Finite Group Databasebeta

← #13126521

Subgroups — #13126521

Order 1664.

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

normal subgroups only

This group has 526 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
1C22×C13×D8C211yesmaximal, characteristic, complemented
2#11719511C212yesmaximal, complemented
3C2×#88166C211yesmaximal, characteristic, complemented
4#11718879C212yesmaximal, complemented
5#11718819C212yesmaximal, complemented
6#11718818C211yesmaximal, characteristic, complemented
7#11718816C211yesmaximal, characteristic, complemented
8#11718814C212yesmaximal, complemented
9D8×Dic13C211yesmaximal, characteristic, complemented
10#11718777C211yesmaximal, characteristic, complemented
11C8×C22⋊D13C211yesmaximal, characteristic, complemented
12C22×D4×C13C2212yes—
13C2×#6129C2212yescomplemented
14C2×C13×D8—24no—
15C2×C13×D8C2212yes—
16C2×C13×D8C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19#88207—22no—
20C2×C22⋊Dic13—22no—
21#88193—22no—
22#88192C2212yescomplemented
23#88190C2212yescomplemented
24#88189—22no—
25D4×Dic13C2212yescomplemented
26C2×#6105C2212yescomplemented
27C2×#6105C2212yescomplemented
28C4×C22⋊D13C2211yescharacteristic
29#88178C2212yes—
30#88166—24no—
31C2×Dic52C2211yescharacteristic, complemented
32C2×C8×D13C2211yescharacteristic, complemented
33#88072C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2211yescharacteristic
36#88060C2211yescharacteristic, complemented
37#88058C2211yescharacteristic, complemented
38#88056C2212yescomplemented
39#88054C2211yescharacteristic, complemented
40C8×Dic13C2211yescharacteristic, complemented
41C24×C13—22no—
42C2×D4×C13—24no—
43C2×D4×C13—22no—
44C2×D4×C13—42no—
45C2×D4×C13C2312yes—
46C2×D4×C13C2312yes—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13D411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53#6129—24no—
54#6129—42no—
55C2×C4×D13C2311yescharacteristic
56C2×Dic26C2312yes—
57C13×D8—24no—
58C13×D8—22no—
59C13×D8D414yescomplemented
60C2×C8×C13—22no—
61C2×C8×C13C2311yescharacteristic
62C2×C8×C13C2311yescharacteristic
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65C22⋊Dic13—22no—
66C22⋊Dic13—22no—
67C22⋊Dic13—22no—
68C22⋊Dic13D411yescharacteristic
69#6105—24no—
70#6105—42no—
71#6103D411yescharacteristic
72C4⋊Dic13C2312yes—
73#6101—22no—
74#6101D411yescharacteristic
75C4×Dic13C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77C2×#1055C2311yescharacteristic
78Dic52—22no—
79C8×D13—22no—
80#3280—131nomaximal, Sylow
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—44no—
84C23×C13—44no—
85C23×C13—82no—
86C23×C13C2×D411yescharacteristic
87C22×D13C2×D411yescharacteristic
88D4×C13—22no—
89D4×C13—22no—
90D4×C13—22no—
91D4×C13—44no—
92D4×C13C2×D414yes—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—22no—
98C22⋊D13—44no—
99C22⋊D13—82no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—44no—
103C2×Dic13—82no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
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×D8D1311yescharacteristic, complemented
117#546—132no—
118#495—131no—
119#467—131no—
120#466—131no—
121#463—132no—
122#450—132no—
123#449—132no—
124C4×D8—131no—
125C8×D4—131no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—24no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—88no—
135C22×C13#13512yescomplemented
136C22×C13C22×D411yescharacteristic
137C2×D13—21no—
138C2×D13—21no—
139C2×D13—21no—
140C4×C13—21no—
141C4×C13C22×D411yescharacteristic
142C4×C13H(5,𝔽2)11yescharacteristic
143Dic13—21no—
144Dic13—21no—
145Dic13—21no—
