Finite Group Databasebeta

← #16779873

Subgroups — #16779873

Order 3328.

564 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 160 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⋊#431C212yesmaximal
2#13129718C214yesmaximal
3#13123468C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5#11719125—22no—
6D13⋊(C22⋊C8)C2214yes—
7#11719119—22no—
8#11719051C414yes—
9D13⋊(C4⋊C8)—22no—
10#11719049C414yes—
11C4×D13⋊C8—22no—
12C13×#423C411yescharacteristic
13#11718787C2212yes—
14M16×Dic13C412yes—
15#11718585C411yescharacteristic
16#11718496—22no—
17#11718494—22no—
18C22×C4×D13Q812yes—
19C22×C4×D13C2311yescharacteristic
20C2×D13⋊C8—24no—
21C2×C13×M16C2×C412yes—
22C2×C42×C13C2×C411yescharacteristic
23C2×C4×Dic13C2×C411yescharacteristic
24C2×C4×Dic13D412yes—
25C2×#6099C2×C412yes—
26C42×D13C2×C412yes—
27C42×D13C2×C412yes—
28C42×D13D412yes—
29C42×D13D412yes—
30C22⋊#1057—24no—
31#88112—24no—
32#88111C2×C418yes—
33C4⋊#1057—24no—
34C4×#1057—24no—
35C4×#1057—24no—
36C13×C4⋊C8—22no—
37#88060—24no—
38#88055—22no—
39C8×Dic13—22no—
40C4⋊#1055—22no—
41#8054—131nomaximal, Sylow
42C23×D13C2×Q811yescharacteristic
43C22×C4×C13C4⋊C412yes—
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13C4⋊C412yes—
46C22×Dic13C2×D411yescharacteristic
47C2×C4×D13—28no—
48C2×C4×D13—41no—
49C2×C4×D13—41no—
50C2×C4×D13C4⋊C412yes—
51C2×C4×D13C4⋊C412yes—
52C2×C4×D13C4⋊C412yes—
53C2×C4×D13C4⋊C412yes—
54C2×C4×D13C22×C412yes—
55C2×C4×D13C2×D412yes—
56C2×#1057—28no—
57D13⋊C8—44no—
58D13⋊C8—44no—
59C13×M16—42no—
60C2×C8×C13—22no—
61C42×C13C4211yescharacteristic
62C42×C13C4211yescharacteristic
63C42×C13C22⋊C412yes—
64C4×Dic13C4212yes—
65C4×Dic13C22⋊C411yescharacteristic
66C4×Dic13C22⋊C411yescharacteristic
67C4×Dic13C22⋊C412yes—
68C4×Dic13C22⋊C412yes—
69C4×Dic13C22⋊C412yes—
70C4×Dic13C22⋊C412yes—
71#6099—42no—
72C2×#1055—22no—
73#2920—131no—
74C2×#431—132no—
75#1298—134no—
76C23×C13C2×C4⋊C411yescharacteristic
77C22×D13—24no—
78C22×D13—41no—
79C22×D13C2×C4⋊C412yes—
80C2×C4×C13—24no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13#9512yes—
84C2×C4×C13#9512yes—
85C2×C4×C13C2×C4211yescharacteristic
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×Dic13—24no—
88C2×Dic13—41no—
89C2×Dic13#9512yes—
90C2×Dic13#9512yes—
91C2×Dic13C2×C22⋊C412yes—
92C4×D13—24no—
93C4×D13—24no—
94C4×D13—22no—
95C4×D13—22no—
96C4×D13—24no—
97C4×D13—42no—
98C4×D13#10818yes—
99#1057—48no—
100C8×C13—42no—
101#1055—42no—
102C22×C42—131no—
103#432—262no—
104#431—134no—
105#431—134no—
106#431—262no—
107#431—262no—
108#431—262no—
109#423—131no—
110#423#26111yescharacteristic
111C2×C4⋊C8—262no—
112#407—132no—
113C2×C22⋊C8—134no—
114C4×M16—132no—
115C2×C4×C8—262no—
116C22×C13—22no—
117C22×C13—21no—
118C22×C13C2×#9511yescharacteristic
119C2×D13—22no—
120C2×D13—22no—
121C2×D13—44no—
122C2×D13C2×#10814yes—
123C4×C13—22no—
124C4×C13—21no—
125C4×C13#34114yes—
126C4×C13#41011yescharacteristic
127C4×C13#41011yescharacteristic
128Dic13—22no—
129Dic13—22no—
130Dic13#34114yes—
131C23×C4—132no—
132C23×C4—131no—
133C2×M16—132no—
134C2×M16C2×#26112yes—
135C22×C8—264no—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42—132no—
139C2×C42—132no—
140C2×C42—132no—
141C2×C42—132no—
142C2×C42C2×#26111yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—264no—
145C4⋊C8—264no—
146C4⋊C8—262no—
147C22⋊C8—138no—
148C22⋊C8—264no—
149C22⋊C8—264no—
150#97—262no—
151C4×C8—262no—
152C4×C8—264no—
153C4×C8—264no—
154C2×C13—41no—
155C2×C13C2×#34112yes—
156C2×C13#174011yescharacteristic
157D13—24no—
158C24—131no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—131no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—132no—
166C22×C4—132no—
167C22×C4—268no—
168C22×C4—521no—
169C22×C4—521no—
170C22×C4C4⋊#26112yes—
171C22×C4C22×#26111yescharacteristic
172M16—42no—
173M16—522no—
174C2×C8—22no—
175C2×C8—268no—
176C2×C8—262no—
177C2×C8—524no—
178C2×C8—524no—
179C42—132no—
180C42—132no—
181C42—132no—
182C42—132no—
183C42—132no—
184C42—131no—
185C42—131no—
186C42C4×#26111yescharacteristic
187C42C4×#26111yescharacteristic
188C42C22⋊#26112yes—
189C13#805411yescharacteristic, complemented, Sylow
190C23—132no—
191C23—264no—
192C23—521no—
193C23C2×C4⋊#26111yescharacteristic
194C2×C4—24no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—132no—
198C2×C4—138no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—264no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—522no—
208C2×C4—521no—
209C2×C4(C2×#261)⋊C412yes—
210C2×C4(C2×#261)⋊C412yes—
211C2×C4C2×C4×#26111yescharacteristic
212C2×C4C2×C22⋊#26111yescharacteristic
213C8—42no—
214C8—528no—
215C8—522no—
216C22—22no—
217C22—21no—
218C22—134no—
219C22—262no—
220C22—262no—
221C22—524no—
222C22C2×(C2×#261)⋊C411yescharacteristic
223C4—22no—
224C4—21no—
225C4—134no—
226C4—262no—
227C4—262no—
228C4#1171827314yes—
229C4#1171914211yescharacteristic
230C4#1171915611yescharacteristic
231C2—41no—
232C2—264no—
233C2C2×#1171827312yes—
234C2#1313053611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#423C4
socleC22×C13C2×#95
prime radicalC23×D13C2×Q8
cosocleC22×C4×D13C23
hypercenter#423#261
hypocenterC13#8054
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
189. C13#8054semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131297182
#131234682
#805413