Finite Group Databasebeta

← #13118186

Subgroups — #13118186

Order 1664.

1232 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 205 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×D4×C13C211yesmaximal, characteristic, complemented
2C2×#88207C212yesmaximal, complemented
3C2×#88192C212yesmaximal, complemented
4C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
5#11718908C212yesmaximal, complemented
6#11718884C212yesmaximal, complemented
7#11718883C212yesmaximal, complemented
8#11718882C212yesmaximal, complemented
9#11718873C211yesmaximal, characteristic, complemented
10C25×C13C2212yes—
11C22×D4×C13—28no—
12C22×D4×C13—24no—
13C22×D4×C13C2212yes—
14C22×D4×C13C2212yes—
15C23×C4×C13C2211yescharacteristic
16C22×C22⋊D13C2211yescharacteristic
17C22×C22⋊D13C2214yescomplemented
18C22×C4×D13C2211yescharacteristic, complemented
19#88207—28no—
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2214yescomplemented
23C2×C22⋊Dic13C2214yescomplemented
24C2×C22⋊Dic13C2214yescomplemented
25#88192—28no—
26C4×C22⋊D13—24no—
27C2×#6103C2211yescharacteristic, complemented
28C2×C4⋊Dic13C2212yescomplemented
29C2×#6101C2211yescharacteristic, complemented
30C2×C4×Dic13C2211yescharacteristic, complemented
31#88071C2212yescomplemented
32C24×C13—28no—
33C24×C13—24no—
34C24×C13—24no—
35C24×C13—24no—
36C24×C13—44no—
37C24×C13C2314yes—
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C2×D4×C13—232no—
41C2×D4×C13—28no—
42C2×D4×C13—24no—
43C2×D4×C13—24no—
44C2×D4×C13—24no—
45C2×D4×C13D418yescomplemented
46C22×C4×C13—24no—
47C22×C4×C13D414yescomplemented
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—28no—
53C2×C22⋊D13—28no—
54C2×C22⋊D13—44no—
55C2×C22⋊D13D414yescomplemented
56C22×Dic13C2314yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C2×C4×D13—22no—
61C2×C4×D13—24no—
62C22⋊Dic13—22no—
63C22⋊Dic13—28no—
64C22⋊Dic13—24no—
65C22⋊Dic13—28no—
66C22⋊Dic13—44no—
67#6103—22no—
68C4⋊Dic13—24no—
69#6101—22no—
70C4×Dic13—22no—
71#2408—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—216no—
75C23×C13—24no—
76C23×C13—24no—
77C23×C13—24no—
78C23×C13—24no—
79C23×C13—24no—
80C23×C13—24no—
81C23×C13—416no—
82C23×C13—416no—
83C23×C13—48no—
84C23×C13—48no—
85C23×C13C2×D418yes—
86C23×C13C2×D412yes—
87C23×C13C2×D412yes—
88C23×C13#4112yes—
89C23×C13C2411yescharacteristic
90C22×D13—21no—
91C22×D13—22no—
92C22×D13—21no—
93C22×D13—22no—
94C22×D13C2×D412yescomplemented
95D4×C13—216no—
96D4×C13—216no—
97C2×C4×C13—22no—
98C2×C4×C13—28no—
99C2×C4×C13C2×D412yes—
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2×D414yes—
102C22⋊D13—28no—
103C22⋊D13—416no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—24no—
109C2×Dic13—22no—
110C2×Dic13—24no—
111C2×Dic13—22no—
112C2×Dic13—24no—
113C2×Dic13C2×D412yescomplemented
114C4×D13—44no—
115C23×D4D1311yescharacteristic, complemented
116C2×#121—132no—
117C2×#120—132no—
118C2×C4×D4—131no—
119#394—132no—
120#392—132no—
121#390—132no—
122#380—131no—
123#379—132no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—24no—
127C22×C13—24no—
128C22×C13—28no—
129C22×C13—28no—
130C22×C13—28no—
131C22×C13—432no—
132C22×C13—44no—
133C22×C13—44no—
134C22×C13—44no—
135C22×C13—44no—
136C22×C13#12114yescomplemented
137C22×C13C22×D411yescharacteristic
138C22×C13C22×D411yescharacteristic
139C22×C13C22×D412yes—
140C22×C13C2×#4111yescharacteristic
141C22×C13H(5,𝔽2)12yes—
142C2×D13—22no—
143C2×D13—24no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—42no—
147C4×C13—22no—
148C4×C13#12014yescomplemented
149Dic13—22no—
150Dic13—41no—
151Dic13—41no—
152Dic13—44no—
153C25C2×D1312yes—
154C22×D4—28no—
155C22×D4—24no—
156C22×D4—131no—
157C22×D4—134no—
158C22×D4C2×D1312yes—
159C22×D4C2×D1312yes—
160C23×C4—131no—
161C23×C4C2×D1311yescharacteristic
162#121—268no—
163#120—268no—
