Finite Group Databasebeta

← #13118193

Subgroups — #13118193

Order 1664.

1232 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C23×D52C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×#88149C212yesmaximal, complemented
4C2×#88136C212yesmaximal, complemented
5C13×#380C211yesmaximal, characteristic, complemented
6#11718649C212yesmaximal, complemented
7#11718616C212yesmaximal, complemented
8#11718333C212yesmaximal, complemented
9#11718332C212yesmaximal, complemented
10C24×D13C2212yes—
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13C2211yescharacteristic
13C22×D52—24no—
14C22×D52—28no—
15C22×D52C2212yes—
16C22×D52C2212yes—
17C22×D52C2214yescomplemented
18C22×C4×D13C2211yescharacteristic, complemented
19C2×C13×C4⋊C4C2212yescomplemented
20C2×C13×C22⋊C4C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22C4×C22⋊D13—24no—
23C2×#6103C2214yescomplemented
24C2×#6103C2214yescomplemented
25C2×#6103C2211yescharacteristic, complemented
26C2×#6103C2214yescomplemented
27C2×#6101C2211yescharacteristic, complemented
28C2×C4×Dic13C2211yescharacteristic, complemented
29#88149—28no—
30#88136—28no—
31C13×#95C2212yescomplemented
32C24×C13C2311yescharacteristic
33C23×D13—24no—
34C23×D13—28no—
35C23×D13—24no—
36C23×D13—24no—
37C23×D13—44no—
38C23×D13C2314yes—
39C23×D13C2311yescharacteristic
40C22×C4×C13—24no—
41C22×C4×C13D414yescomplemented
42C22×C4×C13C2314yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13D414yescomplemented
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C2×D52—232no—
52C2×D52—28no—
53C2×D52—24no—
54C2×D52—24no—
55C2×D52—24no—
56C2×D52—28no—
57C2×D52—28no—
58C2×D52—44no—
59C2×D52D418yescomplemented
60C2×C4×D13—24no—
61C2×C4×D13—22no—
62C13×C4⋊C4—24no—
63C13×C22⋊C4—24no—
64C22⋊Dic13—22no—
65#6103—28no—
66#6103—22no—
67#6103—28no—
68#6103—44no—
69#6101—22no—
70C4×Dic13—22no—
71#2408—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2×D412yes—
76C23×C13#4112yes—
77C23×C13C2411yescharacteristic
78C22×D13—216no—
79C22×D13—21no—
80C22×D13—24no—
81C22×D13—22no—
82C22×D13—24no—
83C22×D13—24no—
84C22×D13—21no—
85C22×D13—24no—
86C22×D13—24no—
87C22×D13—22no—
88C22×D13—24no—
89C22×D13—416no—
90C22×D13—416no—
91C22×D13—48no—
92C22×D13—48no—
93C22×D13C2×D418yes—
94C22×D13C2×D412yescomplemented
95C2×C4×C13—22no—
96C2×C4×C13—28no—
97C2×C4×C13—24no—
98C2×C4×C13—24no—
99C2×C4×C13—24no—
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2×D412yes—
102C2×C4×C13C2×D414yes—
103C22⋊D13—28no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13C2×D412yescomplemented
111D52—216no—
112D52—216no—
113D52—416no—
114C4×D13—44no—
115C23×D4—131no—
116C2×#121—132no—
117C2×#120—132no—
118C2×C4×D4—131no—
119#394—132no—
120#392—132no—
121#390—132no—
122#380D1311yescharacteristic, complemented
123#379—132no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—24no—
127C22×C13—24no—
128C22×C13#12114yescomplemented
129C22×C13C22×D411yescharacteristic
130C22×C13C22×D412yes—
131C22×C13C22×D411yescharacteristic
132C22×C13C2×#4111yescharacteristic
133C22×C13H(5,𝔽2)12yes—
134C2×D13—28no—
135C2×D13—22no—
136C2×D13—24no—
137C2×D13—28no—
138C2×D13—28no—
139C2×D13—432no—
140C2×D13—41no—
141C2×D13—44no—
142C2×D13—41no—
143C2×D13—44no—
144C2×D13—44no—
145C2×D13—42no—
146C2×D13—44no—
147C4×C13—22no—
148C4×C13—44no—
149C4×C13#12014yescomplemented
150Dic13—22no—
151Dic13—41no—
152Dic13—41no—
153C25—132no—
154C22×D4—131no—
155C22×D4—132no—
156C22×D4—132no—
157C22×D4—134no—
158C22×D4—268no—
159C22×D4—264no—
160C23×C4—131no—
161C23×C4C2×D1311yescharacteristic
162#121—268no—
163#120—268no—
164C4×D4—264no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4C2×D1312yescomplemented
