Finite Group Databasebeta

← #15775916

Subgroups — #15775916

Order 3328.

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

normal subgroups only

This group has 394 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#13120209C211yesmaximal, characteristic
2#13113844C212yesmaximal
3#13112841C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2060C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×C4×Dic26—21no—
8C13×#428—21no—
9C13×#384C2211yescharacteristic
10#11718704—22no—
11#11718646—22no—
12#11718644—21no—
13#11718644C2212yes—
14#11718635—22no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C22×Dic26—21no—
20C2×C13×M16—21no—
21C13×C4⋊Q8—41no—
22C13×#125—41no—
23C13×C22⋊Q8—22no—
24C13×#117—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13D412yes—
32C2×#6101—22no—
33C2×C4×Dic13—22no—
34C4×Dic26—42no—
35C4×Dic26—42no—
36C13×#107—41no—
37C13×#106—41no—
38#88075—42no—
39#88071—21no—
40#88071—22no—
41#88071—22no—
42#88071D412yes—
43C22⋊#1055—22no—
44#88048—42no—
45#12247—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×D411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C2×Dic26—24no—
54C2×Dic26—42no—
55C2×Dic26—42no—
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×C13SD1612yes—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72C4⋊Dic13—81no—
73#6101—42no—
74#6101—42no—
75C4×Dic13—44no—
76C2×#1055—42no—
77#2582—131no—
78#2060D1311yescharacteristic
79#1611—132no—
80#1346—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×SD1611yescharacteristic
96C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
97C2×Dic13—24no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103Dic26—48no—
104C8×C13—42no—
105#1055—82no—
106#544C2×D1311yescharacteristic
107C2×C4×Q8—261no—
108#483—262no—
109#428—21no—
110#398—132no—
111#398—261no—
112#391—262no—
113#389—262no—
114#384C2×D1311yescharacteristic
115#343C2×D1311yescharacteristic
116#339—21no—
117#328—262no—
118#324—132no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#45011yescharacteristic
122C22×C13#45611yescharacteristic
123C22×C13B(4,𝔽2)11yescharacteristic
124C4×C13—24no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—42no—
128C4×C13—81no—
129C4×C13—81no—
130C4×C13—81no—
131Dic13—44no—
132Dic13—82no—
133C22×Q8—261no—
134C2×M16—21no—
135C4⋊Q8—41no—
136#125—41no—
137C22⋊Q8—22no—
138C4×Q8—522no—
139C4×Q8—522no—
140#117—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4C22⋊D1311yescharacteristic
147C2×C4⋊C4C22×D1311yescharacteristic
148C2×C42—262no—
149C2×C42C22⋊D1311yescharacteristic
150#107—41no—
151#106—41no—
152#106—522no—
153#103—522no—
154C22⋊C8—262no—
155#95—132no—
156#95—262no—
157#95—261no—
158#95—262no—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#160411yescharacteristic
162C2×C13#219811yescharacteristic
163C2×C13#220511yescharacteristic
164C2×Q8—22no—
165C2×Q8—264no—
166C2×Q8—522no—
167C2×Q8—522no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4D4×D1312yes—
173C22×C4C2×C22⋊D1311yescharacteristic
174M16—22no—
175M16—41no—
176C2×C8—41no—
177C2×C8—522no—
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—522no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C4⋊C4—1041no—
190C22⋊C4—41no—
191C42—21no—
192C42—41no—
193C42—524no—
194C42#610612yes—
195C13#1224711yescharacteristic, complemented, Sylow
196C23#8819111yescharacteristic
197Q8—82no—
198Q8—528no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—264no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4C2×#610611yescharacteristic
217C2×C4#8820311yescharacteristic
218C8—42no—
219C8—1042no—
220C22—21no—
221C22—21no—
222C22#1171869311yescharacteristic
223C22#1171870711yescharacteristic
224C22#1171875611yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4—81no—
231C4—81no—
232C4—524no—
233C4—1042no—
234C2—21no—
235C2—21no—
236C2#1311380411yescharacteristic
237C2#1311683111yescharacteristic
238C2#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#12247
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
195. C13#12247semidirect

Maximal subgroups

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

subgroupindex
#131202092
#131138442
#131128412
#131127822
C13×#20602
#1224713