Finite Group Databasebeta

← #13126522

Subgroups — #13126522

Order 1664.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#88166C211yesmaximal, characteristic, complemented
2C2×D8×D13C211yesmaximal, characteristic, complemented
3#11719259C212yesmaximal, complemented
4C4×C13×D8C211yesmaximal, characteristic, complemented
5#11718677C212yesmaximal, complemented
6#11718548C211yesmaximal, characteristic, complemented
7#11718544C211yesmaximal, characteristic, complemented
8#11718442C212yesmaximal, complemented
9#11718437C212yesmaximal, complemented
10#11718357C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×#6129C2212yescomplemented
13C2×D4×D13C2212yes—
14C2×C13×D8C2211yescharacteristic
15C4×D4×C13C2212yescomplemented
16C2×#6105C2212yescomplemented
17C2×#6104C2212yes—
18#88184—22no—
19C2×#6103—22no—
20#88166—24no—
21D8×D13—24no—
22C2×Dic52C2211yescharacteristic, complemented
23C2×D104C2211yescharacteristic
24C2×#6095C2212yescomplemented
25C2×C8×D13C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic, complemented
27#88151C2212yes—
28#88149C2212yescomplemented
29#88140—22no—
30#88136—22no—
31#88129C2212yescomplemented
32C4×D52C2211yescharacteristic
33C13×#107C2211yescharacteristic, complemented
34C13×#102C2212yescomplemented
35C4×C8×C13C2211yescharacteristic, complemented
36#88060C2211yescharacteristic
37#88060C2211yescharacteristic, complemented
38#88050C2212yescomplemented
39#88049C2212yescomplemented
40C4⋊#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×D4×C13C2312yes—
43C22×C4×C13—22no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C22×Dic13—22no—
47#6129—24no—
48#6129—42no—
49D4×D13—24no—
50D4×D13—42no—
51C2×D52—22no—
52C2×D52D411yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13C2311yescharacteristic
55C2×C4×D13C2311yescharacteristic
56C2×Dic26C2312yes—
57C13×D8D414yescomplemented
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C13×C4⋊C4C2312yes—
61C13×C22⋊C4—22no—
62C42×C13C2311yescharacteristic
63#6105—24no—
64#6104—24no—
65#6103—22no—
66#6103—22no—
67#6103—22no—
68#6103—22no—
69#6103D411yescharacteristic
70#6103D411yescharacteristic
71C4⋊Dic13—22no—
72C4⋊Dic13D411yescharacteristic
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75Dic52—22no—
76D104—22no—
77#6095—42no—
78C8×D13—22no—
79C8×D13—22no—
80#3280—131nomaximal, Sylow
81C23×C13—22no—
82C22×D13—22no—
83C22×D13—44no—
84C22×D13—44no—
85C22×D13—82no—
86C22×D13C2×D411yescharacteristic
87C22×D13C2×D411yescharacteristic
88D4×C13—22no—
89D4×C13C2×D414yes—
90C2×C4×C13—22no—
91C2×C4×C13—82no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—44no—
96C22⋊D13—44no—
97C2×Dic13—22no—
98C2×Dic13—44no—
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101D52—22no—
102D52—22no—
103D52—22no—
104D52—82no—
105C4×D13—21no—
106C4×D13—21no—
107C4×D13—21no—
108C4×D13—21no—
109Dic26—22no—
110Dic26—22no—
111C8×C13—21no—
112C8×C13C2×D412yes—
113#1055—21no—
114#1055—21no—
115C2×#135—131no—
116C22×D8—131no—
117#546—132no—
118#495—131no—
119#467—131no—
120#466—131no—
121#463—132no—
122#450—132no—
123#449—132no—
124C4×D8D1311yescharacteristic, complemented
125C8×D4—131no—
126C22×C13—24no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C2×D13—21no—
131C2×D13—21no—
132C2×D13—21no—
133C2×D13—21no—
134C2×D13—21no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—88no—
139C2×D13#13512yescomplemented
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13C22×D411yescharacteristic
144C4×C13H(5,𝔽2)11yescharacteristic
145Dic13—21no—
146Dic13—21no—
147Dic13—42no—
148C2×#41—132no—
149C22×D4—132no—
150#135—264no—
