Finite Group Databasebeta

← #13130243

Subgroups — #13130243

Order 1664.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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×#88149C211yesmaximal, characteristic
2#11719135C211yesmaximal, characteristic, complemented
3#11719126C211yesmaximal, characteristic, complemented
4#11718240C214yesmaximal, complemented
5C22×D52—21no—
6C22×D52C411yescharacteristic, complemented
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×#6122—21no—
10C2×C13×C4⋊C4C411yescharacteristic, complemented
11C2×#6103—21no—
12#88149—21no—
13#88149—21no—
14#88149C412yescomplemented
15#88149C2212yes—
16(C2×#261)⋊C4—21no—
17(C2×#261)⋊C4C2212yescomplemented
18#88111—21no—
19#88111C2212yescomplemented
20C23×D13—21no—
21C23×D13D411yescharacteristic
22C22×#261—22no—
23C22×C4×C13—21no—
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13D411yescharacteristic
26C2×D52—22no—
27C2×D52—22no—
28C2×D52—21no—
29C2×D52—42no—
30C2×D52—44no—
31C2×D52C2×C412yes—
32C2×C4×D13—42no—
33C2×C4×D13C2×C411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13C2311yescharacteristic
37C22⋊#261—42no—
38#6122—42no—
39C2×#1057—22no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4C2×C412yes—
42#6103—22no—
43#6103—22no—
44#1510—131nomaximal, Sylow
45C23×C13C22⋊C411yescharacteristic
46C22×D13—22no—
47C22×D13—22no—
48C22×D13—22no—
49C22×D13—41no—
50C22×D13—42no—
51C22×D13—42no—
52C22×D13—42no—
53C22×D13C22⋊C411yescharacteristic
54C22×D13C2×D411yescharacteristic
55C2×#261—42no—
56C2×#261—42no—
57C2×#261—42no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—42no—
61C2×C4×C13C22⋊C411yescharacteristic
62C2×C4×C13C22×C411yescharacteristic
63C2×Dic13—22no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—42no—
67D52—42no—
68D52—44no—
69D52—44no—
70C4×D13—41no—
71C4×D13—41no—
72C4×D13—41no—
73C4×D13—41no—
74#1057—42no—
75C2×#121—131no—
76#407—131no—
77#381—131no—
78#327—134no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13#9912yes—
82C22×C13C2×C22⋊C411yescharacteristic
83C2×D13—21no—
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—44no—
89C2×D13—42no—
90C2×D13—42no—
91C2×D13—42no—
92C2×D13—84no—
93C2×D13AGL(1,ℤ/8)12yes—
94#261—82no—
95C4×C13—21no—
96C4×C13—21no—
97C4×C13—42no—
98Dic13—21no—
99Dic13—21no—
100C22×D4—131no—
101C22×D4—261no—
102C23×C4—131no—
103C2×M16—261no—
104#121—132no—
105#121—132no—
106#121—261no—
107#121—261no—
108C2×C4⋊C4#26111yescharacteristic, complemented
109C2×C22⋊C4—261no—
110C2×C22⋊C4—261no—
111C22⋊C8—132no—
112C22⋊C8—261no—
113#95—132no—
114#95—261no—
115C2×C13—22no—
116C2×C13C2×#9911yescharacteristic
117C2×C13#41811yescharacteristic
118C2×C13#42111yescharacteristic
119D13—22no—
120D13—41no—
121D13—82no—
122C24—131no—
123C24—261no—
124C2×D4—132no—
125C2×D4—262no—
126C2×D4—262no—
127C2×D4—261no—
128C2×D4—522no—
129C2×D4—524no—
130C22×C4—21no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—262no—
137C22×C4—522no—
138C22×C4C2×#26111yescharacteristic
139M16—522no—
140C2×C8—262no—
141C4⋊C4—21no—
142C4⋊C4C2×#26112yes—
143C22⋊C4—262no—
144C22⋊C4—262no—
145C22⋊C4—522no—
146C13#151011yescharacteristic, complemented, Sylow
147C23—131no—
148C23—131no—
149C23—262no—
150C23—262no—
151C23—262no—
152C23—521no—
153C23—522no—
154C23—522no—
155C23—522no—
156C23C22⋊#26111yescharacteristic
157D4—522no—
158D4—522no—
159D4—524no—
160D4—524no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—262no—
167C2×C4—521no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—521no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4—522no—
174C2×C4C22⋊#26111yescharacteristic
175C2×C4C22×#26111yescharacteristic
176C8—522no—
177C22—21no—
178C22—21no—
179C22—132no—
180C22—261no—
181C22—261no—
182C22—261no—
183C22—261no—
184C22—261no—
185C22—524no—
186C22—522no—
187C22—522no—
188C22—522no—
189C22—1044no—
190C22#8810712yes—
191C22C2×C22⋊#26111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—261no—
196C4—261no—
197C4—1042no—
198C2—22no—
199C2—262no—
200C2—521no—
201C2—1042no—
202C2C2×#8810711yescharacteristic
203C2#1171913811yescharacteristic
204C2#1171915511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88149C2
cosocleC2×C4×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1510
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719135C2semidirect
3. #11719126C2semidirect
4. #11718240C2semidirect
6. C22×D52C4semidirect
10. C2×C13×C4⋊C4C4semidirect
14. #88149C4semidirect
17. (C2×#261)⋊C4C22semidirect
19. #88111C22semidirect
108. C2×C4⋊C4#261semidirect
146. C13#1510semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
#117191352
#117191262
#117182402
#151013