Finite Group Databasebeta

← #13120550

Subgroups — #13120550

Order 1664.

1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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×C22⋊D13C211yesmaximal, characteristic, complemented
2C2×C13×#120C211yesmaximal, characteristic, complemented
3C2×#88191C211yesmaximal, characteristic, complemented
4C2×#88189C211yesmaximal, characteristic, complemented
5#11718908C211yesmaximal, characteristic, complemented
6#11718884C214yesmaximal, complemented
7#11718620C214yesmaximal, complemented
8#11718616C211yesmaximal, characteristic, complemented
9#11718604C211yesmaximal, characteristic, complemented
10C25×C13C2211yescharacteristic
11C24×D13C2211yescharacteristic
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2212yescomplemented
14C22×C22⋊D13—24no—
15C22×C22⋊D13—24no—
16C22×C22⋊D13—24no—
17C22×C22⋊D13C2214yes—
18C22×C22⋊D13C2212yescomplemented
19C23×Dic13C2211yescharacteristic
20C13×#120—24no—
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2212yescomplemented
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2212yescomplemented
26C2×C22⋊Dic13C2214yescomplemented
27#88191—24no—
28#88189—24no—
29C2×#6103C2212yescomplemented
30C2×#6103C2214yescomplemented
31C2×#6101C2212yescomplemented
32#88071C2214yescomplemented
33C24×C13—22no—
34C24×C13—22no—
35C24×C13—44no—
36C24×C13D414yescomplemented
37C24×C13C2311yescharacteristic
38C24×C13C2312yes—
39C24×C13C2311yescharacteristic
40C23×D13—22no—
41C23×D13—22no—
42C23×D13—44no—
43C23×D13D414yescomplemented
44C23×D13C2312yes—
45C2×D4×C13—22no—
46C2×D4×C13—22no—
47C2×D4×C13—22no—
48C2×D4×C13—24no—
49C2×D4×C13—44no—
50C22×C4×C13C2312yes—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—232no—
53C2×C22⋊D13—28no—
54C2×C22⋊D13—28no—
55C2×C22⋊D13—24no—
56C2×C22⋊D13—28no—
57C2×C22⋊D13—44no—
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13D414yescomplemented
61C22×Dic13C2312yes—
62C22×Dic13C2312yes—
63C22×Dic13C2312yes—
64C13×C22⋊C4—22no—
65C13×C22⋊C4—24no—
66C22⋊Dic13—22no—
67C22⋊Dic13—22no—
68C22⋊Dic13—24no—
69C22⋊Dic13—44no—
70#6103—24no—
71#6103—44no—
72#6101—24no—
73#2613—131nomaximal, Sylow
74C23×C13—24no—
75C23×C13—28no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—24no—
79C23×C13—24no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—24no—
84C23×C13—48no—
85C23×C13—48no—
86C23×C13—48no—
87C23×C13C2×D414yes—
88C23×C13C2×D412yes—
89C23×C13C2×D412yes—
90C23×C13C2×D412yes—
91C23×C13C2411yescharacteristic
92C22×D13—28no—
93C22×D13—22no—
94C22×D13—22no—
95C22×D13—24no—
96C22×D13—24no—
97C22×D13—48no—
98C22×D13—48no—
99C22×D13—48no—
100C22×D13C2×D414yes—
101D4×C13—48no—
102D4×C13—44no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—24no—
108C22⋊D13—232no—
109C22⋊D13—48no—
110C2×Dic13—28no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—24no—
116C2×Dic13—24no—
117C2×Dic13C2×D414yes—
118C23×D4—131no—
119C2×#123—131no—
120C2×#120—131no—
121C2×#120D1311yescharacteristic, complemented
122#394—134no—
123#392—134no—
124#381—131no—
125#379—131no—
126#379—131no—
127C22×C13—24no—
128C22×C13—24no—
129C22×C13—24no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13—24no—
133C22×C13—416no—
134C22×C13—44no—
135C22×C13—44no—
136C22×C13—41no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13#12014yes—
141C22×C13C22×D411yescharacteristic
142C22×C13C22×D411yescharacteristic
143C22×C13C22×D411yescharacteristic
144C22×C13H(5,𝔽2)14yes—
145C2×D13—24no—
146C2×D13—24no—
147C2×D13—24no—
148C2×D13—416no—
149C2×D13—44no—
150C2×D13—44no—
151C4×C13—41no—
152C4×C13—42no—
153Dic13—24no—
154Dic13—42no—
