Finite Group Databasebeta

← #16782187

Subgroups — #16782187

Order 3328.

630 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 140 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#13130692C212yesmaximal
2#13129714C214yesmaximal, complemented
3C2×#11718637C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×#6101—22no—
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9C2×#88112C2214yes—
10#11718637—22no—
11#11718637C412yes—
12#11718637C2212yes—
13#11718290—22no—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×#1057—24no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—42no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C4⋊Dic13—21no—
23C2×C4⋊Dic13—42no—
24C2×C4⋊Dic13C2×C412yes—
25C2×#6101—24no—
26C2×#6101—24no—
27C2×#6101—44no—
28C2×#6101—44no—
29C2×C4×Dic13—24no—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13D412yes—
32C2×C4×Dic13C2311yescharacteristic
33C22⋊#1057—44no—
34#88112—28no—
35#8723—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—42no—
42C22×C4×C13—44no—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13—22no—
48C22×Dic13—42no—
49C22×Dic13—44no—
50C22×Dic13C22⋊C412yes—
51C22×Dic13D814yes—
52C22×Dic13SD1614yes—
53C22×Dic13C2×D412yes—
54C2×#1057—44no—
55C2×#1057—44no—
56C2×#1057—44no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—42no—
59C4⋊Dic13—42no—
60C4⋊Dic13—42no—
61#6101—48no—
62#6101—44no—
63#6101—44no—
64C4×Dic13—22no—
65C4×Dic13—24no—
66C4×Dic13#4114yes—
67C2×#384—131no—
68#1797—132no—
69#1296—134no—
70C23×C13—21no—
71C23×C13—21no—
72C23×C13—22no—
73C23×C13#10012yes—
74C23×C13#10214yes—
75C23×C13C2×C22⋊C411yescharacteristic
76C2×C4×C13—28no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13—84no—
84C2×C4×C13#10112yes—
85C2×C4×C13#11712yes—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—28no—
89C2×Dic13—28no—
90C2×Dic13—42no—
91C2×Dic13—44no—
92C2×Dic13—84no—
93C2×Dic13#10214yes—
94C2×Dic13#12314yes—
95C2×Dic13C2×D812yes—
96C2×Dic13C2×SD1612yes—
97C2×Dic13#13714yes—
98#1057—84no—
99C22×C4⋊C4—131no—
100C22×C4⋊C4—262no—
101C22×C4⋊C4#26111yescharacteristic
102C22×C42—131no—
103C2×C4⋊C8—134no—
104C2×C22⋊C8—262no—
105#384—132no—
106#384—132no—
107#384—262no—
108#336—262no—
109C22×C13—24no—
110C22×C13—22no—
111C22×C13—22no—
112C22×C13—24no—
113C22×C13#33114yes—
114C22×C13#38111yescharacteristic
115C22×C13C2×#10011yescharacteristic
116C22×C13C2×#10111yescharacteristic
117C22×C13C2×#10212yes—
118C22×C13#41912yes—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—82no—
122Dic13—24no—
123Dic13—82no—
124Dic13#48014yes—
125Dic13#48314yes—
126C23×C4—21no—
127C23×C4—132no—
128C23×C4—261no—
129C23×C4C2×#26111yescharacteristic
130C22×C8—264no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—264no—
135C2×C4⋊C4—264no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—522no—
138C2×C4⋊C4—524no—
139C2×C4⋊C4—524no—
140C2×C4⋊C4C2×#26112yes—
141C2×C42—131no—
142C2×C42—132no—
143C2×C42—131no—
144C2×C42—264no—
145C4⋊C8—268no—
146C22⋊C8—524no—
147C2×C13—24no—
148C2×C13C2×#33111yescharacteristic
149C2×C13#154612yes—
150C2×C13#155811yescharacteristic
151C2×C13#182111yescharacteristic
152C2×C13#182312yes—
153C24C22⋊#26111yescharacteristic
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—44no—
159C22×C4—42no—
160C22×C4—132no—
161C22×C4—134no—
162C22×C4—134no—
163C22×C4—132no—
164C22×C4—264no—
165C22×C4—264no—
166C22×C4—262no—
167C22×C4—524no—
168C22×C4—522no—
169C22×C4C22⋊#26111yescharacteristic
170C22×C4C22×#26111yescharacteristic
171C2×C8—524no—
172C2×C8—524no—
173C2×C8—524no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—524no—
179C4⋊C4—524no—
180C4⋊C4—528no—
181C42—134no—
182C42—264no—
183C42—262no—
184C13#872311yescharacteristic, complemented, Sylow
185C23—21no—
186C23—21no—
187C23—22no—
188C23#8811514yes—
189C23#8812112yes—
190C23C2×C22⋊#26111yescharacteristic
191C2×C4—28no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—44no—
198C2×C4—84no—
199C2×C4—134no—
200C2×C4—132no—
201C2×C4—132no—
202C2×C4—134no—
203C2×C4—134no—
204C2×C4—268no—
205C2×C4—268no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—522no—
209C2×C4—524no—
210C2×C4—1044no—
211C2×C4#8811312yes—
212C2×C4#8823712yes—
213C8—1044no—
214C22—24no—
215C22—22no—
216C22—22no—
217C22—24no—
218C22#1171829714yes—
219C22C2×#8811311yescharacteristic
220C22#1171913511yescharacteristic
221C22C2×#8811512yes—
222C22#1171915312yes—
223C22C2×#8812111yescharacteristic
224C4—22no—
225C4—22no—
226C4—82no—
227C4—134no—
228C4—134no—
229C4—264no—
230C4—1042no—
231C2—24no—
232C2C2×#1171829711yescharacteristic
233C2#1313034512yes—
234C2#1313036911yescharacteristic
235C2#1313073511yescharacteristic
236C2#1313073912yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8723
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
184. C13#8723semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
C2×#117186372
#872313