Finite Group Databasebeta

← #15772351

Subgroups — #15772351

Order 3328.

330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116648C212yesmaximal, complemented
2#13112787C212yesmaximal, complemented
3#13112772C212yesmaximal
4C13×#2920C211yesmaximal, characteristic
5C22×C42×C13C411yescharacteristic
6C13×#432—22no—
7C13×#431—22no—
8C13×#423C411yescharacteristic
9C13×#423C2211yescharacteristic
10C13×#407C411yescharacteristic
11C13×#407C2211yescharacteristic
12C4×C13×M16C411yescharacteristic
13C4×C13×M16C2211yescharacteristic
14#11718145C2214yes—
15#11718058—22no—
16#11718055—22no—
17C23×C4×C13—21no—
18C23×C4×C13C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23C2×C42×C13—21no—
24C2×C42×C13—21no—
25C2×C42×C13—21no—
26C2×C42×C13—21no—
27C2×C42×C13—21no—
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C13×C4⋊C8—22no—
31C13×C4⋊C8—22no—
32C13×C22⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#97—21no—
35C13×#97D412yes—
36C4×C8×C13—21no—
37C4×C8×C13D412yes—
38#88052—24no—
39#11521—131nomaximal, Sylow
40C24×C13M1611yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—44no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13M1611yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C13×M16—41no—
55C13×M16—41no—
56C13×M16—41no—
57C13×M16—41no—
58C2×C8×C13—21no—
59C2×C8×C13—21no—
60C2×C8×C13C22⋊C412yes—
61C2×C8×C13C2×D412yes—
62C42×C13—21no—
63C42×C13—21no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—21no—
67C42×C13—21no—
68C42×C13C22⋊C411yescharacteristic
69C42×C13C22⋊C411yescharacteristic
70C42×C13M1611yescharacteristic
71C42×C13M1611yescharacteristic
72#6090—44no—
73#2920D1311yescharacteristic
74#2165—132no—
75#1327—132no—
76#1320—132no—
77C23×C13—21no—
78C23×C13—42no—
79C23×C13—41no—
80C23×C13C2×M1611yescharacteristic
81C2×C4×C13—24no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C8×C13—22no—
101C8×C13—22no—
102C8×C13—41no—
103C8×C13—41no—
104C22×C42Dic1311yescharacteristic
105#432—22no—
106#431—22no—
107#423Dic1311yescharacteristic
108#423C2×D1311yescharacteristic
109#407Dic1311yescharacteristic
110#407C2×D1311yescharacteristic
111C4×M16Dic1311yescharacteristic
112C4×M16C2×D1311yescharacteristic
113#364—262no—
114#349—134no—
115#347—262no—
116C22×C13—22no—
117C22×C13—21no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13—41no—
123C22×C13#40711yescharacteristic
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13—41no—
129C4×C13—41no—
130C4×C13#41011yescharacteristic
131C4×C13#41311yescharacteristic
132C23×C4—21no—
133C23×C4C2×Dic1311yescharacteristic
134C2×M16C2×Dic1311yescharacteristic
135C2×M16C2×Dic1311yescharacteristic
136C2×M16C2×Dic1311yescharacteristic
137C2×M16C22×D1311yescharacteristic
138C2×C42—21no—
139C2×C42—21no—
140C2×C42—21no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42C2×Dic1311yescharacteristic
144C2×C42C2×Dic1311yescharacteristic
145M32—264no—
146C4⋊C8—22no—
147C4⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150#97—21no—
151#97C22⋊D1312yes—
152C4×C8—21no—
153C4×C8C22⋊D1312yes—
154C2×C13—21no—
155C2×C13—42no—
156C2×C13—41no—
157C2×C13#146411yescharacteristic
158C24#609911yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—44no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4#609911yescharacteristic
171C22×C4C22×Dic1311yescharacteristic
172M16—41no—
173M16—41no—
174M16—41no—
175M16—41no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8C22⋊Dic1312yes—
179C2×C8C2×C22⋊D1312yes—
180C42—21no—
181C42—21no—
182C42—21no—
183C42—21no—
184C42—21no—
185C42—21no—
186C42#609911yescharacteristic
187C42#609911yescharacteristic
188C42C22⋊Dic1311yescharacteristic
189C42C22⋊Dic1311yescharacteristic
190C16—524no—
191C13#1152111yescharacteristic, complemented, Sylow
192C23—21no—
193C23—42no—
194C23—41no—
195C23C2×#609911yescharacteristic
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4C2×#609911yescharacteristic
214C2×C4C2×C22⋊Dic1311yescharacteristic
215C8—22no—
216C8—22no—
217C8—41no—
218C8—41no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22#1171886811yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4#1171889811yescharacteristic
234C4#1171890111yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2#1311317011yescharacteristic
subgroupG/H
centerC4#11718901
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2920C2
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×C13×M16C23
hypercenter#2920D13
hypocenterC13#11521
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #13116648C2semidirect
2. #13112787C2semidirect
191. C13#11521semidirect

Maximal subgroups

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

subgroupindex
#131166482
#131127872
#131127722
C13×#29202
#1152113