Finite Group Databasebeta

← #16787118

Subgroups — #16787118

Order 3328.

334 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 70 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#13131210C212yesmaximal, complemented
2#13129771C212yesmaximal, complemented
3#13129768C212yesmaximal, complemented
4#13123539C211yesmaximal, characteristic
5C22×C13×M16C411yescharacteristic
6#11719496C411yescharacteristic
7C2×#88155C411yescharacteristic
8#11718868C2211yescharacteristic
9#11718789—22no—
10#11718788—22no—
11#11718771C2211yescharacteristic
12#11718763C411yescharacteristic
13#11718762C2211yescharacteristic
14#11718284C2214yes—
15#11718262—22no—
16#11718261—22no—
17C23×C4×C13C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C2×C13×M16—21no—
20C2×C13×M16—21no—
21C2×C13×M16—42no—
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2×C411yescharacteristic
24#88207—21no—
25#88184—21no—
26#88183—21no—
27C4×C22⋊D13—22no—
28#88180C2×C411yescharacteristic
29#88178—21no—
30C2×#6099C2×C411yescharacteristic
31C2×#6099C2311yescharacteristic
32#88155—42no—
33C2×#6094—21no—
34C2×C8×D13—21no—
35#88106—24no—
36C22⋊#1055—22no—
37#88060—22no—
38#88055D412yes—
39#88054—22no—
40C8×Dic13D412yes—
41#11538—131nomaximal, Sylow
42C24×C13M1611yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13M1611yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C2×C22⋊D13—21no—
50C2×C22⋊D13—22no—
51#6127—41no—
52#6127—41no—
53C2×D52M1611yescharacteristic
54C2×C4×D13—21no—
55C2×Dic26M1611yescharacteristic
56C13×M16—42no—
57C13×M16—42no—
58C2×C8×C13—22no—
59C2×C8×C13—21no—
60C2×C8×C13—41no—
61C2×C8×C13C22⋊C411yescharacteristic
62C2×C8×C13C22⋊C411yescharacteristic
63C22⋊Dic13—22no—
64C22⋊Dic13—21no—
65#6103—22no—
66C4⋊Dic13—21no—
67#6101—22no—
68C4×Dic13C22⋊C412yes—
69#6099—41no—
70#6099—41no—
71C2×#1055—21no—
72C2×#1055C2×D412yes—
73#6094—42no—
74C8×D13—42no—
75#6092—44no—
76#2930—131no—
77#2166—132no—
78#1321—132no—
79#1320—132no—
80C23×C13—21no—
81C23×C13—41no—
82C23×C13—81no—
83C23×C13C2×M1611yescharacteristic
84C22×D13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—42no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×C4×C13C2×M1611yescharacteristic
94C22⋊D13—42no—
95C22⋊D13—82no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98D52—41no—
99C4×D13—41no—
100C4×D13—41no—
101Dic26—41no—
102C8×C13—21no—
103C8×C13—41no—
104C8×C13#10012yes—
105#1055—22no—
106#1055—41no—
107C2×#131—131no—
108C22×M16#26111yescharacteristic
109#525—131no—
110#436—262no—
111#435—262no—
112#424—131no—
113#408—131no—
114#407—131no—
115#405—131no—
116#364—262no—
117#349—134no—
118#347—262no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—82no—
125C22×C13#40711yescharacteristic
126C2×D13—42no—
127C2×D13—41no—
128C4×C13—21no—
129C4×C13—41no—
130C4×C13#41011yescharacteristic
131C4×C13C2×#10011yescharacteristic
132Dic13—42no—
133Dic13—41no—
134C2×#41—131no—
135C23×C4C2×#26111yescharacteristic
136#131—522no—
137C2×M16—21no—
138C2×M16—21no—
139C2×M16—42no—
140C2×M16—131no—
141C2×M16—131no—
142C2×M16—261no—
143C22×C8—261no—
144C22×C8C2×#26111yescharacteristic
145C22×C8C2×#26111yescharacteristic
146#123—261no—
147C22⋊Q8—261no—
148#121—261no—
149#120—261no—
150C4×D4—262no—
151#117—131no—
152M32—264no—
153C4⋊C8—262no—
154C22⋊C8—262no—
155C22⋊C8—262no—
156#97—132no—
157C4×C8—132no—
158C2×C13—21no—
159C2×C13—41no—
160C2×C13—81no—
161C2×C13#146611yescharacteristic
162D13—81no—
163C24#611811yescharacteristic
164#41—521no—
165#41—521no—
166C2×Q8—131no—
167C2×D4—131no—
168C2×D4—261no—
169C2×D4—262no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—261no—
175C22×C4#611811yescharacteristic
176C22×C4C22×#26111yescharacteristic
177M16—42no—
178M16—42no—
179M16—521no—
180M16—522no—
181M16—521no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—132no—
186C2×C8—261no—
187C2×C8—522no—
188C2×C8C22⋊#26111yescharacteristic
189C2×C8C22⋊#26111yescharacteristic
190C4⋊C4—262no—
191C4⋊C4—261no—
192C22⋊C4—262no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C42—132no—
196C16—524no—
197C13#1153811yescharacteristic, complemented, Sylow
198C23—21no—
199C23—41no—
200C23—81no—
201C23—261no—
202C23C2×#611811yescharacteristic
203Q8—521no—
204D4—521no—
205D4—522no—
206D4—1042no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4D13⋊M1611yescharacteristic
219C2×C4C2×C22⋊#26111yescharacteristic
220C8—21no—
221C8—41no—
222C8—262no—
223C8—521no—
224C8#8812112yes—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—82no—
231C22—522no—
232C22—521no—
233C22#1171912711yescharacteristic
234C4—21no—
235C4—41no—
236C4—522no—
237C4—521no—
238C4#1171911611yescharacteristic
239C4C2×#8812111yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—1041no—
244C2#1313009511yescharacteristic
subgroupG/H
centerC4#11719116
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC2×C13#1466
prime radical#11719496C4
cosocleC2×#6099C23
hypercenterC22×M16#261
hypocenterC13#11538
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #13131210C2semidirect
2. #13129771C2semidirect
3. #13129768C2semidirect
197. C13#11538semidirect

Maximal subgroups

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

subgroupindex
#131312102
#131297712
#131297682
#131235392
#1153813