Finite Group Databasebeta

← #15779191

Subgroups — #15779191

Order 3328.

566 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114760C212yesmaximal
2#13112963C214yesmaximal, complemented
3C13×#2310C211yesmaximal, characteristic
4C23×Q8×C13C2211yescharacteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C411yescharacteristic
7C13×#391—22no—
8C13×#391C412yes—
9C13×#391C2212yes—
10C13×#381—22no—
11C2×#88076—22no—
12C2×#88076C2214yes—
13#11718868—22no—
14C22×Q8×C13—24no—
15C22×Q8×C13—42no—
16C22×Q8×C13—42no—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Q8×C13D412yes—
19C22×Q8×C13C2311yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13D412yes—
22C13×#117—42no—
23C13×#117—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—21no—
28C2×C42×C13—21no—
29C2×C42×C13C2×C412yes—
30C2×#6099—24no—
31C13×#95—24no—
32C13×#95—24no—
33#88076—28no—
34#88076—44no—
35C22⋊#1055—44no—
36#12862—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C2×Q8×C13—24no—
39C2×Q8×C13—22no—
40C2×Q8×C13—24no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×Q8×C13—42no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13—416no—
47C2×Q8×C13#4114yes—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—24no—
52C22×C4×C13—24no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D412yes—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C22⋊C4—42no—
63C13×C22⋊C4—42no—
64C42×C13—42no—
65C42×C13—42no—
66#6099—44no—
67#6099—44no—
68C2×#1055—44no—
69#2310D1311yescharacteristic
70#1784—132no—
71#1394—134no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—42no—
75C23×C13#9912yes—
76C23×C13C2×C22⋊C411yescharacteristic
77Q8×C13—44no—
78Q8×C13—48no—
79Q8×C13—44no—
80C2×C4×C13—28no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—48no—
91C2×C4×C13—44no—
92C2×C4×C13—44no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13#9912yes—
96C2×C4×C13#11712yes—
97C2×C4×C13#12314yes—
98#1055—84no—
99C23×Q8C2×D1311yescharacteristic
100C2×#117Dic1311yescharacteristic
101C2×#117Dic1311yescharacteristic
102C2×#101—134no—
103C2×#101—262no—
104#407—262no—
105#391—22no—
106#391Dic1312yes—
107#391C2×D1312yes—
108#381—22no—
109C22×C13—22no—
110C22×C13—22no—
111C22×C13—24no—
112C22×C13—42no—
113C22×C13—42no—
114C22×C13#38111yescharacteristic
115C22×C13C2×#9911yescharacteristic
116C22×C13C2×#9911yescharacteristic
117C4×C13—24no—
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—42no—
121C4×C13—82no—
122C4×C13—82no—
123C22×Q8—24no—
124C22×Q8—42no—
125C22×Q8—42no—
126C22×Q8C2×Dic1311yescharacteristic
127C22×Q8C22⋊D1312yes—
128C22×Q8C22×D1311yescharacteristic
129C23×C4C2×Dic1311yescharacteristic
130C23×C4C22⋊D1312yes—
131C2×M16—264no—
132#117—42no—
133#117—42no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4C2×Dic1312yes—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—21no—
138C2×C42—21no—
139C2×C42C2×Dic1312yes—
140#101—268no—
141#101—524no—
142C22⋊C8—524no—
143#95—24no—
144#95—24no—
145C2×C13—21no—
146C2×C13—21no—
147C2×C13—42no—
148C2×C13#181911yescharacteristic
149C2×C13#213312yes—
150C24C22⋊Dic1311yescharacteristic
151C2×Q8—24no—
152C2×Q8—22no—
153C2×Q8—24no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—42no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—416no—
160C2×Q8#612714yes—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—42no—
169C22×C4C22⋊Dic1312yes—
170C22×C4C22⋊Dic1311yescharacteristic
171C22×C4C22×Dic1311yescharacteristic
172C22×C4C2×C22⋊D1312yes—
173M16—524no—
174M16—524no—
175C2×C8—524no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C22⋊C4—42no—
179C22⋊C4—42no—
180C42—42no—
181C42—42no—
182C13#1286211yescharacteristic, complemented, Sylow
183C23—21no—
184C23—21no—
185C23—42no—
186C23#8807412yes—
187C23C2×C22⋊Dic1311yescharacteristic
188Q8—44no—
189Q8—48no—
190Q8—44no—
191C2×C4—28no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—48no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4#8807412yes—
207C2×C4#8818012yes—
208C2×C4#8818314yes—
209C8—1044no—
210C22—22no—
211C22—22no—
212C22—24no—
213C22—42no—
214C22—42no—
215C22#1171887211yescharacteristic
216C22C2×#8807411yescharacteristic
217C22C2×#8807411yescharacteristic
218C4—24no—
219C4—22no—
220C4—22no—
221C4—42no—
222C4—82no—
223C4—82no—
224C2—21no—
225C2—21no—
226C2—42no—
227C2#1311491011yescharacteristic
228C2#1311652512yes—
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2310C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#2310D13
hypocenterC13#12862
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13112963C2semidirect
182. C13#12862semidirect

Maximal subgroups

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

subgroupindex
#131147602
#131129632
C13×#23102
#1286213