Finite Group Databasebeta

← #15775973

Subgroups — #15775973

Order 3328.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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#13119865C211yesmaximal, characteristic
2#13113810C212yesmaximal
3#13112865C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2060C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×#88142—22no—
8C13×#428—21no—
9C13×#384C2211yescharacteristic
10#11718711—22no—
11#11718640—21no—
12#11718640C2212yes—
13#11718634—22no—
14C4×C4⋊Dic13—21no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C22×Dic26—21no—
20C22×Dic26D412yes—
21C2×C13×M16—21no—
22C13×C4⋊Q8—41no—
23C13×#125—41no—
24C13×C22⋊Q8—22no—
25C13×#117—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×#6107—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×C4×Dic13—22no—
36#88142—48no—
37C13×#107—41no—
38C13×#106—41no—
39#88071—21no—
40#88071—22no—
41#88071D412yes—
42C22⋊#1055—22no—
43#88050—42no—
44#12256—131nomaximal, Sylow
45C2×Q8×C13—22no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C2×D412yes—
49C22×C4×C13C2×D411yescharacteristic
50C22×Dic13—22no—
51C22×Dic13—22no—
52C2×Dic26—42no—
53C2×Dic26—44no—
54C2×Dic26—44no—
55C2×Dic26—81no—
56C13×M16—22no—
57C13×M16—41no—
58C2×C8×C13—41no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—44no—
65C13×C4⋊C4—42no—
66C13×C22⋊C4—41no—
67C42×C13—21no—
68C42×C13—41no—
69C42×C13Q1612yescomplemented
70#6107—84no—
71C4⋊Dic13—24no—
72C4⋊Dic13—24no—
73#6101—44no—
74#6101—44no—
75C4×Dic13—44no—
76C2×#1055—42no—
77#2551—131no—
78#2060D1311yescharacteristic
79#1605—132no—
80#1354—132no—
81#1325—131no—
82C23×C13#12011yescharacteristic
83Q8×C13—82no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13C2×Q1611yescharacteristic
96C2×C4×C13#13711yescharacteristic
97C2×Dic13—24no—
98C2×Dic13—24no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103Dic26—44no—
104Dic26—82no—
105Dic26—84no—
106C8×C13—42no—
107#1055—82no—
108#544C2×D1311yescharacteristic
109C2×C4⋊Q8—262no—
110#451—262no—
111#428—21no—
112#395—132no—
113#395—261no—
114#389—262no—
115#384C2×D1311yescharacteristic
116C4×C4⋊C4—261no—
117#343C2×D1311yescharacteristic
118#339—21no—
119#328—262no—
120#324—132no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#45111yescharacteristic
124C22×C13#45611yescharacteristic
125C22×C13B(4,𝔽2)11yescharacteristic
126C4×C13—24no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—81no—
131C4×C13—81no—
132C4×C13—81no—
133Dic13—44no—
134Dic13—44no—
135C22×Q8—132no—
136C22×Q8—261no—
137C2×Q16—522no—
138C2×M16—21no—
139C4⋊Q8—41no—
140C4⋊Q8—528no—
141#125—41no—
142C22⋊Q8—22no—
143#117—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4—261no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4C22⋊D1311yescharacteristic
150C2×C4⋊C4C22×D1311yescharacteristic
151C2×C42—262no—
152C2×C42C22⋊D1311yescharacteristic
153#107—41no—
154#106—41no—
155#103—522no—
156C22⋊C8—262no—
157#95—132no—
158#95—261no—
159#95—262no—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#160511yescharacteristic
163C2×C13#219611yescharacteristic
164C2×C13#220511yescharacteristic
165C2×Q8—22no—
166C2×Q8—522no—
167C2×Q8—524no—
168C2×Q8—524no—
169C2×Q8—1041no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4D4×D1312yes—
175C22×C4C2×C22⋊D1311yescharacteristic
176Q16—1044no—
177M16—22no—
178M16—41no—
179C2×C8—41no—
180C2×C8—522no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C4⋊C4—264no—
189C4⋊C4—264no—
190C4⋊C4—524no—
191C4⋊C4—524no—
192C22⋊C4—41no—
193C42—21no—
194C42—41no—
195C42—524no—
196C42#610712yescomplemented
197C13#1225611yescharacteristic, complemented, Sylow
198C23#8819111yescharacteristic
199Q8—82no—
200Q8—524no—
201Q8—1042no—
202Q8—1044no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—264no—
215C2×C4—264no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4C2×#610711yescharacteristic
221C2×C4#8820511yescharacteristic
222C8—42no—
223C8—1042no—
224C22—21no—
225C22—21no—
226C22#1171869311yescharacteristic
227C22#1171871111yescharacteristic
228C22#1171875611yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—81no—
234C4—81no—
235C4—81no—
236C4—524no—
237C4—524no—
238C2—21no—
239C2—21no—
240C2#1311380911yescharacteristic
241C2#1311681911yescharacteristic
242C2#1311686511yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2060C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2060D13
hypocenterC13#12256
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
69. C42×C13Q16semidirect
196. C42#6107semidirect
197. C13#12256semidirect

Maximal subgroups

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

subgroupindex
#131198652
#131138102
#131128652
#131127822
C13×#20602
#1225613