Finite Group Databasebeta

← #16782188

Subgroups — #16782188

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—44no—
29C4⋊C4×D13—44no—
30C42×D13—24no—
31#88112—28no—
32#88111—44no—
33#8723—131nomaximal, Sylow
34C23×D13C22⋊C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13C22⋊C412yes—
37C22×C4×C13C22×C411yescharacteristic
38C22×Dic13—22no—
39C22×Dic13C22⋊C411yescharacteristic
40C22×Dic13C2×D412yes—
41C2×C4×D13—22no—
42C2×C4×D13—22no—
43C2×C4×D13—22no—
44C2×C4×D13—24no—
45C2×C4×D13—24no—
46C2×C4×D13—44no—
47C2×C4×D13—48no—
48C2×C4×D13D814yes—
49C2×C4×D13SD1614yes—
50C2×#1057—44no—
51C2×#1057—44no—
52C2×#1057—44no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—44no—
55C42×C13—22no—
56C4⋊Dic13—44no—
57C4⋊Dic13—42no—
58#6101—44no—
59#6101—44no—
60#6101—44no—
61C4×Dic13—24no—
62C4×Dic13#4114yes—
63C2×#384—131no—
64#1797—132no—
65#1296—134no—
66C23×C13C2×C22⋊C411yescharacteristic
67C22×D13—21no—
68C22×D13—21no—
69C22×D13—22no—
70C22×D13#10012yes—
71C22×D13#10214yes—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—42no—
77C2×C4×C13—44no—
78C2×C4×C13#10214yes—
79C2×C4×C13#11712yes—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—42no—
83C2×Dic13—44no—
84C2×Dic13#10112yes—
85C2×Dic13#12314yes—
86C2×Dic13C2×D812yes—
87C2×Dic13C2×SD1612yes—
88C2×Dic13#13714yes—
89C4×D13—28no—
90C4×D13—28no—
91C4×D13—28no—
92C4×D13—88no—
93#1057—84no—
94C22×C4⋊C4—132no—
95C22×C4⋊C4—262no—
96C22×C42—131no—
97C2×C4⋊C8—134no—
98C2×C22⋊C8—262no—
99#384—132no—
100#384—131no—
101#384—262no—
102#384#26111yescharacteristic
103#336—262no—
104C22×C13#38111yescharacteristic
105C22×C13C2×#10011yescharacteristic
106C22×C13C2×#10111yescharacteristic
107C22×C13C2×#10212yes—
108C22×C13#41912yes—
109C2×D13—24no—
110C2×D13—22no—
111C2×D13—22no—
112C2×D13—24no—
113C2×D13#33114yes—
114C4×C13—22no—
115C4×C13—24no—
116C4×C13—82no—
117Dic13—22no—
118Dic13—82no—
119Dic13#48014yes—
120Dic13#48314yes—
121C23×C4—132no—
122C23×C4—131no—
123C23×C4—262no—
124C22×C8—264no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—262no—
128C2×C4⋊C4—264no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—524no—
131C2×C4⋊C4—524no—
132C2×C4⋊C4—524no—
133C2×C4⋊C4C2×#26112yes—
134C2×C42—131no—
135C2×C42—132no—
136C2×C42—264no—
137C2×C42C2×#26111yescharacteristic
138C4⋊C8—268no—
139C22⋊C8—524no—
140C2×C13C2×#33111yescharacteristic
141C2×C13#154612yes—
142C2×C13#155811yescharacteristic
143C2×C13#182111yescharacteristic
144C2×C13#182312yes—
145D13—24no—
146C24—131no—
147C22×C4—22no—
148C22×C4—132no—
149C22×C4—131no—
150C22×C4—134no—
151C22×C4—134no—
152C22×C4—264no—
153C22×C4—264no—
154C22×C4—262no—
155C22×C4—262no—
156C22×C4—262no—
157C22×C4—262no—
158C22×C4—528no—
159C22×C4—524no—
160C22×C4C22⋊#26112yes—
161C22×C4C22×#26111yescharacteristic
162C2×C8—524no—
163C2×C8—524no—
164C2×C8—524no—
165C4⋊C4—42no—
166C4⋊C4—44no—
167C4⋊C4—522no—
168C4⋊C4—524no—
169C4⋊C4—524no—
170C4⋊C4—524no—
171C4⋊C4—524no—
172C42—22no—
173C42—134no—
174C42—264no—
175C13#872311yescharacteristic, complemented, Sylow
176C23—134no—
177C23—132no—
178C23—261no—
179C23—262no—
180C23—261no—
181C23C2×C22⋊#26111yescharacteristic
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—44no—
187C2×C4—42no—
188C2×C4—134no—
189C2×C4—132no—
190C2×C4—132no—
191C2×C4—134no—
192C2×C4—132no—
193C2×C4—268no—
194C2×C4—268no—
195C2×C4—268no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—524no—
199C2×C4—522no—
200C2×C4—1048no—
201C2×C4#8811514yes—
202C2×C4#8823712yes—
203C8—1044no—
204C22—134no—
205C22—264no—
206C22—262no—
207C22—262no—
208C22—264no—
209C22#1171913511yescharacteristic
210C22C2×#8811512yes—
211C22D13⋊#10011yescharacteristic
212C22#1171915312yes—
213C22D13⋊#10111yescharacteristic
214C4—22no—
215C4—24no—
216C4—82no—
217C4—134no—
218C4—134no—
219C4—262no—
220C4—1042no—
221C2—264no—
222C2D13⋊#33111yescharacteristic
223C2#1313034612yes—
224C2#1313037011yescharacteristic
225C2#1313073611yescharacteristic
226C2#1313073912yes—
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#8723
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
175. C13#8723semidirect

Maximal subgroups

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

subgroupindex
#131306932
#131297142
D13×#3842
#872313