Finite Group Databasebeta

← #27193669

Subgroups — #27193669

Order 13184.

242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 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#20267848C211yesmaximal, characteristic, complemented
2C4×C4⋊Dic103C211yesmaximal, characteristic, complemented
3#20267528C212yesmaximal, complemented
4#20267525C212yesmaximal
5#529×C103C211yesmaximal, characteristic
6C2×C4⋊Dic103—21no—
7C2×C4×Dic103—21no—
8C4⋊(C103⋊C8)—21no—
9C22⋊(C103⋊C8)C2212yes—
10#15692932—21no—
11C103⋊#95C2212yes—
12#126×C103—21no—
13#125×C103C411yescharacteristic, complemented
14#124×C103C411yescharacteristic, complemented
15#123×C103—21no—
16C22⋊Q8×C103C2211yescharacteristic
17#121×C103C2211yescharacteristic
18C4×Q8×C103C411yescharacteristic, complemented
19C4×D4×C103—21no—
20C4×D4×C103C411yescharacteristic, complemented
21#117×C103—21no—
22C2×C42×C103C2211yescharacteristic
23C22×Dic103—22no—
24C2×C103⋊C8—22no—
25C4⋊Dic103—24no—
26C4×Dic103—42no—
27C2×Q8×C103C2×C411yescharacteristic
28C2×D4×C103—21no—
29C2×D4×C103C2×C411yescharacteristic
30C22×C4×C103—21no—
31C22×C4×C103D411yescharacteristic
32C22×C4×C103D411yescharacteristic
33C22×C4×C103C2311yescharacteristic
34C4⋊C4×C103—21no—
35C4⋊C4×C103—21no—
36C4⋊C4×C103—21no—
37C4⋊C4×C103—21no—
38C4⋊C4×C103C2×C411yescharacteristic
39C4⋊C4×C103C2×C411yescharacteristic
40C22⋊C4×C103—21no—
41C22⋊C4×C103—21no—
42C22⋊C4×C103—21no—
43C22⋊C4×C103—21no—
44C22⋊C4×C103—21no—
45C42×C103—21no—
46C42×C103C2×C411yescharacteristic
47C42×C103C2×C411yescharacteristic
48C42×C103D411yescharacteristic
49C42×C103D411yescharacteristic
50C23×C103—21no—
51C23×C103C2×D411yescharacteristic
52Q8×C103—41no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—41no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—22no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—41no—
63C2×C4×C103—42no—
64C2×C4×C103C22⋊C411yescharacteristic
65C2×C4×C103C22⋊C411yescharacteristic
66C2×C4×C103C22⋊C411yescharacteristic
67C2×C4×C103C22⋊C411yescharacteristic
68C2×C4×C103C22×C411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×Dic103—24no—
71C2×Dic103—42no—
72C2×Dic103—42no—
73C103⋊C8—42no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103C2×C22⋊C411yescharacteristic
80C22×C103AGL(1,ℤ/8)11yescharacteristic
81C22×C103#13711yescharacteristic
82C4×C103—21no—
83C4×C103—21no—
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—21no—
87C4×C103—41no—
88C4×C103—41no—
89C4×C103—41no—
90C4×C103#10412yes—
91Dic103—44no—
92C2×C103—21no—
93C2×C103—21no—
94C2×C103—81no—
95C2×C103#41011yescharacteristic
96C2×C103#41711yescharacteristic
97C2×C103C2×#10411yescharacteristic
98#1509—1031nomaximal, Sylow
99C103#150911yescharacteristic, complemented, Sylow
100#529D10311yescharacteristic
101#432—1031no—
102C4×C4⋊C4—1031no—
103#328—1032no—
104#327—1032no—
105#126—21no—
106#125Dic10311yescharacteristic, complemented
107#124Dic10311yescharacteristic, complemented
108#123—21no—
109C22⋊Q8C2×D10311yescharacteristic
110#121C2×D10311yescharacteristic
111C4×Q8Dic10311yescharacteristic, complemented
112C4×D4—21no—
113C4×D4Dic10311yescharacteristic, complemented
114#117—21no—
115C2×C4⋊C4—2061no—
116C2×C42—2061no—
117C2×C42C2×D10311yescharacteristic
118C4⋊C8—2061no—
119C22⋊C8—1032no—
120#97—2061no—
121#95—1032no—
122C2×Q8C2×Dic10311yescharacteristic
123C2×D4—21no—
124C2×D4C2×Dic10311yescharacteristic
125C22×C4—21no—
126C22×C4—2062no—
127C22×C4C22⋊D10311yescharacteristic
128C22×C4C22⋊D10311yescharacteristic
129C22×C4C22×D10311yescharacteristic
130C2×C8—2062no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—2064no—
136C4⋊C4C2×Dic10311yescharacteristic
137C4⋊C4C2×Dic10311yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—4122no—
145C42C2×Dic10311yescharacteristic
146C42C2×Dic10311yescharacteristic
147C42C22⋊D10311yescharacteristic
148C42C22⋊D10311yescharacteristic
149C23—21no—
150C23C2×C22⋊D10311yescharacteristic
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—4122no—
164C2×C4—4122no—
165C2×C4—2064no—
166C2×C4C22⋊Dic10311yescharacteristic
167C2×C4C22⋊Dic10311yescharacteristic
168C2×C4C22⋊Dic10311yescharacteristic
169C2×C4C22⋊Dic10311yescharacteristic
170C2×C4C22×Dic10311yescharacteristic
171C2×C4C2×C22⋊D10311yescharacteristic
172C8—4122no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22C2×C22⋊Dic10311yescharacteristic
179C22#1569304611yescharacteristic
180C22#1569305111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—4124no—
190C4#1569294812yes—
191C2—21no—
192C2—21no—
193C2—81no—
194C2#2026776511yescharacteristic
195C2#2026779211yescharacteristic
196C2C2×#1569294811yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#529×C103C2
socleC22×C103C2×C22⋊C4
prime radical#121×C103C22
cosocleC22×C4×C103C23
hypercenter#529D103
hypocenterC103#1509
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20267848C2semidirect
2. C4×C4⋊Dic103C2semidirect
3. #20267528C2semidirect
13. #125×C103C4semidirect
14. #124×C103C4semidirect
18. C4×Q8×C103C4semidirect
20. C4×D4×C103C4semidirect
99. C103#1509semidirect
106. #125Dic103semidirect
107. #124Dic103semidirect
111. C4×Q8Dic103semidirect
113. C4×D4Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678482
C4×C4⋊Dic1032
#202675282
#202675252
#529×C1032
#1509103