Finite Group Databasebeta

← #13124359

Subgroups — #13124359

Order 1664.

490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×C13×#137C211yesmaximal, characteristic, complemented
2#11719535C211yesmaximal, characteristic
3#11719517C211yesmaximal, characteristic, complemented
4C22×#6106C211yesmaximal, characteristic, complemented
5#11718894C211yesmaximal, characteristic, complemented
6#11718846C214yesmaximal, complemented
7#11718824C214yesmaximal, complemented
8#11718792C211yesmaximal, characteristic, complemented
9#11718780C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic
12C22×D52C2211yescharacteristic
13C13×#137—24no—
14C2×C13×Q16C2212yescomplemented
15C2×C13×SD16C2212yescomplemented
16C2×C13×M16C2211yescharacteristic
17#88201C2212yes—
18Q8×Dic13—22no—
19Q8×Dic13C2214yescomplemented
20C2×#6106—24no—
21C2×#6106C2214yes—
22#88194C2212yes—
23#88191—22no—
24#88184—22no—
25#88180—22no—
26#88180C2211yescharacteristic
27#88180C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29#88075C2212yescomplemented
30#88072C2212yescomplemented
31#88061C2214yes—
32#88054C2214yescomplemented
33C23×D13—21no—
34C13×#41—22no—
35C13×#41—22no—
36C2×Q8×C13—21no—
37C2×Q8×C13—22no—
38C2×Q8×C13D414yescomplemented
39C2×Q8×C13C2311yescharacteristic
40C2×Q8×C13C2312yes—
41C2×D4×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—24no—
47C2×D52—22no—
48C2×D52—22no—
49C2×D52—21no—
50C2×D52C2312yes—
51C13×Q16—24no—
52C13×SD16—24no—
53C13×M16—22no—
54C2×C8×C13C2312yes—
55C22⋊Dic13—21no—
56C22⋊Dic13D412yes—
57#6106—28no—
58#6103—24no—
59C4⋊Dic13—24no—
60C4⋊Dic13D412yes—
61C4⋊Dic13C2312yes—
62C4×Dic13—21no—
63C4×Dic13—24no—
64C4×Dic13C2312yes—
65C2×#1055—22no—
66C2×#1055C2312yes—
67#3043—131nomaximal, Sylow
68C23×C13—21no—
69C23×C13C2×D411yescharacteristic
70C22×D13—22no—
71C22×D13—42no—
72C22×D13—82no—
73Q8×C13—24no—
74Q8×C13—22no—
75Q8×C13—21no—
76Q8×C13—21no—
77Q8×C13C2×D414yes—
78D4×C13—21no—
79D4×C13—21no—
80D4×C13—42no—
81C2×C4×C13—24no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D412yes—
87C2×C4×C13#4112yes—
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—84no—
90C2×Dic13—22no—
91C2×Dic13C2×D414yes—
92D52—22no—
93D52—22no—
94D52—42no—
95C8×C13—22no—
96#1055—22no—
97C2×#137D1311yescharacteristic, complemented
98C22×SD16—131no—
99#535—131no—
100#519—131no—
101#464—134no—
102#460—134no—
103#424—131no—
104#418—131no—
105#416—131no—
106C22×C13—22no—
107C22×C13—41no—
108C22×C13—42no—
109C22×C13#12112yes—
110C22×C13C22×D411yescharacteristic
111C2×D13—42no—
112C2×D13—44no—
113C2×D13—84no—
114C4×C13—24no—
115C4×C13—41no—
116C4×C13#12112yes—
117C4×C13C22×D411yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—24no—
120Dic13—42no—
121C2×#41C2×D1311yescharacteristic
122C22×Q8C2×D1311yescharacteristic
123C22×D4—131no—
124#137—24no—
125C2×Q16C2×D1312yescomplemented
126C2×SD16—134no—
127C2×SD16—264no—
128C2×SD16C2×D1312yescomplemented
129C2×M16C2×D1311yescharacteristic
130C22×C8—131no—
131#127—132no—
132#124—132no—
133#121—262no—
134#120—262no—
135C4×Q8—134no—
136C4×Q8—262no—
137#117—131no—
138#117—131no—
139#117—262no—
140C4⋊C8—134no—
141#103—132no—
142#102—132no—
143#102—134no—
144C2×C13—22no—
145C2×C13—81no—
146C2×C13C2×#12111yescharacteristic
147C2×C13#57712yes—
148D13—82no—
149C24—261no—
150#41—22no—
151#41—22no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8C22⋊D1314yescomplemented
155C2×Q8C22×D1311yescharacteristic
156C2×Q8C22×D1312yes—
157C2×D4—21no—
158C2×D4—132no—
159C2×D4—264no—
160C2×D4—261no—
161C2×D4—262no—
162C2×D4—262no—
163C2×D4C22×D1311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4C22×D1311yescharacteristic
167Q16—24no—
168SD16—24no—
169SD16—268no—
170M16—22no—
171C2×C8—132no—
172C2×C8—262no—
173C2×C8C22×D1312yes—
174C4⋊C4—132no—
175C4⋊C4—132no—
176C4⋊C4—264no—
177C22⋊C4—132no—
178C22⋊C4—264no—
179C22⋊C4—261no—
180C42—132no—
181C42—264no—
182C42—261no—
183C13#304311yescharacteristic, complemented, Sylow
184C23—21no—
185C23—262no—
186C23—522no—
187C23—1042no—
188C23D4×D1311yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D1314yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—262no—
198D4—262no—
199D4—522no—
200D4—1044no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—134no—
206C2×C4—262no—
207C2×C4D4×D1311yescharacteristic
208C2×C4#612912yes—
209C2×C4C2×C22⋊D1312yes—
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—262no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—524no—
217C22—522no—
218C22—1044no—
219C22#8819312yes—
220C22C2×D4×D1311yescharacteristic
221C4—24no—
222C4—41no—
223C4—264no—
224C4—522no—
225C4#8819312yes—
226C4C2×#612911yescharacteristic
227C4C22×C22⋊D1311yescharacteristic
228C2—22no—
229C2—81no—
230C2—1042no—
231C2#1171948312yes—
232C2C2×#8819311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
prime radical#11719535C2
hypercenterC2×#137D13
hypocenterC13#3043
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C13×#137C2semidirect
3. #11719517C2semidirect
4. C22×#6106C2semidirect
5. #11718894C2semidirect
6. #11718846C2semidirect
7. #11718824C2semidirect
8. #11718792C2semidirect
9. #11718780C2semidirect
14. C2×C13×Q16C22semidirect
15. C2×C13×SD16C22semidirect
19. Q8×Dic13C22semidirect
29. #88075C22semidirect
30. #88072C22semidirect
32. #88054C22semidirect
38. C2×Q8×C13D4semidirect
97. C2×#137D13semidirect
125. C2×Q16C2×D13semidirect
128. C2×SD16C2×D13semidirect
154. C2×Q8C22⋊D13semidirect
183. C13#3043semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1372
#117195352
#117195172
C22×#61062
#117188942
#117188462
#117188242
#117187922
#117187802
#304313