Finite Group Databasebeta

← #13115251

Subgroups — #13115251

Order 1664.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#11719496C211yesmaximal, characteristic
2#11719450C211yesmaximal, characteristic, complemented
3C13×#407C211yesmaximal, characteristic, complemented
4#11718868C211yesmaximal, characteristic, complemented
5#11718793C211yesmaximal, characteristic, complemented
6#11718151C211yesmaximal, characteristic, complemented
7#11718148C211yesmaximal, characteristic, complemented
8C23×C4×C13C2211yescharacteristic
9C2×#6127C2211yescharacteristic
10C2×C13×M16C2211yescharacteristic
11C2×C13×M16C2211yescharacteristic
12#88207C412yes—
13#88184—21no—
14#88183C412yes—
15C4×C22⋊D13—22no—
16#88180C2211yescharacteristic
17#88178—21no—
18C2×#6099C2211yescharacteristic
19C2×#6099C2211yescharacteristic
20#88161—22no—
21M16×D13—22no—
22#88155—22no—
23C13×C22⋊C8—22no—
24C22⋊#1055—22no—
25#88064—21no—
26#88063—21no—
27C24×C13C2×C411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13—21no—
34C22×C4×C13C2×C411yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C2×C22⋊D13—22no—
37C2×C22⋊D13C2×C412yes—
38#6127—21no—
39#6127—21no—
40#6127—21no—
41#6127—21no—
42C2×D52D411yescharacteristic
43C2×C4×D13D412yes—
44C2×Dic26D411yescharacteristic
45C13×M16—21no—
46C13×M16—21no—
47C13×M16—21no—
48C13×M16—21no—
49C2×C8×C13—21no—
50C2×C8×C13D412yescomplemented
51C22⋊Dic13—22no—
52C22⋊Dic13C2×C412yes—
53#6103—22no—
54C4⋊Dic13—21no—
55#6101—22no—
56C4×Dic13—21no—
57#6099—21no—
58#6099—21no—
59#6099—21no—
60#6099—21no—
61C2×#1055—21no—
62C2×#1055D412yescomplemented
63#6094—24no—
64C8×D13—24no—
65#1891—131nomaximal, Sylow
66C23×C13—21no—
67C23×C13—21no—
68C23×C13—21no—
69C23×C13—42no—
70C23×C13C22×C411yescharacteristic
71C22×D13C22⋊C412yes—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—41no—
76C2×C4×C13—41no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13#4111yescharacteristic
84C2×C4×C13#4111yescharacteristic
85C22⋊D13—22no—
86C22⋊D13—22no—
87C22⋊D13—44no—
88C2×Dic13—22no—
89C2×Dic13C22⋊C412yes—
90D52—21no—
91D52—21no—
92C4×D13—22no—
93C4×D13—22no—
94Dic26—21no—
95Dic26—21no—
96C8×C13—22no—
97C8×C13—41no—
98#1055—22no—
99#1055—41no—
100#568—131no—
101#525—131no—
102#413—131no—
103#407—131no—
104#407D1311yescharacteristic, complemented
105#344—131no—
106#344—131no—
107C22×C13—22no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13C2×C22⋊C411yescharacteristic
116C22×C13C4×D411yescharacteristic
117C22×C13C4×D411yescharacteristic
118C2×D13—22no—
119C2×D13—42no—
120C4×C13—41no—
121C4×C13#12011yescharacteristic
122C4×C13#12111yescharacteristic
123C4×C13#12111yescharacteristic
124C4×C13#12311yescharacteristic
125Dic13—22no—
126Dic13—42no—
127C2×#41—131no—
128C23×C4C2×D1311yescharacteristic
129#131—262no—
130#131—262no—
131C2×M16—131no—
132C2×M16—131no—
133C2×M16—262no—
134C2×M16C2×D1311yescharacteristic
135C2×M16C2×D1311yescharacteristic
136#123—132no—
137C22⋊Q8—261no—
138#121—261no—
139#120—132no—
140C4×D4—262no—
141#117—131no—
142#101—261no—
143#100—261no—
144C22⋊C8—22no—
145C22⋊C8—262no—
146C2×C13—21no—
147C2×C13—21no—
148C2×C13—21no—
149C2×C13—42no—
150C2×C13#38611yescharacteristic
151D13—42no—
152C24C4×D1311yescharacteristic
153#41—261no—
154#41—261no—
155#41—261no—
156#41—261no—
157C2×Q8—131no—
158C2×D4—132no—
159C2×D4—131no—
160C2×D4—262no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—132no—
168C22×C4C4×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170M16—21no—
171M16—21no—
172M16—21no—
173M16—21no—
174M16—264no—
175M16—261no—
176M16—261no—
177M16—261no—
178M16—261no—
179C2×C8—21no—
180C2×C8—132no—
181C2×C8—264no—
182C2×C8—261no—
183C2×C8C22⋊D1312yescomplemented
184C4⋊C4—262no—
185C4⋊C4—261no—
186C22⋊C4—132no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C42—261no—
190C13#189111yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—132no—
196C23C2×C4×D1311yescharacteristic
197Q8—261no—
198Q8—261no—
199D4—262no—
200D4—262no—
201D4—261no—
202D4—261no—
203D4—524no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—132no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4#612711yescharacteristic
216C2×C4D4×D1311yescharacteristic
217C2×C4D4×D1311yescharacteristic
218C2×C4D4×D1311yescharacteristic
219C2×C4#612911yescharacteristic
220C2×C4C2×C22⋊D1311yescharacteristic
221C8—22no—
222C8—41no—
223C8—262no—
224C8—521no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—262no—
234C22—522no—
235C22C22⋊C4×D1311yescharacteristic
236C22#8813511yescharacteristic
237C22C4×C22⋊D1311yescharacteristic
238C4—41no—
239C4—262no—
240C4—522no—
241C4#8813711yescharacteristic
242C4#8813811yescharacteristic
243C4#8819111yescharacteristic
244C4#8819211yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—522no—
250C2#1171861711yescharacteristic
subgroupG/H
centerC4#88191
commutatorC23×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#407C2
socleC2×C13#386
prime radical#11719496C2
cosocleC22×C4×C13C23
hypercenter#407D13
hypocenterC13#1891
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #11719450C2semidirect
3. C13×#407C2semidirect
4. #11718868C2semidirect
5. #11718793C2semidirect
6. #11718151C2semidirect
7. #11718148C2semidirect
50. C2×C8×C13D4semidirect
62. C2×#1055D4semidirect
104. #407D13semidirect
183. C2×C8C22⋊D13semidirect
190. C13#1891semidirect

Maximal subgroups

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

subgroupindex
#117194962
#117194502
C13×#4072
#117188682
#117187932
#117181512
#117181482
#189113