Finite Group Databasebeta

← #16782191

Subgroups — #16782191

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—48no—
28C2×C4×Dic13—24no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13D412yes—
31C2×C4×Dic13C2311yescharacteristic
32C22⋊#1057—44no—
33#88112—28no—
34#8725—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—44no—
41C22×C4×C13—42no—
42C22×C4×C13C22⋊C411yescharacteristic
43C22×C4×C13C22×C411yescharacteristic
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—22no—
47C22×Dic13—44no—
48C22×Dic13—42no—
49C22×Dic13C22⋊C412yes—
50C22×Dic13SD1614yes—
51C22×Dic13Q1614yes—
52C22×Dic13C2×D412yes—
53C2×#1057—44no—
54C2×#1057—44no—
55C2×#1057—44no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—42no—
58C4⋊Dic13—42no—
59C4⋊Dic13—42no—
60#6101—48no—
61#6101—48no—
62C4×Dic13—22no—
63C4×Dic13—24no—
64C4×Dic13#4114yes—
65C2×#384—131no—
66#1797—132no—
67#1296—134no—
68C23×C13—21no—
69C23×C13—21no—
70C23×C13—22no—
71C23×C13#10012yes—
72C23×C13#10314yes—
73C23×C13C2×C22⋊C411yescharacteristic
74C2×C4×C13—28no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—42no—
80C2×C4×C13—44no—
81C2×C4×C13—84no—
82C2×C4×C13#10112yes—
83C2×C4×C13#11712yes—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—28no—
87C2×Dic13—28no—
88C2×Dic13—42no—
89C2×Dic13—44no—
90C2×Dic13—84no—
91C2×Dic13#10314yes—
92C2×Dic13#12314yes—
93C2×Dic13C2×SD1612yes—
94C2×Dic13C2×Q1612yes—
95C2×Dic13AGL(1,ℤ/8)14yes—
96#1057—84no—
97C22×C4⋊C4—131no—
98C22×C4⋊C4—262no—
99C22×C4⋊C4#26111yescharacteristic
100C22×C42—131no—
101C2×C4⋊C8—134no—
102C2×C22⋊C8—262no—
103#384—132no—
104#384—132no—
105#384—262no—
106#336—262no—
107C22×C13—24no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13—24no—
111C22×C13#33314yes—
112C22×C13#38111yescharacteristic
113C22×C13C2×#10011yescharacteristic
114C22×C13C2×#10111yescharacteristic
115C22×C13C2×#10312yes—
116C22×C13#41812yes—
117C4×C13—22no—
118C4×C13—22no—
119C4×C13—82no—
120Dic13—24no—
121Dic13—82no—
122Dic13#48114yes—
123Dic13#48414yes—
124C23×C4—21no—
125C23×C4—132no—
126C23×C4—261no—
127C23×C4C2×#26111yescharacteristic
128C22×C8—264no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—264no—
133C2×C4⋊C4—264no—
134C2×C4⋊C4—261no—
135C2×C4⋊C4—522no—
136C2×C4⋊C4—528no—
137C2×C4⋊C4C2×#26112yes—
138C2×C42—131no—
139C2×C42—132no—
140C2×C42—131no—
141C2×C42—264no—
142C4⋊C8—268no—
143C22⋊C8—524no—
144C2×C13—24no—
145C2×C13C2×#33311yescharacteristic
146C2×C13#154912yes—
147C2×C13#155511yescharacteristic
148C2×C13#182111yescharacteristic
149C2×C13#182412yes—
150C24C22⋊#26111yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4—42no—
157C22×C4—132no—
158C22×C4—134no—
159C22×C4—134no—
160C22×C4—132no—
161C22×C4—264no—
162C22×C4—264no—
163C22×C4—262no—
164C22×C4—524no—
165C22×C4—522no—
166C22×C4C22⋊#26111yescharacteristic
167C22×C4C22×#26111yescharacteristic
168C2×C8—524no—
169C2×C8—524no—
170C2×C8—524no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—522no—
174C4⋊C4—522no—
175C4⋊C4—528no—
176C4⋊C4—528no—
177C42—134no—
178C42—264no—
179C42—262no—
180C13#872511yescharacteristic, complemented, Sylow
181C23—21no—
182C23—21no—
183C23—22no—
184C23#8811714yes—
185C23#8812112yes—
186C23C2×C22⋊#26111yescharacteristic
187C2×C4—28no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—84no—
195C2×C4—134no—
196C2×C4—134no—
197C2×C4—132no—
198C2×C4—132no—
199C2×C4—134no—
200C2×C4—268no—
201C2×C4—268no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—522no—
205C2×C4—524no—
206C2×C4—1044no—
207C2×C4#8811312yes—
208C2×C4#8823712yes—
209C8—1044no—
210C22—24no—
211C22—22no—
212C22—22no—
213C22—24no—
214C22#1171830314yes—
215C22C2×#8811311yescharacteristic
216C22#1171913511yescharacteristic
217C22#1171913812yes—
218C22C2×#8811712yes—
219C22C2×#8812111yescharacteristic
220C4—22no—
221C4—22no—
222C4—82no—
223C4—134no—
224C4—134no—
225C4—264no—
226C4—1042no—
227C2—24no—
228C2C2×#1171830311yescharacteristic
229C2#1313035112yes—
230C2#1313036311yescharacteristic
231C2#1313073511yescharacteristic
232C2#1313074012yes—
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#8725
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
180. C13#8725semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
C2×#117186372
#872513