Finite Group Databasebeta

← #15773208

Subgroups — #15773208

Order 3328.

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

normal subgroups only

This group has 448 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#13112857C214yesmaximal
4C13×#2628C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C2×#88180—21no—
8C13×#400—21no—
9C13×#399—21no—
10C13×#395C412yescomplemented
11C13×#393C2212yes—
12C13×#389—21no—
13C13×#382C411yescharacteristic, complemented
14C13×#380—21no—
15#11718586—21no—
16#11718120—21no—
17#11718118—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×Q8×C13C2×C412yes—
21C23×C4×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×#117—41no—
25C13×#117—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2311yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13—22no—
38#88180—24no—
39#88180—42no—
40C2×C4⋊Dic13—41no—
41C2×C4×Dic13—41no—
42C13×#95—22no—
43C13×#95—21no—
44C13×#95—22no—
45C13×#95C2×C412yes—
46C22⋊#1055—22no—
47C4⋊#1055—41no—
48C4×#1055—41no—
49#11717—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13SD1612yes—
63C22×C4×C13Q1612yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—82no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—82no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C22⋊Dic13—24no—
82C22⋊Dic13—42no—
83C4⋊Dic13—44no—
84C4×Dic13—44no—
85C2×#1055—42no—
86#2628D1311yescharacteristic
87#1740—131no—
88#1458—131no—
89#1351—134no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13C2×SD1611yescharacteristic
96C23×C13C2×Q1611yescharacteristic
97Q8×C13—84no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#10312yes—
121C2×C4×C13#10312yes—
122C2×C4×C13#10412yes—
123C2×Dic13—44no—
124C2×Dic13—82no—
125C2×Dic13—82no—
126#1055—82no—
127C2×C4⋊Q8Dic1311yescharacteristic, complemented
128C2×#117—261no—
129C2×#117C2×D1311yescharacteristic
130#431—261no—
131#400—21no—
132#399—21no—
133#395Dic1312yescomplemented
134#393C2×D1312yes—
135#389—21no—
136#382Dic1311yescharacteristic, complemented
137#380—21no—
138#342—132no—
139#342—261no—
140#324—261no—
141#323—132no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—81no—
151C22×C13C2×#9911yescharacteristic
152C22×C13C2×#10311yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C4×C13—22no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—82no—
160C4×C13—82no—
161C4×C13#32812yes—
162C4×C13#32812yes—
163Dic13—84no—
164C22×Q8C2×Dic1312yes—
165C23×C4C22⋊D1311yescharacteristic
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168#117—41no—
169#117—41no—
170#117—264no—
171#117—522no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—521no—
177C2×C4⋊C4C2×Dic1311yescharacteristic
178C2×C4⋊C4C22⋊D1311yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4C22⋊D1311yescharacteristic
182C2×C22⋊C4C22×D1311yescharacteristic
183C2×C42—521no—
184C2×C42C2×Dic1311yescharacteristic
185C2×C42C22⋊D1311yescharacteristic
186C4⋊C8—521no—
187C22⋊C8—262no—
188C4×C8—521no—
189#95—22no—
190#95—21no—
191#95—22no—
192#95C2×Dic1312yes—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—41no—
196C2×C13—41no—
197C2×C13C2×#32811yescharacteristic
198C2×C13#212211yescharacteristic
199C2×C13#212911yescharacteristic
200C24C2×C22⋊D1311yescharacteristic
201C2×Q8—42no—
202C2×Q8—82no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—522no—
209C22×C4#610612yes—
210C22×C4#610712yes—
211C22×C4C22⋊Dic1311yescharacteristic
212C22×C4C22⋊Dic1311yescharacteristic
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22⋊Dic1311yescharacteristic
215C22×C4C22×Dic1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C2×C8—522no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C4⋊C4—524no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—264no—
230C22⋊C4—522no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—524no—
236C13#1171711yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23C2×#610611yescharacteristic
242C23C2×#610711yescharacteristic
243C23C2×C22⋊Dic1311yescharacteristic
244Q8—84no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—524no—
266C2×C4—1042no—
267C2×C4—1042no—
268C2×C4#8807411yescharacteristic
269C2×C4#8807411yescharacteristic
270C2×C4#8807512yes—
271C2×C4#8807512yes—
272C2×C4#8807712yes—
273C8—1042no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22C2×#8807411yescharacteristic
284C22C2×#8807511yescharacteristic
285C22C2×#8807711yescharacteristic
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4—1044no—
294C4#1171813012yes—
295C4#1171813012yes—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2C2×#1171813011yescharacteristic
301C2#1311648611yescharacteristic
302C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2628C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2628D13
hypocenterC13#11717
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
10. C13×#395C4semidirect
13. C13×#382C4semidirect
127. C2×C4⋊Q8Dic13semidirect
133. #395Dic13semidirect
136. #382Dic13semidirect
236. C13#11717semidirect

Maximal subgroups

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

subgroupindex
#131145692
#131131502
#131128572
C13×#26282
#1171713