155Dic13—42no—
156C25—131no—
157C25C2×D1311yescharacteristic
158C22×D4—134no—
159C22×D4—132no—
160C22×D4—264no—
161C22×D4—264no—
162C22×D4—264no—
163C22×D4C2×D1311yescharacteristic
164C22×D4C2×D1312yescomplemented
165C23×C4—131no—
166#123—264no—
167#120—24no—
168#120—264no—
169C2×C4⋊C4—132no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—134no—
175C2×C22⋊C4—134no—
176C2×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C4C2×D1312yescomplemented
178#95—134no—
179C2×C13—24no—
180C2×C13—44no—
181C2×C13—81no—
182C2×C13C2×#12011yescharacteristic
183C2×C13#53412yes—
184C2×C13#53412yes—
185C2×C13#53512yes—
186D13—44no—
187C24—22no—
188C24—22no—
189C24—44no—
190C24—132no—
191C24—134no—
192C24—262no—
193C24—262no—
194C24—524no—
195C24C22⋊D1314yescomplemented
196C24C22×D1311yescharacteristic
197C24C22×D1312yes—
198C24C22×D1311yescharacteristic
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—24no—
203C2×D4—44no—
204C2×D4—268no—
205C2×D4—268no—
206C2×D4—2632no—
207C2×D4—268no—
208C2×D4—264no—
209C2×D4—524no—
210C22×C4—134no—
211C22×C4—132no—
212C22×C4—132no—
213C22×C4—132no—
214C22×C4—262no—
215C22×C4—262no—
216C22×C4C22×D1312yes—
217C22×C4C22×D1311yescharacteristic
218C4⋊C4—264no—
219C22⋊C4—22no—
220C22⋊C4—24no—
221C22⋊C4—264no—
222C22⋊C4—264no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—524no—
226C22⋊C4—524no—
227C13#261311yescharacteristic, complemented, Sylow
228C23—24no—
229C23—28no—
230C23—22no—
231C23—22no—
232C23—24no—
233C23—24no—
234C23—21no—
235C23—21no—
236C23—24no—
237C23—21no—
238C23—48no—
239C23—48no—
240C23—48no—
241C23—134no—
242C23—268no—
243C23—262no—
244C23—264no—
245C23—264no—
246C23—262no—
247C23—528no—
248C23—528no—
249C23—528no—
250C23D4×D1312yes—
251C23D4×D1312yes—
252C23C2×C22⋊D1314yes—
253C23C2×C22⋊D1312yes—
254C23C23×D1311yescharacteristic
255D4—48no—
256D4—44no—
257D4—2632no—
258D4—528no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—134no—
265C2×C4—268no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—264no—
271C2×C4—264no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—416no—
279C22—44no—
280C22—44no—
281C22—41no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—264no—
286C22—264no—
287C22—264no—
288C22—5216no—
289C22—524no—
290C22—524no—
291C22#8819114yes—
292C22C2×D4×D1311yescharacteristic
293C22C2×D4×D1311yescharacteristic
294C22#8825114yes—
295C22C22×C22⋊D1311yescharacteristic
296C4—41no—
297C4—42no—
298C4—264no—
299C4—522no—
300C4—522no—
301C2—24no—
302C2—44no—
303C2—81no—
304C2—524no—
305C2#1171929412yes—
306C2#1171929712yes—
307C2C2×#8819111yescharacteristic
308C2#1171950912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#120C2
hypercenterC2×#120D13
hypocenterC13#2613
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D13C2semidirect
2. C2×C13×#120C2semidirect
3. C2×#88191C2semidirect
4. C2×#88189C2semidirect
5. #11718908C2semidirect
6. #11718884C2semidirect
7. #11718620C2semidirect
8. #11718616C2semidirect
9. #11718604C2semidirect
13. C22×D4×C13C22semidirect
18. C22×C22⋊D13C22semidirect
22. C2×C13×C22⋊C4C22semidirect
25. C2×C22⋊Dic13C22semidirect
26. C2×C22⋊Dic13C22semidirect
29. C2×#6103C22semidirect
30. C2×#6103C22semidirect
31. C2×#6101C22semidirect
32. #88071C22semidirect
36. C24×C13D4semidirect
43. C23×D13D4semidirect
60. C22×Dic13D4semidirect
121. C2×#120D13semidirect
164. C22×D4C2×D13semidirect
177. C2×C22⋊C4C2×D13semidirect
195. C24C22⋊D13semidirect
227. C13#2613semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D132
C2×C13×#1202
C2×#881912
C2×#881892
#117189082
#117188842
#117186202
#117186162
#117186042
#261313