Finite Group Databasebeta

← #15779188

Subgroups — #15779188

Order 3328.

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

normal subgroups only

This group has 642 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#13114764C212yesmaximal
2#13112963C214yesmaximal, complemented
3C13×#2297C211yesmaximal, characteristic
4C22×C13×#41C2211yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C42×C13C411yescharacteristic
7C13×#391C2212yes—
8C13×#390C412yes—
9C13×#386—22no—
10C4×C13×C22⋊C4—22no—
11C2×#88076C2214yes—
12C2×#88073—22no—
13#11718868—22no—
14C2×C13×#41—24no—
15C2×C13×#41—42no—
16C2×C13×#41—42no—
17C22×Q8×C13C2311yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13D412yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D412yes—
23C13×#117—42no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C13×C22⋊C4—24no—
26C2×C13×C22⋊C4—21no—
27C2×C42×C13—21no—
28C2×C42×C13—21no—
29C2×C42×C13—42no—
30C2×C42×C13C2×C412yes—
31C2×#6099—24no—
32C13×#95—24no—
33#88076—28no—
34#88073—44no—
35C22⋊#1055—44no—
36#12861—131nomaximal, Sylow
37C24×C13C22⋊C412yes—
38C24×C13C22⋊C411yescharacteristic
39C13×#41—416no—
40C2×Q8×C13—41no—
41C2×Q8×C13—41no—
42C2×Q8×C13#4114yes—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—24no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—42no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—24no—
54C22×C4×C13—24no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—44no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—48no—
64C13×C22⋊C4—42no—
65C42×C13—42no—
66C42×C13—42no—
67C42×C13—42no—
68#6099—44no—
69#6099—44no—
70C2×#1055—44no—
71#2297D1311yescharacteristic
72#1785—132no—
73#1394—134no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—42no—
80C23×C13—44no—
81C23×C13#9912yes—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—44no—
84D4×C13—48no—
85D4×C13—44no—
86C2×C4×C13—28no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—24no—
94C2×C4×C13—48no—
95C2×C4×C13—42no—
96C2×C4×C13—48no—
97C2×C4×C13—42no—
98C2×C4×C13—44no—
99C2×C4×C13—42no—
100C2×C4×C13#9912yes—
101C2×C4×C13#11712yes—
102C2×C4×C13#12314yes—
103#1055—84no—
104C22×#41C2×D1311yescharacteristic
105C2×#117Dic1311yescharacteristic
106C22×C42Dic1311yescharacteristic
107C2×#101—134no—
108C2×#100—262no—
109#407—262no—
110#391C2×D1312yes—
111#390Dic1312yes—
112#386—22no—
113C4×C22⋊C4—22no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—44no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—44no—
122C22×C13—82no—
123C22×C13#38111yescharacteristic
124C22×C13C2×#9911yescharacteristic
125C22×C13C2×#9911yescharacteristic
126C4×C13—24no—
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—44no—
130C4×C13—82no—
131C2×#41—24no—
132C2×#41—42no—
133C2×#41—42no—
134C22×Q8C22×D1311yescharacteristic
135C22×D4C2×Dic1311yescharacteristic
136C22×D4C22⋊D1312yes—
137C23×C4—21no—
138C23×C4C2×Dic1311yescharacteristic
139C23×C4C22⋊D1312yes—
140C2×M16—264no—
141#117—42no—
142C2×C4⋊C4C2×Dic1312yes—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—24no—
145C2×C42—21no—
146C2×C42—21no—
147C2×C42—42no—
148C2×C42C2×Dic1312yes—
149#101—268no—
150#100—524no—
151C22⋊C8—524no—
152#95—24no—
153C2×C13—21no—
154C2×C13—21no—
155C2×C13—42no—
156C2×C13—82no—
157C2×C13#181911yescharacteristic
158C2×C13#213212yes—
159C24C22⋊Dic1312yes—
160C24C22⋊Dic1311yescharacteristic
161#41—416no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8#612714yes—
165C2×D4—24no—
166C2×D4—22no—
167C2×D4—24no—
168C2×D4—41no—
169C2×D4—41no—
170C2×D4—42no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—44no—
180C22×C4—42no—
181C22×C4C22⋊Dic1311yescharacteristic
182C22×C4C22×Dic1311yescharacteristic
183C22×C4C2×C22⋊D1312yes—
184M16—524no—
185M16—524no—
186C2×C8—524no—
187C4⋊C4—42no—
188C22⋊C4—48no—
189C22⋊C4—42no—
190C42—42no—
191C42—42no—
192C42—42no—
193C13#1286111yescharacteristic, complemented, Sylow
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—42no—
200C23—44no—
201C23#8807412yes—
202C23C2×C22⋊Dic1311yescharacteristic
203Q8—44no—
204D4—48no—
205D4—44no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—48no—
215C2×C4—42no—
216C2×C4—48no—
217C2×C4—42no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4#8807412yes—
221C2×C4#8818012yes—
222C2×C4#8818314yes—
223C8—1044no—
224C22—22no—
225C22—22no—
226C22—42no—
227C22—42no—
228C22—44no—
229C22—42no—
230C22—42no—
231C22—44no—
232C22—82no—
233C22#1171887211yescharacteristic
234C22C2×#8807411yescharacteristic
235C22C2×#8807411yescharacteristic
236C4—24no—
237C4—22no—
238C4—22no—
239C4—44no—
240C4—82no—
241C2—21no—
242C2—21no—
243C2—42no—
244C2—82no—
245C2#1311491011yescharacteristic
246C2#1311652112yes—
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2297C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×Q8×C13C23
hypercenter#2297D13
hypocenterC13#12861
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. #13112963C2semidirect
193. C13#12861semidirect

Maximal subgroups

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

subgroupindex
#131147642
#131129632
C13×#22972
#1286113