Finite Group Databasebeta

← #13118486

Subgroups — #13118486

Order 1664.

1088 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D13C211yesmaximal, characteristic
2C2×#88190C211yesmaximal, characteristic, complemented
3C2×#88151C211yesmaximal, characteristic, complemented
4C2×#88129C211yesmaximal, characteristic, complemented
5C13×#390C211yesmaximal, characteristic, complemented
6#11718649C211yesmaximal, characteristic, complemented
7#11718622C214yesmaximal, complemented
8#11718616C214yesmaximal, complemented
9C4×#6103C211yesmaximal, characteristic, complemented
10C24×D13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C2×D4×D13—24no—
14C2×D4×D13—24no—
15C2×D4×D13—24no—
16C22×D52C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic, complemented
19C2×C13×C4⋊C4C2211yescharacteristic, complemented
20C2×C13×C22⋊C4C2214yescomplemented
21C2×C42×C13C2211yescharacteristic, complemented
22C2×C22⋊Dic13C2214yescomplemented
23#88190—24no—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2214yescomplemented
27C2×#6103C2214yescomplemented
28C2×C4⋊Dic13C2212yescomplemented
29C2×C4×Dic13C2211yescharacteristic, complemented
30#88151—24no—
31#88129—24no—
32#88071C2212yescomplemented
33C24×C13C2312yes—
34C23×D13—24no—
35C23×D13—24no—
36C23×D13—24no—
37C23×D13—28no—
38C23×D13—44no—
39C23×D13C2312yes—
40C23×D13C2311yescharacteristic
41C2×D4×C13—22no—
42C2×D4×C13—22no—
43C2×D4×C13D414yes—
44C22×C4×C13C2312yes—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—24no—
48C2×C22⋊D13—24no—
49C2×C22⋊D13—24no—
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53D4×D13—232no—
54C2×D52—22no—
55C2×D52—22no—
56C2×D52D414yes—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13D414yes—
60C2×Dic26—22no—
61C2×Dic26—22no—
62C2×Dic26—22no—
63C13×C4⋊C4—22no—
64C13×C22⋊C4—44no—
65C42×C13—22no—
66C22⋊Dic13—28no—
67#6103—28no—
68#6103—24no—
69#6103—24no—
70#6103—44no—
71C4⋊Dic13—24no—
72C4×Dic13—22no—
73#2435—131nomaximal, Sylow
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—24no—
77C23×C13—24no—
78C23×C13C2×D414yes—
79C23×C13C2411yescharacteristic
80C22×D13—21no—
81C22×D13—21no—
82C22×D13—22no—
83C22×D13—216no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—24no—
87C22×D13—24no—
88C22×D13—416no—
89C22×D13—416no—
90C22×D13—48no—
91C22×D13—48no—
92C22×D13C2×D414yes—
93C22×D13C2×D412yes—
94C22×D13#4114yes—
95D4×C13—28no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—24no—
100C2×C4×C13—22no—
101C2×C4×C13C2×D412yes—
102C2×C4×C13C2×D412yes—
103C2×C4×C13C2×D412yes—
104C22⋊D13—216no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13C2×D412yes—
114D52—28no—
115C4×D13—28no—
116Dic26—44no—
117C23×D4—131no—
118C2×#124—131no—
119C2×#124—131no—
120C2×C22⋊Q8—131no—
121#394—134no—
122#390—131no—
123#390D1311yescharacteristic, complemented
124#379—134no—
125C4×C22⋊C4—131no—
126C22×C13—24no—
127C22×C13—28no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—44no—
131C22×C13C22×D411yescharacteristic
132C22×C13C22×D411yescharacteristic
133C22×C13C22×D411yescharacteristic
134C22×C13C2×#4112yes—
135C22×C13H(5,𝔽2)12yes—
136C2×D13—22no—
137C2×D13—22no—
138C2×D13—24no—
139C2×D13—24no—
140C2×D13—24no—
141C2×D13—28no—
142C2×D13—432no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—44no—
146C2×D13#12414yescomplemented
147C4×C13—42no—
148C4×C13—42no—
149C4×C13#12014yes—
150Dic13—22no—
151Dic13—42no—
152Dic13—42no—
153C25—132no—
154C22×Q8—131no—
155C22×D4—132no—
156C22×D4—131no—
157C22×D4—264no—
158C22×D4—264no—
159C22×D4—264no—
