Finite Group Databasebeta

← #13126626

Subgroups — #13126626

Order 1664.

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

normal subgroups only

This group has 460 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#11719483C212yesmaximal, complemented
3C13×#456C211yesmaximal, characteristic, complemented
4#11718864C212yesmaximal, complemented
5#11718756C211yesmaximal, characteristic, complemented
6#11718746C211yesmaximal, characteristic, complemented
7#11718485C212yesmaximal, complemented
8#11718483C212yesmaximal, complemented
9#11718415C212yesmaximal, complemented
10C13×2−1+4C2211yescharacteristic
11#88256C2212yescomplemented
12#88254C2211yescharacteristic
13C13×#137C2212yescomplemented
14C13×C4⋊Q8C2211yescharacteristic, complemented
15#88204—22no—
16#88204C2212yes—
17#88203—22no—
18#88203C2212yes—
19#88202C2212yescomplemented
20#88196—22no—
21#88196C2212yescomplemented
22C2×#6106—22no—
23C2×#6106C2212yescomplemented
24C2×#6106C2212yescomplemented
25#88173—22no—
26#88172—22no—
27#88168—22no—
28SD16×D13—22no—
29#88162C2212yes—
30#88161C2212yescomplemented
31#88128C2211yescharacteristic
32C13×#104C2212yescomplemented
33C13×#101C2211yescharacteristic, complemented
34#88076C2211yescharacteristic, complemented
35#88063C2212yescomplemented
36#88062C2212yescomplemented
37#88045C2212yescomplemented
38C4×#1055C2211yescharacteristic, complemented
39C13×#41—22no—
40C13×#41—41no—
41C13×#41C2312yes—
42C2×Q8×C13—22no—
43C2×Q8×C13C2311yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45#6131—22no—
46#6131—22no—
47Q8×D13—22no—
48D4×D13—22no—
49D4×D13—42no—
50#6127—22no—
51#6127—41no—
52#6127C2312yes—
53C2×D52—22no—
54C2×D52—41no—
55C2×D52C2312yes—
56C13×Q16—22no—
57C13×SD16—22no—
58C13×M16C2312yes—
59C13×C4⋊C4—41no—
60C42×C13C2311yescharacteristic
61#6107—22no—
62#6107D412yescomplemented
63#6106—22no—
64#6106—22no—
65#6106—22no—
66#6106—22no—
67#6106—22no—
68#6106—22no—
69#6106D412yescomplemented
70#6105D412yescomplemented
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#3291—131nomaximal, Sylow
82C22×D13—22no—
83C22×D13—42no—
84Q8×C13—22no—
85Q8×C13—22no—
86Q8×C13—41no—
87Q8×C13C2×D412yes—
88D4×C13—22no—
89D4×C13—41no—
90D4×C13C2×D412yes—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—42no—
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—22no—
98C22⋊D13—42no—
99D52—22no—
100D52—22no—
101D52—42no—
102D52—41no—
103D52—82no—
104D52C2×D412yes—
105C4×D13—22no—
106C4×D13—42no—
107C4×D13—42no—
108Dic26—41no—
109Dic26C2×D412yes—
110C8×C13—22no—
111#1055—22no—
112#1055C2×D412yes—
113#1055C2×D412yes—
114#577—132no—
115#577—132no—
116#492—131no—
117#471—132no—
118#471—132no—
119#456—131no—
120#456D1311yescharacteristic, complemented
121#453—132no—
122#443—132no—
123C22×C13—22no—
124C22×C13H(5,𝔽2)11yescharacteristic
125C2×D13—22no—
126C2×D13—42no—
127C2×D13—82no—
128C2×D13—162no—
129C4×C13—22no—
130C4×C13—22no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13C22×D412yes—
134Dic13—22no—
1352−1+4—131no—
1362−1+4C2×D1311yescharacteristic
137H(5,𝔽2)—132no—
138#137—132no—
139#137—262no—
140#137—262no—
141#137C2×D1312yescomplemented
142AGL(1,ℤ/8)—132no—
143AGL(1,ℤ/8)—132no—
144AGL(1,ℤ/8)—262no—
