Finite Group Databasebeta

← #16786869

Subgroups — #16786869

Order 3328.

398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×C22⋊#6092C212yesmaximal, complemented
2#13129775C212yesmaximal, complemented
3#13129759C212yesmaximal, complemented
4#13123526C211yesmaximal, characteristic
5#11719496C411yescharacteristic
6C23×#1055C2211yescharacteristic
7C2×#88161C411yescharacteristic
8C22×#6092—22no—
9C13×#407C411yescharacteristic
10#11718790C2211yescharacteristic
11#11718783C411yescharacteristic
12#11718780C2211yescharacteristic
13#11718391—22no—
14#11718386—22no—
15C22⋊#6092—22no—
16C22⋊#6092C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21#88207—21no—
22#88184C812yes—
23#88183—21no—
24C4×C22⋊D13—22no—
25#88180C2×C411yescharacteristic
26#88178C812yes—
27C22×#1055—42no—
28C22×#1055C2×C411yescharacteristic
29C22×#1055D412yes—
30C22×#1055D412yes—
31C22×#1055C2311yescharacteristic
32#88161—42no—
33C2×#6094—21no—
34C2×C8×D13—21no—
35C2×#6092—24no—
36C2×#6092—44no—
37C13×C22⋊C8—22no—
38#88060—22no—
39#88055—21no—
40#88054—22no—
41C8×Dic13—21no—
42#11468—131nomaximal, Sylow
43C24×C13M1611yescharacteristic
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13C22⋊C412yes—
47C22×C4×C13C2×C812yes—
48C22×C4×C13M1611yescharacteristic
49C22×C4×C13C22×C411yescharacteristic
50C2×C22⋊D13—22no—
51C2×C22⋊D13—21no—
52#6127—41no—
53#6127—41no—
54C2×D52C2×C811yescharacteristic
55C2×C4×D13—21no—
56C2×Dic26C2×C811yescharacteristic
57C13×M16—41no—
58C13×M16—41no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C22⋊Dic13—22no—
62C22⋊Dic13—21no—
63#6103—22no—
64C4⋊Dic13C2×C812yes—
65#6101—22no—
66C4×Dic13—21no—
67C2×#1055—24no—
68C2×#1055—22no—
69C2×#1055—42no—
70C2×#1055—41no—
71C2×#1055C22⋊C411yescharacteristic
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D412yes—
74#6094—42no—
75C8×D13—42no—
76#6092—44no—
77#2929—131no—
78C2×C22⋊C16—132no—
79#1323—132no—
80#1315—132no—
81C23×C13—24no—
82C23×C13—41no—
83C23×C13C22⋊C812yes—
84C23×C13C2×M1611yescharacteristic
85C22×D13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13C22⋊C812yes—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13C22×C811yescharacteristic
95C22⋊D13—42no—
96C22⋊D13—44no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99D52—41no—
100C4×D13—41no—
101C4×D13—41no—
102Dic26—41no—
103C8×C13—41no—
104C8×C13—41no—
105#1055—22no—
106#1055—21no—
107#1055#9912yes—
108C2×#131—131no—
109C23×C8—131no—
110#525—131no—
111C22×C16—262no—
112#435—262no—
113C8×D4—262no—
114#424—131no—
115#408—131no—
116#407#26111yescharacteristic
117#405—131no—
118C22⋊C16—134no—
119C22⋊C16—262no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—21no—
124C22×C13—44no—
125C22×C13#35014yes—
126C22×C13C2×C22⋊C811yescharacteristic
127C2×D13—42no—
128C2×D13—41no—
129C4×C13—21no—
130C4×C13—22no—
131C4×C13C2×#9911yescharacteristic
132C4×C13#41311yescharacteristic
133Dic13—42no—
134Dic13—41no—
135C2×#41—131no—
136C23×C4C2×#26111yescharacteristic
137#131—522no—
138C2×M16—261no—
139C2×M16C2×#26111yescharacteristic
140C2×M16C2×#26111yescharacteristic
141C22×C8—132no—
142C22×C8—131no—
143C22×C8—132no—
144C22×C8—131no—
145C22×C8—261no—
146C22×C8—522no—
147#123—261no—
148C22⋊Q8—132no—
149#121—132no—
150#120—261no—
151C4×D4—262no—
152#117—131no—
153C2×C16—264no—
154C2×C16—524no—
155C4⋊C8—262no—
156C22⋊C8—22no—
157C22⋊C8—262no—
158#97—261no—
159C4×C8—261no—
160C2×C13—24no—
161C2×C13—41no—
162C2×C13#145911yescharacteristic
163C2×C13C2×#35012yes—
164D13—81no—
165C24#611811yescharacteristic
166#41—521no—
167#41—521no—
168C2×Q8—131no—
169C2×D4—131no—
170C2×D4—262no—
171C2×D4—261no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—261no—
175C22×C4D13⋊C812yes—
176C22×C4#611811yescharacteristic
177C22×C4C22⋊#26112yes—
178C22×C4C22×#26111yescharacteristic
179M16—41no—
180M16—41no—
181M16—522no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—131no—
185C2×C8—131no—
186C2×C8—132no—
187C2×C8—264no—
188C2×C8—262no—
189C2×C8—522no—
190C2×C8—521no—
191C2×C8—522no—
192C4⋊C4—132no—
193C4⋊C4—262no—
194C22⋊C4—262no—
195C22⋊C4—261no—
196C22⋊C4—262no—
197C42—261no—
198C16—524no—
199C13#1146811yescharacteristic, complemented, Sylow
200C23—24no—
201C23—41no—
202C23—261no—
203C23#8811112yes—
204C23C2×#611811yescharacteristic
205Q8—521no—
206D4—521no—
207D4—522no—
208D4—524no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4#8811112yes—
220C2×C4C2×D13⋊C811yescharacteristic
221C2×C4C2×C22⋊#26111yescharacteristic
222C8—41no—
223C8—41no—
224C8—132no—
225C8—262no—
226C8—261no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—44no—
232C22—522no—
233C22—521no—
234C22#1171827014yes—
235C22C2×#8811111yescharacteristic
236C4—22no—
237C4—21no—
238C4—522no—
239C4—521no—
240C4D13⋊#9911yescharacteristic
241C4#1171914811yescharacteristic
242C2—24no—
243C2—41no—
244C2—1041no—
245C2#1313007411yescharacteristic
246C2C2×#1171827012yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#407C4
socleC22×C13C2×C22⋊C8
prime radical#11719496C4
cosocleC22×#1055C23
hypercenter#407#261
hypocenterC13#11468
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊#6092C2semidirect
2. #13129775C2semidirect
3. #13129759C2semidirect
199. C13#11468semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊#60922
#131297752
#131297592
#131235262
#1146813