Finite Group Databasebeta

← #13126661

Subgroups — #13126661

Order 1664.

462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D52C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3C8×D4×C13C211yesmaximal, characteristic, complemented
4#11718775C212yesmaximal, complemented
5C2×#88061C212yesmaximal, complemented
6#11718509C211yesmaximal, characteristic, complemented
7#11718503C211yesmaximal, characteristic, complemented
8#11718396C212yesmaximal, complemented
9#11718392C212yesmaximal, complemented
10#11718355C211yesmaximal, characteristic, complemented
11C4×#6095C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C22×D52C2212yes—
14C22×C8×C13C2212yescomplemented
15C4×D4×C13C2211yescharacteristic
16D4×Dic13—21no—
17#88184C2212yes—
18C2×C4⋊Dic13C2212yescomplemented
19#88178C2212yescomplemented
20C2×#6095C2211yescharacteristic
21C2×#6095C2212yescomplemented
22#88149—21no—
23#88144—21no—
24#88136—22no—
25#88132—22no—
26#88128C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic, complemented
29C4×Dic26C2211yescharacteristic, complemented
30C13×C4⋊C8C2211yescharacteristic, complemented
31C13×C22⋊C8C2212yescomplemented
32C4×C8×C13C2211yescharacteristic, complemented
33#88061C2212yes—
34#88061C2211yescharacteristic
35#88061C2212yescomplemented
36#88061C2212yescomplemented
37#88061C2212yescomplemented
38#88057C2212yescomplemented
39#88057C2211yescharacteristic, complemented
40#88056C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×D4×C13D411yescharacteristic
43C22×C4×C13C2312yes—
44C2×C22⋊D13—22no—
45C22×Dic13—22no—
46D4×D13—44no—
47C2×D52—24no—
48C2×D52—21no—
49C2×D52—22no—
50C2×D52—21no—
51C2×D52—42no—
52C2×D52C2312yes—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×Dic26—21no—
56C2×Dic26C2311yescharacteristic
57C2×C8×C13—42no—
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2312yes—
61C13×C4⋊C4D411yescharacteristic
62C13×C22⋊C4D412yes—
63C42×C13C2311yescharacteristic
64C22⋊Dic13—22no—
65#6103—21no—
66#6103—22no—
67C4⋊Dic13—21no—
68C4⋊Dic13—22no—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2312yes—
71C4⋊Dic13C2311yescharacteristic
72#6101—21no—
73#6101—22no—
74C4×Dic13—21no—
75#6095—22no—
76#6095—42no—
77#3295—131nomaximal, Sylow
78C23×C13C2×D412yes—
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—44no—
82C22×D13—44no—
83C22×D13—82no—
84D4×C13SD1614yescomplemented
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—44no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—82no—
97D52—22no—
98D52—21no—
99D52—22no—
100D52—44no—
101D52—42no—
102D52—81no—
103D52#4112yes—
104C4×D13—42no—
105Dic26—21no—
106Dic26—21no—
107Dic26—81no—
108C8×C13—21no—
109C8×C13—22no—
110C8×C13—21no—
111#554—131no—
112D42—131no—
113#486—131no—
114#481—132no—
115#476—131no—
116#465—132no—
117#460—131no—
118#450—132no—
119C4×SD16—131no—
120C8×D4D1311yescharacteristic, complemented
121C2×#102—132no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13C2×SD1614yes—
125C22×C13C22×D411yescharacteristic
126C2×D13—22no—
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—42no—
132C2×D13—88no—
133C4×C13—22no—
134C4×C13—21no—
135C4×C13C2×SD1612yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—41no—
139Dic13—41no—
140Dic13—42no—
141Dic13—41no—
142C22×D4—132no—
143C22×D4—261no—
144C2×SD16—131no—
145C2×SD16—132no—
146C22×C8C2×D1312yescomplemented
147C4⋊Q8—131no—
148#127—131no—
149#125—261no—
150C22⋊Q8—132no—
151C22⋊Q8—262no—
152#121—132no—