146Dic13—42no—
147Dic13—42no—
148C2×#41—132no—
149C22×D4C2×D1312yes—
150#135—264no—
151C2×Q16—131no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8—24no—
155C2×D8C2×D1312yes—
156C2×D8C2×D1311yescharacteristic
157C2×D8C2×D1311yescharacteristic
158C22×C8—131no—
159C22×C8C2×D1311yescharacteristic
160#124—132no—
161#123—262no—
162C22⋊Q8—132no—
163#121—132no—
164#121—262no—
165#120—262no—
166C4×D4—131no—
167C4×D4—132no—
168C2×C22⋊C4—262no—
169#107—131no—
170C4⋊C8—131no—
171#103—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—131no—
175C22⋊C8—131no—
176C4×C8—131no—
177C2×C13—22no—
178C2×C13—44no—
179C2×C13—82no—
180C2×C13D4211yescharacteristic
181C2×C13C2×#13511yescharacteristic
182C2×C13#57611yescharacteristic
183D13—41no—
184C24—22no—
185#41—264no—
186#41—522no—
187C2×Q8—132no—
188C2×D4—24no—
189C2×D4—22no—
190C2×D4—42no—
191C2×D4—131no—
192C2×D4—262no—
193C2×D4—262no—
194C2×D4C22×D1312yes—
195C2×D4C22×D1312yes—
196C22×C4—131no—
197C22×C4—262no—
198C22×C4—262no—
199C22×C4C22×D1311yescharacteristic
200Q16—262no—
201SD16—264no—
202SD16—522no—
203D8—24no—
204D8—22no—
205D8C22⋊D1314yescomplemented
206C2×C8—22no—
207C2×C8—131no—
208C2×C8—131no—
209C2×C8—262no—
210C2×C8C22×D1311yescharacteristic
211C2×C8C22×D1311yescharacteristic
212C4⋊C4—131no—
213C4⋊C4—132no—
214C4⋊C4—262no—
215C22⋊C4—131no—
216C22⋊C4—131no—
217C22⋊C4—262no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42—131no—
223C13#328011yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—44no—
227C23—44no—
228C23—82no—
229C23—131no—
230C23D4×D1311yescharacteristic
231Q8—262no—
232Q8—262no—
233D4—22no—
234D4—22no—
235D4—22no—
236D4—44no—
237D4—262no—
238D4—524no—
239D4—1042no—
240D4C2×C22⋊D1314yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—524no—
251C2×C4—1042no—
252C2×C4D4×D1311yescharacteristic
253C2×C4C23×D1311yescharacteristic
254C8—21no—
255C8—261no—
256C8—261no—
257C8C2×C22⋊D1312yes—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—88no—
267C22—261no—
268C22—261no—
269C22—261no—
270C22#8816612yescomplemented
271C22C2×D4×D1311yescharacteristic
272C4—21no—
273C4—261no—
274C4—261no—
275C4—261no—
276C4—522no—
277C4—522no—
278C4#8825111yescharacteristic
279C4C22×C22⋊D1311yescharacteristic
280C2—22no—
281C2—44no—
282C2—82no—
283C2—521no—
284C2C2×#8816611yescharacteristic
285C2#1171946211yescharacteristic
286C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×D8C2
socleC22×C13C22×D4
hypercenterC22×D8D13
hypocenterC13#3280
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C13×D8C2semidirect
2. #11719511C2semidirect
3. C2×#88166C2semidirect
4. #11718879C2semidirect
5. #11718819C2semidirect
6. #11718818C2semidirect
7. #11718816C2semidirect
8. #11718814C2semidirect
9. D8×Dic13C2semidirect
10. #11718777C2semidirect
11. C8×C22⋊D13C2semidirect
13. C2×#6129C22semidirect
22. #88192C22semidirect
23. #88190C22semidirect
25. D4×Dic13C22semidirect
26. C2×#6105C22semidirect
27. C2×#6105C22semidirect
31. C2×Dic52C22semidirect
32. C2×C8×D13C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
36. #88060C22semidirect
37. #88058C22semidirect
38. #88056C22semidirect
39. #88054C22semidirect
40. C8×Dic13C22semidirect
59. C13×D8D4semidirect
116. C22×D8D13semidirect
135. C22×C13#135semidirect
205. D8C22⋊D13semidirect
223. C13#3280semidirect
270. C22#88166semidirect

Maximal subgroups

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

subgroupindex
C22×C13×D82
#117195112
C2×#881662
#117188792
#117188192
#117188182
#117188162
#117188142
D8×Dic132
#117187772
C8×C22⋊D132
#328013