Finite Group Databasebeta

← #20243921

Subgroups — #20243921

Order 6016.

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

normal subgroups only

This group has 362 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
1#15689598C211yesmaximal, characteristic, complemented
2#15689140C212yesmaximal, complemented
3C2×#13093941C211yesmaximal, characteristic, complemented
4#15688879C212yesmaximal, complemented
5C47×#535C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7D4×Dic47—24no—
8#13093983C2212yes—
9C2×C22⋊Dic47—22no—
10#13093951—24no—
11#13093941—22no—
12C2×#41×C47C2211yescharacteristic
13C22×D4×C47C2211yescharacteristic
14#127×C47C412yescomplemented
15#124×C47C412yescomplemented
16#121×C47—22no—
17#120×C47—22no—
18#117×C47C2211yescharacteristic
19C24×C47D412yes—
20#41×C47—22no—
21#41×C47—22no—
22C2×Q8×C47C2×C411yescharacteristic, complemented
23C2×D4×C47—21no—
24C2×D4×C47—24no—
25C2×D4×C47—22no—
26C2×D4×C47—22no—
27C2×D4×C47C2×C412yes—
28C2×D4×C47C2×C411yescharacteristic, complemented
29C2×D4×C47D412yes—
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—24no—
33C4⋊C4×C47—21no—
34C22⋊C4×C47—24no—
35C22⋊C4×C47—21no—
36C42×C47C2×C412yescomplemented
37C22⋊Dic47—24no—
38C22⋊Dic47—22no—
39C4⋊Dic47—22no—
40C4×Dic47D414yescomplemented
41#10625329—22no—
42#10625329—22no—
43C2×C47⋊C8—22no—
44C23×C47—22no—
45C23×C47—22no—
46C23×C47—21no—
47C23×C47—82no—
48C23×C47C22⋊C414yes—
49C23×C47C2×D411yescharacteristic
50Q8×C47—22no—
51D4×C47—24no—
52D4×C47—22no—
53D4×C47—24no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—84no—
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—42no—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4112yes—
64C2×Dic47—24no—
65C2×Dic47—84no—
66C47⋊C8—42no—
67C22×C47—24no—
68C22×C47—41no—
69C22×C47—44no—
70C22×C47—44no—
71C22×C47—42no—
72C22×C47—41no—
73C22×C47—82no—
74C22×C47C2×C22⋊C411yescharacteristic
75C22×C47#12011yescharacteristic
76C22×C47#12311yescharacteristic
77C4×C47—42no—
78C4×C47—41no—
79C4×C47C4×D412yes—
80C4×C47#12112yes—
81Dic47—44no—
82#1911—471nomaximal, Sylow
83C2×C47—21no—
84C2×C47—21no—
85C2×C47—21no—
86C2×C47—44no—
87C2×C47—81no—
88C2×C47#38611yescharacteristic
89#535D4711yescharacteristic
90#518—471no—
91#421—472no—
92C2×#100—471no—
93H(3,ℤ/4)—472no—
94C47#191111yescharacteristic, complemented, Sylow
95C2×#41C2×D4711yescharacteristic
96C22×D4C2×D4711yescharacteristic
97C2×M16—472no—
98#127Dic4712yescomplemented
99#124Dic4712yescomplemented
100#121—22no—
101#120—22no—
102C4×D4—944no—
103#117—472no—
104#117C2×D4711yescharacteristic
105C2×C22⋊C4—942no—
106#104—944no—
107#100—942no—
108C24C22⋊D4712yes—
109#41—22no—
110#41—22no—
111C2×Q8C2×Dic4711yescharacteristic, complemented
112C2×D4—21no—
113C2×D4—24no—
114C2×D4—22no—
115C2×D4—22no—
116C2×D4C2×Dic4712yes—
117C2×D4C2×Dic4711yescharacteristic, complemented
118C2×D4C22⋊D4712yes—
119C22×C4—21no—
120C22×C4—944no—
121C22×C4C22×D4711yescharacteristic
122M16—942no—
123M16—942no—
124C2×C8—942no—
125C4⋊C4—21no—
126C4⋊C4—942no—
127C22⋊C4—24no—
128C22⋊C4—21no—
129C22⋊C4—944no—
130C22⋊C4—942no—
131C42—474no—
132C42C2×Dic4712yescomplemented
133C23—22no—
134C23—22no—
135C23—21no—
136C23—82no—
137C23C22⋊Dic4714yes—
138C23C2×C22⋊D4711yescharacteristic
139Q8—22no—
140D4—24no—
141D4—22no—
142D4—24no—
143D4—41no—
144D4—41no—
145D4—84no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—42no—
149C2×C4—944no—
150C2×C4—3764no—
151C2×C4D4×D4712yes—
152C2×C4#1062535212yes—
153C2×C4C22×Dic4711yescharacteristic
154C2×C4C2×C22⋊D4711yescharacteristic
155C8—1882no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—42no—
161C22—41no—
162C22—82no—
163C22C2×C22⋊Dic4711yescharacteristic
164C22#1309399211yescharacteristic
165C22#1309400511yescharacteristic
166C4—42no—
167C4—41no—
168C4—1884no—
169C4D4×Dic4712yes—
170C4#1309399612yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—81no—
176C2#1568900311yescharacteristic
subgroupG/H
centerC2#15689003
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#535C2
socleC2×C47#386
hypercenter#535D47
hypocenterC47#1911
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689598C2semidirect
2. #15689140C2semidirect
3. C2×#13093941C2semidirect
4. #15688879C2semidirect
14. #127×C47C4semidirect
15. #124×C47C4semidirect
22. C2×Q8×C47C2×C4semidirect
28. C2×D4×C47C2×C4semidirect
36. C42×C47C2×C4semidirect
40. C4×Dic47D4semidirect
94. C47#1911semidirect
98. #127Dic47semidirect
99. #124Dic47semidirect
111. C2×Q8C2×Dic47semidirect
117. C2×D4C2×Dic47semidirect
132. C42C2×Dic47semidirect