Finite Group Databasebeta

← #13125301

Subgroups — #13125301

Order 1664.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88169C212yesmaximal, complemented
2C2×#88165C212yesmaximal, complemented
3#11719421C211yesmaximal, characteristic, complemented
4D13×#124C211yesmaximal, characteristic, complemented
5C13×#496C211yesmaximal, characteristic, complemented
6#11718829C212yesmaximal, complemented
7#11718816C212yesmaximal, complemented
8#11718735C211yesmaximal, characteristic, complemented
9#11718721C211yesmaximal, characteristic, complemented
10#11718376C211yesmaximal, characteristic, complemented
11#11718368C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×#6129C2212yes—
14C2×D4×D13C2211yescharacteristic
15C2×C13×SD16C2212yescomplemented
16C2×C13×D8C2212yes—
17C13×#127C2211yescharacteristic, complemented
18C13×#124C2211yescharacteristic
19#88201C2211yescharacteristic
20C2×#6107C2212yescomplemented
21#88192—22no—
22#88190C2211yescharacteristic
23#88190C2212yescomplemented
24D4×Dic13—22no—
25C2×#6105C2212yes—
26C2×#6105C2212yescomplemented
27C2×#6104C2212yes—
28#88169—28no—
29#88165—28no—
30C2×Dic52C2212yescomplemented
31C2×#6095C2212yes—
32C2×#6094C2212yes—
33#88139—22no—
34C22⋊C4×D13—22no—
35#88129C2211yescharacteristic
36C42×D13C2211yescharacteristic
37#88123C2211yescharacteristic, complemented
38C13×#97C2211yescharacteristic, complemented
39C8×Dic13C2212yescomplemented
40#88043C2211yescharacteristic, complemented
41C23×D13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×D4×C13—22no—
44C2×D4×C13C2312yes—
45C2×D4×C13C2311yescharacteristic
46C2×C22⋊D13—22no—
47C2×C22⋊D13—21no—
48C22×Dic13—22no—
49Q8×D13—24no—
50#6129—24no—
51#6129—24no—
52D4×D13—24no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13D412yes—
56C2×C4×D13C2311yescharacteristic
57C2×Dic26—21no—
58C2×Dic26C2312yes—
59C2×Dic26C2311yescharacteristic
60C13×SD16—24no—
61C13×D8—24no—
62C2×C8×C13C2312yes—
63C13×C22⋊C4—22no—
64C42×C13C2311yescharacteristic
65C22⋊Dic13—22no—
66C22⋊Dic13—24no—
67#6107—24no—
68#6105—24no—
69#6105—24no—
70#6104—24no—
71#6103—22no—
72#6103—22no—
73C4⋊Dic13—22no—
74C4×Dic13D412yes—
75C4×Dic13C2311yescharacteristic
76C2×#1055C2312yes—
77Dic52—24no—
78#6095—24no—
79#6094D418yescomplemented
80#3153—131nomaximal, Sylow
81C23×C13—21no—
82C23×C13—22no—
83C22×D13—21no—
84C22×D13—44no—
85C22×D13—42no—
86C22×D13C2×D411yescharacteristic
87Q8×C13—22no—
88D4×C13—22no—
89D4×C13—22no—
90D4×C13—22no—
91D4×C13—44no—
92C2×C4×C13—21no—
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—44no—
96C22⋊D13—42no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—44no—
100C2×Dic13C2×D412yes—
101C2×Dic13C2×D411yescharacteristic
102D52—22no—
103C4×D13—42no—
104C4×D13—42no—
105C4×D13C2×D414yes—
106Dic26—22no—
107Dic26—22no—
108Dic26—22no—
109Dic26—42no—
110C8×C13C2×D414yes—
111#1055C2×D414yes—
112C2×#137—132no—
113C2×AGL(1,ℤ/8)—132no—
114#532—131no—
115C2×#124—131no—
116#497—131no—
117#497—131no—
118#496—131no—
119#496D1311yescharacteristic, complemented
120#495—132no—
121#495—132no—
122C4×M16—131no—
123C22×C13—42no—
124C22×C13—41no—
125C22×C13—44no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C2×D13—22no—
129C2×D13—41no—
130C2×D13—42no—
131C2×D13—84no—
132C2×D13#12712yes—
133C4×C13—22no—
134C4×C13—41no—
135C4×C13C22×D412yes—
136Dic13—22no—
