Finite Group Databasebeta

← #15773108

Subgroups — #15773108

Order 3328.

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

normal subgroups only

This group has 468 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#13114569C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112836C214yesmaximal
4C13×#2621C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×C22⋊Q8—21no—
7C2×C13×#117C2211yescharacteristic
8C2×#88180—21no—
9C13×#398—21no—
10C13×#398C412yescomplemented
11C13×#397—21no—
12C13×#397C2212yes—
13C13×#391—21no—
14C13×#382C411yescharacteristic, complemented
15#11718586—21no—
16#11718120—21no—
17#11718118—21no—
18#11718118C2212yes—
19#11718117C2212yes—
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⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2311yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C22⋊Dic13—22no—
40#88180—24no—
41#88180—42no—
42C2×C4⋊Dic13—41no—
43C2×C4×Dic13—41no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95C2×C412yes—
48C22⋊#1055—22no—
49C4⋊#1055—41no—
50C4×#1055—41no—
51#11694—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
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×C13C22⋊C411yescharacteristic
66C22×C4×C13D812yes—
67C22×C4×C13SD1612yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—44no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—42no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C22⋊Dic13—24no—
86C22⋊Dic13—42no—
87C4⋊Dic13—44no—
88C4×Dic13—44no—
89C2×#1055—42no—
90#2621D1311yescharacteristic
91#1740—131no—
92#1458—131no—
93#1344—134no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13C2×D811yescharacteristic
100C23×C13C2×SD1611yescharacteristic
101Q8×C13—82no—
102Q8×C13—82no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#10212yes—
126C2×C4×C13#10212yes—
127C2×C4×C13#10412yes—
128C2×Dic13—44no—
129C2×Dic13—82no—
130C2×Dic13—82no—
131#1055—82no—
132C2×C4⋊Q8Dic1311yescharacteristic, complemented
133C2×C22⋊Q8—21no—
134C2×#117—261no—
135C2×#117C2×D1311yescharacteristic
136#431—261no—
137#398—21no—
138#398Dic1312yescomplemented
139#397—21no—
140#397C2×D1312yes—
141#391—21no—
142#382Dic1311yescharacteristic, complemented
143#342—132no—
144#342—261no—
145#324—261no—
146#323—132no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10211yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—82no—
165C4×C13—82no—
166C4×C13#32712yes—
167C4×C13#32712yes—
168Dic13—84no—
169C22×Q8—21no—
170C23×C4C22⋊D1311yescharacteristic
171C4⋊Q8—41no—
172C4⋊Q8—41no—
173C22⋊Q8—42no—
174C22⋊Q8—42no—
175#117—41no—
176#117—41no—
177#117—264no—
178#117—522no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—521no—
183C2×C4⋊C4C2×Dic1312yes—
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4C22⋊D1311yescharacteristic
189C2×C22⋊C4C22×D1311yescharacteristic
190C2×C42—521no—
191C2×C42C2×Dic1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C4⋊C8—521no—
194C22⋊C8—262no—
195C4×C8—521no—
196#95—21no—
197#95—22no—
198#95—22no—
199#95C2×Dic1312yes—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—41no—
203C2×C13—41no—
204C2×C13C2×#32711yescharacteristic
205C2×C13#212311yescharacteristic
206C2×C13#212911yescharacteristic
207C24C2×C22⋊D1311yescharacteristic
208C2×Q8—42no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—42no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—522no—
218C22×C4#610412yes—
219C22×C4#610512yes—
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22×Dic1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C2×C8—522no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—524no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—264no—
239C22⋊C4—522no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—524no—
245C13#1169411yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×#610411yescharacteristic
251C23C2×#610511yescharacteristic
252C23C2×C22⋊Dic1311yescharacteristic
253Q8—82no—
254Q8—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—524no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4#8807212yes—
279C2×C4#8807212yes—
280C2×C4#8807411yescharacteristic
281C2×C4#8807411yescharacteristic
282C2×C4#8807712yes—
283C8—1042no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#8807211yescharacteristic
294C22C2×#8807411yescharacteristic
295C22C2×#8807711yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—82no—
302C4—82no—
303C4—1044no—
304C4#1171812912yes—
305C4#1171812912yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#1171812911yescharacteristic
311C2#1311649011yescharacteristic
312C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2621C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2621D13
hypocenterC13#11694
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
5. C2×C13×C4⋊Q8C4semidirect
10. C13×#398C4semidirect
14. C13×#382C4semidirect
132. C2×C4⋊Q8Dic13semidirect
138. #398Dic13semidirect
142. #382Dic13semidirect
245. C13#11694semidirect

Maximal subgroups

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

subgroupindex
#131145692
#131131502
#131128362
C13×#26212
#1169413