Finite Group Databasebeta

← #13119112

Subgroups — #13119112

Order 1664.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#6103C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C13×#381C211yesmaximal, characteristic, complemented
4#11718616C212yesmaximal
5#11718611C212yesmaximal, complemented
6#11718338C212yesmaximal, complemented
7#11718335C212yesmaximal, complemented
8#11718331C214yesmaximal, complemented
9C24×D13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C2×C13×C22⋊C4C2212yes—
13C2×C22⋊Dic13C2212yes—
14C2×#6103—24no—
15C2×#6103C2212yes—
16C2×#6103C2212yes—
17C2×#6103C2214yes—
18C2×#6103C2214yes—
19#88180—24no—
20C2×C4⋊Dic13C2211yescharacteristic, complemented
21C2×C4⋊Dic13C2211yescharacteristic, complemented
22C2×C4⋊Dic13C2214yescomplemented
23C2×C4×Dic13C2212yescomplemented
24C13×#95C2212yescomplemented
25C13×#95C2212yescomplemented
26#88071C2214yescomplemented
27C24×C13C2311yescharacteristic
28C23×D13—22no—
29C23×D13—24no—
30C23×D13—24no—
31C23×D13—42no—
32C23×D13C2312yes—
33C22×C4×C13—24no—
34C22×C4×C13D414yes—
35C22×C4×C13C2314yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13—22no—
39C22×Dic13—42no—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C13×C22⋊C4—24no—
44C22⋊Dic13—24no—
45#6103—28no—
46#6103—24no—
47#6103—24no—
48#6103—44no—
49C4⋊Dic13—22no—
50C4⋊Dic13—22no—
51C4⋊Dic13—44no—
52C4×Dic13—24no—
53#2482—131nomaximal, Sylow
54C23×C13—22no—
55C23×C13—22no—
56C23×C13C2×D412yes—
57C23×C13#4114yes—
58C23×C13C2411yescharacteristic
59C22×D13—28no—
60C22×D13—22no—
61C22×D13—22no—
62C22×D13—24no—
63C22×D13—24no—
64C22×D13—416no—
65C22×D13—44no—
66C22×D13—44no—
67C22×D13#4114yes—
68C2×C4×C13—28no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—24no—
72C2×C4×C13—24no—
73C2×C4×C13—24no—
74C2×C4×C13C2×D412yes—
75C2×C4×C13C2×D412yes—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81C2×Dic13—24no—
82C2×Dic13—44no—
83C2×#117—131no—
84C22×C22⋊C4—131no—
85#399—132no—
86#397—132no—
87#388—134no—
88#385—132no—
89#381D1311yescharacteristic, complemented
90#379—132no—
91C22×C13—22no—
92C22×C13—22no—
93C22×C13—28no—
94C22×C13#12314yes—
95C22×C13C22×D411yescharacteristic
96C22×C13C2×#4112yes—
97C22×C13C2×#4112yes—
98C22×C13H(5,𝔽2)12yes—
99C2×D13—24no—
100C2×D13—28no—
101C2×D13—416no—
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—44no—
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—44no—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111C25—131no—
112C23×C4—131no—
113C23×C4C2×D1311yescharacteristic
114#117—264no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—134no—
118C2×C22⋊C4—132no—
119C2×C22⋊C4—132no—
120C2×C22⋊C4—132no—
121C2×C22⋊C4—134no—
122C2×C22⋊C4—134no—
123C2×C22⋊C4—264no—
124C2×C22⋊C4C2×D1312yes—
125C2×C42—132no—
126#95—134no—
127#95C2×D1312yescomplemented
128#95C2×D1312yescomplemented
129C2×C13—24no—
130C2×C13C2×#12311yescharacteristic
131C2×C13#52511yescharacteristic
132C2×C13#53511yescharacteristic
133C2×C13#55114yes—
134D13—44no—
135C24—132no—
136C24—264no—
137C24—262no—
138C24—264no—
139C24—522no—
140C24C22×D1311yescharacteristic
141C22×C4—24no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—262no—
146C22×C4—522no—
147C22×C4D5214yes—
148C22×C4C22×D1314yes—
149C22×C4C22×D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—524no—
154C22⋊C4—24no—
155C22⋊C4—268no—
156C22⋊C4—264no—
157C22⋊C4—264no—
158C22⋊C4—264no—
159C22⋊C4—524no—
160C42—264no—
161C13#248211yescharacteristic, complemented, Sylow
162C23—22no—
163C23—22no—
164C23—134no—
165C23—268no—
166C23—262no—
167C23—264no—
168C23—262no—
169C23—264no—
170C23—5216no—
171C23—524no—
172C23—524no—
173C23C2×D5212yes—
174C23#612914yes—
175C23C23×D1311yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—264no—
186C2×C4—264no—
187C2×C4—264no—
188C2×C4—524no—
189C2×C4C2×D5212yes—
190C2×C4C2×D5212yes—
191C22—22no—
192C22—22no—
193C22—28no—
194C22—264no—
195C22—268no—
196C22—5216no—
197C22—522no—
198C22—522no—
199C22—524no—
200C22#8814014yes—
201C22C22×D5211yescharacteristic
202C22C2×#612912yes—
203C22#41×D1312yes—
204C22#8825612yes—
205C4—22no—
206C4—22no—
207C4—44no—
208C4—522no—
209C4—522no—
210C4—522no—
211C2—24no—
212C2—524no—
213C2C2×#8814011yescharacteristic
214C2#1171922911yescharacteristic
215C2#1171923011yescharacteristic
216C2#1171936314yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC24×D13C22
hypercenter#381D13
hypocenterC13#2482
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C13×#381C2semidirect
5. #11718611C2semidirect
6. #11718338C2semidirect
7. #11718335C2semidirect
8. #11718331C2semidirect
20. C2×C4⋊Dic13C22semidirect
21. C2×C4⋊Dic13C22semidirect
22. C2×C4⋊Dic13C22semidirect
23. C2×C4×Dic13C22semidirect
24. C13×#95C22semidirect
25. C13×#95C22semidirect
26. #88071C22semidirect
89. #381D13semidirect
127. #95C2×D13semidirect
128. #95C2×D13semidirect
161. C13#2482semidirect

Maximal subgroups

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

subgroupindex
C22×#61032
C2×#881802
C13×#3812
#117186162
#117186112
#117183382
#117183352
#117183312
#248213