Finite Group Databasebeta

← #13120647

Subgroups — #13120647

Order 1664.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#6103C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic, complemented
3C13×#385C211yesmaximal, characteristic, complemented
4#11718871C211yesmaximal, characteristic, complemented
5#11718655C212yesmaximal, complemented
6#11718653C212yesmaximal, complemented
7#11718616C211yesmaximal, characteristic
8#11718616C211yesmaximal, characteristic
9#11718603C211yesmaximal, characteristic, complemented
10#11718337C212yesmaximal, complemented
11#11718334C212yesmaximal, complemented
12C24×D13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic, complemented
16C2×C13×C4⋊C4C2212yescomplemented
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C22⋊Dic13C2211yescharacteristic
20C2×C22⋊Dic13C2211yescharacteristic
21C2×#6103—24no—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6103C2212yes—
28C2×C4⋊Dic13C2211yescharacteristic, complemented
29C2×#6101C2211yescharacteristic, complemented
30C2×#6101C2211yescharacteristic, complemented
31C2×#6101C2212yescomplemented
32C2×#6101C2212yescomplemented
33#88132—24no—
34C13×#95C2212yescomplemented
35#88071C2212yescomplemented
36#88071C2212yescomplemented
37C24×C13C2311yescharacteristic
38C23×D13—22no—
39C23×D13—22no—
40C23×D13—42no—
41C23×D13—42no—
42C23×D13Q814yescomplemented
43C23×D13C2312yes—
44C22×C4×C13—22no—
45C22×C4×C13—42no—
46C22×C4×C13C2312yes—
47C22×C4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—42no—
51C22×Dic13D414yes—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2311yescharacteristic
57C2×Dic26—22no—
58C2×Dic26—42no—
59C13×C4⋊C4—42no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C22⋊Dic13—22no—
63C22⋊Dic13—22no—
64#6103—24no—
65#6103—24no—
66#6103—42no—
67#6103—42no—
68#6103—42no—
69#6103—42no—
70C4⋊Dic13—22no—
71#6101—22no—
72#6101—22no—
73#6101—42no—
74#6101—42no—
75#2626—131nomaximal, Sylow
76C23×C13—22no—
77C23×C13—22no—
78C23×C13C2×D412yes—
79C23×C13C2×Q812yes—
80C23×C13#4112yes—
81C23×C13C2411yescharacteristic
82C22×D13—28no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—48no—
90C22×D13—44no—
91C22×D13—44no—
92C22×D13—48no—
93C22×D13C2×Q814yes—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
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×C13—44no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—44no—
115C2×Dic13C2×D412yes—
116C2×Dic13C2×D412yes—
117Dic26—44no—
118C2×C22⋊Q8—131no—
119C22×C22⋊C4—131no—
120#399—132no—
121#396—132no—
122#396—132no—
123#393—132no—
124#385—131no—
125#385D1311yescharacteristic, complemented
126#380—131no—
127#379—131no—
128#379—131no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—24no—
132C22×C13—24no—
133C22×C13C22⋊Q814yes—
134C22×C13C22×D411yescharacteristic
135C22×C13C22×Q811yescharacteristic
136C22×C13C2×#4111yescharacteristic
137C22×C13H(5,𝔽2)12yes—
138C22×C13H(5,𝔽2)12yes—
139C2×D13—24no—
140C2×D13—24no—
141C2×D13—24no—
142C2×D13—416no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—42no—
147C4×C13—41no—
148C4×C13—41no—
149C4×C13—42no—
150C4×C13—42no—
151Dic13—22no—
152Dic13—22no—
153Dic13—41no—
154Dic13—41no—
155Dic13—42no—
156C25—131no—
157C22×Q8—131no—
158C23×C4—131no—
159C23×C4C2×D1311yescharacteristic
160C22⋊Q8—264no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4C2×D1312yescomplemented
167C2×C22⋊C4—131no—
168C2×C22⋊C4—131no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—264no—
176C2×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C4C2×D1311yescharacteristic
178#95—132no—
179#95—132no—
180#95C2×D1312yescomplemented
181C2×C13—24no—
182C2×C13C2×C22⋊Q811yescharacteristic
183C2×C13#53411yescharacteristic
184C2×C13#53511yescharacteristic
185C2×C13#53812yes—
186C2×C13#54312yes—
187D13—44no—
188C24—132no—
189C24—134no—
190C24—262no—
191C24—262no—
192C24—522no—
193C24—522no—
194C24C22×D1311yescharacteristic
195C2×Q8—262no—
196C2×Q8—522no—
197C22×C4—22no—
198C22×C4—42no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—134no—
202C22×C4—132no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—522no—
206C22×C4C22×D1312yes—
207C22×C4C22×D1312yes—
208C22×C4C22×D1311yescharacteristic
209C22×C4C22×D1311yescharacteristic
210C4⋊C4—42no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—262no—
214C4⋊C4—522no—
215C4⋊C4—522no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—264no—
219C22⋊C4—264no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C22⋊C4—522no—
223C22⋊C4—522no—
224C22⋊C4—522no—
225C22⋊C4—522no—
226C13#262611yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—134no—
230C23—268no—
231C23—262no—
232C23—262no—
233C23—262no—
234C23—262no—
235C23—262no—
236C23—262no—
237C23—528no—
238C23—528no—
239C23—524no—
240C23—524no—
241C23#612712yes—
242C23D4×D1312yes—
243C23Q8×D1312yes—
244C23C23×D1311yescharacteristic
245Q8—524no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—44no—
257C2×C4—132no—
258C2×C4—132no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—524no—
269C22—24no—
270C22—22no—
271C22—24no—
272C22—22no—
273C22—264no—
274C22—264no—
275C22—264no—
276C22—5216no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—522no—
281C22#8815014yes—
282C22C2×#612711yescharacteristic
283C22C2×D4×D1311yescharacteristic
284C22#8825112yes—
285C22C2×Q8×D1311yescharacteristic
286C22#8825612yes—
287C4—42no—
288C4—41no—
289C4—42no—
290C4—41no—
291C4—262no—
292C4—262no—
293C4—522no—
294C4—521no—
295C4—521no—
296C2—24no—
297C2—524no—
298C2C2×#8815011yescharacteristic
299C2#1171926512yes—
300C2#1171929711yescharacteristic
301C2#1171933912yes—
302C2#1171935811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC24×D13C22
hypercenter#385D13
hypocenterC13#2626
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#88132C2semidirect
3. C13×#385C2semidirect
4. #11718871C2semidirect
5. #11718655C2semidirect
6. #11718653C2semidirect
9. #11718603C2semidirect
10. #11718337C2semidirect
11. #11718334C2semidirect
15. C22×Dic26C22semidirect
16. C2×C13×C4⋊C4C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C2×#6101C22semidirect
30. C2×#6101C22semidirect
31. C2×#6101C22semidirect
32. C2×#6101C22semidirect
34. C13×#95C22semidirect
35. #88071C22semidirect
36. #88071C22semidirect
42. C23×D13Q8semidirect
125. #385D13semidirect
166. C2×C4⋊C4C2×D13semidirect
180. #95C2×D13semidirect
226. C13#2626semidirect

Maximal subgroups

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

subgroupindex
C22×#61032
C2×#881322
C13×#3852
#117188712
#117186552
#117186532
#117186162
#117186032
#117183372
#117183342
#262613