Finite Group Databasebeta

← #13124895

Subgroups — #13124895

Order 1664.

434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719421C211yesmaximal, characteristic, complemented
2C4×#6131C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718833C212yesmaximal, complemented
5SD16×Dic13C212yesmaximal, complemented
6#11718733C211yesmaximal, characteristic, complemented
7#11718682C211yesmaximal, characteristic, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic, complemented
10#11718440C212yesmaximal, complemented
11#11718417C212yesmaximal, complemented
12C2×#6131C2211yescharacteristic
13C2×#6129—21no—
14C2×C13×SD16C2212yes—
15C13×#127C2211yescharacteristic
16C4×Q8×C13C2211yescharacteristic
17Q8×Dic13C2211yescharacteristic
18#88192—21no—
19#88192C2212yes—
20#88190—21no—
21D4×Dic13—21no—
22D4×Dic13C2212yes—
23C2×#6104C2212yes—
24#88147—21no—
25#88147C2211yescharacteristic
26#88146—21no—
27#88146C2211yescharacteristic
28C4×D52—21no—
29C4×D52C2211yescharacteristic
30C42×D13—21no—
31C42×D13C2211yescharacteristic
32#88123C2211yescharacteristic
33C13×C4⋊C8C2211yescharacteristic
34C13×#102C2212yes—
35#88075C2212yes—
36#88072C2212yes—
37#88061C2212yes—
38#88060C2212yes—
39#88057C2212yes—
40C8×Dic13C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13C2312yes—
47C2×C22⋊D13—22no—
48C22×Dic13—22no—
49#6131—22no—
50#6131—22no—
51#6129—44no—
52C2×D52—21no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—21no—
56C2×C4×D13—21no—
57C2×C4×D13D411yescharacteristic
58C2×C4×D13D411yescharacteristic
59C2×C4×D13C2311yescharacteristic
60C2×Dic26—21no—
61C13×SD16—24no—
62C2×C8×C13C2312yes—
63C13×C4⋊C4—21no—
64C13×C4⋊C4C2311yescharacteristic
65C42×C13—21no—
66C42×C13C2311yescharacteristic
67C22⋊Dic13—22no—
68C22⋊Dic13—22no—
69#6104—24no—
70#6103—21no—
71#6103—21no—
72#6103—21no—
73C4⋊Dic13—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13C2311yescharacteristic
76C4⋊Dic13C2312yes—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13D411yescharacteristic
80C4×Dic13D411yescharacteristic
81C4×Dic13C2311yescharacteristic
82C2×#1055C2312yes—
83#3106—131nomaximal, Sylow
84C23×C13—22no—
85C22×D13—21no—
86C22×D13C2×D411yescharacteristic
87Q8×C13—21no—
88Q8×C13#4112yescomplemented
89D4×C13—22no—
90D4×C13—22no—
91D4×C13—42no—
92D4×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—44no—
99C2×Dic13—21no—
100C2×Dic13—22no—
101C2×Dic13—44no—
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—24no—
106D52—21no—
107D52#4112yescomplemented
108C4×D13—24no—
109C4×D13—22no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13—22no—
113C4×D13—42no—
114C4×D13—42no—
115Dic26—42no—
116C8×C13—22no—
117#1055—22no—
118#532—131no—
119C4×#41—131no—
120#482—132no—
121#477—131no—
122#476—131no—
123#460D1311yescharacteristic, complemented
124#459—131no—
125#449—132no—
126C4×SD16—132no—
127C4×D8—132no—
128#431—131no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13C22×D411yescharacteristic
133C2×D13—21no—
134C2×D13—22no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—41no—
138C2×D13—41no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13#13512yes—
143C4×C13C2×#4111yescharacteristic
144C4×C13C2×#4111yescharacteristic
145Dic13—21no—
146Dic13—21no—
