Finite Group Databasebeta

← #13126004

Subgroups — #13126004

Order 1664.

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

normal subgroups only

This group has 334 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
1C2×C13×#125C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic
3#11718729C212yesmaximal, complemented
4#11718727C212yesmaximal, complemented
5#11718725C212yesmaximal, complemented
6#11718724C212yesmaximal, complemented
7#11718632C211yesmaximal, characteristic, complemented
8#11718631C211yesmaximal, characteristic, complemented
9#11718629C211yesmaximal, characteristic
10#11718628C211yesmaximal, characteristic
11#11718586C211yesmaximal, characteristic, complemented
12C13×#125—21no—
13C13×#125—21no—
14C13×#125C2212yes—
15C13×#125C2212yes—
16C2×C13×C4⋊C4—21no—
17C2×C13×C4⋊C4—21no—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21#88184C2211yescharacteristic
22#88183—21no—
23C4×C22⋊D13—21no—
24#88178C2211yescharacteristic
25#88130—21no—
26#88129C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88126—21no—
29#88124C2211yescharacteristic
30C4×Dic26C2211yescharacteristic
31C22⋊#1055C2211yescharacteristic
32C22⋊#1055C2211yescharacteristic
33#88050C2212yes—
34#88050C2212yes—
35#88049C2212yes—
36#88049C2212yes—
37#88048C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40#88047C2212yes—
41C4⋊#1055C2212yes—
42C4×#1055C2212yes—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13D411yescharacteristic
46C22×C4×C13D411yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C2×D52C2311yescharacteristic
50C2×C4×D13—21no—
51C2×Dic26C2311yescharacteristic
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C13×C4⋊C4C2312yes—
60C42×C13D411yescharacteristic
61C42×C13D411yescharacteristic
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65#6103—21no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13—21no—
76C2×#1055C2312yes—
77C2×#1055C2312yes—
78#3232—131nomaximal, Sylow
79C23×C13C2×D411yescharacteristic
80C22×D13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—42no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98D52—22no—
99C4×D13—42no—
100Dic26—22no—
101#1055—22no—
102#1055—22no—
103#529—131no—
104C2×#125D1311yescharacteristic, complemented
105#499—132no—
106#488—132no—
107#484—131no—
108#483—131no—
109#481—131no—
110#480—131no—
111#479—132no—
112#478—132no—
113#431—131no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#13512yes—
117C22×C13C22×D411yescharacteristic
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—41no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—42no—
128C4×C132−1+412yes—
129Dic13—41no—
130Dic13—41no—
131Dic13—41no—
132#126—261no—
133#125—21no—
134#125—21no—
135#125—131no—
136#125C2×D1312yes—
137#125C2×D1312yes—
138#124—131no—
139#123—261no—
140C22⋊Q8—131no—
141#121—131no—
142C4×Q8—131no—
143C4×D4—131no—
144C4×D4—261no—
145#117—261no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×D1311yescharacteristic
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C42C2×D1311yescharacteristic
151#107—132no—
152#107—132no—
153#106—132no—
154#106—132no—
155C4⋊C8—132no—
156#103—132no—
157#103—132no—
158#102—132no—
159#102—132no—
160C22⋊C8—131no—
161C22⋊C8—131no—
162C4×C8—132no—
163C2×C13—22no—
164C2×C13#53611yescharacteristic
165C2×C13C2×#13511yescharacteristic
166C2×C13#57511yescharacteristic
167D13—81no—
168C2×Q8—131no—
169C2×D4—131no—
170C2×D4—261no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—261no—
174C22×C4C22⋊D1311yescharacteristic
175C22×C4C22⋊D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C2×C8—132no—
178C2×C8—132no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—131no—
186C4⋊C4—131no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4C22×D1312yes—
192C4⋊C4C22×D1312yes—
193C22⋊C4—261no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C42—261no—
199C42C22⋊D1311yescharacteristic
200C42C22⋊D1311yescharacteristic
201C42C22×D1311yescharacteristic
202C42C22×D1311yescharacteristic
203C13#323211yescharacteristic, complemented, Sylow
204C23—261no—
205C23C2×C22⋊D1311yescharacteristic
206Q8—262no—
207D4—262no—
208D4—522no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—261no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—522no—
220C2×C4C2×C22⋊D1311yescharacteristic
221C2×C4C2×C22⋊D1311yescharacteristic
222C2×C4C2×C22⋊D1311yescharacteristic
223C2×C4C2×C22⋊D1311yescharacteristic
224C2×C4C2×C22⋊D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—262no—
227C8—262no—
228C22—21no—
229C22—21no—
230C22—521no—
231C22—521no—
232C22—521no—
233C22#8820412yes—
234C22C22×C22⋊D1311yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—521no—
243C4—521no—
244C4—521no—
245C4#8825412yes—
246C2—22no—
247C2—1041no—
248C2#1171952111yescharacteristic
249C2C2×#8820411yescharacteristic
250C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#125C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenterC2×#125D13
hypocenterC13#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
3. #11718729C2semidirect
4. #11718727C2semidirect
5. #11718725C2semidirect
6. #11718724C2semidirect
7. #11718632C2semidirect
8. #11718631C2semidirect
11. #11718586C2semidirect
104. C2×#125D13semidirect
203. C13#3232semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
#117191842
#117187292
#117187272
#117187252
#117187242
#117186322
#117186312
#117186292
#117186282
#117185862
#323213