Finite Group Databasebeta

← #16782192

Subgroups — #16782192

Order 3328.

630 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 132 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#13130693C212yesmaximal
2#13129714C214yesmaximal, complemented
3D13×#384C211yesmaximal, characteristic
4C2×C4⋊C4×D13—22no—
5C2×C4⋊C4×D13C412yes—
6C2×C42×D13C2211yescharacteristic
7C2×#88112C2214yes—
8C2×#88111—22no—
9C13×#384C411yescharacteristic
10#11718637—22no—
11#11718637C2212yes—
12#11718596C411yescharacteristic
13#11718290—22no—
14C22×C4×D13—22no—
15C22×C4×D13C2×C411yescharacteristic
16C22×C4×D13D412yes—
17C22×#1057—24no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4C2×C412yes—
20C2×C42×C13C2×C411yescharacteristic
21C2×C4⋊Dic13—22no—
22C2×C4⋊Dic13C2×C412yes—
23C2×#6101—22no—
24C2×#6101—24no—
25C2×C4×Dic13D412yes—
26C2×C4×Dic13C2311yescharacteristic
27C4⋊C4×D13—44no—
28C4⋊C4×D13—48no—
29C42×D13—24no—
30#88112—28no—
31#88111—44no—
32#8725—131nomaximal, Sylow
33C23×D13C22⋊C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13C22⋊C412yes—
36C22×C4×C13C22×C411yescharacteristic
37C22×Dic13—22no—
38C22×Dic13C22⋊C411yescharacteristic
39C22×Dic13C2×D412yes—
40C2×C4×D13—22no—
41C2×C4×D13—22no—
42C2×C4×D13—22no—
43C2×C4×D13—24no—
44C2×C4×D13—24no—
45C2×C4×D13—48no—
46C2×C4×D13—44no—
47C2×C4×D13SD1614yes—
48C2×C4×D13Q1614yes—
49C2×#1057—44no—
50C2×#1057—44no—
51C2×#1057—44no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—44no—
54C42×C13—22no—
55C4⋊Dic13—44no—
56C4⋊Dic13—42no—
57#6101—44no—
58#6101—48no—
59C4×Dic13—24no—
60C4×Dic13#4114yes—
61C2×#384—131no—
62#1797—132no—
63#1296—134no—
64C23×C13C2×C22⋊C411yescharacteristic
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—22no—
68C22×D13#10012yes—
69C22×D13#10314yes—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13—44no—
76C2×C4×C13#10314yes—
77C2×C4×C13#11712yes—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—42no—
81C2×Dic13—44no—
82C2×Dic13#10112yes—
83C2×Dic13#12314yes—
84C2×Dic13C2×SD1612yes—
85C2×Dic13C2×Q1612yes—
86C2×Dic13AGL(1,ℤ/8)14yes—
87C4×D13—28no—
88C4×D13—28no—
89C4×D13—28no—
90C4×D13—88no—
91#1057—84no—
92C22×C4⋊C4—132no—
93C22×C4⋊C4—262no—
94C22×C42—131no—
95C2×C4⋊C8—134no—
96C2×C22⋊C8—262no—
97#384—132no—
98#384—131no—
99#384—262no—
100#384#26111yescharacteristic
101#336—262no—
102C22×C13#38111yescharacteristic
103C22×C13C2×#10011yescharacteristic
104C22×C13C2×#10111yescharacteristic
105C22×C13C2×#10312yes—
106C22×C13#41812yes—
107C2×D13—24no—
108C2×D13—22no—
109C2×D13—22no—
110C2×D13—24no—
111C2×D13#33314yes—
112C4×C13—22no—
113C4×C13—24no—
114C4×C13—82no—
115Dic13—22no—
116Dic13—82no—
117Dic13#48114yes—
118Dic13#48414yes—
119C23×C4—132no—
120C23×C4—131no—
121C23×C4—262no—
122C22×C8—264no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—262no—
126C2×C4⋊C4—264no—
127C2×C4⋊C4—262no—
128C2×C4⋊C4—524no—
129C2×C4⋊C4—528no—
130C2×C4⋊C4C2×#26112yes—
131C2×C42—131no—
132C2×C42—132no—
133C2×C42—264no—
134C2×C42C2×#26111yescharacteristic
135C4⋊C8—268no—
136C22⋊C8—524no—
137C2×C13C2×#33311yescharacteristic
138C2×C13#154912yes—
139C2×C13#155511yescharacteristic
140C2×C13#182111yescharacteristic
141C2×C13#182412yes—
142D13—24no—
143C24—131no—
144C22×C4—22no—
145C22×C4—132no—
146C22×C4—131no—
147C22×C4—134no—
148C22×C4—134no—
149C22×C4—264no—
150C22×C4—264no—
151C22×C4—262no—
152C22×C4—262no—
153C22×C4—262no—
154C22×C4—262no—
155C22×C4—524no—
156C22×C4—528no—
157C22×C4C22⋊#26112yes—
158C22×C4C22×#26111yescharacteristic
159C2×C8—524no—
160C2×C8—524no—
161C2×C8—524no—
162C4⋊C4—42no—
163C4⋊C4—44no—
164C4⋊C4—522no—
165C4⋊C4—524no—
166C4⋊C4—528no—
167C4⋊C4—524no—
168C42—22no—
169C42—134no—
170C42—264no—
171C13#872511yescharacteristic, complemented, Sylow
172C23—132no—
173C23—134no—
174C23—261no—
175C23—262no—
176C23—261no—
177C23C2×C22⋊#26111yescharacteristic
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—42no—
184C2×C4—134no—
185C2×C4—134no—
186C2×C4—132no—
187C2×C4—132no—
188C2×C4—132no—
189C2×C4—268no—
190C2×C4—268no—
191C2×C4—268no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—524no—
195C2×C4—522no—
196C2×C4—1048no—
197C2×C4#8811714yes—
198C2×C4#8823712yes—
199C8—1044no—
200C22—134no—
201C22—264no—
202C22—262no—
203C22—262no—
204C22—264no—
205C22#1171913511yescharacteristic
206C22#1171913812yes—
207C22D13⋊#10011yescharacteristic
208C22C2×#8811712yes—
209C22D13⋊#10111yescharacteristic
210C4—22no—
211C4—24no—
212C4—82no—
213C4—134no—
214C4—134no—
215C4—262no—
216C4—1042no—
217C2—264no—
218C2D13⋊#33311yescharacteristic
219C2#1313035212yes—
220C2#1313036411yescharacteristic
221C2#1313073611yescharacteristic
222C2#1313074012yes—
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#8725
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. #13129714C2semidirect
171. C13#8725semidirect

Maximal subgroups

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

subgroupindex
#131306932
#131297142
D13×#3842
#872513