Finite Group Databasebeta

← #15772087

Subgroups — #15772087

Order 3328.

434 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 131 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#13113150C212yesmaximal
2#13112782C214yesmaximal, complemented
3C13×#2317C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×C13×#117C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#389—22no—
8C13×#385—22no—
9C13×#384C2212yes—
10C13×#382C412yes—
11#11718586—22no—
12#11718120C2214yes—
13#11718117—22no—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C13×#117—22no—
17C13×#117—42no—
18C13×#117C814yescomplemented
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—24no—
22C2×C13×C4⋊C4—42no—
23C2×C13×C4⋊C4C2×C412yes—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4D412yes—
28C2×C42×C13C2×C412yes—
29C2×C42×C13D412yes—
30C13×#95—24no—
31C22⋊#1055—24no—
32C4⋊#1055—42no—
33C4×#1055—42no—
34#11450—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—42no—
41C22×C4×C13—82no—
42C22×C4×C13C22⋊C412yes—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C2×C812yes—
45C22×C4×C13M1612yes—
46C22×C4×C13C22×C411yescharacteristic
47C22×C4×C13C2×D412yes—
48C13×C4⋊C4—24no—
49C13×C4⋊C4—41no—
50C13×C4⋊C4—41no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—84no—
54C13×C22⋊C4—24no—
55C13×C22⋊C4—42no—
56C42×C13—22no—
57C42×C13—22no—
58C42×C13—22no—
59C42×C13C2×C814yes—
60C2×#1055—44no—
61#2317D1311yescharacteristic
62#1458—132no—
63#1325—134no—
64C23×C13—21no—
65C23×C13—21no—
66C23×C13—41no—
67C23×C13—41no—
68C23×C13C22⋊C812yes—
69C23×C13C2×C22⋊C411yescharacteristic
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—24no—
73C2×C4×C13—24no—
74C2×C4×C13—24no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—44no—
82C2×C4×C13—42no—
83C2×C4×C13—84no—
84C2×C4×C13C22⋊C812yes—
85C2×C4×C13#9912yes—
86C2×C4×C13#10112yes—
87C2×C4×C13C22×C811yescharacteristic
88C2×C4×C13C2×M1611yescharacteristic
89#1055—84no—
90C2×#117Dic1311yescharacteristic
91C2×#117C2×D1311yescharacteristic
92C22×C4⋊C4Dic1311yescharacteristic
93#431—262no—
94#389—22no—
95#385—22no—
96#384C2×D1312yes—
97#382Dic1312yes—
98#324—134no—
99#323—262no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—22no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13C2×C22⋊C811yescharacteristic
108C22×C13C2×#9911yescharacteristic
109C22×C13C2×#10111yescharacteristic
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—44no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13—82no—
116C4×C13#32414yes—
117C23×C4—21no—
118C23×C4C2×Dic1311yescharacteristic
119#117—22no—
120#117—42no—
121#117#105514yescomplemented
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4C2×Dic1312yes—
127C2×C4⋊C4C2×Dic1311yescharacteristic
128C2×C4⋊C4C22×D1311yescharacteristic
129C2×C22⋊C4—21no—
130C2×C22⋊C4C22⋊D1312yes—
131C2×C42C2×Dic1312yes—
132C2×C42C22⋊D1312yes—
133C4⋊C8—522no—
134C22⋊C8—264no—
135C4×C8—522no—
136#95—24no—
137C2×C13—21no—
138C2×C13—21no—
139C2×C13—42no—
140C2×C13C2×#32411yescharacteristic
141C2×C13#212811yescharacteristic
142C2×C13#213511yescharacteristic
143C24C22⋊Dic1311yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—82no—
150C22×C4C2×#105512yes—
151C22×C4#609912yes—
152C22×C4C22⋊Dic1312yes—
153C22×C4C22⋊Dic1311yescharacteristic
154C22×C4C22×Dic1311yescharacteristic
155C22×C4C2×C22⋊D1312yes—
156C2×C8—524no—
157C4⋊C4—24no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—84no—
163C22⋊C4—24no—
164C22⋊C4—42no—
165C42—22no—
166C42—22no—
167C42—22no—
168C42C2×#105514yes—
169C13#1145011yescharacteristic, complemented, Sylow
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23C22⋊#105512yes—
175C23C2×C22⋊Dic1311yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4C22⋊#105512yes—
191C2×C4#8807412yes—
192C2×C4#8807612yes—
193C2×C4C22×#105511yescharacteristic
194C2×C4C2×#609911yescharacteristic
195C8—1044no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×C22⋊#105511yescharacteristic
204C22C2×#8807411yescharacteristic
205C22C2×#8807611yescharacteristic
206C4—21no—
207C4—21no—
208C4—44no—
209C4—42no—
210C4—42no—
211C4—82no—
212C4#1171812014yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×#1171812011yescharacteristic
217C2#1311650811yescharacteristic
218C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2317C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2317D13
hypocenterC13#11450
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #13112782C2semidirect
18. C13×#117C8semidirect
121. #117#1055semidirect
169. C13#11450semidirect

Maximal subgroups

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

subgroupindex
#131131502
#131127822
C13×#23172
#1145013