Finite Group Databasebeta

← #13126660

Subgroups — #13126660

Order 1664.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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
1D42×C13C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3#11718879C212yesmaximal, complemented
4C2×#88072C212yesmaximal, complemented
5#11718736C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718702C212yesmaximal, complemented
8#11718695C212yesmaximal, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10D4×#1055C211yesmaximal, characteristic, complemented
11#11718669C211yesmaximal, characteristic, complemented
12C22×D4×C13—21no—
13C22×D4×C13C2212yes—
14C13×#127C2211yescharacteristic
15C13×#121—21no—
16C13×#121C2212yes—
17C13×#120—22no—
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20D4×Dic13—21no—
21C2×#6105C2211yescharacteristic
22C2×#6105C2212yescomplemented
23C2×C4⋊Dic13C2212yescomplemented
24#88178C2212yescomplemented
25C22×#1055C2212yescomplemented
26#88144—21no—
27#88132—22no—
28#88123C2211yescharacteristic, complemented
29C4×Dic26C2211yescharacteristic, complemented
30#88072C2212yes—
31#88072C2211yescharacteristic
32#88072C2212yescomplemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2212yescomplemented
36#88050C2211yescharacteristic, complemented
37#88048C2212yescomplemented
38#88048C2211yescharacteristic, complemented
39C4⋊#1055C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C24×C13—22no—
42C2×D4×C13—24no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13—44no—
49C2×D4×C13D411yescharacteristic
50C2×D4×C13C2312yes—
51C2×D4×C13C2311yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13C2312yes—
54C22×Dic13—22no—
55C2×Dic26—21no—
56C2×Dic26C2311yescharacteristic
57C13×C4⋊C4D411yescharacteristic
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4D412yes—
62C42×C13C2311yescharacteristic
63C22⋊Dic13—22no—
64#6105—22no—
65#6105—42no—
66C4⋊Dic13—21no—
67C4⋊Dic13—22no—
68C4⋊Dic13C2311yescharacteristic
69C4⋊Dic13C2312yes—
70#6101—21no—
71#6101—22no—
72C4×Dic13—21no—
73C2×#1055—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3295—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13—22no—
80C23×C13—44no—
81C23×C13—44no—
82C23×C13—82no—
83C23×C13C2×D412yes—
84D4×C13—22no—
85D4×C13—21no—
86D4×C13—22no—
87D4×C13—44no—
88D4×C13—44no—
89D4×C13—42no—
90D4×C13—81no—
91D4×C13SD1614yescomplemented
92D4×C13#4112yes—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—82no—
105Dic26—21no—
106Dic26—21no—
107Dic26—81no—
108#1055—21no—
109#1055—21no—
110#1055—22no—
111#554—131no—
112D42D1311yescharacteristic
113#486—131no—
114#481—132no—
115#476—131no—
116#465—132no—
117#460—131no—
118#450—132no—
119C4×SD16—131no—
120C8×D4—131no—
121C2×#102—132no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—88no—
131C22×C13C2×SD1614yes—
132C22×C13C22×D411yescharacteristic
133C4×C13—22no—
134C4×C13—21no—
135C4×C13—41no—
136C4×C13C2×SD1612yes—
137C4×C13C2×#4111yescharacteristic
138C4×C13H(5,𝔽2)11yescharacteristic
139Dic13—41no—
140Dic13—42no—
141Dic13—41no—
142C22×D4—21no—
143C22×D4C2×D1312yes—
144C2×SD16—131no—
145C2×SD16—132no—
146C22×C8—132no—
147C4⋊Q8—131no—
148#127C2×D1311yescharacteristic
149#125—261no—
150C22⋊Q8—132no—
151C22⋊Q8—262no—
152#121—21no—
153#121C2×D1312yes—
154#120—22no—
155C4×Q8—131no—
156C4×D4—261no—
157C4×D4C2×D1311yescharacteristic
158C4×D4C2×D1311yescharacteristic
159C2×C4⋊C4—132no—
160#106—131no—
161#106—132no—
162C4⋊C8—131no—
163#103—131no—
164#102—131no—
165#102—132no—
166#102—132no—
167#102—132no—
168#102—132no—
169C22⋊C8—132no—
170C4×C8—131no—
171C2×C13—24no—
172C2×C13—42no—
173C2×C13—82no—
174C2×C13#54611yescharacteristic
175C2×C13C22×SD1611yescharacteristic
176C2×C13#57611yescharacteristic
177C24—22no—
178C2×Q8—131no—
179C2×Q8—261no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—42no—
186C2×D4—44no—
187C2×D4C22⋊D1311yescharacteristic
188C2×D4C22×D1312yes—
189C2×D4C22×D1311yescharacteristic
190C22×C4—21no—
191C22×C4—262no—
192C22×C4C22×D1312yes—
193SD16—262no—
194SD16—522no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—132no—
198C2×C8—522no—
199C4⋊C4—131no—
200C4⋊C4—132no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—262no—
205C4⋊C4C22⋊D1311yescharacteristic
206C4⋊C4C22×D1311yescharacteristic
207C22⋊C4—21no—
208C22⋊C4—22no—
209C22⋊C4—262no—
210C22⋊C4C22⋊D1312yes—
211C42—261no—
212C42C22×D1311yescharacteristic
213C13#329511yescharacteristic, complemented, Sylow
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D1312yes—
220Q8—261no—
221Q8—261no—
222Q8—1041no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#610514yescomplemented
231D4#612912yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—1042no—
240C2×C4C2×C22⋊D1311yescharacteristic
241C2×C4C2×C22⋊D1312yes—
242C2×C4C2×C22⋊D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—261no—
245C8—261no—
246C8—262no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#610514yes—
257C22C22×C22⋊D1311yescharacteristic
258C4—22no—
259C4—21no—
260C4—41no—
261C4—521no—
262C4—521no—
263C4—522no—
264C4C2×#610512yes—
265C4C2×#612911yescharacteristic
266C4#8825111yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2C22×#610511yescharacteristic
271C2#1171951111yescharacteristic
272C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3295
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. #11718879C2semidirect
4. C2×#88072C2semidirect
5. #11718736C2semidirect
6. #11718731C2semidirect
7. #11718702C2semidirect
8. #11718695C2semidirect
9. C4×#6105C2semidirect
10. D4×#1055C2semidirect
11. #11718669C2semidirect
22. C2×#6105C22semidirect
23. C2×C4⋊Dic13C22semidirect
24. #88178C22semidirect
25. C22×#1055C22semidirect
28. #88123C22semidirect
29. C4×Dic26C22semidirect
32. #88072C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
35. C22⋊#1055C22semidirect
36. #88050C22semidirect
37. #88048C22semidirect
38. #88048C22semidirect
39. C4⋊#1055C22semidirect
40. C4×#1055C22semidirect
91. D4×C13SD16semidirect
213. C13#3295semidirect
230. D4#6105semidirect

Maximal subgroups

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

subgroupindex
D42×C132
#117192482
#117188792
C2×#880722
#117187362
#117187312
#117187022
#117186952
C4×#61052
D4×#10552
#117186692
#329513