147Dic13—41no—
148Dic13—42no—
149Dic13AGL(1,ℤ/8)12yes—
150C2×#41—131no—
151C2×#41—261no—
152C2×SD16C2×D1312yes—
153C2×D8—132no—
154C4⋊Q8—131no—
155#127C2×D1311yescharacteristic
156#124—261no—
157#121—132no—
158#121—261no—
159C4×Q8—131no—
160C4×Q8C2×D1311yescharacteristic
161C4×D4—132no—
162C4×D4—131no—
163C4×D4—131no—
164C4×D4—261no—
165C4×D4—261no—
166C4×D4—261no—
167#117—131no—
168#117—261no—
169C2×C42—131no—
170C2×C42—261no—
171#107—132no—
172#106—132no—
173C4⋊C8—131no—
174C4⋊C8C2×D1311yescharacteristic
175#103—132no—
176#102—132no—
177#102—132no—
178#102C2×D1312yes—
179C22⋊C8—132no—
180C4×C8—132no—
181C2×C13—82no—
182C2×C13#52511yescharacteristic
183C2×C13C2×#13511yescharacteristic
184C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
185D13—41no—
186D13—42no—
187#41—262no—
188#41—262no—
189#41—524no—
190C2×Q8—261no—
191C2×Q8C22×D1311yescharacteristic
192C2×D4—21no—
193C2×D4—21no—
194C2×D4—131no—
195C2×D4—261no—
196C2×D4—262no—
197C2×D4C22×D1312yes—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4—262no—
204C22×C4—261no—
205SD16—24no—
206D8—264no—
207C2×C8—132no—
208C2×C8C22×D1312yes—
209C4⋊C4—21no—
210C4⋊C4—131no—
211C4⋊C4—132no—
212C4⋊C4—261no—
213C4⋊C4—261no—
214C4⋊C4C22×D1311yescharacteristic
215C22⋊C4—261no—
216C22⋊C4—261no—
217C22⋊C4—262no—
218C22⋊C4—262no—
219C22⋊C4—261no—
220C42—21no—
221C42—131no—
222C42—131no—
223C42—131no—
224C42—261no—
225C42—261no—
226C42C22×D1311yescharacteristic
227C13#310611yescharacteristic, complemented, Sylow
228C23—22no—
229C23—131no—
230C23—261no—
231Q8—21no—
232Q8—522no—
233Q8#612912yescomplemented
234D4—22no—
235D4—22no—
236D4—42no—
237D4—42no—
238D4—132no—
239D4—264no—
240D4—261no—
241D4—524no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—262no—
248C2×C4—264no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—262no—
254C2×C4—522no—
255C2×C4—524no—
256C2×C4—522no—
257C2×C4D4×D1311yescharacteristic
258C2×C4D4×D1311yescharacteristic
259C2×C4C23×D1311yescharacteristic
260C8—22no—
261C8—262no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—261no—
266C22—261no—
267C22—262no—
268C22—261no—
269C22—521no—
270C22—521no—
271C22C2×D4×D1311yescharacteristic
272C4—21no—
273C4—22no—
274C4—41no—
275C4—132no—
276C4—261no—
277C4—261no—
278C4—521no—
279C4—522no—
280C4#8817012yes—
281C4C2×#612911yescharacteristic
282C4#41×D1311yescharacteristic
283C2—82no—
284C2—521no—
285C2—522no—
286C2#1171931111yescharacteristic
287C2C2×#8817011yescharacteristic
288C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
hypercenter#460D13
hypocenterC13#3106
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #11719421C2semidirect
2. C4×#6131C2semidirect
3. C13×#460C2semidirect
4. #11718833C2semidirect
5. SD16×Dic13C2semidirect
6. #11718733C2semidirect
7. #11718682C2semidirect
8. #11718503C2semidirect
9. #11718494C2semidirect
10. #11718440C2semidirect
11. #11718417C2semidirect
88. Q8×C13#41semidirect
107. D52#41semidirect
123. #460D13semidirect
227. C13#3106semidirect
233. Q8#6129semidirect

Maximal subgroups

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

subgroupindex
#117194212
C4×#61312
C13×#4602
#117188332
SD16×Dic132
#117187332
#117186822
#117185032
#117184942
#117184402
#117184172
#310613