Finite Group Databasebeta

← #15755422

Subgroups — #15755422

Order 3328.

818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11719240C211yesmaximal, characteristic
2#13114913C211yesmaximal, characteristic, complemented
3#13113366C214yesmaximal, complemented
4C13×#1822C211yesmaximal, characteristic, complemented
5C2×C13×#117C2211yescharacteristic
6C2×#88184C2212yes—
7#11719240—28no—
8C2×#88148—22no—
9C2×#88138—22no—
10C2×#88128C411yescharacteristic, complemented
11C2×C4×D52C412yescomplemented
12C2×#88124C411yescharacteristic, complemented
13C13×#407C2212yes—
14#11718872C2212yes—
15C13×#343—22no—
16#11718118—22no—
17#11718062—28no—
18C23×C4×C13C2311yescharacteristic
19C22×C22⋊D13—22no—
20C22×D52—22no—
21C22×D52C2×C412yes—
22C22×C4×D13—22no—
23C2×C13×M16—22no—
24C13×#117—24no—
25C2×C13×C4⋊C4D412yes—
26C2×C13×C22⋊C4D412yes—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C22⋊Dic13—22no—
30#88184—24no—
31#88184D418yes—
32C2×#6103—22no—
33C2×#6103—22no—
34C2×C4⋊Dic13C2×C412yes—
35C2×#6101—22no—
36#88148—216no—
37#88138—216no—
38#88128—24no—
39C4×D52—24no—
40C4×D52—24no—
41#88124—24no—
42C13×C22⋊C8—24no—
43#88071—24no—
44#8518—131nomaximal, Sylow
45C24×C13C2×D411yescharacteristic
46C23×D13—22no—
47C22×C4×C13—42no—
48C22×C4×C13C22⋊C412yes—
49C22×C4×C13C22⋊C412yes—
50C22×C4×C13C22×C411yescharacteristic
51C22×C4×C13C2×D414yes—
52C22×C4×C13C2×D411yescharacteristic
53C2×C22⋊D13—28no—
54C2×C22⋊D13—84no—
55C22×Dic13—22no—
56C22×Dic13—42no—
57C2×D52—22no—
58C2×D52—28no—
59C2×D52—44no—
60C2×D52—84no—
61C2×D52C22⋊C414yes—
62C2×C4×D13—28no—
63C2×C4×D13—84no—
64C13×M16—44no—
65C2×C8×C13—42no—
66C13×C4⋊C4—24no—
67C13×C22⋊C4—24no—
68C42×C13—22no—
69C42×C13—22no—
70C22⋊Dic13—44no—
71#6103—28no—
72#6103—28no—
73C4⋊Dic13—22no—
74C4⋊Dic13C22⋊C414yes—
75#6101—28no—
76C2×#540—131no—
77#1822D1311yescharacteristic, complemented
78#1820—131no—
79#1510—134no—
80C23×C13—22no—
81C23×C13—42no—
82C23×C13C2×C22⋊C411yescharacteristic
83C23×C13#12012yes—
84C22×D13—24no—
85C22×D13—44no—
86C22×D13—44no—
87C22×D13—44no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—44no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13C2×C22⋊C412yes—
96C2×C4×C13#12012yes—
97C22⋊D13—88no—
98C2×Dic13—24no—
99C2×Dic13—44no—
100C2×Dic13—82no—
101C2×Dic13—84no—
102D52—44no—
103D52—44no—
104D52—88no—
105C4×D13—88no—
106C8×C13—82no—
107#540—268no—
108C2×#127—131no—
109C2×#125—131no—
110C2×#123—262no—
111C2×#121—132no—
112C2×#121—262no—
113C2×C4×D4—132no—
114C2×#117C2×D1311yescharacteristic
115#407C2×D1312yes—
116#381—132no—
117#343—22no—
118#342—262no—
119#327—268no—
120C22×C13—22no—
121C22×C13—24no—
122C22×C13—22no—
123C22×C13—82no—
124C22×C13#37911yescharacteristic
125C22×C13#41012yes—
126C2×D13—44no—
127C2×D13—44no—
128C2×D13—44no—
129C2×D13—88no—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—42no—
133C4×C13—42no—
134Dic13—44no—
135Dic13—162no—
136C22×D4—132no—
137C22×D4—262no—
138C22×D4—262no—
139C23×C4—262no—
140C23×C4C22×D1311yescharacteristic
141C2×M16—22no—
142#127—264no—
143#125—264no—
144#123—2616no—
145#121—138no—
146#121—2616no—
147#121—264no—
148C4×D4—264no—
149C4×D4—264no—
150#117—24no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—262no—
153C2×C4⋊C4C22⋊D1312yes—
154C2×C22⋊C4—262no—
155C2×C22⋊C4—262no—
156C2×C22⋊C4—262no—
157C2×C22⋊C4D5212yes—
158C2×C42C4×D1311yescharacteristic
159C2×C42C4×D1311yescharacteristic
160C22⋊C8—24no—
161#95—264no—
162C2×C13—22no—
163C2×C13—42no—
164C2×C13#178211yescharacteristic
165C2×C13#179512yes—
166D13—84no—
167C24—262no—
168C24C2×D5211yescharacteristic
169C2×D4—134no—
170C2×D4—268no—
171C2×D4—268no—
172C2×D4—262no—
173C2×D4—524no—
174C2×D4—1044no—
175C2×D4—1044no—
176C22×C4—42no—
177C22×C4—268no—
178C22×C4—262no—
179C22×C4—522no—
180C22×C4—1044no—
181C22×C4#610312yes—
182C22×C4#610312yes—
183C22×C4C2×C4×D1311yescharacteristic
184C22×C4D4×D1314yes—
185C22×C4C2×C22⋊D1311yescharacteristic
186M16—44no—
187C2×C8—42no—
188C4⋊C4—24no—
189C4⋊C4—134no—
190C4⋊C4—268no—
191C4⋊C4—262no—
192C22⋊C4—24no—
193C22⋊C4—268no—
194C22⋊C4—268no—
195C22⋊C4—524no—
196C42—22no—
197C42—22no—
198C13#851811yescharacteristic, complemented, Sylow
199C23—22no—
200C23—42no—
201C23—264no—
202C23—524no—
203C23—524no—
204C23—524no—
205C23#8813612yes—
206C23C2×#610311yescharacteristic
207D4—524no—
208D4—524no—
209D4—1048no—
210D4—1048no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—264no—
219C2×C4—524no—
220C2×C4—1048no—
221C2×C4—1042no—
222C2×C4—1044no—
223C2×C4C22⋊C4×D1312yes—
224C2×C4#8819112yes—
225C8—82no—
226C22—22no—
227C22—22no—
228C22—24no—
229C22—82no—
230C22—524no—
231C22—524no—
232C22—524no—
233C22—1048no—
234C22#1171861611yescharacteristic
235C22#1171866712yes—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—524no—
241C4—2082no—
242C2—22no—
243C2—42no—
244C2—1044no—
245C2#1311475311yescharacteristic
246C2#1311480712yes—
subgroupG/H
centerC22#11718616
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1822C2
socleC22×C13#379
prime radicalC2×#11719240C2
cosocleC23×C4×C13C23
hypercenter#1822D13
hypocenterC13#8518
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. #13114913C2semidirect
3. #13113366C2semidirect
4. C13×#1822C2semidirect
10. C2×#88128C4semidirect
11. C2×C4×D52C4semidirect
12. C2×#88124C4semidirect
77. #1822D13semidirect
198. C13#8518semidirect

Maximal subgroups

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

subgroupindex
C2×#117192402
#131149132
#131133662
C13×#18222
#851813