Finite Group Databasebeta

← #20242356

Subgroups — #20242356

Order 6016.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689704C211yesmaximal, characteristic
2#15689262C212yesmaximal, complemented
3#15688856C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#395C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7C2×#10625336—22no—
8#13094004—22no—
9#13093999—22no—
10#13093998—21no—
11#13093998C2212yes—
12#13093948—22no—
13C22⋊(C47⋊C8)C2212yes—
14C22×Q8×C47C2211yescharacteristic
15C2×C4⋊C4×C47—21no—
16C2×C4⋊C4×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47C2211yescharacteristic
19C2×Q8×C47—22no—
20C2×Q8×C47—42no—
21C22×C4×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—22no—
27#10625350—42no—
28#10625350—42no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C2×C4×D47—22no—
33C2×Dic94—21no—
34C4⋊C4×C47—22no—
35C4⋊C4×C47—42no—
36#10625336—44no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47D412yes—
41C2×C47⋊C8—22no—
42C23×C47C2×D411yescharacteristic
43C22×D47—22no—
44Q8×C47—24no—
45Q8×C47—42no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—22no—
49C2×C4×C47—22no—
50C2×C4×C47—21no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47SD1612yescomplemented
58C2×C4×C47C2×D412yes—
59C22⋊D47—42no—
60C22⋊D47—42no—
61C2×Dic47—22no—
62D188—42no—
63D188—42no—
64D188—81no—
65C4×D47—44no—
66Dic94—42no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47#12011yescharacteristic
71C22×C47C2×SD1611yescharacteristic
72C22×C47AGL(1,ℤ/8)11yescharacteristic
73C2×D47—42no—
74C2×D47—42no—
75C2×D47—42no—
76C4×C47—22no—
77C4×C47—22no—
78C4×C47—42no—
79C4×C47—41no—
80C4×C47—42no—
81Dic47—42no—
82#1604—471nomaximal, Sylow
83C2×C47—21no—
84C2×C47—21no—
85C2×C47#45011yescharacteristic
86C2×C47#45611yescharacteristic
87C2×C47B(4,𝔽2)11yescharacteristic
88D47—82no—
89#537—471no—
90#448—472no—
91#395D4711yescharacteristic, complemented
92#327—472no—
93#324—471no—
94C47#160411yescharacteristic, complemented, Sylow
95C2×#41—941no—
96C22×Q8C2×D4711yescharacteristic
97C2×SD16—942no—
98C22⋊Q8—942no—
99#121—472no—
100#121—942no—
101#121—941no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D4711yescharacteristic
104#103—942no—
105C22⋊C8—472no—
106#95—21no—
107#95C2×D4711yescharacteristic
108#41—1882no—
109#41—1882no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—941no—
113C2×D4—472no—
114C2×D4—941no—
115C2×D4—941no—
116C2×D4—942no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—942no—
120C22×C4C22⋊D4711yescharacteristic
121C22×C4C22⋊D4711yescharacteristic
122C22×C4C22×D4711yescharacteristic
123SD16—1884no—
124C2×C8—942no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—472no—
128C4⋊C4—941no—
129C22⋊C4—942no—
130C22⋊C4—942no—
131C23—942no—
132C23C2×C22⋊D4711yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—1882no—
136D4—3761no—
137D4—1882no—
138D4—1882no—
139D4—1882no—
140D4—1882no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—942no—
153C2×C4—1884no—
154C2×C4#1062533612yescomplemented
155C2×C4D4×D4712yes—
156C8—1882no—
157C22—21no—
158C22—21no—
159C22—1882no—
160C22—1882no—
161C22—1882no—
162C22#1309399211yescharacteristic
163C22C2×#1062533611yescharacteristic
164C22#1309404911yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—1882no—
171C2—21no—
172C2—21no—
173C2—3762no—
174C2#1568927311yescharacteristic
175C2#1568930511yescharacteristic
176C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#395C2
socleC22×C47#120
hypercenter#395D47
hypocenterC47#1604
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #15689262C2semidirect
3. #15688856C2semidirect
4. #15688849C2semidirect
5. C47×#395C2semidirect
57. C2×C4×C47SD16semidirect
91. #395D47semidirect
94. C47#1604semidirect
154. C2×C4#10625336semidirect