137Dic13—41no—
138Dic13—42no—
139Dic13#12712yes—
140C2×#41—132no—
141C22×Q8—131no—
142C22×D4—131no—
143#137—268no—
144AGL(1,ℤ/8)—268no—
145C2×Q16—132no—
146C2×Q16—132no—
147C2×SD16—132no—
148C2×SD16—132no—
149C2×SD16—132no—
150C2×SD16C2×D1312yescomplemented
151C2×D8—132no—
152C2×D8C2×D1312yes—
153C2×M16—132no—
154C4⋊Q8—131no—
155#127C2×D1311yescharacteristic, complemented
156#124—131no—
157#124—131no—
158#124—132no—
159#124—131no—
160#124—262no—
161#124C2×D1311yescharacteristic
162#121—262no—
163C4×D4—262no—
164C2×C22⋊C4—262no—
165C2×C42—131no—
166#97—131no—
167#97C2×D1311yescharacteristic, complemented
168C4×C8—132no—
169C2×C13—81no—
170C2×C13—82no—
171C2×C13C2×#12711yescharacteristic
172C2×C13#57512yes—
173D13—22no—
174D13—81no—
175C24—261no—
176#41—264no—
177#41—264no—
178C2×Q8—131no—
179C2×Q8—132no—
180C2×Q8—261no—
181C2×Q8—264no—
182C2×Q8C22×D1311yescharacteristic
183C2×D4—22no—
184C2×D4—131no—
185C2×D4—264no—
186C2×D4—261no—
187C2×D4—262no—
188C2×D4C22×D1311yescharacteristic
189C2×D4C22×D1312yes—
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—261no—
193C22×C4—262no—
194Q16—264no—
195Q16—264no—
196SD16—24no—
197SD16—264no—
198SD16—264no—
199SD16—264no—
200D8—24no—
201D8—264no—
202M16—138no—
203C2×C8—132no—
204C2×C8C22×D1312yes—
205C4⋊C4—262no—
206C22⋊C4—22no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4—264no—
210C22⋊C4—262no—
211C42—132no—
212C42—131no—
213C42C22×D1311yescharacteristic
214C13#315311yescharacteristic, complemented, Sylow
215C23—21no—
216C23—22no—
217C23—131no—
218C23—261no—
219C23—522no—
220C23—524no—
221Q8—22no—
222Q8—262no—
223Q8—262no—
224Q8—262no—
225Q8—522no—
226D4—22no—
227D4—22no—
228D4—22no—
229D4—44no—
230D4—262no—
231D4—522no—
232D4—524no—
233C2×C4—21no—
234C2×C4—131no—
235C2×C4—134no—
236C2×C4—132no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—524no—
242C2×C4D4×D1312yes—
243C2×C4C23×D1311yescharacteristic
244C8—134no—
245C8D4×D1314yes—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—132no—
251C22—262no—
252C22—522no—
253C22—521no—
254C22—1044no—
255C22C2×D4×D1311yescharacteristic
256C4—22no—
257C4—41no—
258C4—132no—
259C4—262no—
260C4—522no—
261C4—521no—
262C4C2×D4×D1312yes—
263C2—81no—
264C2—82no—
265C2—262no—
266C2—1041no—
267C2D13×#12711yescharacteristic
268C2#1171947812yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3153
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#88169C2semidirect
2. C2×#88165C2semidirect
3. #11719421C2semidirect
4. D13×#124C2semidirect
5. C13×#496C2semidirect
6. #11718829C2semidirect
7. #11718816C2semidirect
8. #11718735C2semidirect
9. #11718721C2semidirect
10. #11718376C2semidirect
11. #11718368C2semidirect
15. C2×C13×SD16C22semidirect
17. C13×#127C22semidirect
20. C2×#6107C22semidirect
23. #88190C22semidirect
26. C2×#6105C22semidirect
30. C2×Dic52C22semidirect
37. #88123C22semidirect
38. C13×#97C22semidirect
39. C8×Dic13C22semidirect
40. #88043C22semidirect
79. #6094D4semidirect
119. #496D13semidirect
150. C2×SD16C2×D13semidirect
155. #127C2×D13semidirect
167. #97C2×D13semidirect
214. C13#3153semidirect

Maximal subgroups

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

subgroupindex
C2×#881692
C2×#881652
#117194212
D13×#1242
C13×#4962
#117188292
#117188162
#117187352
#117187212
#117183762
#117183682
#315313