Finite Group Databasebeta

← #15872187

Subgroups — #15872187

Order 3328.

1334 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 315 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#13117439C212yesmaximal, complemented
2#13115673C218yesmaximal, complemented
3#13114754C214yesmaximal, complemented
4C2×C13×#537C211yesmaximal, characteristic
5C22×C13×#41C2212yes—
6C13×#537—28no—
7C2×C13×C22⋊Q8C414yescomplemented
8C2×C13×#121C414yescomplemented
9C2×C13×#121C2214yes—
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×#88074C22116yes—
12#11718873C2214yes—
13#11718872C2214yes—
14C4×C22⋊Dic13C2214yes—
15#11718642—28no—
16C2×C13×#41—28no—
17C2×C13×#41—48no—
18C22×Q8×C13C2×C412yes—
19C22×D4×C13C2×C412yes—
20C22×D4×C13C2×C414yes—
21C22×D4×C13C2314yes—
22C23×C4×C13C2×C414yes—
23C23×C4×C13C2311yescharacteristic
24C23×C4×C13C2312yes—
25C13×C22⋊Q8—216no—
26C13×#121—28no—
27C13×#121—28no—
28C13×#121—216no—
29C2×C13×C4⋊C4C2×C414yes—
30C2×C13×C4⋊C4C2×C414yes—
31C2×C13×C4⋊C4D418yes—
32C2×C13×C22⋊C4C2×C418yes—
33C2×C22⋊Dic13C2318yes—
34C2×C4⋊Dic13—24no—
35C2×C4×Dic13—24no—
36#88074—416no—
37#88071—24no—
38#88071—28no—
39#88071—24no—
40#21796—131nomaximal, Sylow
41C24×C13C22×C414yes—
42C24×C13C2411yescharacteristic
43C13×#41—432no—
44C2×Q8×C13—24no—
45C2×Q8×C13—44no—
46C2×D4×C13—28no—
47C2×D4×C13—216no—
48C2×D4×C13—24no—
49C2×D4×C13—28no—
50C2×D4×C13—44no—
51C2×D4×C13—84no—
52C22×C4×C13—24no—
53C22×C4×C13—28no—
54C22×C4×C13—48no—
55C22×C4×C13—82no—
56C22×C4×C13C22×C414yes—
57C22×C4×C13C22×C412yes—
58C22×C4×C13C22×C414yes—
59C22×C4×C13C2×D414yes—
60C22×C4×C13C2×D414yes—
61C22×C4×C13C2×D414yes—
62C22×Dic13—28no—
63C13×C4⋊C4—28no—
64C13×C4⋊C4C22⋊C4116yes—
65C13×C22⋊C4—216no—
66C22⋊Dic13—216no—
67C4⋊Dic13—84no—
68C4×Dic13—84no—
69C2×#537D1311yescharacteristic
70#2313—132no—
71#1964—138no—
72#1782—134no—
73C23×C13—24no—
74C23×C13—28no—
75C23×C13—41no—
76C23×C13—41no—
77C23×C13—44no—
78C23×C13—44no—
79C23×C13C23×C411yescharacteristic
80C23×C13C22×D412yes—
81C23×C13H(5,𝔽2)14yes—
82Q8×C13—48no—
83D4×C13—48no—
84D4×C13—416no—
85D4×C13—88no—
86C2×C4×C13—24no—
87C2×C4×C13—28no—
88C2×C4×C13—24no—
89C2×C4×C13—28no—
90C2×C4×C13—44no—
91C2×C4×C13—44no—
92C2×C4×C13—44no—
93C2×C4×C13—416no—
94C2×C4×C13C2×C22⋊C418yes—
95C2×C4×C13C2×C22⋊C414yes—
96C2×Dic13—48no—
97C2×Dic13—48no—
98C2×Dic13—48no—
99C22×#41C2×D1312yes—
100#537—28no—
101C2×C22⋊Q8Dic1314yescomplemented
102C2×#121Dic1314yescomplemented
103C2×#121C2×D1314yes—
104C22×C4⋊C4C2×D1311yescharacteristic
105C2×#99—1316no—
106#387—268no—
107#381—134no—
108#380—134no—
109C4×C22⋊C4—134no—
110C22×C13—22no—
111C22×C13—21no—
112C22×C13—22no—
113C22×C13—21no—
114C22×C13—44no—
115C22×C13—44no—
116C22×C13—44no—
117C22×C13—44no—
118C22×C13—88no—
