Finite Group Databasebeta

← #13123128

Subgroups — #13123128

Order 1664.

1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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
1C24×C4×C13C211yesmaximal, characteristic, complemented
2C2×#88207C211yesmaximal, characteristic
3C2×#88183C212yesmaximal, complemented
4#11718908C211yesmaximal, characteristic, complemented
5#11718874C214yesmaximal, complemented
6#11718872C212yesmaximal, complemented
7#11718871C214yesmaximal, complemented
8C25×C13C2211yescharacteristic
9C23×C4×C13—24no—
10C23×C4×C13—28no—
11C23×C4×C13C2214yes—
12C23×C4×C13C2212yes—
13C22×C22⋊D13C2211yescharacteristic
14C22×C22⋊D13C2212yes—
15#88207—24no—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2214yes—
20#88183—28no—
21C2×#6103C2214yescomplemented
22C2×#6101C2214yescomplemented
23#88071C2218yescomplemented
24C24×C13—24no—
25C24×C13—28no—
26C24×C13D414yes—
27C24×C13C2311yescharacteristic
28C24×C13C2312yes—
29C23×D13C2311yescharacteristic
30C22×C4×C13—232no—
31C22×C4×C13—28no—
32C22×C4×C13—24no—
33C22×C4×C13—24no—
34C22×C4×C13—216no—
35C22×C4×C13D418yescomplemented
36C22×C4×C13C2314yes—
37C2×C22⋊D13—24no—
38C2×C22⋊D13—22no—
39C2×C22⋊D13—24no—
40C2×C22⋊D13—28no—
41C22×Dic13C2312yes—
42C22×Dic13C2314yes—
43C22×Dic13C2311yescharacteristic
44C22⋊Dic13—24no—
45C22⋊Dic13—22no—
46C22⋊Dic13—24no—
47C22⋊Dic13—28no—
48#6103—28no—
49#6101—28no—
50#2849—131nomaximal, Sylow
51C23×C13—232no—
52C23×C13—28no—
53C23×C13—216no—
54C23×C13—24no—
55C23×C13—24no—
56C23×C13—24no—
57C23×C13C2×D412yes—
58C23×C13C2×D414yes—
59C23×C13C2×D414yes—
60C23×C13#4118yes—
61C23×C13C2411yescharacteristic
62C22×D13—22no—
63C22×D13—21no—
64C22×D13—24no—
65C2×C4×C13—232no—
66C2×C4×C13—216no—
67C2×C4×C13—24no—
68C2×C4×C13—24no—
69C2×C4×C13C2×D418yes—
70C22⋊D13—44no—
71C22⋊D13—48no—
72C2×Dic13—22no—
73C2×Dic13—24no—
74C2×Dic13—21no—
75C2×Dic13—22no—
76C2×Dic13—28no—
77C2×Dic13—24no—
78C24×C4D1311yescharacteristic, complemented
79C2×#123—132no—
80C2×#120—131no—
81#386—134no—
82#385—134no—
83#381—132no—
84#379—131no—
85C22×C13—232no—
86C22×C13—24no—
87C22×C13—24no—
88C22×C13—24no—
89C22×C13—28no—
90C22×C13—216no—
91C22×C13#12014yes—
92C22×C13#12318yescomplemented
93C22×C13C22×D411yescharacteristic
94C22×C13C22×D412yes—
95C22×C13C2×#4114yes—
96C2×D13—41no—
97C2×D13—42no—
98C2×D13—44no—
99C4×C13—28no—
100Dic13—41no—
101Dic13—42no—
102Dic13—44no—
103C25C2×D1311yescharacteristic
104C22×D4—131no—
105C22×D4—132no—
106C23×C4—24no—
107C23×C4—28no—
108C23×C4C2×D1314yes—
109C23×C4C2×D1312yes—
110#123—268no—
111#120—264no—
112C2×C4⋊C4—134no—
113C2×C22⋊C4—131no—
114C2×C22⋊C4—132no—
115C2×C22⋊C4—132no—
116C2×C22⋊C4—134no—
117C2×C22⋊C4—134no—
118#95—138no—
119C2×C13—24no—
120C2×C13—28no—
121C2×C13C2×#12011yescharacteristic
122C2×C13C2×#12312yes—
123C2×C13#52514yes—
124D13—81no—
125C24—28no—
126C24—24no—
127C24—131no—
128C24C22⋊D1314yes—
129C24C22×D1312yes—
130C24C22×D1311yescharacteristic
131C2×D4—268no—
132C2×D4—264no—
133C2×D4—262no—
134C2×D4—264no—
135C22×C4—232no—
136C22×C4—28no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—216no—
140C22×C4—132no—
141C22×C4—134no—
142C22×C4—131no—
143C22×C4C22⋊D1318yescomplemented
144C22×C4C22×D1314yes—
145C4⋊C4—268no—
146C22⋊C4—268no—
147C22⋊C4—264no—
148C22⋊C4—262no—
149C22⋊C4—264no—
150C22⋊C4—268no—
151C13#284911yescharacteristic, complemented, Sylow
152C23—232no—
153C23—216no—
154C23—28no—
155C23—24no—
156C23—24no—
157C23—24no—
158C23—264no—
159C23—262no—
160C23—261no—
161C23#612718yes—
162C23C2×C22⋊D1314yes—
163C23C2×C22⋊D1312yes—
164C23C2×C22⋊D1314yes—
165C23C23×D1311yescharacteristic
166D4—528no—
167D4—524no—
168C2×C4—232no—
169C2×C4—216no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—268no—
173C2×C4—264no—
174C2×C4—264no—
175C2×C4—262no—
176C2×C4—261no—
177C2×C4—262no—
178C2×C4C2×C22⋊D1318yes—
179C22—232no—
180C22—24no—
181C22—24no—
182C22—216no—
183C22—28no—
184C22—24no—
185C22—522no—
186C22—524no—
187C22—521no—
188C22#8818318yescomplemented
189C22#8820714yes—
190C22C2×#612714yes—
191C22C22×C22⋊D1311yescharacteristic
192C22C22×C22⋊D1312yes—
193C4—28no—
194C4—522no—
195C4—524no—
196C4—521no—
197C2—28no—
198C2—24no—
199C2—1041no—
200C2C2×#8818312yes—
201C2#1171949614yes—
202C2C2×#8820711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC24×C4×C13C2
prime radicalC2×#88207C2
hypercenterC24×C4D13
hypocenterC13#2849
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C24×C4×C13C2semidirect
3. C2×#88183C2semidirect
4. #11718908C2semidirect
5. #11718874C2semidirect
6. #11718872C2semidirect
7. #11718871C2semidirect
21. C2×#6103C22semidirect
22. C2×#6101C22semidirect
23. #88071C22semidirect
35. C22×C4×C13D4semidirect
78. C24×C4D13semidirect
92. C22×C13#123semidirect
143. C22×C4C22⋊D13semidirect
151. C13#2849semidirect
188. C22#88183semidirect

Maximal subgroups

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

subgroupindex
C24×C4×C132
C2×#882072
C2×#881832
#117189082
#117188742
#117188722
#117188712
#284913