164C4×D4—264no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—132no—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—134no—
170C2×C22⋊C4—134no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—134no—
173C2×C42—131no—
174#95—132no—
175C2×C13—24no—
176C2×C13—48no—
177C2×C13C2×#12011yescharacteristic
178C2×C13C2×#12111yescharacteristic
179C2×C13#53511yescharacteristic
180C2×C13D4212yes—
181C2×C13#54612yes—
182D13—42no—
183C24—28no—
184C24—24no—
185C24—24no—
186C24—24no—
187C24—44no—
188C24—131no—
189C24C22×D1314yes—
190C24C22×D1311yescharacteristic
191C2×D4—232no—
192C2×D4—28no—
193C2×D4—24no—
194C2×D4—24no—
195C2×D4—24no—
196C2×D4—134no—
197C2×D4—262no—
198C2×D4—262no—
199C2×D4—268no—
200C2×D4—268no—
201C2×D4—524no—
202C2×D4C22⋊D1318yescomplemented
203C22×C4—24no—
204C22×C4—131no—
205C22×C4—134no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—262no—
209C22×C4—264no—
210C22×C4C22⋊D1314yescomplemented
211C22×C4C22×D1311yescharacteristic
212C22×C4C22×D1311yescharacteristic
213C4⋊C4—262no—
214C4⋊C4—264no—
215C22⋊C4—268no—
216C22⋊C4—264no—
217C22⋊C4—262no—
218C22⋊C4—268no—
219C22⋊C4—262no—
220C22⋊C4—524no—
221C42—262no—
222C13#240811yescharacteristic, complemented, Sylow
223C23—22no—
224C23—22no—
225C23—216no—
226C23—24no—
227C23—24no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—24no—
232C23—416no—
233C23—416no—
234C23—48no—
235C23—48no—
236C23—132no—
237C23—261no—
238C23—262no—
239C23—261no—
240C23—262no—
241C23D4×D1312yes—
242C23#612912yes—
243C23C2×C22⋊D1318yes—
244C23C2×C22⋊D1312yes—
245C23C23×D1311yescharacteristic
246D4—216no—
247D4—216no—
248D4—268no—
249D4—5216no—
250C2×C4—22no—
251C2×C4—28no—
252C2×C4—132no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—264no—
256C2×C4—262no—
257C2×C4—264no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—261no—
261C2×C4—264no—
262C2×C4—524no—
263C2×C4C2×C22⋊D1312yes—
264C2×C4C2×C22⋊D1312yes—
265C2×C4C2×C22⋊D1314yes—
266C22—24no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—28no—
271C22—28no—
272C22—28no—
273C22—432no—
274C22—44no—
275C22—44no—
276C22—44no—
277C22—44no—
278C22—262no—
279C22—264no—
280C22—521no—
281C22—522no—
282C22—521no—
283C22#8819214yescomplemented
284C22C2×D4×D1311yescharacteristic
285C22C2×#612911yescharacteristic
286C22#8825112yes—
287C22C22×C22⋊D1311yescharacteristic
288C22C22×C22⋊D1312yes—
289C4—22no—
290C4—262no—
291C4—524no—
292C4—521no—
293C4—521no—
294C4#8820714yescomplemented
295C2—24no—
296C2—48no—
297C2—522no—
298C2C2×#8819211yescharacteristic
299C2D4×C22⋊D1312yes—
300C2#1171951011yescharacteristic
301C2#1171951112yes—
302C2C2×#8820711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC23×D4×C13C2
hypercenterC23×D4D13
hypocenterC13#2408
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D4×C13C2semidirect
2. C2×#88207C2semidirect
3. C2×#88192C2semidirect
4. C2×C4×C22⋊D13C2semidirect
5. #11718908C2semidirect
6. #11718884C2semidirect
7. #11718883C2semidirect
8. #11718882C2semidirect
9. #11718873C2semidirect
17. C22×C22⋊D13C22semidirect
18. C22×C4×D13C22semidirect
22. C2×C22⋊Dic13C22semidirect
23. C2×C22⋊Dic13C22semidirect
24. C2×C22⋊Dic13C22semidirect
27. C2×#6103C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C2×#6101C22semidirect
30. C2×C4×Dic13C22semidirect
31. #88071C22semidirect
45. C2×D4×C13D4semidirect
47. C22×C4×C13D4semidirect
55. C2×C22⋊D13D4semidirect
94. C22×D13C2×D4semidirect
113. C2×Dic13C2×D4semidirect
115. C23×D4D13semidirect
136. C22×C13#121semidirect
148. C4×C13#120semidirect
202. C2×D4C22⋊D13semidirect
210. C22×C4C22⋊D13semidirect
222. C13#2408semidirect
283. C22#88192semidirect
294. C4#88207semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C132
C2×#882072
C2×#881922
C2×C4×C22⋊D132
#117189082
#117188842
#117188832
#117188822
#117188732
#240813