119C22×C13C22×C22⋊C411yescharacteristic
120C22×C13#51812yes—
121C22×C13#53514yes—
122C4×C13—24no—
123C4×C13—28no—
124C4×C13—44no—
125Dic13—88no—
126C2×#41—28no—
127C2×#41—48no—
128C22×Q8C2×Dic1312yes—
129C22×D4C2×Dic1312yes—
130C22×D4C2×Dic1314yes—
131C22×D4C22×D1314yes—
132C23×C4C2×Dic1314yes—
133C23×C4C22×D1311yescharacteristic
134C23×C4C22×D1312yes—
135C22⋊Q8—216no—
136#121—28no—
137#121—28no—
138#121—216no—
139C2×C4⋊C4—264no—
140C2×C4⋊C4C2×Dic1314yes—
141C2×C4⋊C4C2×Dic1314yes—
142C2×C4⋊C4C22⋊D1318yes—
143C2×C22⋊C4—138no—
144C2×C22⋊C4C2×Dic1318yes—
145C2×C42—264no—
146#99—5216no—
147#95—264no—
148#95—264no—
149#95—268no—
150C2×C13—24no—
151C2×C13—22no—
152C2×C13—84no—
153C2×C13#230911yescharacteristic
154C2×C13#288311yescharacteristic
155C2×C13#288411yescharacteristic
156C24C22×Dic1314yes—
157C24C23×D1311yescharacteristic
158#41—432no—
159C2×Q8—24no—
160C2×Q8—44no—
161C2×D4—216no—
162C2×D4—28no—
163C2×D4—24no—
164C2×D4—28no—
165C2×D4—44no—
166C2×D4—84no—
167C22×C4—24no—
168C22×C4—28no—
169C22×C4—48no—
170C22×C4—82no—
171C22×C4—268no—
172C22×C4C22×Dic1314yes—
173C22×C4C22×Dic1312yes—
174C22×C4C22×Dic1314yes—
175C22×C4C2×C22⋊D1314yes—
176C22×C4C2×C22⋊D1314yes—
177C22×C4C2×C22⋊D1314yes—
178C4⋊C4—28no—
179C4⋊C4—1044no—
180C4⋊C4C22⋊Dic13116yes—
181C22⋊C4—216no—
182C22⋊C4—2616no—
183C42—1044no—
184C13#2179611yescharacteristic, complemented, Sylow
185C23—24no—
186C23—28no—
187C23—41no—
188C23—41no—
189C23—44no—
190C23—44no—
191C23#8825114yes—
192C23C23×Dic1311yescharacteristic
193C23C22×C22⋊D1312yes—
194Q8—48no—
195D4—48no—
196D4—416no—
197D4—88no—
198C2×C4—24no—
199C2×C4—28no—
200C2×C4—28no—
201C2×C4—24no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—44no—
205C2×C4—416no—
206C2×C4—528no—
207C2×C4—528no—
208C2×C4—528no—
209C2×C4C2×C22⋊Dic1318yes—
210C2×C4C2×C22⋊Dic1314yes—
211C22—22no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—44no—
216C22—44no—
217C22—44no—
218C22—44no—
219C22—88no—
220C22#1171950312yes—
221C22#1171951014yes—
222C22C22×C22⋊Dic1311yescharacteristic
223C4—28no—
224C4—24no—
225C4—44no—
226C4—1048no—
227C2—24no—
228C2—22no—
229C2—84no—
230C2#1311741811yescharacteristic
231C2#1312329711yescharacteristic
232C2#1312330011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
Fitting, prime radicalC2×C13×#537C2
socleC22×C13C22×C22⋊C4
cosocleC24×C13C24
hypercenterC2×#537D13
hypocenterC13#21796
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13117439C2semidirect
2. #13115673C2semidirect
3. #13114754C2semidirect
7. C2×C13×C22⋊Q8C4semidirect
8. C2×C13×#121C4semidirect
101. C2×C22⋊Q8Dic13semidirect
102. C2×#121Dic13semidirect
184. C13#21796semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131156732
#131147542
C2×C13×#5372
#2179613