Finite Group Databasebeta

← #13118484

Subgroups — #13118484

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×C13×#124C211yesmaximal, characteristic, complemented
3C2×#88201C211yesmaximal, characteristic, complemented
4C2×#88200C211yesmaximal, characteristic, complemented
5#11718882C211yesmaximal, characteristic, complemented
6#11718620C214yesmaximal, complemented
7#11718616C214yesmaximal, complemented
8#11718600C211yesmaximal, characteristic, complemented
9C4×#6103C211yesmaximal, characteristic, complemented
10C24×D13C2212yes—
11C22×Q8×C13C2211yescharacteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C2×D4×D13—24no—
15C2×D4×D13—24no—
16C2×D4×D13—24no—
17C22×D52C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C13×#124—24no—
20C2×C13×C22⋊C4C2214yescomplemented
21C2×C42×C13C2211yescharacteristic, complemented
22C2×C22⋊Dic13C2214yescomplemented
23#88201—24no—
24#88200—24no—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6103C2214yescomplemented
28C2×#6103C2214yescomplemented
29C2×C4⋊Dic13C2211yescharacteristic, complemented
30C2×#6101C2212yescomplemented
31C2×C4×Dic13C2211yescharacteristic, complemented
32#88071C2212yescomplemented
33C24×C13C2312yes—
34C23×D13—24no—
35C23×D13—24no—
36C23×D13—24no—
37C23×D13—28no—
38C23×D13—44no—
39C23×D13C2312yes—
40C23×D13C2311yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13D414yes—
47C22×C4×C13C2312yes—
48C22×C4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—24no—
51C2×C22⋊D13—24no—
52C2×C22⋊D13—24no—
53C22×Dic13C2312yes—
54C22×Dic13C2312yes—
55C22×Dic13C2311yescharacteristic
56D4×D13—232no—
57C2×D52—22no—
58C2×D52—22no—
59C2×D52D414yes—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13D414yes—
63C13×C22⋊C4—28no—
64C42×C13—22no—
65C22⋊Dic13—44no—
66#6103—24no—
67#6103—28no—
68#6103—24no—
69#6103—44no—
70C4⋊Dic13—22no—
71#6101—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—
95Q8×C13—44no—
96D4×C13—28no—
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×C13C2×D412yes—
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C22⋊D13—216no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—24no—
113C2×Dic13—22no—
114C2×Dic13C2×D412yes—
115D52—28no—
116C4×D13—28no—
117C23×D4—131no—
118C2×#124—131no—
119C2×#124D1311yescharacteristic, complemented
120C2×C22⋊Q8—131no—
121#394—134no—
122#390—131no—
123#390—131no—
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×Q8C2×D1311yescharacteristic, complemented
155C22×D4—132no—
156C22×D4—131no—
157C22×D4—264no—
158C22×D4—264no—
159C22×D4—264no—
160C22×D4C2×D1311yescharacteristic
161C23×C4—131no—
162#124—24no—
163#124—264no—
164C22⋊Q8—264no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—131no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—134no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—134no—
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—22no—
193C2×Q8—22no—
194C2×Q8—22no—
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×D4C22⋊D1314yes—
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—264no—
215C4⋊C4—262no—
216C22⋊C4—28no—
217C22⋊C4—264no—
218C22⋊C4—268no—
219C22⋊C4—264no—
220C22⋊C4—524no—
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—262no—
235C23—261no—
236C23—262no—
237C23—264no—
238C23—264no—
239C23—262no—
240C23—5216no—
241C23—528no—
242C23—5216no—
243C23—528no—
244C23C2×C22⋊D1314yes—
245C23C23×D1311yescharacteristic
246Q8—44no—
247D4—28no—
248D4—2616no—
249D4—268no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—132no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—268no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—264no—
264C2×C4—262no—
265C2×C4D4×D1312yes—
266C2×C4D4×D1312yes—
267C2×C4C2×C22⋊D1312yes—
268C22—24no—
269C22—28no—
270C22—42no—
271C22—42no—
272C22—44no—
273C22—134no—
274C22—262no—
275C22—264no—
276C22—262no—
277C22—264no—
278C22—264no—
279C22—268no—
280C22—5232no—
281C22—524no—
282C22—522no—
283C22—522no—
284C22C2×D4×D1311yescharacteristic
285C22C2×D4×D1311yescharacteristic
286C22#41×D1312yes—
287C22#8825612yes—
288C22C22×C22⋊D1311yescharacteristic
289C4—42no—
290C4—42no—
291C4—262no—
292C4—522no—
293C4—522no—
294C4#8819114yes—
295C2—44no—
296C2—264no—
297C2—524no—
298C2D13×#12411yescharacteristic
299C2#1171937911yescharacteristic
300C2#1171938112yes—
301C2C2×#8819111yescharacteristic
302C2#1171953412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
prime radicalC22×D4×D13C2
hypercenterC2×#124D13
hypocenterC13#2435
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×C13×#124C2semidirect
3. C2×#88201C2semidirect
4. C2×#88200C2semidirect
5. #11718882C2semidirect
6. #11718620C2semidirect
7. #11718616C2semidirect
8. #11718600C2semidirect
9. C4×#6103C2semidirect
11. C22×Q8×C13C22semidirect
20. C2×C13×C22⋊C4C22semidirect
21. C2×C42×C13C22semidirect
22. C2×C22⋊Dic13C22semidirect
27. C2×#6103C22semidirect
28. C2×#6103C22semidirect
29. C2×C4⋊Dic13C22semidirect
30. C2×#6101C22semidirect
31. C2×C4×Dic13C22semidirect
32. #88071C22semidirect
119. C2×#124D13semidirect
146. C2×D13#124semidirect
154. C22×Q8C2×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×C13×#1242
C2×#882012
C2×#882002
#117188822
#117186202
#117186162
#117186002
C4×#61032
#243513