Finite Group Databasebeta

← #13126631

Subgroups — #13126631

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#11719541C212yesmaximal, complemented
2#11719480C212yesmaximal, complemented
3C13×#453C211yesmaximal, characteristic, complemented
4#11718861C212yesmaximal, complemented
5#11718738C211yesmaximal, characteristic, complemented
6#11718737C211yesmaximal, characteristic, complemented
7#11718487C212yesmaximal, complemented
8#11718485C212yesmaximal, complemented
9#11718409C212yesmaximal, complemented
10C13×H(5,𝔽2)C2211yescharacteristic, complemented
11#88257C2212yes—
12#88251C2211yescharacteristic, complemented
13C13×AGL(1,ℤ/8)C2212yes—
14C13×#127C2211yescharacteristic
15#88205—22no—
16#88205C2212yescomplemented
17#88204—22no—
18#88204C2212yes—
19#88202C2212yescomplemented
20C2×#6105—22no—
21C2×#6105C2212yescomplemented
22C2×#6105C2212yescomplemented
23#88186—22no—
24#88186C2212yes—
25#88169—22no—
26SD16×D13—22no—
27#88166—22no—
28#88165—22no—
29#88163C2212yescomplemented
30#88161C2212yescomplemented
31#88123C2211yescharacteristic, complemented
32C13×#104C2212yescomplemented
33C13×#100C2211yescharacteristic, complemented
34#88073C2211yescharacteristic, complemented
35#88064C2212yescomplemented
36#88062C2212yescomplemented
37#88045C2212yescomplemented
38C4×#1055C2211yescharacteristic, complemented
39C13×#41—22no—
40C13×#41C2312yes—
41C2×D4×C13—22no—
42C2×D4×C13—41no—
43C2×D4×C13—41no—
44C2×D4×C13C2311yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C2×C22⋊D13—41no—
47Q8×D13—22no—
48#6129—22no—
49#6129—22no—
50#6129—42no—
51D4×D13—22no—
52#6127—22no—
53#6127C2312yes—
54C2×Dic26—22no—
55C2×Dic26C2312yes—
56C13×SD16—22no—
57C13×D8—22no—
58C13×M16C2312yes—
59C42×C13C2311yescharacteristic
60#6107—22no—
61#6107D412yescomplemented
62#6106D412yescomplemented
63#6105—22no—
64#6105—22no—
65#6105—22no—
66#6105—22no—
67#6105—22no—
68#6105—22no—
69#6105D412yescomplemented
70#6104—22no—
71#6104D412yescomplemented
72C4⋊Dic13—41no—
73#6099—22no—
74#6099C2312yes—
75C2×#1055—22no—
76C2×#1055C2312yes—
77Dic52—22no—
78#6095—22no—
79#6094—22no—
80C8×D13—22no—
81#3291—131nomaximal, Sylow
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—41no—
85C22×D13—41no—
86Q8×C13C2×D412yes—
87D4×C13—22no—
88D4×C13—22no—
89D4×C13—22no—
90D4×C13—42no—
91D4×C13—82no—
92D4×C13C2×D412yes—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—22no—
98C22⋊D13—42no—
99C22⋊D13—42no—
100C2×Dic13—22no—
101C2×Dic13—41no—
102C2×Dic13—42no—
103D52C2×D412yes—
104C4×D13—22no—
105C4×D13—42no—
106Dic26—22no—
107Dic26—22no—
108Dic26—42no—
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—132no—
120#453—131no—
121#453D1311yescharacteristic, complemented
122#443—132no—
123C22×C13—22no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—81no—
127C22×C13—81no—
128C22×C13—161no—
129C22×C13H(5,𝔽2)11yescharacteristic
130C2×D13—22no—
131C2×D13—161no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13C22×D412yes—
135Dic13—22no—
136Dic13—42no—
1372−1+4—132no—
138H(5,𝔽2)—131no—
139H(5,𝔽2)C2×D1311yescharacteristic, complemented
140#137—132no—
141#137—132no—
142#137—262no—
143#137—262no—
144AGL(1,ℤ/8)—132no—
145AGL(1,ℤ/8)—262no—
