Finite Group Databasebeta

← #13126535

Subgroups — #13126535

Order 1664.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×SD16×D13C212yesmaximal, complemented
2#11719432C211yesmaximal, characteristic, complemented
3D4×D52C211yesmaximal, characteristic
4C13×#461C211yesmaximal, characteristic, complemented
5#11718830C212yesmaximal, complemented
6#11718746C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718509C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic, complemented
10#11718468C212yesmaximal, complemented
11#11718467C212yesmaximal, complemented
12C2×Q8×D13C2212yescomplemented
13C2×D4×D13C2212yes—
14C22×D52—21no—
15C2×C13×SD16C2212yes—
16C13×C4⋊Q8C2211yescharacteristic, complemented
17C4×D4×C13C2211yescharacteristic
18#88200C2212yescomplemented
19C2×#6106C2212yescomplemented
20C2×#6106C2212yescomplemented
21C2×#6105C2211yescharacteristic
22#88184—21no—
23SD16×D13—28no—
24C2×#6095C2212yescomplemented
25C2×C8×D13C2212yescomplemented
26#88150—22no—
27#88149C2212yes—
28#88147—21no—
29#88142—21no—
30#88136—22no—
31#88128C2211yescharacteristic
32C4×D52C2211yescharacteristic
33C4×Dic26C2211yescharacteristic, complemented
34C13×C4⋊C8C2211yescharacteristic, complemented
35C13×#103C2212yescomplemented
36#88072C2211yescharacteristic
37#88061C2212yescomplemented
38#88060C2212yescomplemented
39#88050C2211yescharacteristic, complemented
40#88048C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×Q8×C13C2312yes—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C2×C22⋊D13—22no—
47Q8×D13—24no—
48Q8×D13—42no—
49D4×D13—24no—
50D4×D13—42no—
51C2×D52—22no—
52C2×D52—21no—
53C2×D52—21no—
54C2×D52—44no—
55C2×D52D411yescharacteristic
56C2×D52C2312yes—
57C2×C4×D13—22no—
58C2×C4×D13C2312yes—
59C2×Dic26—22no—
60C2×Dic26C2311yescharacteristic
61C13×SD16—24no—
62C2×C8×C13C2312yes—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C42×C13C2311yescharacteristic
68#6106—24no—
69#6106—42no—
70#6105D414yescomplemented
71#6103—22no—
72#6103—22no—
73#6103D412yes—
74C4⋊Dic13D411yescharacteristic
75C4⋊Dic13C2311yescharacteristic
76#6101—21no—
77#6101—22no—
78C4×Dic13—21no—
79C2×#1055C2311yescharacteristic
80C2×#1055C2311yescharacteristic
81#6095—24no—
82C8×D13—24no—
83D4×SD16—131nomaximal, Sylow
84C23×C13—21no—
85C22×D13—22no—
86C22×D13—44no—
87C22×D13—44no—
88C22×D13—82no—
89C22×D13C2×D412yes—
90Q8×C13—22no—
91Q8×C13—22no—
92D4×C13—21no—
93D4×C13C2×D412yes—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—44no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13C2×D412yes—
104D52—22no—
105D52—22no—
106D52—44no—
107D52—42no—
108D52—81no—
109D52SD1614yescomplemented
110C4×D13—22no—
111C4×D13—22no—
112C4×D13—44no—
113Dic26—21no—
114Dic26—44no—
115Dic26C2×D412yescomplemented
116C8×C13—22no—
117#1055—21no—
118#1055C2×D412yescomplemented
119C22×SD16—132no—
120D4×Q8—131no—
121D42—131no—
122#492—131no—
123#465—132no—
124#461D1311yescharacteristic, complemented
125#460—131no—
126#450—132no—
127#448—132no—
128C4×SD16—131no—
129C8×D4—131no—
130C22×C13—22no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13C22×D411yescharacteristic
134C2×D13—22no—
135C2×D13—22no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—88no—
140C2×D13C2×SD1614yescomplemented
141C4×C13—21no—
142C4×C13—42no—
143C4×C13—41no—
144C4×C13C2×SD1612yescomplemented
145C4×C13C22×D411yescharacteristic
146C4×C13H(5,𝔽2)11yescharacteristic
147Dic13—22no—
148Dic13—22no—
149Dic13—41no—
150C22×Q8—132no—
151C22×D4—132no—
152C22×D4—261no—
153C2×SD16—131no—
154C2×SD16—132no—
155C2×SD16—132no—
156C2×SD16—132no—
157C2×SD16—268no—
158C2×SD16C2×D1312yes—
159C22×C8—132no—
160C4⋊Q8—261no—
