Finite Group Databasebeta

← #13125283

Subgroups — #13125283

Order 1664.

656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#88168C214yesmaximal, complemented
2#11719430C211yesmaximal, characteristic, complemented
3D13×#127C211yesmaximal, characteristic, complemented
4C13×#492C211yesmaximal, characteristic, complemented
5#11718837C214yesmaximal, complemented
6#11718746C211yesmaximal, characteristic, complemented
7#11718734C211yesmaximal, characteristic, complemented
8#11718356C211yesmaximal, characteristic, complemented
9C4×#6094C211yesmaximal, characteristic, complemented
10C2×#6131C2212yes—
11C2×D4×D13—22no—
12C2×D4×D13C2212yes—
13C2×C13×SD16C2214yescomplemented
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C13×#127C2211yescharacteristic
16#88201C2212yescomplemented
17C2×#6106C2214yescomplemented
18#88194—22no—
19#88194C2212yes—
20C2×#6104C2214yescomplemented
21#88168—216no—
22C2×D104C2214yescomplemented
23C2×#6094C2212yes—
24#88149—22no—
25#88147—22no—
26#88128C2211yescharacteristic
27#88128C2211yescharacteristic, complemented
28C42×D13C2211yescharacteristic
29C4×C8×C13C2211yescharacteristic, complemented
30#88055C2212yescomplemented
31C4×#1055C2211yescharacteristic, complemented
32C23×D13—22no—
33C2×Q8×C13C2312yes—
34C2×D4×C13—22no—
35C2×D4×C13C2312yes—
36C2×C22⋊D13—22no—
37C2×C22⋊D13—24no—
38#6131—28no—
39D4×D13—28no—
40D4×D13—48no—
41C2×D52—22no—
42C2×D52—22no—
43C2×D52—22no—
44C2×D52C2312yes—
45C2×D52C2312yes—
46C2×C4×D13—22no—
47C2×C4×D13D412yes—
48C2×C4×D13C2311yescharacteristic
49C13×SD16—28no—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—22no—
52C42×C13C2311yescharacteristic
53#6106—28no—
54#6104—28no—
55#6103—24no—
56C4×Dic13D412yes—
57C4×Dic13C2311yescharacteristic
58C2×#1055C2312yes—
59D104—28no—
60#6094D418yescomplemented
61#3151—131nomaximal, Sylow
62C23×C13—22no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—48no—
66C22×D13—44no—
67C22×D13C2×D411yescharacteristic
68Q8×C13—24no—
69D4×C13—24no—
70D4×C13—44no—
71C2×C4×C13—22no—
72C2×C4×C13C2×D412yes—
73C2×C4×C13C2411yescharacteristic
74C22⋊D13—48no—
75C22⋊D13—44no—
76C2×Dic13C2×D412yes—
77C2×Dic13C2×D411yescharacteristic
78D52—24no—
79D52—24no—
80D52—44no—
81D52—44no—
82D52—44no—
83C4×D13—24no—
84C4×D13—44no—
85C4×D13C2×D414yes—
86C8×C13C2×D414yescomplemented
87#1055C2×D414yescomplemented
88C2×AGL(1,ℤ/8)—134no—
89#532—131no—
90C2×#127—131no—
91#496—134no—
92#493—131no—
93#493—131no—
94#492—131no—
95#492D1311yescharacteristic, complemented
96C4×M16—131no—
97C22×C13—42no—
98C22×C13—44no—
99C22×C13C22×D411yescharacteristic
100C2×D13—22no—
101C2×D13—42no—
102C2×D13—42no—
103C2×D13—44no—
104C2×D13—44no—
105C2×D13—88no—
106C2×D13#12712yes—
107C4×C13—42no—
108C4×C13AGL(1,ℤ/8)14yescomplemented
109C4×C13C22×D412yes—
110Dic13—22no—
111Dic13#12712yes—
112C2×#41—132no—
113C22×D4—132no—
114C22×D4—262no—
115AGL(1,ℤ/8)—2616no—
116C2×SD16—134no—