146AGL(1,ℤ/8)—262no—
147AGL(1,ℤ/8)C2×D1312yes—
148#135—132no—
149#135—262no—
150#135—262no—
151C2×SD16—132no—
152C2×SD16—132no—
153C2×SD16—262no—
154C2×SD16—262no—
155#131—132no—
156#131—132no—
157C4⋊Q8—131no—
158#127C2×D1311yescharacteristic
159#108—132no—
160#104—132no—
161#104C2×D1312yescomplemented
162#101—132no—
163#100—131no—
164#100C2×D1311yescharacteristic, complemented
165C4×C8—131no—
166C2×C13—21no—
167C2×C13—42no—
168C2×C13—81no—
169C2×C13—81no—
170C2×C13D4211yescharacteristic
171D13—42no—
172#41—22no—
173#41—132no—
174#41—262no—
175#41—262no—
176#41—262no—
177#41—522no—
178#41C22×D1312yes—
179C2×Q8—132no—
180C2×Q8—262no—
181C2×Q8—262no—
182C2×D4—22no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4—262no—
186C2×D4—521no—
187C2×D4C22×D1311yescharacteristic
188C2×D4C22×D1311yescharacteristic
189Q16—132no—
190Q16—262no—
191Q16—262no—
192SD16—22no—
193SD16—132no—
194SD16—132no—
195SD16—262no—
196SD16—262no—
197SD16—262no—
198SD16—262no—
199SD16—262no—
200SD16—262no—
201SD16—262no—
202D8—22no—
203D8—132no—
204D8—262no—
205M16—132no—
206M16—262no—
207M16—262no—
208M16C22×D1312yes—
209C2×C8—132no—
210C2×C8—262no—
211C2×C8—262no—
212C4⋊C4—521no—
213C42C22×D1311yescharacteristic
214C13#329111yescharacteristic, complemented, Sylow
215C23—21no—
216C23—21no—
217C23—41no—
218C23—521no—
219Q8—132no—
220Q8—262no—
221Q8—262no—
222Q8—522no—
223Q8D4×D1312yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—132no—
230D4—262no—
231D4—522no—
232D4—522no—
233D4D4×D1312yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—522no—
240C2×C4—521no—
241C2×C4—522no—
242C2×C4C23×D1311yescharacteristic
243C8—22no—
244C8—132no—
245C8—132no—
246C8—262no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—262no—
254C22—2081no—
255C22#8825111yescharacteristic
256C4—22no—
257C4—22no—
258C4—262no—
259C4—522no—
260C4C2×D4×D1312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—522no—
266C2#1171929511yescharacteristic
subgroupG/H
centerC2#11719295
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#453C2
socleC2×C13D42
hypercenter#453D13
hypocenterC13#3291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11719541C2semidirect
2. #11719480C2semidirect
3. C13×#453C2semidirect
4. #11718861C2semidirect
5. #11718738C2semidirect
6. #11718737C2semidirect
7. #11718487C2semidirect
8. #11718485C2semidirect
9. #11718409C2semidirect
10. C13×H(5,𝔽2)C22semidirect
12. #88251C22semidirect
16. #88205C22semidirect
19. #88202C22semidirect
21. C2×#6105C22semidirect
22. C2×#6105C22semidirect
29. #88163C22semidirect
30. #88161C22semidirect
31. #88123C22semidirect
32. C13×#104C22semidirect
33. C13×#100C22semidirect
34. #88073C22semidirect
35. #88064C22semidirect
36. #88062C22semidirect
37. #88045C22semidirect
38. C4×#1055C22semidirect
61. #6107D4semidirect
62. #6106D4semidirect
69. #6105D4semidirect
71. #6104D4semidirect
121. #453D13semidirect
139. H(5,𝔽2)C2×D13semidirect
161. #104C2×D13semidirect
164. #100C2×D13semidirect
214. C13#3291semidirect

Maximal subgroups

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

subgroupindex
#117195412
#117194802
C13×#4532
#117188612
#117187382
#117187372
#117184872
#117184852
#117184092
#329113