Finite Group Databasebeta

← #13126604

Subgroups — #13126604

Order 1664.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719542C212yesmaximal, complemented
2#11719479C212yesmaximal, complemented
3C13×#454C211yesmaximal, characteristic, complemented
4#11718860C212yesmaximal, complemented
5#11718722C211yesmaximal, characteristic, complemented
6#11718719C211yesmaximal, characteristic, complemented
7#11718484C212yesmaximal, complemented
8#11718483C212yesmaximal, complemented
9#11718415C212yesmaximal, complemented
10C13×2−1+4C2211yescharacteristic, complemented
11#88256C2212yescomplemented
12#88251C2211yescharacteristic
13C13×AGL(1,ℤ/8)C2212yescomplemented
14C13×#124C2211yescharacteristic, complemented
15#88204—22no—
16#88204C2212yes—
17#88203—22no—
18#88203C2212yescomplemented
19#88202C2212yescomplemented
20#88196—22no—
21#88196C2212yescomplemented
22C2×#6106—22no—
23C2×#6106C2212yescomplemented
24C2×#6104C2212yescomplemented
25#88170—22no—
26#88168—22no—
27#88165—22no—
28D8×D13—22no—
29#88162C2212yes—
30#88161C2212yescomplemented
31#88128C2211yescharacteristic, complemented
32C13×#104C2212yescomplemented
33C13×#101C2211yescharacteristic, complemented
34#88073C2211yescharacteristic, complemented
35#88063C2212yescomplemented
36#88062C2212yescomplemented
37#88045C2212yescomplemented
38#88043C2211yescharacteristic, complemented
39C13×#41—22no—
40C13×#41—41no—
41C13×#41C2312yes—
42C2×Q8×C13—22no—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13C2311yescharacteristic
45C2×C22⋊D13—41no—
46#6131—22no—
47#6129—22no—
48D4×D13—22no—
49D4×D13—22no—
50D4×D13—42no—
51#6127—22no—
52#6127C2312yes—
53C2×D52—22no—
54C2×D52—41no—
55C2×D52C2312yes—
56C13×SD16—22no—
57C13×D8—22no—
58C13×M16C2312yes—
59C13×C22⋊C4—41no—
60C42×C13C2311yescharacteristic
61#6107—22no—
62#6107D412yescomplemented
63#6106—22no—
64#6106—22no—
65#6106—22no—
66#6106—22no—
67#6106D412yescomplemented
68#6105D412yescomplemented
69#6104—22no—
70#6104—22no—
71#6104—22no—
72#6104D412yescomplemented
73#6099—22no—
74#6099C2312yes—
75C2×#1055—22no—
76C2×#1055C2312yes—
77D104—22no—
78#6095—22no—
79#6094—22no—
80C8×D13—22no—
81#3288—131nomaximal, Sylow
82C23×C13—21no—
83C22×D13—22no—
84C22×D13—41no—
85C22×D13—42no—
86Q8×C13—22no—
87Q8×C13—41no—
88Q8×C13C2×D412yes—
89D4×C13—22no—
90D4×C13—22no—
91D4×C13—41no—
92D4×C13C2×D412yes—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—22no—
99C22⋊D13—42no—
100C22⋊D13—42no—
101C2×Dic13—41no—
102D52—22no—
103D52—22no—
104D52—42no—
105D52—82no—
106D52C2×D412yes—
107C4×D13—22no—
108C4×D13—42no—
109Dic26C2×D412yes—
110C8×C13—22no—
111#1055—22no—
112#1055C2×D412yes—
113#1055C2×D412yes—
114#577—132no—
115#576—132no—
116#496—131no—
117#472—132no—
118#471—132no—
119#455—131no—
120#454D1311yescharacteristic, complemented
121#453—132no—
122#444—132no—
123C22×C13—22no—
124C22×C13—41no—
125C22×C13—81no—
126C22×C13H(5,𝔽2)11yescharacteristic
127C2×D13—22no—
128C2×D13—42no—
129C2×D13—82no—
130C2×D13—161no—
131C2×D13—162no—
132C4×C13—22no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13C22×D412yes—
136Dic13—22no—
1372−1+4C2×D1311yescharacteristic, complemented
138H(5,𝔽2)—132no—
139H(5,𝔽2)—131no—
140#137—132no—
141#137—262no—
142AGL(1,ℤ/8)—132no—
143AGL(1,ℤ/8)—132no—
144AGL(1,ℤ/8)—262no—
145AGL(1,ℤ/8)—262no—
146AGL(1,ℤ/8)—262no—
147AGL(1,ℤ/8)C2×D1312yescomplemented