145AGL(1,ℤ/8)—262no—
146#135—132no—
147#135—262no—
148#135—262no—
149C2×SD16—132no—
150C2×SD16—132no—
151C2×SD16—262no—
152C2×SD16—262no—
153#131—132no—
154#131—132no—
155C4⋊Q8C2×D1311yescharacteristic, complemented
156#127—131no—
157#108—132no—
158#104—132no—
159#104C2×D1312yescomplemented
160#101—131no—
161#101C2×D1311yescharacteristic, complemented
162#100—132no—
163C4×C8—131no—
164C2×C13—21no—
165C2×C13—42no—
166C2×C13D4211yescharacteristic
167D13—42no—
168D13—82no—
169#41—22no—
170#41—41no—
171#41—132no—
172#41—262no—
173#41—262no—
174#41—262no—
175#41—521no—
176#41C22×D1312yes—
177C2×Q8—22no—
178C2×Q8—262no—
179C2×Q8C22×D1311yescharacteristic
180C2×Q8C22×D1311yescharacteristic
181C2×D4—132no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—521no—
185C2×D4—522no—
186Q16—22no—
187Q16—132no—
188Q16—262no—
189SD16—22no—
190SD16—132no—
191SD16—132no—
192SD16—262no—
193SD16—262no—
194SD16—262no—
195SD16—262no—
196SD16—262no—
197SD16—262no—
198SD16—262no—
199D8—132no—
200D8—262no—
201D8—262no—
202M16—132no—
203M16—262no—
204M16—262no—
205M16C22×D1312yes—
206C2×C8—132no—
207C2×C8—262no—
208C2×C8—262no—
209C4⋊C4—41no—
210C42C22×D1311yescharacteristic
211C13#329111yescharacteristic, complemented, Sylow
212C23—262no—
213C23—522no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—132no—
218Q8—521no—
219Q8D4×D1312yes—
220D4—22no—
221D4—41no—
222D4—132no—
223D4—262no—
224D4—262no—
225D4—262no—
226D4—522no—
227D4—521no—
228D4—522no—
229D4—1042no—
230D4D4×D1312yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—262no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4C23×D1311yescharacteristic
240C8—22no—
241C8—132no—
242C8—132no—
243C8—262no—
244C22—22no—
245C22—262no—
246C22—522no—
247C22—1042no—
248C22—2082no—
249C22#8825111yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—262no—
255C4C2×D4×D1312yes—
256C2—21no—
257C2—42no—
258C2—522no—
259C2—1042no—
260C2#1171929511yescharacteristic
subgroupG/H
centerC2#11719295
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#456C2
socleC2×C13D42
hypercenter#456D13
hypocenterC13#3291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11719542C2semidirect
2. #11719483C2semidirect
3. C13×#456C2semidirect
4. #11718864C2semidirect
5. #11718756C2semidirect
6. #11718746C2semidirect
7. #11718485C2semidirect
8. #11718483C2semidirect
9. #11718415C2semidirect
11. #88256C22semidirect
13. C13×#137C22semidirect
14. C13×C4⋊Q8C22semidirect
19. #88202C22semidirect
21. #88196C22semidirect
23. C2×#6106C22semidirect
24. C2×#6106C22semidirect
30. #88161C22semidirect
32. C13×#104C22semidirect
33. C13×#101C22semidirect
34. #88076C22semidirect
35. #88063C22semidirect
36. #88062C22semidirect
37. #88045C22semidirect
38. C4×#1055C22semidirect
62. #6107D4semidirect
69. #6106D4semidirect
70. #6105D4semidirect
72. #6104D4semidirect
120. #456D13semidirect
141. #137C2×D13semidirect
155. C4⋊Q8C2×D13semidirect
159. #104C2×D13semidirect
161. #101C2×D13semidirect
211. C13#3291semidirect

Maximal subgroups

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

subgroupindex
#117195422
#117194832
C13×#4562
#117188642
#117187562
#117187462
#117184852
#117184832
#117184152
#329113