Finite Group Databasebeta

← #16782183

Subgroups — #16782183

Order 3328.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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
1#13130563C212yesmaximal
2#13129712C214yesmaximal, complemented
3#13117241C211yesmaximal, characteristic
4C2×#88146C412yes—
5C2×C42×D13C2211yescharacteristic
6C2×#88111—22no—
7C2×#88110C2214yes—
8C13×#384C411yescharacteristic
9#11718648—22no—
10#11718638C2212yes—
11C4⋊C4×Dic13—22no—
12#11718596C411yescharacteristic
13#11718290—22no—
14C22×C4×D13C2×C411yescharacteristic
15C22×C4×D13D412yes—
16C22×#1057—24no—
17C2×C13×C4⋊C4—22no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C42×C13C2×C411yescharacteristic
20C2×#6103—22no—
21C2×C4⋊Dic13—22no—
22C2×C4⋊Dic13C2×C412yes—
23C2×C4×Dic13—22no—
24C2×C4×Dic13D412yes—
25C2×C4×Dic13C2311yescharacteristic
26#88146—44no—
27C42×D13—24no—
28#88111—28no—
29#88110—28no—
30#88071—24no—
31#8721—131nomaximal, Sylow
32C23×D13C22⋊C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13C22⋊C412yes—
35C22×C4×C13C22×C411yescharacteristic
36C22×Dic13—22no—
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C2×D412yes—
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13—22no—
42C2×C4×D13—24no—
43C2×C4×D13—24no—
44C2×C4×D13—42no—
45C2×#1057—28no—
46C2×#1057—44no—
47C2×#1057—44no—
48C13×C4⋊C4—42no—
49C13×C4⋊C4—44no—
50C42×C13—22no—
51#6103—44no—
52C4⋊Dic13—44no—
53C4⋊Dic13—42no—
54C4×Dic13—24no—
55C4×Dic13—44no—
56C4×Dic13#4114yes—
57#2285—131no—
58#1749—132no—
59#1295—134no—
60C23×C13C2×C22⋊C411yescharacteristic
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—22no—
65C22×D13#10112yes—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—42no—
71C2×C4×C13—44no—
72C2×C4×C13#10414yes—
73C2×C4×C13#11712yes—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—42no—
79C2×Dic13—44no—
80C2×Dic13#10012yes—
81C2×Dic13#12314yes—
82C4×D13—28no—
83C4×D13—48no—
84#1057—48no—
85C2×#117—132no—
86C22×C42—131no—
87C2×C22⋊C8—262no—
88C2×#97—134no—
89#384—131no—
90#384#26111yescharacteristic
91#382—132no—
92#380—262no—
93C4×C4⋊C4—262no—
94#336—262no—
95C22×C13#38111yescharacteristic
96C22×C13C2×#10011yescharacteristic
97C22×C13C2×#10111yescharacteristic
98C22×C13C2×#10412yes—
99C22×C13#42112yes—
100C2×D13—22no—
101C2×D13—24no—
102C2×D13—41no—
103C2×D13—42no—
104C2×D13—41no—
105C4×C13—22no—
106C4×C13—24no—
107C4×C13—82no—
108Dic13—22no—
109Dic13—24no—
110Dic13—82no—
111C23×C4—131no—
112C23×C4—132no—
113C22×C8—264no—
114#117—524no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—262no—
118C2×C4⋊C4C2×#26112yes—
119C2×C22⋊C4—262no—
120C2×C42—131no—
121C2×C42—132no—
122C2×C42—264no—
123C2×C42—262no—
124C2×C42C2×#26111yescharacteristic
125C22⋊C8—268no—
126#97—268no—
127#95—264no—
128C2×C13#152511yescharacteristic
129C2×C13#153112yes—
130C2×C13#153611yescharacteristic
131C2×C13#182111yescharacteristic
132C2×C13#182612yes—
133D13—42no—
134C24—131no—
135C22×C4—22no—
136C22×C4—132no—
137C22×C4—131no—
138C22×C4—262no—
139C22×C4—264no—
140C22×C4—262no—
141C22×C4—262no—
142C22×C4—264no—
143C22×C4—262no—
144C22×C4—522no—
145C22×C4C22⋊#26112yes—
146C22×C4C22×#26111yescharacteristic
147C2×C8—268no—
148C2×C8—524no—
149C2×C8—524no—
150C4⋊C4—42no—
151C4⋊C4—44no—
152C4⋊C4—522no—
153C4⋊C4—524no—
154C22⋊C4—524no—
155C42—22no—
156C42—134no—
157C42—264no—
158C42—524no—
159C13#872111yescharacteristic, complemented, Sylow
160C23—132no—
161C23—261no—
162C23—262no—
163C23—261no—
164C23—262no—
165C23C2×C22⋊#26111yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—44no—
171C2×C4—42no—
172C2×C4—134no—
173C2×C4—132no—
174C2×C4—268no—
175C2×C4—261no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—261no—
179C2×C4—528no—
180C2×C4—522no—
181C2×C4—524no—
182C2×C4#8811614yes—
183C2×C4#8823712yes—
184C8—528no—
185C22—264no—
186C22—262no—
187C22—521no—
188C22—521no—
189C22—522no—
190C22#1171913511yescharacteristic
191C22C2×#8811612yes—
192C22D13⋊#10011yescharacteristic
193C22#1171915512yes—
194C22D13⋊#10111yescharacteristic
195C4—22no—
196C4—24no—
197C4—82no—
198C4—262no—
199C4—264no—
200C4—1042no—
201C2—522no—
202C2#1313029111yescharacteristic
203C2#1313030912yes—
204C2#1313032611yescharacteristic
205C2#1313073611yescharacteristic
206C2#1313074212yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#8721
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #13129712C2semidirect
159. C13#8721semidirect

Maximal subgroups

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

subgroupindex
#131305632
#131297122
#131172412
#872113