148#135—132no—
149#135—262no—
150#135—262no—
151C2×SD16—132no—
152C2×SD16—262no—
153C2×D8—132no—
154C2×D8—262no—
155#131—132no—
156#131—132no—
157#127—131no—
158#124C2×D1311yescharacteristic, complemented
159#108—132no—
160#104—132no—
161#104C2×D1312yescomplemented
162#101C2×D1311yescharacteristic, complemented
163#100—131no—
164#100—132no—
165#97—131no—
166C2×C13—21no—
167C2×C13—42no—
168C2×C13—81no—
169C2×C13D4211yescharacteristic
170D13—42no—
171D13—82no—
172#41—22no—
173#41—41no—
174#41—132no—
175#41—262no—
176#41—262no—
177#41—262no—
178#41C22×D1312yes—
179C2×Q8—22no—
180C2×Q8C22×D1311yescharacteristic
181C2×D4—132no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—521no—
186C2×D4—522no—
187C2×D4—521no—
188C2×D4C22×D1311yescharacteristic
189Q16—132no—
190Q16—262no—
191SD16—22no—
192SD16—132no—
193SD16—132no—
194SD16—262no—
195SD16—262no—
196SD16—262no—
197SD16—262no—
198SD16—262no—
199D8—22no—
200D8—132no—
201D8—262no—
202D8—262no—
203D8—262no—
204D8—262no—
205M16—132no—
206M16—262no—
207M16—262no—
208M16C22×D1312yes—
209C2×C8—132no—
210C2×C8—262no—
211C2×C8—262no—
212C22⋊C4—41no—
213C42C22×D1311yescharacteristic
214C13#328811yescharacteristic, complemented, Sylow
215C23—21no—
216C23—262no—
217C23—522no—
218C23—521no—
219Q8—22no—
220Q8—41no—
221Q8—132no—
222Q8D4×D1312yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—132no—
227D4—262no—
228D4—262no—
229D4—262no—
230D4—522no—
231D4—522no—
232D4—522no—
233D4—1042no—
234D4D4×D1312yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—262no—
240C2×C4—522no—
241C2×C4—521no—
242C2×C4C23×D1311yescharacteristic
243C8—22no—
244C8—132no—
245C8—132no—
246C8—262no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—262no—
251C22—522no—
252C22—1042no—
253C22—2082no—
254C22—2081no—
255C22#8825111yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—262no—
260C4C2×D4×D1312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—522no—
265C2—1042no—
266C2#1171929511yescharacteristic
subgroupG/H
centerC2#11719295
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#454C2
socleC2×C13D42
hypercenter#454D13
hypocenterC13#3288
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #11719542C2semidirect
2. #11719479C2semidirect
3. C13×#454C2semidirect
4. #11718860C2semidirect
5. #11718722C2semidirect
6. #11718719C2semidirect
7. #11718484C2semidirect
8. #11718483C2semidirect
9. #11718415C2semidirect
10. C13×2−1+4C22semidirect
11. #88256C22semidirect
13. C13×AGL(1,ℤ/8)C22semidirect
14. C13×#124C22semidirect
18. #88203C22semidirect
19. #88202C22semidirect
21. #88196C22semidirect
23. C2×#6106C22semidirect
24. C2×#6104C22semidirect
30. #88161C22semidirect
31. #88128C22semidirect
32. C13×#104C22semidirect
33. C13×#101C22semidirect
34. #88073C22semidirect
35. #88063C22semidirect
36. #88062C22semidirect
37. #88045C22semidirect
38. #88043C22semidirect
62. #6107D4semidirect
67. #6106D4semidirect
68. #6105D4semidirect
72. #6104D4semidirect
120. #454D13semidirect
137. 2−1+4C2×D13semidirect
147. AGL(1,ℤ/8)C2×D13semidirect
158. #124C2×D13semidirect
161. #104C2×D13semidirect
162. #101C2×D13semidirect
214. C13#3288semidirect

Maximal subgroups

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

subgroupindex
#117195422
#117194792
C13×#4542
#117188602
#117187222
#117187192
#117184842
#117184832
#117184152
#328813