117C2×SD16C2×D1314yescomplemented
118C2×D8—134no—
119C2×D8—134no—
120C2×M16—132no—
121C4⋊Q8C2×D1311yescharacteristic, complemented
122#127—132no—
123#127—131no—
124#127—131no—
125#127—262no—
126#127C2×D1311yescharacteristic
127#124—132no—
128#121—262no—
129C4×D4—262no—
130C2×C42—131no—
131#97—132no—
132C4×C8—131no—
133C4×C8C2×D1311yescharacteristic, complemented
134C2×C13—82no—
135C2×C13C2×#12711yescharacteristic
136C2×C13C2×AGL(1,ℤ/8)12yes—
137D13—22no—
138D13—82no—
139D13—82no—
140C24—262no—
141#41—268no—
142C2×Q8C22×D1312yes—
143C2×D4—22no—
144C2×D4—132no—
145C2×D4—132no—
146C2×D4—262no—
147C2×D4—268no—
148C2×D4—264no—
149C2×D4—262no—
150C2×D4—262no—
151C2×D4—262no—
152C2×D4—528no—
153C2×D4C22×D1312yes—
154C22×C4—131no—
155C22×C4—132no—
156C22×C4—262no—
157SD16—28no—
158SD16—268no—
159D8—268no—
160D8—268no—
161M16—138no—
162C2×C8—132no—
163C2×C8C22×D1312yes—
164C4⋊C4—22no—
165C22⋊C4—264no—
166C42—132no—
167C42—131no—
168C42C22×D1311yescharacteristic
169C13#315111yescharacteristic, complemented, Sylow
170C23—22no—
171C23—131no—
172C23—262no—
173C23—262no—
174C23—524no—
175C23—528no—
176Q8—24no—
177D4—24no—
178D4—44no—
179D4—264no—
180D4—264no—
181D4—524no—
182D4—524no—
183D4—528no—
184D4—524no—
185D4—524no—
186C2×C4—22no—
187C2×C4—131no—
188C2×C4—134no—
189C2×C4—132no—
190C2×C4—264no—
191C2×C4—524no—
192C2×C4D4×D1312yes—
193C2×C4C23×D1311yescharacteristic
194C8—134no—
195C8D4×D1314yescomplemented
196C22—44no—
197C22—42no—
198C22—132no—
199C22—262no—
200C22—524no—
201C22—524no—
202C22—522no—
203C22—522no—
204C22—1048no—
205C22C2×D4×D1311yescharacteristic
206C4—42no—
207C4—132no—
208C4—262no—
209C4#8816814yescomplemented
210C4C2×D4×D1312yes—
211C2—82no—
212C2—262no—
213C2—1042no—
214C2—1042no—
215C2D13×#12711yescharacteristic
216C2C2×#8816812yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#492C2
socleC22×C13C22×D4
hypercenter#492D13
hypocenterC13#3151
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#88168C2semidirect
2. #11719430C2semidirect
3. D13×#127C2semidirect
4. C13×#492C2semidirect
5. #11718837C2semidirect
6. #11718746C2semidirect
7. #11718734C2semidirect
8. #11718356C2semidirect
9. C4×#6094C2semidirect
13. C2×C13×SD16C22semidirect
14. C13×C4⋊Q8C22semidirect
16. #88201C22semidirect
17. C2×#6106C22semidirect
20. C2×#6104C22semidirect
22. C2×D104C22semidirect
27. #88128C22semidirect
29. C4×C8×C13C22semidirect
30. #88055C22semidirect
31. C4×#1055C22semidirect
60. #6094D4semidirect
86. C8×C13C2×D4semidirect
87. #1055C2×D4semidirect
95. #492D13semidirect
108. C4×C13AGL(1,ℤ/8)semidirect
117. C2×SD16C2×D13semidirect
121. C4⋊Q8C2×D13semidirect
133. C4×C8C2×D13semidirect
169. C13#3151semidirect
195. C8D4×D13semidirect
209. C4#88168semidirect

Maximal subgroups

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

subgroupindex
C2×#881682
#117194302
D13×#1272
C13×#4922
#117188372
#117187462
#117187342
#117183562
C4×#60942
#315113