151C2×Q16—131no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8—132no—
155C2×D8—131no—
156C2×D8—264no—
157C2×D8C2×D1311yescharacteristic
158C22×C8—131no—
159C22×C8—131no—
160#124—132no—
161#123—262no—
162C22⋊Q8—132no—
163#121—132no—
164#121—262no—
165#120—262no—
166C4×D4—131no—
167C4×D4C2×D1312yescomplemented
168C2×C22⋊C4—262no—
169#107C2×D1311yescharacteristic, complemented
170C4⋊C8—131no—
171#103—132no—
172#102—132no—
173#102C2×D1312yescomplemented
174C22⋊C8—131no—
175C22⋊C8—131no—
176C4×C8C2×D1311yescharacteristic, complemented
177C2×C13—44no—
178C2×C13D4211yescharacteristic
179C2×C13C2×#13511yescharacteristic
180C2×C13#57611yescharacteristic
181D13—22no—
182D13—41no—
183D13—82no—
184C24—262no—
185#41—264no—
186#41—522no—
187C2×Q8—132no—
188C2×D4—131no—
189C2×D4—132no—
190C2×D4—262no—
191C2×D4—262no—
192C2×D4—264no—
193C2×D4—262no—
194C2×D4—522no—
195C2×D4C22×D1312yes—
196C22×C4—22no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—262no—
200Q16—262no—
201SD16—264no—
202SD16—522no—
203D8—264no—
204D8—262no—
205D8D5214yescomplemented
206C2×C8—131no—
207C2×C8—131no—
208C2×C8—262no—
209C2×C8—262no—
210C2×C8C22×D1311yescharacteristic
211C2×C8C22×D1311yescharacteristic
212C4⋊C4—131no—
213C4⋊C4—262no—
214C4⋊C4C22×D1312yes—
215C22⋊C4—22no—
216C22⋊C4—131no—
217C22⋊C4—131no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42C22×D1311yescharacteristic
223C13#328011yescharacteristic, complemented, Sylow
224C23—22no—
225C23—131no—
226C23—131no—
227C23—262no—
228C23—524no—
229C23—524no—
230C23—1042no—
231Q8—262no—
232Q8—262no—
233D4—22no—
234D4—262no—
235D4—262no—
236D4—262no—
237D4—524no—
238D4—524no—
239D4—1042no—
240D4C2×D5214yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—524no—
251C2×C4D4×D1311yescharacteristic
252C2×C4D4×D1311yescharacteristic
253C2×C4C23×D1311yescharacteristic
254C8—21no—
255C8—261no—
256C8—261no—
257C8C2×D5212yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—132no—
262C22—261no—
263C22—261no—
264C22—261no—
265C22—261no—
266C22—261no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22—1048no—
271C22C2×D4×D1311yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—261no—
276C4—261no—
277C4—522no—
278C4C22×D5211yescharacteristic
279C4#8825611yescharacteristic
280C2—44no—
281C2—262no—
282C2—521no—
283C2—1042no—
284C2D4×D5211yescharacteristic
285C2#1171946211yescharacteristic
286C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3280
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#88166C2semidirect
2. C2×D8×D13C2semidirect
3. #11719259C2semidirect
4. C4×C13×D8C2semidirect
5. #11718677C2semidirect
6. #11718548C2semidirect
7. #11718544C2semidirect
8. #11718442C2semidirect
9. #11718437C2semidirect
10. #11718357C2semidirect
11. C8×D52C2semidirect
12. C2×#6129C22semidirect
15. C4×D4×C13C22semidirect
16. C2×#6105C22semidirect
22. C2×Dic52C22semidirect
24. C2×#6095C22semidirect
26. C2×C8×D13C22semidirect
28. #88149C22semidirect
31. #88129C22semidirect
33. C13×#107C22semidirect
34. C13×#102C22semidirect
35. C4×C8×C13C22semidirect
37. #88060C22semidirect
38. #88050C22semidirect
39. #88049C22semidirect
40. C4⋊#1055C22semidirect
57. C13×D8D4semidirect
124. C4×D8D13semidirect
139. C2×D13#135semidirect
167. C4×D4C2×D13semidirect
169. #107C2×D13semidirect
173. #102C2×D13semidirect
176. C4×C8C2×D13semidirect
205. D8D52semidirect
223. C13#3280semidirect

Maximal subgroups

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

subgroupindex
C2×#881662
C2×D8×D132
#117192592
C4×C13×D82
#117186772
#117185482
#117185442
#117184422
#117184372
#117183572
C8×D522
#328013