Dic1311yescharacteristic
247Q8—82no—
248Q8—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4#8807212yes—
270C2×C4#8807411yescharacteristic
271C2×C4#8807411yescharacteristic
272C2×C4#8807712yes—
273C2×C4C2×#610411yescharacteristic
274C2×C4C2×#610511yescharacteristic
275C8—524no—
276C8—1042no—
277C22—21no—
278C22—21no—
279C22—22no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—81no—
284C22C2×#8807211yescharacteristic
285C22C2×#8807411yescharacteristic
286C22C2×#8807711yescharacteristic
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4#1171812912yes—
296C4#1171812912yes—
297C2—21no—
298C2—21no—
299C2—42no—
300C2C2×#1171812911yescharacteristic
301C2#1311649011yescharacteristic
302C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2621C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2621D13
hypocenterC13#11700
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
3. #13112842C2semidirect
240. C13#11700semidirect

Maximal subgroups

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

subgroupindex
#131145752
#131131502
#131128422
C13×#26212
#1170013