Finite Group Databasebeta

← #16782128

Subgroups — #16782128

Order 3328.

530 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130727C212yesmaximal
2#13129674C214yesmaximal
3C2×#11718638C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057C2214yes—
8C2×#88071C412yes—
9C2×#88071C2212yes—
10#11718638—22no—
11#11718638—22no—
12#11718290—22no—
13#11718290—22no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13C2311yescharacteristic
19C22×#1057—24no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—42no—
23C2×C4⋊Dic13—21no—
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—42no—
26C2×C4×Dic13—24no—
27C2×C4×Dic13D412yes—
28C2×C4×Dic13D412yes—
29C22⋊#1057—28no—
30#88071—24no—
31#88071—24no—
32#8703—131nomaximal, Sylow
33C24×C13C22×C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—24no—
39C22×C4×C13—42no—
40C22×C4×C13—42no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22⋊C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—22no—
45C22×Dic13—22no—
46C22×Dic13—22no—
47C22×Dic13—24no—
48C22×Dic13—41no—
49C22×Dic13—41no—
50C22×Dic13—42no—
51C22×Dic13—42no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C22×Dic13#4114yes—
55C2×#1057—44no—
56C2×#1057—44no—
57C2×#1057—44no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—42no—
60C4⋊Dic13—42no—
61C4⋊Dic13—42no—
62C4×Dic13—24no—
63C4×Dic13—24no—
64C2×#382—131no—
65#1817—132no—
66#1280—134no—
67C23×C13—21no—
68C23×C13—21no—
69C23×C13—21no—
70C23×C13—21no—
71C23×C13C2×C22⋊C411yescharacteristic
72C23×C13#11712yes—
73C23×C13#13112yes—
74C23×C13#13112yes—
75C2×C4×C13—28no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—84no—
84C2×C4×C13#10012yes—
85C2×C4×C13#10112yes—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—44no—
92C2×Dic13—44no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—84no—
97C2×Dic13#12314yes—
98#1057—84no—
99C22×C4⋊C4—131no—
100C22×C4⋊C4#26111yescharacteristic
101C22×C42—131no—
102C2×C22⋊C8—134no—
103#382—262no—
104#382—262no—
105C2×#95—132no—
106C2×#95—132no—
107#336—262no—
108#336—262no—
109C22×C13—22no—
110C22×C13—22no—
111C22×C13—22no—
112C22×C13—22no—
113C22×C13—22no—
114C22×C13—22no—
115C22×C13#38111yescharacteristic
116C22×C13#40811yescharacteristic
117C22×C13#40811yescharacteristic
118C22×C13#41011yescharacteristic
119C22×C13#41011yescharacteristic
120C22×C13C2×#10011yescharacteristic
121C22×C13C2×#10111yescharacteristic
122C22×C13#43314yes—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—82no—
126Dic13—24no—
127Dic13—42no—
128Dic13—82no—
129C23×C4—131no—
130C23×C4—131no—
131C23×C4—132no—
132C23×C4C2×#26112yes—
133C23×C4C2×#26111yescharacteristic
134C22×C8—264no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4—261no—
140C2×C4⋊C4—522no—
141C2×C42—132no—
142C2×C42—132no—
143C2×C42—264no—
144C22⋊C8—268no—
145#95—264no—
146#95—264no—
147C2×C13—24no—
148C2×C13#146911yescharacteristic
149C2×C13#146911yescharacteristic
150C2×C13#147011yescharacteristic
151C2×C13#147011yescharacteristic
152C2×C13#181811yescharacteristic
153C2×C13#182011yescharacteristic
154C2×C13#182111yescharacteristic
155C24C22×#26111yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—132no—
164C22×C4—134no—
165C22×C4—132no—
166C22×C4—262no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4—264no—
171C22×C4—521no—
172C22×C4—521no—
173C22×C4—522no—
174C22×C4—522no—
175C22×C4C22⋊#26111yescharacteristic
176C22×C4C22⋊#26111yescharacteristic
177C2×C8—524no—
178C2×C8—524no—
179C2×C8—524no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—522no—
183C4⋊C4—522no—
184C42—264no—
185C42—264no—
186C13#870311yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—21no—
190C23—21no—
191C23#8823712yes—
192C23#8823812yes—
193C23#8824012yes—
194C23C2×C22⋊#26111yescharacteristic
195C2×C4—28no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—84no—
204C2×C4—134no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—524no—
211C2×C4—524no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—1044no—
216C2×C4#8811312yes—
217C2×C4#8812112yes—
218C8—1044no—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#1171907714yes—
226C22C2×#8811311yescharacteristic
227C22#1171913511yescharacteristic
228C22#1171914211yescharacteristic
229C22#1171914711yescharacteristic
230C22#1171915611yescharacteristic
231C22#1171915911yescharacteristic
232C22C2×#8812111yescharacteristic
233C4—22no—
234C4—22no—
235C4—82no—
236C4—264no—
237C4—522no—
238C4—1042no—
239C2—24no—
240C2#1313010611yescharacteristic
241C2#1313010711yescharacteristic
242C2#1313010911yescharacteristic
243C2#1313011011yescharacteristic
244C2#1313073011yescharacteristic
245C2#1313073411yescharacteristic
246C2#1313073511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8703
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
186. C13#8703semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131296742
C2×#117186382
#870313