Finite Group Databasebeta

← #13127976

Subgroups — #13127976

Order 1664.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#11719474C211yesmaximal, characteristic, complemented
2#11719462C211yesmaximal, characteristic, complemented
3C13×#509C211yesmaximal, characteristic, complemented
4#11718855C211yesmaximal, characteristic, complemented
5C2×#88066C211yesmaximal, characteristic, complemented
6#11718577C212yesmaximal, complemented
7#11718575C212yesmaximal, complemented
8#11718572C212yesmaximal, complemented
9D13×D16C212yesmaximal, complemented
10#11718569C211yesmaximal, characteristic, complemented
11#11718568C211yesmaximal, characteristic, complemented
12#88256—21no—
13#88251—21no—
14C13×#135C2211yescharacteristic, complemented
15C2×C13×D8C2211yescharacteristic, complemented
16#88203—21no—
17#88186—21no—
18#88173C2212yescomplemented
19#88168—22no—
20#88166C2212yescomplemented
21#88165—22no—
22D8×D13C2212yescomplemented
23D8×D13C2212yescomplemented
24#88158C2211yescharacteristic, complemented
25C2×D104C2211yescharacteristic, complemented
26#88155C2211yescharacteristic
27C13×SD32C2212yescomplemented
28C13×D16C2212yescomplemented
29C13×M32C2211yescharacteristic, complemented
30#88069C2211yescharacteristic, complemented
31#88068C2211yescharacteristic, complemented
32#88067C2211yescharacteristic, complemented
33#88066C2212yescomplemented
34#88066C2212yescomplemented
35#88066C2211yescharacteristic, complemented
36C2×#6090C2211yescharacteristic, complemented
37#88040C2212yescomplemented
38D208C2212yescomplemented
39#88038C2212yescomplemented
40C16×D13C2212yescomplemented
41C13×#41—21no—
42C2×D4×C13—21no—
43C2×C22⋊D13—42no—
44#6131—22no—
45#6129—22no—
46#6129—41no—
47D4×D13—22no—
48D4×D13—22no—
49D4×D13—42no—
50D4×D13—41no—
51#6127—21no—
52#6127—41no—
53#6127D411yescharacteristic
54C2×D52—21no—
55C2×D52—41no—
56C13×Q16C2311yescharacteristic
57C13×SD16—21no—
58C13×D8—21no—
59C13×D8C2312yes—
60C13×D8C2311yescharacteristic
61C2×C8×C13C2311yescharacteristic
62#6106—22no—
63#6105—22no—
64#6104—22no—
65#6104—22no—
66#6099D411yescharacteristic
67Dic52C2311yescharacteristic
68D104—21no—
69D104C2312yes—
70D104C2311yescharacteristic
71#6095—21no—
72#6094D412yes—
73C8×D13C2312yes—
74C13×C16C2312yes—
75#6090C2311yescharacteristic
76#6090C2311yescharacteristic
77#3415—131nomaximal, Sylow
78C23×C13—41no—
79C22×D13—41no—
80C22×D13—42no—
81C22×D13—42no—
82Q8×C13—21no—
83D4×C13—21no—
84D4×C13—22no—
85D4×C13—41no—
86D4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13C2×D411yescharacteristic
89C22⋊D13—41no—
90C22⋊D13—42no—
91C22⋊D13—42no—
92C22⋊D13—42no—
93C22⋊D13D812yes—
94C2×Dic13—42no—
95D52—21no—
96D52—22no—
97D52—42no—
98D52—41no—
99D52D811yescharacteristic
100C4×D13—41no—
101C4×D13—42no—
102C4×D13C2×D412yes—
103Dic26—21no—
104Dic26D811yescharacteristic
105C8×C13C2×D411yescharacteristic
106C8×C13C2411yescharacteristic
107#1055C2×D412yes—
108#576—131no—
109#576—131no—
110#509—132no—
111#509—132no—
112#509—131no—
113#509D1311yescharacteristic, complemented
114#508—131no—
115#508—132no—
116C2×D16—131no—
117C2×D16—132no—
118#504—131no—
119C22×C13—42no—
120C22×C13—41no—
121C22×C13—161no—
122C22×C13C2×D811yescharacteristic
123C2×D13—42no—
124C2×D13—41no—
125C2×D13—162no—
126C2×D13—162no—
127C2×D13—161no—
128C2×D13C2×D812yes—
129C4×C13—41no—
130C4×C13C2×D811yescharacteristic
131C4×C13C22×D411yescharacteristic
132Dic13—41no—
133Dic13C2×D812yes—
134H(5,𝔽2)—261no—
135H(5,𝔽2)—261no—
136AGL(1,ℤ/8)—262no—
137AGL(1,ℤ/8)—262no—
138AGL(1,ℤ/8)—261no—
