Finite Group Databasebeta

← #20245404

Subgroups — #20245404

Order 6016.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#15689865C211yesmaximal, characteristic, complemented
2#15689296C212yesmaximal, complemented
3#15688920C211yesmaximal, characteristic, complemented
4#15688919C212yesmaximal, complemented
5C47×#454C211yesmaximal, characteristic, complemented
6#13094049—22no—
7#13094013C2212yes—
8#13094012—21no—
9#13094010—22no—
10#13093994—22no—
11#13093992—21no—
12#13093951—22no—
13#13093943C2212yescomplemented
142−1+4×C47C2211yescharacteristic, complemented
15AGL(1,ℤ/8)×C47—21no—
16#124×C47C2211yescharacteristic
17#104×C47—21no—
18#101×C47C2211yescharacteristic, complemented
19C23×D47—21no—
20#41×C47—21no—
21#41×C47—22no—
22#41×C47—41no—
23C2×Q8×C47—41no—
24C2×Q8×C47C2311yescharacteristic
25C2×D4×C47D411yescharacteristic
26C2×C22⋊D47—22no—
27C2×D188—21no—
28C2×D188D412yes—
29C2×Dic94—21no—
30SD16×C47—41no—
31D8×C47—41no—
32M16×C47—21no—
33C22⋊C4×C47—22no—
34C42×C47D411yescharacteristic
35C22⋊Dic47—21no—
36#10625336—42no—
37#10625334—42no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41C4×Dic47D412yes—
42#10625329—22no—
43C23×C47—21no—
44C22×D47—22no—
45C22×D47—82no—
46C22×D47—81no—
47Q8×C47—22no—
48Q8×C47—21no—
49Q8×C47—41no—
50D4×C47—22no—
51D4×C47—21no—
52D4×C47—41no—
53D4×C47—41no—
54C2×C4×C47—21no—
55C2×C4×C47—42no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D412yes—
58C2×C4×C47C2×D411yescharacteristic
59C22⋊D47—82no—
60C2×Dic47—22no—
61D188—42no—
62D188—81no—
63Dic94—81no—
64C8×C47—41no—
65C47⋊C8—42no—
66C22×C47—42no—
67C22×C47—41no—
68C22×C47—41no—
69C22×C47#12011yescharacteristic
70C2×D47—42no—
71C2×D47—42no—
72C2×D47—42no—
73C2×D47—84no—
74C4×C47—22no—
75C4×C47—21no—
76C4×C47—41no—
77C4×C47—41no—
78Dic47—42no—
79#2202—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—81no—
82C2×C47—81no—
83C2×C47B(4,𝔽2)11yescharacteristic
84D47—82no—
85H(3,𝔽4)—471no—
86#454—472no—
87#454D4711yescharacteristic, complemented
88#355—471no—
89#355—472no—
90C47#220211yescharacteristic, complemented, Sylow
912−1+4C2×D4711yescharacteristic, complemented
92AGL(1,ℤ/8)—21no—
93AGL(1,ℤ/8)—942no—
94#124—472no—
95#124—942no—
96#124—941no—
97#124C2×D4711yescharacteristic
98#120—942no—
99#120—941no—
100#104—21no—
101#104—942no—
102#101—472no—
103#101C2×D4711yescharacteristic, complemented
104C24—941no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—941no—
110C2×Q8C22×D4711yescharacteristic
111C2×D4—472no—
112C2×D4—941no—
113C2×D4—942no—
114C2×D4C22⋊D4711yescharacteristic
115SD16—41no—
116SD16—1882no—
117D8—41no—
118D8—1882no—
119M16—21no—
120M16—942no—
121C22⋊C4—22no—
122C22⋊C4—942no—
123C22⋊C4—941no—
124C22⋊C4—942no—
125C22⋊C4—942no—
126C42—472no—
127C42C22⋊D4711yescharacteristic
128C23—21no—
129C23—942no—
130C23—3762no—
131C23—3761no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—3761no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—3761no—
141D4—3762no—
142D4—1882no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—942no—
147C2×C4D4×D4712yes—
148C2×C4C2×C22⋊D4711yescharacteristic
149C8—41no—
150C8—1882no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—3764no—
155C22—1882no—
156C22—1882no—
157C22—1882no—
158C22#1309399211yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—1882no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—3762no—
168C2#1568930911yescharacteristic
subgroupG/H
centerC2#15689309
commutatorC2×Q8×C47C23
FrattiniC2×Q8C22×D47
FittingC47×#454C2
socleC2×C47B(4,𝔽2)
hypercenter#454D47
hypocenterC47#2202
LCSG ▷ C2×Q8×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #15689865C2semidirect
2. #15689296C2semidirect
3. #15688920C2semidirect
4. #15688919C2semidirect
5. C47×#454C2semidirect
13. #13093943C22semidirect
14. 2−1+4×C47C22semidirect
18. #101×C47C22semidirect
87. #454D47semidirect
90. C47#2202semidirect
91. 2−1+4C2×D47semidirect
103. #101C2×D47semidirect