Finite Group Databasebeta

← #13120548

Subgroups — #13120548

Order 1664.

1134 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×D4×C13C211yesmaximal, characteristic, complemented
2C2×#88207C212yesmaximal, complemented
3C2×#88183C211yesmaximal, characteristic, complemented
4#11718908C212yesmaximal, complemented
5#11718884C214yesmaximal, complemented
6#11718883C214yesmaximal, complemented
7#11718872C211yesmaximal, characteristic, complemented
8C25×C13C2212yes—
9C22×D4×C13—28no—
10C22×D4×C13—24no—
11C22×D4×C13C2214yes—
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C22⋊D13C2214yescomplemented
15#88207—28no—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2214yescomplemented
19C2×C22⋊Dic13C2218yescomplemented
20#88183—24no—
21C2×#6103C2212yescomplemented
22C2×#6101C2212yescomplemented
23#88071C2214yescomplemented
24C24×C13—24no—
25C24×C13—24no—
26C24×C13—48no—
27C24×C13D418yescomplemented
28C24×C13C2314yes—
29C24×C13C2311yescharacteristic
30C23×D13C2311yescharacteristic
31C2×D4×C13—232no—
32C2×D4×C13—216no—
33C2×D4×C13—28no—
34C22×C4×C13—24no—
35C22×C4×C13D414yescomplemented
36C22×C4×C13C2312yes—
37C2×C22⋊D13—22no—
38C2×C22⋊D13—24no—
39C2×C22⋊D13—28no—
40C2×C22⋊D13—48no—
41C22×Dic13C2314yes—
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22⋊Dic13—22no—
45C22⋊Dic13—24no—
46C22⋊Dic13—28no—
47C22⋊Dic13—48no—
48#6103—24no—
49#6101—24no—
50#2613—131nomaximal, Sylow
51C23×C13—24no—
52C23×C13—216no—
53C23×C13—24no—
54C23×C13—24no—
55C23×C13—28no—
56C23×C13—28no—
57C23×C13—416no—
58C23×C13—416no—
59C23×C13—416no—
60C23×C13C2×D418yes—
61C23×C13C2×D414yes—
62C23×C13C2×D412yes—
63C23×C13C2411yescharacteristic
64C22×D13—21no—
65C22×D13—22no—
66C22×D13—24no—
67D4×C13—232no—
68C2×C4×C13—28no—
69C2×C4×C13—24no—
70C2×C4×C13C2×D414yes—
71C22⋊D13—416no—
72C22⋊D13—44no—
73C2×Dic13—21no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—24no—
77C2×Dic13—24no—
78C2×Dic13—28no—
79C23×D4D1311yescharacteristic, complemented
80C2×#123—131no—
81C2×#120—132no—
82#394—134no—
83#392—134no—
84#381—131no—
85#379—132no—
86C22×C13—28no—
87C22×C13—24no—
88C22×C13—28no—
89C22×C13—28no—
90C22×C13—28no—
91C22×C13—432no—
92C22×C13—48no—
93C22×C13—48no—
94C22×C13#12014yes—
95C22×C13C22×D412yes—
96C22×C13C22×D411yescharacteristic
97C22×C13H(5,𝔽2)14yes—
98C2×D13—41no—
99C2×D13—44no—
100C2×D13—42no—
101C4×C13—24no—
102Dic13—41no—
103Dic13—44no—
104Dic13—42no—
105C25C2×D1312yes—
106C22×D4—28no—
107C22×D4—24no—
108C22×D4—131no—
109C22×D4—134no—
110C22×D4C2×D1314yes—
111C23×C4C2×D1311yescharacteristic
112#123—264no—
113#120—268no—
114C2×C4⋊C4—132no—
115C2×C22⋊C4—132no—
116C2×C22⋊C4—134no—
117C2×C22⋊C4—131no—
118C2×C22⋊C4—132no—
119C2×C22⋊C4—138no—
120#95—134no—
121C2×C13—24no—
122C2×C13—48no—
123C2×C13C2×#12011yescharacteristic
124C2×C13#53414yes—
125C2×C13#53512yes—
126D13—81no—
127C24—24no—
128C24—24no—
129C24—48no—
130C24—131no—
131C24C22⋊D1318yescomplemented
132C24C22×D1314yes—
133C24C22×D1311yescharacteristic
134C2×D4—232no—
135C2×D4—216no—
136C2×D4—28no—
137C2×D4—268no—
138C2×D4—264no—
139C2×D4—262no—
140C2×D4—528no—
141C22×C4—24no—
142C22×C4—134no—
143C22×C4—132no—
144C22×C4—131no—
145C22×C4C22⋊D1314yescomplemented
146C22×C4C22×D1312yes—
147C4⋊C4—264no—
148C22⋊C4—268no—
149C22⋊C4—264no—
150C22⋊C4—262no—
151C22⋊C4—264no—
152C22⋊C4—528no—
153C13#261311yescharacteristic, complemented, Sylow
154C23—24no—
155C23—216no—
156C23—28no—
157C23—28no—
158C23—24no—
159C23—24no—
160C23—416no—
161C23—416no—
162C23—416no—
163C23—264no—
164C23—261no—
165C23—262no—
166C23C2×C22⋊D1318yes—
167C23C2×C22⋊D1314yes—
168C23C2×C22⋊D1312yes—
169C23C23×D1311yescharacteristic
170D4—232no—
171D4—5216no—
172D4—524no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—264no—
176C2×C4—268no—
177C2×C4—262no—
178C2×C4—264no—
179C2×C4—262no—
180C2×C4—261no—
181C2×C4C2×C22⋊D1314yes—
182C22—28no—
183C22—24no—
184C22—28no—
185C22—28no—
186C22—28no—
187C22—432no—
188C22—48no—
189C22—48no—
190C22—524no—
191C22—522no—
192C22—521no—
193C22#8820714yes—
194C22#8825114yes—
195C22C22×C22⋊D1312yes—
196C22C22×C22⋊D1311yescharacteristic
197C4—24no—
198C4—524no—
199C4—522no—
200C4—521no—
201C2—24no—
202C2—48no—
203C2—1041no—
204C2#1171950914yes—
205C2#1171951012yes—
206C2C2×#8820711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC23×D4×C13C2
hypercenterC23×D4D13
hypocenterC13#2613
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D4×C13C2semidirect
2. C2×#88207C2semidirect
3. C2×#88183C2semidirect
4. #11718908C2semidirect
5. #11718884C2semidirect
6. #11718883C2semidirect
7. #11718872C2semidirect
14. C22×C22⋊D13C22semidirect
18. C2×C22⋊Dic13C22semidirect
19. C2×C22⋊Dic13C22semidirect
21. C2×#6103C22semidirect
22. C2×#6101C22semidirect
23. #88071C22semidirect
27. C24×C13D4semidirect
35. C22×C4×C13D4semidirect
79. C23×D4D13semidirect
131. C24C22⋊D13semidirect
145. C22×C4C22⋊D13semidirect
153. C13#2613semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C132
C2×#882072
C2×#881832
#117189082
#117188842
#117188832
#117188722
#261313