139AGL(1,ℤ/8)—261no—
140#135—132no—
141#135—132no—
142#135—131no—
143#135C2×D1311yescharacteristic, complemented
144C2×D8—132no—
145C2×D8—132no—
146C2×D8—131no—
147C2×D8C2×D1311yescharacteristic, complemented
148#131—131no—
149Q32—131no—
150SD32—131no—
151SD32—131no—
152SD32—132no—
153SD32C2×D1312yescomplemented
154D16—132no—
155D16—131no—
156D16—132no—
157D16—132no—
158D16C2×D1312yescomplemented
159M32—132no—
160M32C2×D1311yescharacteristic, complemented
161C2×C16—131no—
162C2×C16—132no—
163C2×C13—21no—
164C2×C13—81no—
165C2×C13—82no—
166C2×C13C22×D811yescharacteristic
167D13—22no—
168D13—82no—
169D13—81no—
170#41—21no—
171#41—131no—
172#41—262no—
173#41—262no—
174#41—261no—
175#41—521no—
176#41—521no—
177C2×D4—21no—
178C2×D4—262no—
179C2×D4—262no—
180C2×D4—261no—
181C2×D4—521no—
182C2×D4—522no—
183C2×D4—521no—
184C2×D4—522no—
185Q16—131no—
186Q16C22×D1311yescharacteristic
187SD16—21no—
188SD16—262no—
189SD16—262no—
190SD16—261no—
191D8—21no—
192D8—132no—
193D8—131no—
194D8—262no—
195D8—262no—
196D8—261no—
197D8C22×D1312yes—
198D8C22×D1311yescharacteristic
199M16—131no—
200M16—132no—
201C2×C8—132no—
202C2×C8C22×D1311yescharacteristic
203C16—131no—
204C16—131no—
205C16C22×D1312yes—
206C13#341511yescharacteristic, complemented, Sylow
207C23—41no—
208C23—522no—
209C23—522no—
210C23—521no—
211Q8—21no—
212Q8—131no—
213Q8—261no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—132no—
219D4—131no—
220D4—261no—
221D4—262no—
222D4—522no—
223D4—522no—
224D4—522no—
225D4—522no—
226D4—521no—
227D4—521no—
228C2×C4—41no—
229C2×C4—132no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4—521no—
233C2×C4D4×D1311yescharacteristic
234C8—132no—
235C8D4×D1311yescharacteristic
236C8C23×D1311yescharacteristic
237C22—41no—
238C22—42no—
239C22—132no—
240C22—161no—
241C22—522no—
242C22—521no—
243C22—2081no—
244C22—2082no—
245C22—2082no—
246C22D8×D1311yescharacteristic
247C4—41no—
248C4—132no—
249C4—521no—
250C4D8×D1311yescharacteristic
251C4C2×D4×D1311yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—262no—
256C2—1042no—
257C2—1041no—
258C2C2×D8×D1311yescharacteristic
subgroupG/H
centerC2C2×D8×D13
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC13×#509C2
socleC2×C13C22×D8
hypercenter#509D13
hypocenterC13#3415
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #11719474C2semidirect
2. #11719462C2semidirect
3. C13×#509C2semidirect
4. #11718855C2semidirect
5. C2×#88066C2semidirect
6. #11718577C2semidirect
7. #11718575C2semidirect
8. #11718572C2semidirect
9. D13×D16C2semidirect
10. #11718569C2semidirect
11. #11718568C2semidirect
14. C13×#135C22semidirect
15. C2×C13×D8C22semidirect
18. #88173C22semidirect
20. #88166C22semidirect
22. D8×D13C22semidirect
23. D8×D13C22semidirect
24. #88158C22semidirect
25. C2×D104C22semidirect
27. C13×SD32C22semidirect
28. C13×D16C22semidirect
29. C13×M32C22semidirect
30. #88069C22semidirect
31. #88068C22semidirect
32. #88067C22semidirect
33. #88066C22semidirect
34. #88066C22semidirect
35. #88066C22semidirect
36. C2×#6090C22semidirect
37. #88040C22semidirect
38. D208C22semidirect
39. #88038C22semidirect
40. C16×D13C22semidirect
113. #509D13semidirect
143. #135C2×D13semidirect
147. C2×D8C2×D13semidirect
153. SD32C2×D13semidirect
158. D16C2×D13semidirect
160. M32C2×D13semidirect
206. C13#3415semidirect

Maximal subgroups

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

subgroupindex
#117194742
#117194622
C13×#5092
#117188552
C2×#880662
#117185772
#117185752
#117185722
D13×D162
#117185692
#117185682
#341513