Finite Group Databasebeta

← #13125226

Subgroups — #13125226

Order 1664.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719421C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718731C211yesmaximal, characteristic, complemented
6#11718432C214yesmaximal, complemented
7#11718426C214yesmaximal, complemented
8C4×#6094C211yesmaximal, characteristic, complemented
9#11718342C211yesmaximal, characteristic, complemented
10C2×Q8×D13—21no—
11C2×#6129C2212yes—
12C13×C4⋊Q8C2211yescharacteristic
13C13×#127C2211yescharacteristic
14#88198—21no—
15#88192—21no—
16#88192—21no—
17#88190C2212yes—
18D4×Dic13—21no—
19D4×Dic13—21no—
20C2×#6094C2212yes—
21C4⋊C4×D13—21no—
22C4⋊C4×D13C2212yes—
23#88142—21no—
24#88142C2212yes—
25C42×D13C2211yescharacteristic
26#88123C2211yescharacteristic
27#88123C2211yescharacteristic
28C13×#102C2214yes—
29C4×C8×C13C2211yescharacteristic
30#88072C2214yes—
31#88056C2214yes—
32#88055C2212yes—
33#88050C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C2×C22⋊D13—22no—
40C22×Dic13—22no—
41Q8×D13—44no—
42#6129—28no—
43C2×C4×D13—22no—
44C2×C4×D13D411yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×C4×D13C2311yescharacteristic
47C2×Dic26—21no—
48C2×Dic26—22no—
49C2×Dic26C2312yes—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2312yes—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—21no—
59C4⋊Dic13C2312yes—
60#6101—22no—
61#6101—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66#6094—24no—
67#3141—131nomaximal, Sylow
68C23×C13—22no—
69C22×D13C2×D411yescharacteristic
70Q8×C13—42no—
71D4×C13—24no—
72D4×C13—42no—
73D4×C13—42no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2411yescharacteristic
78C22⋊D13—44no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—44no—
82C2×Dic13C2×D411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C4×D13—22no—
86C4×D13—22no—
87C4×D13—44no—
88C4×D13#4114yes—
89Dic26—24no—
90Dic26—44no—
91Dic26—42no—
92C8×C13—22no—
93#1055—22no—
94#532—131no—
95C2×C4⋊Q8—131no—
96#489—134no—
97#487—131no—
98#487—131no—
99#486—131no—
100#486D1311yescharacteristic, complemented
101#417—134no—
102C4×M16—131no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13C22×D411yescharacteristic
107C2×D13—21no—
108C2×D13—21no—
109C2×D13#12412yes—
110C4×C13—42no—
111C4×C13AGL(1,ℤ/8)12yes—
112C4×C13#13712yes—
113C4×C13C2×#4112yes—
114Dic13—21no—
115Dic13—21no—
116Dic13—42no—
117Dic13—42no—
118Dic13#12412yes—
119C2×#41—132no—
120C22×Q8—261no—
121C2×M16—132no—
122C4⋊Q8—132no—
123C4⋊Q8—131no—
124C4⋊Q8—131no—
125C4⋊Q8—261no—
126C4⋊Q8—261no—
127C4⋊Q8C2×D1311yescharacteristic
128#127C2×D1311yescharacteristic
129#124—132no—
130#121—261no—
131#121—261no—
132C4×D4—261no—
133C4×D4—261no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—261no—
136C2×C42—131no—
137#103—134no—
138#103—134no—
139#102—134no—
140#102C2×D1314yes—
141#97—132no—
142C4×C8—131no—
143C4×C8C2×D1311yescharacteristic
144C2×C13—82no—
145C2×C13C2×#12411yescharacteristic
146C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C13C2×#13711yescharacteristic
148D13—22no—
149#41—268no—
150C2×Q8—21no—
151C2×Q8—132no—
152C2×Q8—262no—
153C2×Q8—261no—
154C2×Q8—524no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—262no—
158C2×D4C22×D1312yes—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—262no—
163C22×C4—262no—
164M16—264no—
165C2×C8—132no—
166C2×C8C22×D1312yes—
167C4⋊C4—21no—
168C4⋊C4—132no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4—261no—
174C4⋊C4C22×D1312yes—
175C22⋊C4—262no—
176C22⋊C4—262no—
177C42—131no—
178C42—131no—
179C42—131no—
180C42C22×D1311yescharacteristic
181C13#314111yescharacteristic, complemented, Sylow
182C23—22no—
183C23—131no—
184Q8—42no—
185Q8—264no—
186Q8—524no—
187Q8—522no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—524no—
192C2×C4—22no—
193C2×C4—131no—
194C2×C4—134no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—524no—
202C2×C4—524no—
203C2×C4D4×D1311yescharacteristic
204C2×C4D4×D1311yescharacteristic
205C2×C4C23×D1311yescharacteristic
206C8—22no—
207C8—262no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—132no—
212C22—261no—
213C22—261no—
214C22C2×D4×D1311yescharacteristic
215C4—42no—
216C4—132no—
217C4—261no—
218C4—261no—
219C4—522no—
220C4—522no—
221C4#8816512yes—
222C4#8816912yes—
223C4#41×D1312yes—
224C2—82no—
225C2—262no—
226C2D13×#12411yescharacteristic
227C2C2×#8816511yescharacteristic
228C2C2×#8816911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719421C2
hypercenter#486D13
hypocenterC13#3141
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. D13×C4⋊Q8C2semidirect
3. C13×#486C2semidirect
4. #11718754C2semidirect
5. #11718731C2semidirect
6. #11718432C2semidirect
7. #11718426C2semidirect
8. C4×#6094C2semidirect
9. #11718342C2semidirect
100. #486D13semidirect
181. C13#3141semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117194212
C13×#4862
#117187542
#117187312
#117184322
#117184262
C4×#60942
#117183422
#314113