Finite Group Databasebeta

← #16780241

Subgroups — #16780241

Order 3328.

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

normal subgroups only

This group has 524 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
1D13⋊#432C212yesmaximal
2#13129742C214yesmaximal, complemented
3#13123467C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5#11719130C2214yes—
6#11719128C414yes—
7D13⋊(C22⋊C8)C414yes—
8#11719055—22no—
9#11719054—22no—
10D13⋊(C4⋊C8)—22no—
11#11719047—22no—
12C4×C13×M16C411yescharacteristic
13#11718787C412yes—
14#11718779C2212yes—
15C4×#6099C411yescharacteristic
16#11718366—22no—
17#11718346—22no—
18C22×C4×D13C2×C411yescharacteristic
19C22×C4×D13C2×C412yes—
20C2×D13⋊C8—24no—
21C2×C13×M16C2×C412yes—
22C2×C42×C13C2×C411yescharacteristic
23C2×C4×Dic13C2×C412yes—
24C2×C4×Dic13C2311yescharacteristic
25C2×#6099C2×C412yes—
26C42×D13D412yes—
27C42×D13D412yes—
28C42×D13D412yes—
29C42×D13Q812yes—
30C22⋊#1057C2×C418yes—
31#88112—24no—
32#88111—24no—
33#88110—24no—
34#88110—24no—
35C4⋊#1057—24no—
36C13×#97—21no—
37C4×C8×C13—21no—
38#88060—24no—
39#88054—24no—
40#88043—21no—
41C4×#1055—21no—
42#8120—131nomaximal, Sylow
43C23×D13C4211yescharacteristic
44C22×C4×C13C4212yes—
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13C4211yescharacteristic
47C22×Dic13C22×C412yes—
48C2×C4×D13—42no—
49C2×C4×D13—44no—
50C2×C4×D13C22⋊C412yes—
51C2×C4×D13C22⋊C412yes—
52C2×C4×D13C22⋊C412yes—
53C2×C4×D13C4⋊C412yes—
54C2×C4×D13C4⋊C412yes—
55C2×C4×D13C4⋊C412yes—
56C2×#1057—28no—
57D13⋊C8—48no—
58C13×M16—42no—
59C2×C8×C13—22no—
60C42×C13C22⋊C411yescharacteristic
61C42×C13C22⋊C411yescharacteristic
62C42×C13C4⋊C412yes—
63C4×Dic13C22⋊C412yes—
64C4×Dic13C22⋊C412yes—
65C4×Dic13C4⋊C412yes—
66C4×Dic13C4⋊C412yes—
67C4×Dic13C2×D411yescharacteristic
68C4×Dic13C2×D412yes—
69C4×Dic13C2×Q811yescharacteristic
70#6099—42no—
71C2×#1055—22no—
72#2920—131no—
73C2×#432—132no—
74#1307—134no—
75C23×C13C2×C4211yescharacteristic
76C22×D13—24no—
77C22×D13—41no—
78C22×D13#9512yes—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13#9512yes—
82C2×C4×C13#9512yes—
83C2×C4×C13C2×C22⋊C411yescharacteristic
84C2×C4×C13C2×C4⋊C411yescharacteristic
85C2×Dic13—41no—
86C2×Dic13—42no—
87C2×Dic13#9512yes—
88C2×Dic13C2×C22⋊C412yes—
89C2×Dic13C2×C4⋊C412yes—
90C4×D13—24no—
91C4×D13—24no—
92C4×D13—24no—
93C4×D13—42no—
94C4×D13—42no—
95C4×D13—42no—
96#1057—48no—
97C8×C13—42no—
98#1055—42no—
99C22×C42—131no—
100#432—134no—
101#432—134no—
102#432—262no—
103#432—262no—
104#432—262no—
105#431—262no—
106#423—132no—
107C2×C4⋊C8—262no—
108#407—132no—
109C2×C22⋊C8—134no—
110C4×M16—131no—
111C4×M16#26111yescharacteristic
112C2×#97—262no—
113C22×C13—21no—
114C22×C13—22no—
115C22×C13C2×#9511yescharacteristic
116C2×D13—22no—
117C2×D13—22no—
118C2×D13—44no—
119C2×D13#34414yes—
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13#41312yes—
124Dic13—22no—
125Dic13—22no—
126Dic13—22no—
127C23×C4—132no—
128C23×C4—131no—
129C2×M16—132no—
130C2×M16C2×#26112yes—
131C22×C8—264no—
132C2×C42—132no—
133C2×C42—131no—
134C2×C42—132no—
135C2×C42—132no—
136C2×C42—132no—
137C2×C42—132no—
138C2×C42C2×#26111yescharacteristic
139C4⋊C8—264no—
140C4⋊C8—264no—
141C4⋊C8—264no—
142C22⋊C8—138no—
143C22⋊C8—264no—
144C22⋊C8—264no—
145#97—21no—
146#97—264no—
147#97—264no—
148#97—261no—
149C4×C8—21no—
150C4×C8—261no—
151C2×C13—41no—
152C2×C13#174211yescharacteristic
153C2×C13C2×#34412yes—
154D13—24no—
155C24—131no—
156C22×C4—132no—
157C22×C4—131no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—522no—
165C22×C4—524no—
166C22×C4C4×#26112yes—
167C22×C4C22×#26111yescharacteristic
168M16—42no—
169M16—522no—
170C2×C8—22no—
171C2×C8—268no—
172C2×C8—262no—
173C2×C8—528no—
174C42—132no—
175C42—132no—
176C42—132no—
177C42—132no—
178C42—131no—
179C42—131no—
180C42—132no—
181C42C4⋊#26112yes—
182C42C22⋊#26111yescharacteristic
183C42C22⋊#26111yescharacteristic
184C13#812011yescharacteristic, complemented, Sylow
185C23—132no—
186C23—264no—
187C23—521no—
188C23C2×C4×#26111yescharacteristic
189C2×C4—22no—
190C2×C4—42no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—264no—
195C2×C4—264no—
196C2×C4—264no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—521no—
201C2×C4—522no—
202C2×C4(C2×#261)⋊C412yes—
203C2×C4(C2×#261)⋊C412yes—
204C2×C4C2×C4⋊#26111yescharacteristic
205C2×C4C2×C22⋊#26111yescharacteristic
206C8—42no—
207C8—528no—
208C8—522no—
209C22—21no—
210C22—22no—
211C22—134no—
212C22—262no—
213C22—262no—
214C22—524no—
215C22C2×(C2×#261)⋊C411yescharacteristic
216C4—21no—
217C4—22no—
218C4—22no—
219C4—262no—
220C4—262no—
221C4—262no—
222C4#1171913212yes—
223C2—41no—
224C2—264no—
225C2#1313054111yescharacteristic
226C2#1313054812yes—
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC22×C4C22×#261
FittingC4×C13×M16C4
socleC22×C13C2×#95
prime radicalC23×D13C42
cosocleC2×C4×Dic13C23
hypercenterC4×M16#261
hypocenterC13#8120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #13129742C2semidirect
184. C13#8120semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4322
#131297422
#131234672
#812013