167C2×C22⋊C4—131no—
168C2×C22⋊C4—131no—
169C2×C22⋊C4—134no—
170C2×C22⋊C4—134no—
171C2×C22⋊C4—134no—
172C2×C22⋊C4C2×D1312yes—
173C2×C42—131no—
174#95C2×D1312yescomplemented
175C2×C13—24no—
176C2×C13C2×#12011yescharacteristic
177C2×C13C2×#12111yescharacteristic
178C2×C13#53511yescharacteristic
179C2×C13D4212yes—
180C2×C13#54612yes—
181D13—42no—
182D13—48no—
183C24—134no—
184C24—131no—
185C24—268no—
186C24—264no—
187C24—264no—
188C24—264no—
189C24—524no—
190C24C22×D1311yescharacteristic
191C2×D4—134no—
192C2×D4—138no—
193C2×D4—268no—
194C2×D4—2632no—
195C2×D4—268no—
196C2×D4—268no—
197C2×D4—262no—
198C2×D4—262no—
199C2×D4—264no—
200C2×D4—264no—
201C2×D4—264no—
202C2×D4—524no—
203C22×C4—24no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—262no—
208C22×C4—264no—
209C22×C4D5214yescomplemented
210C22×C4C22×D1314yes—
211C22×C4C22×D1311yescharacteristic
212C22×C4C22×D1311yescharacteristic
213C4⋊C4—24no—
214C4⋊C4—262no—
215C22⋊C4—24no—
216C22⋊C4—268no—
217C22⋊C4—268no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C22⋊C4—524no—
221C42—262no—
222C13#240811yescharacteristic, complemented, Sylow
223C23—22no—
224C23—22no—
225C23—138no—
226C23—132no—
227C23—2616no—
228C23—261no—
229C23—264no—
230C23—264no—
231C23—262no—
232C23—264no—
233C23—261no—
234C23—264no—
235C23—264no—
236C23—262no—
237C23—264no—
238C23—5216no—
239C23—5216no—
240C23—528no—
241C23—528no—
242C23C2×D5212yes—
243C23D4×D1312yes—
244C23#613112yes—
245C23C23×D1311yescharacteristic
246D4—2616no—
247D4—268no—
248D4—2616no—
249D4—5216no—
250C2×C4—22no—
251C2×C4—28no—
252C2×C4—24no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—132no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—524no—
263C2×C4C2×D5212yes—
264C2×C4C2×D5212yes—
265C2×C4D4×D1314yes—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—268no—
271C22—262no—
272C22—264no—
273C22—268no—
274C22—268no—
275C22—5232no—
276C22—521no—
277C22—524no—
278C22—521no—
279C22—524no—
280C22—524no—
281C22—522no—
282C22—524no—
283C22#8814914yescomplemented
284C22C22×D5211yescharacteristic
285C22C2×D4×D1312yes—
286C22C2×D4×D1311yescharacteristic
287C22C2×#613111yescharacteristic
288C22#8825612yes—
289C4—22no—
290C4—44no—
291C4—262no—
292C4—521no—
293C4—521no—
294C4#8813614yescomplemented
295C2—24no—
296C2—528no—
297C2—522no—
298C2C2×#8813611yescharacteristic
299C2C2×#8814911yescharacteristic
300C2#1171923011yescharacteristic
301C2#1171931412yes—
302C2#1171933512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
hypercenter#380D13
hypocenterC13#2408
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C23×D52C2semidirect
2. C2×C4×C22⋊D13C2semidirect
3. C2×#88149C2semidirect
4. C2×#88136C2semidirect
5. C13×#380C2semidirect
6. #11718649C2semidirect
7. #11718616C2semidirect
8. #11718333C2semidirect
9. #11718332C2semidirect
17. C22×D52C22semidirect
18. C22×C4×D13C22semidirect
19. C2×C13×C4⋊C4C22semidirect
23. C2×#6103C22semidirect
24. C2×#6103C22semidirect
25. C2×#6103C22semidirect
26. C2×#6103C22semidirect
27. C2×#6101C22semidirect
28. C2×C4×Dic13C22semidirect
31. C13×#95C22semidirect
41. C22×C4×C13D4semidirect
47. C2×C22⋊D13D4semidirect
59. C2×D52D4semidirect
94. C22×D13C2×D4semidirect
110. C2×Dic13C2×D4semidirect
122. #380D13semidirect
128. C22×C13#121semidirect
149. C4×C13#120semidirect
166. C2×C4⋊C4C2×D13semidirect
174. #95C2×D13semidirect
209. C22×C4D52semidirect
222. C13#2408semidirect
283. C22#88149semidirect
294. C4#88136semidirect

Maximal subgroups

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

subgroupindex
C23×D522
C2×C4×C22⋊D132
C2×#881492
C2×#881362
C13×#3802
#117186492
#117186162
#117183332
#117183322
#240813