Finite Group Databasebeta

← #16786809

Subgroups — #16786809

Order 3328.

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

normal subgroups only

This group has 462 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#13130067C212yesmaximal
2#13129780C214yesmaximal
3#13117320C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7#11719119—22no—
8#11718646—22no—
9#11718611C412yes—
10#11718611C2212yes—
11C4×C4⋊Dic13—22no—
12#11718305C2214yes—
13#11718285—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C412yes—
16C13×#117—22no—
17C13×#117C814yescomplemented
18C2×C13×C4⋊C4—21no—
19C2×C13×C22⋊C4C2×C412yes—
20C2×C42×C13—21no—
21C2×C22⋊Dic13C2×C411yescharacteristic
22C2×C22⋊Dic13C2311yescharacteristic
23#88180—41no—
24#88180—41no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13D412yes—
28C2×C4×Dic13—21no—
29C2×C4×Dic13—21no—
30C2×C4×Dic13—41no—
31C2×C4×Dic13—41no—
32C2×C4×Dic13D412yes—
33C22⋊#1057—24no—
34C4⋊#1057—42no—
35C4×#1057—42no—
36#88071—22no—
37#88071—22no—
38#11452—131nomaximal, Sylow
39C24×C13C22×C411yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13C22⋊C411yescharacteristic
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C2×C812yes—
47C22×C4×C13M1612yes—
48C22×Dic13—22no—
49C22×Dic13—44no—
50C22×Dic13—42no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C2×D412yes—
53C2×#1057—44no—
54C13×C4⋊C4—24no—
55C13×C22⋊C4—22no—
56C13×C22⋊C4C2×C814yes—
57C42×C13—24no—
58C22⋊Dic13—41no—
59C22⋊Dic13—41no—
60C4⋊Dic13—42no—
61C4⋊Dic13—44no—
62C4⋊Dic13—44no—
63C4×Dic13—22no—
64C4×Dic13—22no—
65C4×Dic13—42no—
66C4×Dic13—41no—
67C4×Dic13—41no—
68#2296—131no—
69#1458—132no—
70#1326—134no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—42no—
74C23×C13C2×C22⋊C411yescharacteristic
75C23×C13C22×C811yescharacteristic
76C23×C13C2×M1611yescharacteristic
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—24no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13C22⋊C812yes—
87C2×C4×C13C22⋊C812yes—
88C2×C4×C13#9911yescharacteristic
89C2×C4×C13#9911yescharacteristic
90C2×C4×C13#10112yes—
91C2×Dic13—24no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—42no—
95C2×Dic13—44no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—44no—
100#1057—84no—
101C2×#117—131no—
102C2×#117#26111yescharacteristic
103C22×C42—131no—
104#431—262no—
105#389—262no—
106#385—132no—
107#385—132no—
108C4×C4⋊C4—262no—
109#324—262no—
110#323—134no—
111C22×C13—22no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13C2×C22⋊C811yescharacteristic
119C22×C13C2×#9911yescharacteristic
120C22×C13C2×#10111yescharacteristic
121C4×C13—22no—
122C4×C13—44no—
123C4×C13#32412yes—
124C4×C13#32412yes—
125Dic13—42no—
126Dic13—42no—
127Dic13—44no—
128C23×C4—132no—
129C23×C4C2×#26111yescharacteristic
130#117—22no—
131#117—521no—
132#117—521no—
133#117#105714yescomplemented
134C2×C4⋊C4—21no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—262no—
137C2×C4⋊C4—262no—
138C2×C22⋊C4—131no—
139C2×C22⋊C4—131no—
140C2×C22⋊C4C2×#26112yes—
141C2×C42—21no—
142C2×C42—132no—
143C2×C42—261no—
144C2×C42—261no—
145C2×C42—521no—
146C2×C42—521no—
147C4⋊C8—522no—
148C22⋊C8—264no—
149C4×C8—522no—
150#95—262no—
151#95—262no—
152C2×C13—21no—
153C2×C13—21no—
154C2×C13—41no—
155C2×C13—41no—
156C2×C13C2×#32411yescharacteristic
157C2×C13#212012yes—
158C24C22×#26111yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—262no—
166C22×C4—524no—
167C22×C4—522no—
168C22×C4C2×#105712yes—
169C22×C4#612212yes—
170C22×C4C22⋊#26111yescharacteristic
171C22×C4C22⋊#26111yescharacteristic
172C2×C8—524no—
173C4⋊C4—24no—
174C4⋊C4—522no—
175C4⋊C4—524no—
176C4⋊C4—524no—
177C22⋊C4—22no—
178C22⋊C4—521no—
179C22⋊C4—521no—
180C22⋊C4C2×#105714yes—
181C42—24no—
182C42—262no—
183C42—262no—
184C42—522no—
185C42—521no—
186C42—521no—
187C13#1145211yescharacteristic, complemented, Sylow
188C23—21no—
189C23—21no—
190C23—42no—
191C23C22×#105711yescharacteristic
192C23C2×#612211yescharacteristic
193C23C2×C22⋊#26111yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—264no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—522no—
207C2×C4—524no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—524no—
212C2×C4#8810711yescharacteristic
213C2×C4#8810711yescharacteristic
214C2×C4#8811312yes—
215C2×C4C22⋊#105712yes—
216C2×C4C22⋊#105712yes—
217C8—1044no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×#8810711yescharacteristic
226C22C2×#8811311yescharacteristic
227C22C2×C22⋊#105711yescharacteristic
228C4—22no—
229C4—44no—
230C4—522no—
231C4—522no—
232C4—524no—
233C4#1171828512yes—
234C4#1171828512yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#1171828511yescharacteristic
240C2#1313108912yes—
subgroupG/H
centerC2×C4#88107
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22×C4
cosocleC2×C22⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11452
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
17. C13×#117C8semidirect
133. #117#1057semidirect
187. C13#11452semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297802
#131173202
#1145213