Finite Group Databasebeta

← #27195542

Subgroups — #27195542

Order 13184.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15693017C211yesmaximal, characteristic
2#20267795C212yesmaximal, complemented
3C2×#15692938C211yesmaximal, characteristic, complemented
4#20267550C212yesmaximal, complemented
5#518×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C22×C22⋊D103—22no—
8C2×#13110089C2212yes—
9#15693017—22no—
10#15693017C414yescomplemented
11C2×C4×Dic103C2211yescharacteristic
12#15692941—24no—
13#15692938—22no—
14C22×D4×C103C2211yescharacteristic
15C4×D4×C103—24no—
16#117×C103C2212yes—
17C2×C22⋊C4×C103—22no—
18C23×D103—21no—
19C2×D412—22no—
20C2×D412—22no—
21C2×D412—21no—
22C2×D412C2×C412yescomplemented
23C2×C22⋊D103—28no—
24C2×C22⋊D103—48no—
25C22×Dic103—21no—
26#13110089—22no—
27#13110089—22no—
28C2×C103⋊C8—22no—
29C4×Dic103—21no—
30C4×Dic103C2×C412yescomplemented
31C24×C103D412yes—
32C2×D4×C103—22no—
33C2×D4×C103—22no—
34C2×D4×C103C2×C412yes—
35C2×D4×C103D412yes—
36C22×C4×C103—24no—
37C22×C4×C103C2311yescharacteristic
38C4⋊C4×C103D414yescomplemented
39C22⋊C4×C103—24no—
40C22⋊C4×C103—22no—
41C42×C103—22no—
42C23×C103—22no—
43C23×C103—22no—
44C23×C103—44no—
45C23×C103C22⋊C414yes—
46C23×C103C2×D411yescharacteristic
47C22×D103—22no—
48C22×D103—44no—
49C22×D103—41no—
50C22×D103—41no—
51D4×C103—24no—
52D4×C103—24no—
53C2×C4×C103—24no—
54C2×C4×C103—84no—
55C2×C4×C103C22×C411yescharacteristic
56C2×C4×C103C2×D412yes—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103#4112yes—
59C22⋊D103—416no—
60C2×Dic103—24no—
61C2×Dic103—22no—
62D412—24no—
63D412—42no—
64C103⋊C8—42no—
65C22×C103—22no—
66C22×C103—24no—
67C22×C103—44no—
68C22×C103—44no—
69C22×C103—82no—
70C22×C103C2×C22⋊C411yescharacteristic
71C22×C103#12011yescharacteristic
72C22×C103#12311yescharacteristic
73C2×D103—44no—
74C2×D103—42no—
75C2×D103—82no—
76C2×D103—82no—
77C4×C103—44no—
78C4×C103C4×D412yes—
79C4×C103#12112yes—
80Dic103—24no—
81C2×C103—21no—
82C2×C103—21no—
83C2×C103—44no—
84C2×C103#38611yescharacteristic
85C2×C103#45312yes—
86D103—82no—
87#1887—1031nomaximal, Sylow
88C103#188711yescharacteristic, complemented, Sylow
89C2×#127—1031no—
90#518D10311yescharacteristic, complemented
91#418—1032no—
92C2×#100—1031no—
93#339—1032no—
94C22×D4—1031no—
95C22×D4—2062no—
96C22×D4C2×D10311yescharacteristic
97C2×M16—1032no—
98#127—1034no—
99#127—2062no—
100C4×D4—24no—
101#117C2×D10312yes—
102C2×C22⋊C4—22no—
103C2×C42—1031no—
104#102—2064no—
105#100—2062no—
106C24—2061no—
107C24C22⋊D10312yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—1032no—
111C2×D4—4128no—
112C2×D4—2068no—
113C2×D4—2062no—
114C2×D4—2061no—
115C2×D4—2062no—
116C2×D4C4×D10312yes—
117C2×D4D41212yes—
118C22×C4—24no—
119C22×C4—2061no—
120C22×C4C22×D10311yescharacteristic
121M16—2062no—
122M16—2062no—
123C2×C8—2062no—
124C4⋊C4C22⋊D10314yescomplemented
125C22⋊C4—24no—
126C22⋊C4—22no—
127C42—22no—
128C42—1032no—
129C42—2061no—
130C23—22no—
131C23—22no—
132C23—44no—
133C23—4124no—
134C23—4121no—
135C23—4121no—
136C23—2062no—
137C23(C2×D103)⋊C414yes—
138C23C2×C22⋊D10311yescharacteristic
139D4—24no—
140D4—24no—
141D4—41216no—
142D4—4122no—
143D4—2064no—
144C2×C4—24no—
145C2×C4—84no—
146C2×C4—2064no—
147C2×C4—2062no—
148C2×C4C2×C4×D10311yescharacteristic
149C2×C4C2×C22⋊D10312yes—
150C2×C4C2×D41211yescharacteristic
151C2×C4#1311010512yes—
152C8—4122no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—82no—
158C22—8242no—
159C22—8242no—
160C22—4124no—
161C22—4122no—
162C22C2×(C2×D103)⋊C411yescharacteristic
163C22#1569299011yescharacteristic
164C22#1569300411yescharacteristic
165C4—44no—
166C4—2064no—
167C4C4×C22⋊D10312yes—
168C4#1569299512yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—8242no—
173C2#2026767011yescharacteristic
174C2#2026795912yes—
subgroupG/H
centerC22#15692990
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#518×C103C2
socleC22×C103#120
prime radicalC2×#15693017C2
cosocleC22×C4×C103C23
hypercenter#518D103
hypocenterC103#1887
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #20267795C2semidirect
3. C2×#15692938C2semidirect
4. #20267550C2semidirect
5. #518×C103C2semidirect
10. #15693017C4semidirect
22. C2×D412C2×C4semidirect
30. C4×Dic103C2×C4semidirect
38. C4⋊C4×C103D4semidirect
88. C103#1887semidirect
90. #518D103semidirect
124. C4⋊C4C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930172
#202677952
C2×#156929382
#202675502
#518×C1032
#1887103