Finite Group Databasebeta

← #27193682

Subgroups — #27193682

Order 13184.

222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 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
2#20267657C211yesmaximal, characteristic, complemented
3#20267528C212yesmaximal, complemented
4#20267525C212yesmaximal
5#529×C103C211yesmaximal, characteristic
6C2×C4⋊Dic103—21no—
7C4⋊(C103⋊C8)—21no—
8C22⋊(C103⋊C8)C2212yes—
9#15692932—21no—
10C103⋊#95—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—42no—
26C2×Q8×C103C2×C411yescharacteristic
27C2×D4×C103—21no—
28C2×D4×C103C2×C411yescharacteristic
29C22×C4×C103—21no—
30C22×C4×C103D411yescharacteristic
31C22×C4×C103D411yescharacteristic
32C22×C4×C103C2311yescharacteristic
33C4⋊C4×C103—21no—
34C4⋊C4×C103—21no—
35C4⋊C4×C103—21no—
36C4⋊C4×C103—21no—
37C4⋊C4×C103C2×C411yescharacteristic
38C4⋊C4×C103C2×C411yescharacteristic
39C22⋊C4×C103—21no—
40C22⋊C4×C103—21no—
41C22⋊C4×C103—21no—
42C22⋊C4×C103—21no—
43C22⋊C4×C103—21no—
44C42×C103—21no—
45C42×C103C2×C411yescharacteristic
46C42×C103C2×C411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103D411yescharacteristic
49C23×C103—21no—
50C23×C103C2×D411yescharacteristic
51Q8×C103—41no—
52D4×C103—41no—
53D4×C103—41no—
54D4×C103—41no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—41no—
61C2×C4×C103—41no—
62C2×C4×C103—42no—
63C2×C4×C103C22⋊C411yescharacteristic
64C2×C4×C103C22⋊C411yescharacteristic
65C2×C4×C103C22⋊C411yescharacteristic
66C2×C4×C103C22⋊C411yescharacteristic
67C2×C4×C103C22×C411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C2×Dic103—42no—
70C2×Dic103—42no—
71C2×Dic103—42no—
72C103⋊C8—42no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—41no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103C2×C22⋊C411yescharacteristic
79C22×C103AGL(1,ℤ/8)11yescharacteristic
80C22×C103#13711yescharacteristic
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—21no—
84C4×C103—21no—
85C4×C103—21no—
86C4×C103—21no—
87C4×C103—41no—
88C4×C103—41no—
89C4×C103—41no—
90Dic103—82no—
91C2×C103—21no—
92C2×C103—21no—
93C2×C103—81no—
94C2×C103#41011yescharacteristic
95C2×C103#41711yescharacteristic
96C2×C103#42111yescharacteristic
97#1512—1031nomaximal, Sylow
98C103#151211yescharacteristic, complemented, Sylow
99#529D10311yescharacteristic
100#432—1031no—
101#382—1031no—
102#328—1032no—
103#327—1032no—
104#126—21no—
105#125Dic10311yescharacteristic, complemented
106#124Dic10311yescharacteristic, complemented
107#123—21no—
108C22⋊Q8C2×D10311yescharacteristic
109#121C2×D10311yescharacteristic
110C4×Q8Dic10311yescharacteristic, complemented
111C4×D4—21no—
112C4×D4Dic10311yescharacteristic, complemented
113#117—21no—
114C2×C4⋊C4—2061no—
115C2×C42C2×D10311yescharacteristic
116C4⋊C8—2061no—
117C22⋊C8—1032no—
118#97—2061no—
119#95—1032no—
120#95—2061no—
121C2×Q8C2×Dic10311yescharacteristic
122C2×D4—21no—
123C2×D4C2×Dic10311yescharacteristic
124C22×C4—21no—
125C22×C4—2062no—
126C22×C4C22⋊D10311yescharacteristic
127C22×C4C22⋊D10311yescharacteristic
128C22×C4C22×D10311yescharacteristic
129C2×C8—2062no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4122no—
135C4⋊C4C2×Dic10311yescharacteristic
136C4⋊C4C2×Dic10311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C2×Dic10311yescharacteristic
144C42C2×Dic10311yescharacteristic
145C42C22⋊D10311yescharacteristic
146C42C22⋊D10311yescharacteristic
147C23—21no—
148C23C2×C22⋊D10311yescharacteristic
149Q8—41no—
150D4—41no—
151D4—41no—
152D4—41no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—4122no—
162C2×C4—4122no—
163C2×C4—4122no—
164C2×C4C22⋊Dic10311yescharacteristic
165C2×C4C22⋊Dic10311yescharacteristic
166C2×C4C22⋊Dic10311yescharacteristic
167C2×C4C22⋊Dic10311yescharacteristic
168C2×C4C22×Dic10311yescharacteristic
169C2×C4C2×C22⋊D10311yescharacteristic
170C8—4122no—
171C22—21no—
172C22—21no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22C2×C22⋊Dic10311yescharacteristic
177C22#1569304611yescharacteristic
178C22#1569305111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—8242no—
189C2—21no—
190C2—21no—
191C2—81no—
192C2#2026776511yescharacteristic
193C2#2026779211yescharacteristic
194C2#2026780811yescharacteristic
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#1512
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. #20267657C2semidirect
3. #20267528C2semidirect
13. #125×C103C4semidirect
14. #124×C103C4semidirect
18. C4×Q8×C103C4semidirect
20. C4×D4×C103C4semidirect
98. C103#1512semidirect
105. #125Dic103semidirect
106. #124Dic103semidirect
110. C4×Q8Dic103semidirect
112. C4×D4Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678482
#202676572
#202675282
#202675252
#529×C1032
#1512103