161C4⋊Q8C2×D1311yescharacteristic, complemented
162#127—131no—
163C22⋊Q8—132no—
164C22⋊Q8—262no—
165#121—132no—
166#121—261no—
167#120—262no—
168C4×Q8—131no—
169C4×D4—131no—
170C4×D4—261no—
171C4×D4C2×D1311yescharacteristic
172#106—131no—
173C4⋊C8C2×D1311yescharacteristic, complemented
174#103—131no—
175#103C2×D1312yescomplemented
176#102—131no—
177#102—132no—
178C22⋊C8—132no—
179C4×C8—131no—
180C2×C13—42no—
181C2×C13D4211yescharacteristic
182C2×C13C22×SD1611yescharacteristic
183C2×C13#57711yescharacteristic
184D13—24no—
185D13—82no—
186C24—262no—
187C2×Q8—131no—
188C2×Q8—262no—
189C2×Q8—264no—
190C2×Q8—522no—
191C2×Q8C22×D1312yes—
192C2×D4—131no—
193C2×D4—132no—
194C2×D4—262no—
195C2×D4—262no—
196C2×D4—264no—
197C2×D4—261no—
198C2×D4—261no—
199C2×D4—524no—
200C2×D4—522no—
201C2×D4C22×D1311yescharacteristic
202C22×C4—21no—
203C22×C4—132no—
204C22×C4—262no—
205SD16—24no—
206SD16—134no—
207SD16—264no—
208SD16—264no—
209SD16—522no—
210C2×C8—131no—
211C2×C8—131no—
212C2×C8—264no—
213C2×C8C22×D1312yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—131no—
217C4⋊C4—131no—
218C4⋊C4—262no—
219C4⋊C4—261no—
220C4⋊C4C22×D1311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—132no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C42—261no—
226C42C22×D1311yescharacteristic
227C13D4×SD1611yescharacteristic, complemented, Sylow
228C23—21no—
229C23—132no—
230C23—262no—
231C23—524no—
232C23—524no—
233C23—1042no—
234Q8—22no—
235Q8—22no—
236Q8—132no—
237Q8—261no—
238Q8—524no—
239D4—21no—
240D4—134no—
241D4—262no—
242D4—262no—
243D4—524no—
244D4—524no—
245D4—522no—
246D4—1041no—
247D4D4×D1312yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—132no—
252C2×C4—261no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—261no—
256C2×C4—524no—
257C2×C4D4×D1311yescharacteristic
258C2×C4D4×D1311yescharacteristic
259C2×C4C23×D1311yescharacteristic
260C8—22no—
261C8—132no—
262C8—261no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—134no—
267C22—262no—
268C22—262no—
269C22—522no—
270C22—522no—
271C22—522no—
272C22—1048no—
273C22C2×D4×D1311yescharacteristic
274C4—21no—
275C4—41no—
276C4—42no—
277C4—262no—
278C4—262no—
279C4—521no—
280C4SD16×D1312yescomplemented
281C4C2×D4×D1311yescharacteristic
282C4#8825611yescharacteristic
283C2—42no—
284C2—264no—
285C2—1042no—
286C2#1171931411yescharacteristic
287C2C2×SD16×D1311yescharacteristic
288C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalD4×D52C2
hypercenter#461D13
hypocenterC13D4×SD16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D13C2semidirect
2. #11719432C2semidirect
4. C13×#461C2semidirect
5. #11718830C2semidirect
6. #11718746C2semidirect
7. C4×#6105C2semidirect
8. #11718509C2semidirect
9. #11718495C2semidirect
10. #11718468C2semidirect
11. #11718467C2semidirect
12. C2×Q8×D13C22semidirect
16. C13×C4⋊Q8C22semidirect
18. #88200C22semidirect
19. C2×#6106C22semidirect
20. C2×#6106C22semidirect
24. C2×#6095C22semidirect
25. C2×C8×D13C22semidirect
33. C4×Dic26C22semidirect
34. C13×C4⋊C8C22semidirect
35. C13×#103C22semidirect
37. #88061C22semidirect
38. #88060C22semidirect
39. #88050C22semidirect
40. #88048C22semidirect
41. C4×#1055C22semidirect
70. #6105D4semidirect
109. D52SD16semidirect
115. Dic26C2×D4semidirect
118. #1055C2×D4semidirect
124. #461D13semidirect
140. C2×D13C2×SD16semidirect
144. C4×C13C2×SD16semidirect
161. C4⋊Q8C2×D13semidirect
173. C4⋊C8C2×D13semidirect
175. #103C2×D13semidirect
227. C13D4×SD16semidirect
280. C4SD16×D13semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D132
#117194322
D4×D522
C13×#4612
#117188302
#117187462
C4×#61052
#117185092
#117184952
#117184682
#117184672
D4×SD1613