Finite Group Databasebeta

← #20243911

Subgroups — #20243911

Order 6016.

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

normal subgroups only

This group has 312 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#15689890C211yesmaximal, characteristic
2#15689132C212yesmaximal, complemented
3#15689097C211yesmaximal, characteristic
4#15688879C212yesmaximal, complemented
5C47×#536C211yesmaximal, characteristic
6#13094031—24no—
7C2×#10625329—22no—
8C2×#10625329C2212yes—
9#13093983C2212yes—
10#13093948—24no—
11#13093939—22no—
12C2×#41×C47C2211yescharacteristic
13C22×Q8×C47C2211yescharacteristic
14C4⋊Q8×C47C412yescomplemented
15#124×C47C412yescomplemented
16#123×C47—22no—
17C22⋊Q8×C47—22no—
18#117×C47C2211yescharacteristic
19#41×C47—22no—
20#41×C47—22no—
21C2×Q8×C47—21no—
22C2×Q8×C47—22no—
23C2×Q8×C47—22no—
24C2×Q8×C47C2×C412yes—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47C2×C411yescharacteristic
27C2×D4×C47D412yes—
28C22×C4×C47—21no—
29C22×C4×C47D412yes—
30C22×C4×C47C2311yescharacteristic
31C4⋊C4×C47—24no—
32C4⋊C4×C47—21no—
33C22⋊C4×C47—24no—
34C22⋊C4×C47—21no—
35C42×C47C2×C412yes—
36C22⋊Dic47—22no—
37C4⋊Dic47—22no—
38C4×Dic47—22no—
39#10625329—24no—
40#10625329—22no—
41#10625329—22no—
42C2×C47⋊C8—24no—
43C2×C47⋊C8D414yes—
44C23×C47C22⋊C412yes—
45C23×C47C2×D411yescharacteristic
46Q8×C47—22no—
47Q8×C47—24no—
48Q8×C47—41no—
49Q8×C47—41no—
50D4×C47—24no—
51D4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—42no—
57C2×C4×C47C22⋊C412yes—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D412yes—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47#4112yes—
62C2×Dic47—42no—
63C47⋊C8—24no—
64C22×C47—22no—
65C22×C47—41no—
66C22×C47—42no—
67C22×C47C2×C22⋊C411yescharacteristic
68C22×C47#12112yes—
69C4×C47—22no—
70C4×C47—42no—
71C4×C47—42no—
72C4×C47C4×D412yes—
73C4×C47#12011yescharacteristic
74C4×C47#12311yescharacteristic
75Dic47—82no—
76#1909—471nomaximal, Sylow
77C2×C47—22no—
78C2×C47—21no—
79C2×C47—42no—
80C2×C47#38611yescharacteristic
81#568—471no—
82#536D4711yescharacteristic
83#419—472no—
84#410—471no—
85H(3,ℤ/4)—472no—
86C47#190911yescharacteristic, complemented, Sylow
87C2×#41C2×D4711yescharacteristic
88C22×Q8C2×D4711yescharacteristic
89#131—944no—
90C2×M16—472no—
91C2×M16—942no—
92C4⋊Q8Dic4712yescomplemented
93#124Dic4712yescomplemented
94#123—22no—
95C22⋊Q8—22no—
96#117—472no—
97#117C2×D4711yescharacteristic
98#103—944no—
99#99—942no—
100#41—22no—
101#41—22no—
102C2×Q8—21no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic4712yes—
106C2×Q8C2×Dic4711yescharacteristic
107C2×D4C2×Dic4711yescharacteristic
108C2×D4C22⋊D4712yes—
109C22×C4—21no—
110C22×C4C22⋊D4712yes—
111C22×C4C22×D4711yescharacteristic
112M16—944no—
113M16—942no—
114M16—942no—
115C2×C8—474no—
116C2×C8—944no—
117C4⋊C4—24no—
118C4⋊C4—21no—
119C4⋊C4—942no—
120C22⋊C4—24no—
121C22⋊C4—21no—
122C22⋊C4—942no—
123C42—942no—
124C42C2×Dic4712yes—
125C23C22⋊Dic4712yes—
126C23C2×C22⋊D4711yescharacteristic
127Q8—22no—
128Q8—24no—
129Q8—41no—
130Q8—41no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—1882no—
139C2×C4C22⋊Dic4712yes—
140C2×C4D4×D4712yes—
141C2×C4#1062535212yes—
142C2×C4C22×Dic4711yescharacteristic
143C2×C4C2×C22⋊D4711yescharacteristic
144C8—944no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×C22⋊Dic4711yescharacteristic
149C22#1309399612yes—
150C4—22no—
151C4—42no—
152C4—42no—
153C4—3762no—
154C4D4×Dic4712yes—
155C4#1309399211yescharacteristic
156C4#1309400511yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#1568900311yescharacteristic
subgroupG/H
centerC2#15689003
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#536C2
socleC2×C47#386
hypercenter#536D47
hypocenterC47#1909
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #15689132C2semidirect
4. #15688879C2semidirect
14. C4⋊Q8×C47C4semidirect
15. #124×C47C4semidirect
86. C47#1909semidirect
92. C4⋊Q8Dic47semidirect
93. #124Dic47semidirect