Finite Group Databasebeta

← #13119990

Subgroups — #13119990

Order 1664.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#88200C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718616C212yesmaximal
6#11718614C211yesmaximal, characteristic, complemented
7#11718605C212yesmaximal, complemented
8#11718335C211yesmaximal, characteristic, complemented
9#11718330C212yesmaximal, complemented
10#11718327C211yesmaximal, characteristic, complemented
11#11718325C212yesmaximal, complemented
12C24×D13C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic, complemented
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20#88200—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×C4⋊Dic13C2211yescharacteristic, complemented
28C2×#6101C2212yescomplemented
29C2×C4×Dic13C2212yescomplemented
30C22⋊C4×D13—24no—
31C13×#95C2212yescomplemented
32C13×#95C2211yescharacteristic, complemented
33#88071C2212yescomplemented
34#88071C2212yescomplemented
35#88071C2212yescomplemented
36#88071C2211yescharacteristic, complemented
37C24×C13C2311yescharacteristic
38C23×D13—22no—
39C23×D13—22no—
40C23×D13—22no—
41C23×D13—24no—
42C23×D13—42no—
43C23×D13C2311yescharacteristic
44C23×D13C2311yescharacteristic
45C2×Q8×C13—22no—
46C2×Q8×C13—42no—
47C22×C4×C13C2311yescharacteristic
48C22×C4×C13C2312yes—
49C22×C4×C13C2312yes—
50C22×C4×C13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—24no—
57C2×C4×D13—42no—
58C2×C4×D13D414yes—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—42no—
61C22⋊Dic13—24no—
62C22⋊Dic13—22no—
63#6103—24no—
64#6103—24no—
65#6103—24no—
66#6103—22no—
67#6103—22no—
68#6103—42no—
69C4⋊Dic13—22no—
70#6101—24no—
71C4×Dic13—42no—
72#2561—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13#4112yes—
78C23×C13C2411yescharacteristic
79C22×D13—21no—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13—28no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—48no—
88C22×D13—48no—
89C22×D13—44no—
90C22×D13—44no—
91C22×D13C2×D412yes—
92C22×D13#4112yes—
93C22×D13#4114yes—
94Q8×C13—44no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13C2×D412yes—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13C2×D412yes—
115C4×D13—44no—
116C4×D13—44no—
117C2×C22⋊Q8—131no—
118C22×C22⋊C4—131no—
119#397—131no—
120#397—131no—
121#393—131no—
122#393D1311yescharacteristic, complemented
123#388—132no—
124#388—132no—
125#381—132no—
126#379—132no—
127C4×C22⋊C4—131no—
128C22×C13—22no—
129C22×C13—24no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—42no—
133C22×C13C22×D411yescharacteristic
134C22×C13C2×#4111yescharacteristic
135C22×C13C2×#4111yescharacteristic
136C22×C13C2×#4112yes—
137C22×C13H(5,𝔽2)12yes—
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—24no—
141C2×D13—24no—
142C2×D13—22no—
143C2×D13—24no—
144C2×D13—416no—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—42no—
148C2×D13#12414yes—
149C4×C13—22no—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13—42no—
153Dic13—22no—
154Dic13—42no—
155Dic13—41no—
156Dic13—42no—
157C25—131no—
158C22×Q8C2×D1311yescharacteristic, complemented
159C23×C4—131no—
160C23×C4—131no—
161C22⋊Q8—264no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—131no—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—131no—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—264no—
173C2×C22⋊C4C2×D1311yescharacteristic
174C2×C22⋊C4C2×D1312yes—
175C2×C42—132no—
176#95—131no—
177#95—132no—
178#95—132no—
179#95—132no—
180#95C2×D1311yescharacteristic, complemented
181#95C2×D1312yescomplemented
182C2×C13—42no—
183C2×C13#52511yescharacteristic
184C2×C13C2×#12411yescharacteristic
185C2×C13#53411yescharacteristic
186C2×C13#55112yes—
187C2×C13#55112yes—
188D13—24no—
189D13—42no—
190C24—131no—
191C24—131no—
192C24—262no—
193C24—262no—
194C24—264no—
195C24—262no—
196C24—522no—
197C24C22×D1311yescharacteristic
198C2×Q8—22no—
199C2×Q8—42no—
200C22×C4—131no—
201C22×C4—134no—
202C22×C4—131no—
203C22×C4—132no—
204C22×C4—132no—
205C22×C4—262no—
206C22×C4—264no—
207C22×C4—522no—
208C22×C4C22×D1311yescharacteristic
209C22×C4C22×D1312yes—
210C22×C4C22×D1312yes—
211C22×C4C22×D1311yescharacteristic
212C4⋊C4—264no—
213C4⋊C4—262no—
214C22⋊C4—22no—
215C22⋊C4—42no—
216C22⋊C4—262no—
217C22⋊C4—264no—
218C22⋊C4—264no—
219C22⋊C4—264no—
220C22⋊C4—262no—
221C22⋊C4—264no—
222C22⋊C4—262no—
223C22⋊C4—522no—
224C42—522no—
225C13#256111yescharacteristic, complemented, Sylow
226C23—21no—
227C23—22no—
228C23—21no—
229C23—22no—
230C23—132no—
231C23—134no—
232C23—132no—
233C23—268no—
234C23—262no—
235C23—261no—
236C23—261no—
237C23—261no—
238C23—262no—
239C23—261no—
240C23—262no—
241C23—528no—
242C23—524no—
243C23—528no—
244C23—524no—
245C23#613112yes—
246C23C23×D1311yescharacteristic
247Q8—44no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—132no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—524no—
268C2×C4—524no—
269C2×C4D4×D1312yes—
270C22—22no—
271C22—24no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—134no—
276C22—262no—
277C22—262no—
278C22—264no—
279C22—264no—
280C22—262no—
281C22—264no—
282C22—5216no—
283C22—521no—
284C22—522no—
285C22—521no—
286C22C2×D4×D1311yescharacteristic
287C22#8825112yes—
288C22C2×#613111yescharacteristic
289C22#41×D1311yescharacteristic
290C22#41×D1312yes—
291C4—22no—
292C4—42no—
293C4—41no—
294C4—42no—
295C4—262no—
296C4—522no—
297C4—522no—
298C4—521no—
299C2—42no—
300C2—264no—
301C2—522no—
302C2#1171929411yescharacteristic
303C2#1171933211yescharacteristic
304C2#1171934212yes—
305C2D13×#12411yescharacteristic
306C2#1171938412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×D13C22
hypercenter#393D13
hypocenterC13#2561
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
6. #11718614C2semidirect
7. #11718605C2semidirect
8. #11718335C2semidirect
9. #11718330C2semidirect
10. #11718327C2semidirect
11. #11718325C2semidirect
13. C22×Q8×C13C22semidirect
27. C2×C4⋊Dic13C22semidirect
28. C2×#6101C22semidirect
29. C2×C4×Dic13C22semidirect
31. C13×#95C22semidirect
32. C13×#95C22semidirect
33. #88071C22semidirect
34. #88071C22semidirect
35. #88071C22semidirect
36. #88071C22semidirect
122. #393D13semidirect
158. C22×Q8C2×D13semidirect
180. #95C2×D13semidirect
181. #95C2×D13semidirect
225. C13#2561semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×C22⋊C4×D132
C13×#3932
#117188922
#117186162
#117186142
#117186052
#117183352
#117183302
#117183272
#117183252
#256113