Finite Group Databasebeta

← #13125557

Subgroups — #13125557

Order 1664.

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

normal subgroups only

This group has 402 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#11719433C211yesmaximal, characteristic, complemented
2#11719430C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718746C211yesmaximal, characteristic, complemented
5#11718739C211yesmaximal, characteristic, complemented
6#11718478C214yesmaximal, complemented
7#11718473C214yesmaximal, complemented
8#11718355C211yesmaximal, characteristic, complemented
9C4×#6094C211yesmaximal, characteristic, complemented
10C2×#6131—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13#88201—21no—
14#88200C2212yes—
15Q8×Dic13C2212yes—
16C2×#6106C2214yes—
17C2×#6094C2212yes—
18#88151—21no—
19#88149—21no—
20#88149C2212yes—
21#88147—21no—
22#88147C2212yes—
23#88146—21no—
24#88144—21no—
25#88141—21no—
26#88128C2211yescharacteristic
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#103C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88061C2214yes—
32#88055C2212yes—
33#88047C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37#6131—44no—
38C2×D52—22no—
39C2×D52—21no—
40C2×D52—21no—
41C2×D52C2312yes—
42C2×C4×D13—22no—
43C2×C4×D13D411yescharacteristic
44C2×C4×D13D411yescharacteristic
45C2×C4×D13C2311yescharacteristic
46C2×Dic26—21no—
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C42×C13C2311yescharacteristic
53#6106—28no—
54#6103—22no—
55#6103—22no—
56#6103—22no—
57C4⋊Dic13—21no—
58C4⋊Dic13—22no—
59C4⋊Dic13C2312yes—
60#6101—22no—
61C4×Dic13—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66#6094—24no—
67#3182—131nomaximal, Sylow
68C22×D13—22no—
69C22×D13C2×D411yescharacteristic
70Q8×C13—24no—
71Q8×C13—42no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—22no—
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—24no—
82D52—44no—
83D52—42no—
84D52—42no—
85C4×D13—22no—
86C4×D13—22no—
87C4×D13—22no—
88C4×D13—44no—
89Dic26—42no—
90C8×C13—22no—
91#1055#4114yescomplemented
92#533—131no—
93#532—131no—
94#500—131no—
95#492—131no—
96#487D1311yescharacteristic, complemented
97#486—131no—
98#468—134no—
99#440—134no—
100C4×M16—131no—
101C22×C13C22×D411yescharacteristic
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C4×C13—42no—
109C4×C13—42no—
110C4×C13AGL(1,ℤ/8)12yes—
111C4×C13#13712yes—
112C4×C13C2×#4112yes—
113Dic13—21no—
114Dic13—21no—
115Dic13—21no—
116Dic13—42no—
117C2×#41—261no—
118C2×SD16—134no—
119C2×M16—132no—
120C4⋊Q8—131no—
121C4⋊Q8C2×D1311yescharacteristic
122C4⋊Q8C2×D1311yescharacteristic
123#127—131no—
124#125—261no—
125#124—261no—
126C22⋊Q8—132no—
127C22⋊Q8—261no—
128#121—132no—
129#121—261no—
130C4×Q8—132no—
131C4×Q8—261no—
132C4×D4—132no—
133C4×D4—261no—
134#117—261no—
135C2×C42—131no—
136#107—134no—
137#103C2×D1314yes—
138#102—134no—
139#97—132no—
140C4×C8—131no—
141C4×C8C2×D1311yescharacteristic
142C2×C13#53211yescharacteristic
143C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C13C2×#13711yescharacteristic
145D13—41no—
146D13—82no—
147#41—524no—
148C2×Q8—21no—
149C2×Q8—261no—
150C2×Q8C22×D1312yes—
151C2×D4—132no—
152C2×D4—262no—
153C2×D4—261no—
154C2×D4—261no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—262no—
159SD16—268no—
160M16—264no—
161C2×C8—132no—
162C2×C8C22×D1312yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—132no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—261no—
170C4⋊C4C22×D1312yes—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C22⋊C4—262no—
174C42—131no—
175C42—131no—
176C42—131no—
177C42—262no—
178C42C22×D1311yescharacteristic
179C13#318211yescharacteristic, complemented, Sylow
180C23—131no—
181C23—262no—
182Q8—24no—
183Q8—42no—
184Q8—522no—
185D4—264no—
186D4—524no—
187D4—522no—
188D4—522no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—524no—
199C2×C4D4×D1311yescharacteristic
200C2×C4D4×D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—22no—
203C8—134no—
204C22—261no—
205C22—261no—
206C22—261no—
207C22—522no—
208C22—522no—
209C22—522no—
210C22C2×D4×D1311yescharacteristic
211C4—42no—
212C4—42no—
213C4—261no—
214C4—261no—
215C4—261no—
216C4—522no—
217C4#8816812yes—
218C4#8817212yes—
219C4#41×D1312yes—
220C2—521no—
221C2—1042no—
222C2#1171937311yescharacteristic
223C2C2×#8816811yescharacteristic
224C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#487D13
hypocenterC13#3182
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#487C2semidirect
4. #11718746C2semidirect
5. #11718739C2semidirect
6. #11718478C2semidirect
7. #11718473C2semidirect
8. #11718355C2semidirect
9. C4×#6094C2semidirect
91. #1055#41semidirect
96. #487D13semidirect
179. C13#3182semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117194302
C13×#4872
#117187462
#117187392
#117184782
#117184732
#117183552
C4×#60942
#318213