Finite Group Databasebeta

← #13120616

Subgroups — #13120616

Order 1664.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#88183C211yesmaximal, characteristic
3#11718874C212yesmaximal
4#11718872C211yesmaximal, characteristic, complemented
5#11718871C212yesmaximal, complemented
6#11718654C212yesmaximal, complemented
7#11718653C212yesmaximal, complemented
8#11718643C212yesmaximal, complemented
9#11718641C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C23×C4×C13C2212yes—
12C22×C22⋊D13C2211yescharacteristic
13C2×C13×C4⋊C4—24no—
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C4⋊C4C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18#88183—24no—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2214yes—
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2214yes—
25#88071C2214yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C23×D13C2311yescharacteristic
31C22×C4×C13—24no—
32C22×C4×C13—24no—
33C22×C4×C13—44no—
34C22×C4×C13D414yes—
35C22×C4×C13C2314yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39C2×C22⋊D13—24no—
40C22×Dic13C2311yescharacteristic
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2314yes—
43C22×Dic13C2311yescharacteristic
44C13×C4⋊C4—24no—
45C13×C4⋊C4—24no—
46C22⋊Dic13—22no—
47C22⋊Dic13—24no—
48#6103—22no—
49#6103—22no—
50#6103—44no—
51#6101—22no—
52#6101—22no—
53#6101—44no—
54#2623—131nomaximal, Sylow
55C23×C13—22no—
56C23×C13—22no—
57C23×C13C2×D412yes—
58C23×C13#4114yes—
59C23×C13C2411yescharacteristic
60C22×D13—21no—
61C22×D13—22no—
62C22×D13—22no—
63C22×D13—22no—
64C2×C4×C13—28no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—24no—
68C2×C4×C13—24no—
69C2×C4×C13—24no—
70C2×C4×C13—48no—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×D412yes—
73C22⋊D13—44no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—24no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13—24no—
83C2×#123—131no—
84C22×C4⋊C4D1311yescharacteristic, complemented
85#400—132no—
86#399—132no—
87#398—132no—
88#397—132no—
89#386—132no—
90#385—132no—
91#381—131no—
92C22×C13—22no—
93C22×C13—22no—
94C22×C13—28no—
95C22×C13#12314yes—
96C22×C13C22×D411yescharacteristic
97C22×C13C2×#4112yes—
98C22×C13H(5,𝔽2)12yes—
99C22×C132−1+412yes—
100C2×D13—41no—
101C2×D13—41no—
102C2×D13—41no—
103C2×D13—44no—
104C4×C13—22no—
105C4×C13—22no—
106C4×C13—44no—
107Dic13—41no—
108Dic13—41no—
109Dic13—41no—
110Dic13—44no—
111C22×D4—131no—
112C23×C4C2×D1311yescharacteristic
113C23×C4C2×D1312yes—
114#123—264no—
115C2×C4⋊C4—24no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—134no—
119C2×C4⋊C4C2×D1312yes—
120C2×C4⋊C4C2×D1312yes—
121C2×C22⋊C4—131no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—131no—
124C2×C22⋊C4—131no—
125C2×C22⋊C4—134no—
126#95—132no—
127#95—132no—
128#95—134no—
129#95—134no—
130C2×C13—24no—
131C2×C13C2×#12311yescharacteristic
132C2×C13#53511yescharacteristic
133C2×C13#53611yescharacteristic
134C2×C13#53914yes—
135D13—81no—
136C24—131no—
137C24C22×D1311yescharacteristic
138C2×D4—264no—
139C2×D4—262no—
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—44no—
143C22×C4—134no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4C22⋊D1314yes—
148C22×C4C22×D1314yes—
149C22×C4C22×D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4—524no—
156C22⋊C4—264no—
157C22⋊C4—262no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4—524no—
161C13#262311yescharacteristic, complemented, Sylow
162C23—22no—
163C23—22no—
164C23—262no—
165C23—262no—
166C23—262no—
167C23—261no—
168C23#612714yes—
169C23C2×C22⋊D1312yes—
170C23C23×D1311yescharacteristic
171D4—524no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—48no—
179C2×C4—264no—
180C2×C4—262no—
181C2×C4—264no—
182C2×C4—262no—
183C2×C4—264no—
184C2×C4—262no—
185C2×C4—261no—
186C2×C4—261no—
187C2×C4—261no—
188C2×C4C2×C22⋊D1312yes—
189C2×C4C2×C22⋊D1312yes—
190C22—28no—
191C22—22no—
192C22—22no—
193C22—524no—
194C22—521no—
195C22—521no—
196C22—521no—
197C22#8818314yes—
198C22C2×#612712yes—
199C22#8825112yes—
200C22#8825412yes—
201C22C22×C22⋊D1311yescharacteristic
202C4—22no—
203C4—22no—
204C4—44no—
205C4—524no—
206C4—521no—
207C4—521no—
208C4—521no—
209C2—24no—
210C2—1041no—
211C2#1171922014yes—
212C2C2×#8818311yescharacteristic
213C2#1171951011yescharacteristic
214C2#1171952111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC22×C22⋊D13C22
hypercenterC22×C4⋊C4D13
hypocenterC13#2623
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
4. #11718872C2semidirect
5. #11718871C2semidirect
6. #11718654C2semidirect
7. #11718653C2semidirect
8. #11718643C2semidirect
9. #11718641C2semidirect
84. C22×C4⋊C4D13semidirect
161. C13#2623semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×#881832
#117188742
#117188722
#117188712
#117186542
#117186532
#117186432
#117186412
#262313