160C22×D4C2×D1311yescharacteristic
161C23×C4—131no—
162#124—264no—
163#124—264no—
164C22⋊Q8—264no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4C2×D1311yescharacteristic, complemented
167C2×C22⋊C4—134no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—134no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—134no—
172C2×C22⋊C4C2×D1314yescomplemented
173C2×C42—131no—
174C2×C42C2×D1311yescharacteristic, complemented
175#95—132no—
176C2×C13—44no—
177C2×C13C2×#12011yescharacteristic
178C2×C13C2×#12411yescharacteristic
179C2×C13#53511yescharacteristic
180C2×C13#54612yes—
181C2×C13#54612yes—
182D13—24no—
183D13—44no—
184C24—131no—
185C24—132no—
186C24—264no—
187C24—264no—
188C24—268no—
189C24—264no—
190C24—524no—
191C24C22×D1312yes—
192C2×Q8—262no—
193C2×Q8—262no—
194C2×Q8—262no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—134no—
198C2×D4—264no—
199C2×D4—2632no—
200C2×D4—264no—
201C2×D4—264no—
202C2×D4—262no—
203C2×D4—262no—
204C2×D4D5214yes—
205C22×C4—131no—
206C22×C4—134no—
207C22×C4—132no—
208C22×C4—132no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4C22×D1312yes—
212C22×C4C22×D1312yes—
213C22×C4C22×D1311yescharacteristic
214C4⋊C4—22no—
215C4⋊C4—264no—
216C22⋊C4—44no—
217C22⋊C4—264no—
218C22⋊C4—268no—
219C22⋊C4—264no—
220C22⋊C4—268no—
221C22⋊C4—524no—
222C42—22no—
223C42—262no—
224C13#243511yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—24no—
228C23—24no—
229C23—132no—
230C23—134no—
231C23—134no—
232C23—2616no—
233C23—261no—
234C23—261no—
235C23—262no—
236C23—262no—
237C23—262no—
238C23—264no—
239C23—264no—
240C23—5216no—
241C23—528no—
242C23—5216no—
243C23—528no—
244C23C2×D5214yes—
245C23C23×D1311yescharacteristic
246Q8—524no—
247D4—28no—
248D4—2616no—
249D4—268no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—132no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—268no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4C2×D5212yes—
266C2×C4D4×D1312yes—
267C2×C4D4×D1312yes—
268C22—24no—
269C22—28no—
270C22—44no—
271C22—42no—
272C22—42no—
273C22—134no—
274C22—262no—
275C22—264no—
276C22—264no—
277C22—262no—
278C22—264no—
279C22—268no—
280C22—5232no—
281C22—524no—
282C22—522no—
283C22—522no—
284C22C22×D5211yescharacteristic
285C22C2×D4×D1311yescharacteristic
286C22C2×D4×D1311yescharacteristic
287C22#8825112yes—
288C22#41×D1312yes—
289C4—42no—
290C4—42no—
291C4—262no—
292C4—522no—
293C4—522no—
294C4#8813614yes—
295C2—44no—
296C2—264no—
297C2—524no—
298C2C2×#8813611yescharacteristic
299C2#1171925912yes—
300C2#1171931712yes—
301C2D13×#12411yescharacteristic
302C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×D13C2
hypercenter#390D13
hypocenterC13#2435
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#88190C2semidirect
3. C2×#88151C2semidirect
4. C2×#88129C2semidirect
5. C13×#390C2semidirect
6. #11718649C2semidirect
7. #11718622C2semidirect
8. #11718616C2semidirect
9. C4×#6103C2semidirect
18. C22×Dic26C22semidirect
19. C2×C13×C4⋊C4C22semidirect
20. C2×C13×C22⋊C4C22semidirect
21. C2×C42×C13C22semidirect
22. C2×C22⋊Dic13C22semidirect
26. C2×#6103C22semidirect
27. C2×#6103C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C2×C4×Dic13C22semidirect
32. #88071C22semidirect
123. #390D13semidirect
146. C2×D13#124semidirect
166. C2×C4⋊C4C2×D13semidirect
172. C2×C22⋊C4C2×D13semidirect
174. C2×C42C2×D13semidirect
224. C13#2435semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D132
C2×#881902
C2×#881512
C2×#881292
C13×#3902
#117186492
#117186222
#117186162
C4×#61032
#243513