153#121—261no—
154#120—262no—
155C4×Q8—131no—
156C4×D4—131no—
157C4×D4—261no—
158C4×D4C2×D1311yescharacteristic
159C2×C4⋊C4—132no—
160#106—131no—
161#106—132no—
162C4⋊C8C2×D1311yescharacteristic, complemented
163#103—131no—
164#102—131no—
165#102—132no—
166#102—132no—
167#102—132no—
168#102—132no—
169C22⋊C8C2×D1312yescomplemented
170C4×C8C2×D1311yescharacteristic, complemented
171C2×C13—24no—
172C2×C13#54611yescharacteristic
173C2×C13C22×SD1611yescharacteristic
174C2×C13#57611yescharacteristic
175D13—42no—
176D13—82no—
177C24—262no—
178C2×Q8—131no—
179C2×Q8—261no—
180C2×D4—131no—
181C2×D4—132no—
182C2×D4—264no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—261no—
186C2×D4—261no—
187C2×D4—522no—
188C2×D4—524no—
189C2×D4D5211yescharacteristic
190C22×C4—262no—
191C22×C4—261no—
192C22×C4C22×D1312yes—
193SD16—262no—
194SD16—522no—
195C2×C8—42no—
196C2×C8C22×D1311yescharacteristic
197C2×C8C22×D1311yescharacteristic
198C2×C8C22×D1312yes—
199C4⋊C4—131no—
200C4⋊C4—132no—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—262no—
206C4⋊C4D5211yescharacteristic
207C22⋊C4—262no—
208C22⋊C4—261no—
209C22⋊C4—262no—
210C22⋊C4D5212yes—
211C42—261no—
212C42C22×D1311yescharacteristic
213C13#329511yescharacteristic, complemented, Sylow
214C23—261no—
215C23—262no—
216C23—524no—
217C23—524no—
218C23—1042no—
219C23C2×D5212yes—
220Q8—261no—
221Q8—261no—
222Q8—1041no—
223D4—132no—
224D4—261no—
225D4—262no—
226D4—262no—
227D4—524no—
228D4—524no—
229D4—522no—
230D4—1041no—
231D4#609514yescomplemented
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4—522no—
239C2×C4—1042no—
240C2×C4C2×D5211yescharacteristic
241C2×C4C2×D5212yes—
242C2×C4C2×D5211yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—21no—
245C8—22no—
246C8—21no—
247C22—22no—
248C22—22no—
249C22—262no—
250C22—521no—
251C22—521no—
252C22—522no—
253C22—522no—
254C22—522no—
255C22—1048no—
256C22C2×#609514yes—
257C22C22×D5211yescharacteristic
258C4—21no—
259C4—22no—
260C4—521no—
261C4—521no—
262C4—522no—
263C4—521no—
264C4C2×#609512yes—
265C4#8825111yescharacteristic
266C4#41×D1311yescharacteristic
267C2—24no—
268C2—522no—
269C2—1042no—
270C2#1171925911yescharacteristic
271C2C22×#609511yescharacteristic
272C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC8×D4×C13C2
socleC22×C13C22×D4
prime radicalD4×D52C2
hypercenterC8×D4D13
hypocenterC13#3295
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. C8×D4×C13C2semidirect
4. #11718775C2semidirect
5. C2×#88061C2semidirect
6. #11718509C2semidirect
7. #11718503C2semidirect
8. #11718396C2semidirect
9. #11718392C2semidirect
10. #11718355C2semidirect
11. C4×#6095C2semidirect
14. C22×C8×C13C22semidirect
18. C2×C4⋊Dic13C22semidirect
19. #88178C22semidirect
21. C2×#6095C22semidirect
28. #88123C22semidirect
29. C4×Dic26C22semidirect
30. C13×C4⋊C8C22semidirect
31. C13×C22⋊C8C22semidirect
32. C4×C8×C13C22semidirect
35. #88061C22semidirect
36. #88061C22semidirect
37. #88061C22semidirect
38. #88057C22semidirect
39. #88057C22semidirect
40. #88056C22semidirect
84. D4×C13SD16semidirect
120. C8×D4D13semidirect
146. C22×C8C2×D13semidirect
162. C4⋊C8C2×D13semidirect
169. C22⋊C8C2×D13semidirect
170. C4×C8C2×D13semidirect
213. C13#3295semidirect
231. D4#6095semidirect

Maximal subgroups

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

subgroupindex
D4×D522
#117192482
C8×D4×C132
#117187752
C2×#880612
#117185092
#117185032
#117183962
#117183922
#117183552
C4×#60952
#329513