Finite Group Databasebeta

← #20242427

Subgroups — #20242427

Order 6016.

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

normal subgroups only

This group has 246 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#15689442C212yesmaximal, complemented
3#15689062C211yesmaximal, characteristic, complemented
4#15688858C212yesmaximal, complemented
5C47×#324C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7#13094004—22no—
8#13093999—22no—
9#13093998—21no—
10#13093998C2212yes—
11C2×C4⋊Dic47C2211yescharacteristic
12#13093956—22no—
13#13093946—22no—
14C47⋊#95—21no—
15C47⋊#95—21no—
16C47⋊#95C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C2×C22⋊D47—22no—
23C22×Dic47—21no—
24C22×Dic47—21no—
25#10625350—42no—
26#10625350—42no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188D412yes—
30C2×C4×D47—22no—
31C2×Dic94—21no—
32C2×C8×C47—22no—
33C4⋊C4×C47—22no—
34(C2×D47)⋊C4—22no—
35(C2×D47)⋊C4—22no—
36C4⋊Dic47—21no—
37C4⋊Dic47—22no—
38C4⋊Dic47D412yes—
39C23×C47C2×D411yescharacteristic
40C22×D47—22no—
41C2×C4×C47—21no—
42C2×C4×C47—21no—
43C2×C4×C47—21no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47SD1612yes—
47C2×C4×C47C2×D412yes—
48C22⋊D47—42no—
49C22⋊D47—42no—
50C2×Dic47—22no—
51C2×Dic47—41no—
52C2×Dic47—41no—
53C2×Dic47—42no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56D188—42no—
57D188—42no—
58D188—81no—
59C4×D47—44no—
60Dic94—42no—
61C8×C47—42no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47#12011yescharacteristic
65C22×C47C2×SD1611yescharacteristic
66C22×C47AGL(1,ℤ/8)11yescharacteristic
67C2×D47—42no—
68C2×D47—42no—
69C2×D47—42no—
70C4×C47—22no—
71C4×C47—22no—
72C4×C47—41no—
73Dic47—42no—
74Dic47—81no—
75Dic47—81no—
76#1616—471nomaximal, Sylow
77C2×C47—21no—
78C2×C47—21no—
79C2×C47#45011yescharacteristic
80C2×C47#45411yescharacteristic
81C2×C47#45811yescharacteristic
82D47—82no—
83#537—471no—
84#481—472no—
85#400—471no—
86#327—472no—
87#324D4711yescharacteristic, complemented
88C47#161611yescharacteristic, complemented, Sylow
89C2×#41—941no—
90C22⋊Q8—942no—
91#121—472no—
92#121—942no—
93#121—941no—
94C2×C4⋊C4—471no—
95C2×C4⋊C4C2×D4711yescharacteristic
96#106—942no—
97#102—942no—
98C22⋊C8C2×D4712yes—
99#95—471no—
100#95—941no—
101#95—941no—
102#41—1882no—
103#41—1882no—
104C2×Q8—941no—
105C2×D4—472no—
106C2×D4—941no—
107C2×D4—941no—
108C2×D4—942no—
109C22×C4—942no—
110C22×C4—941no—
111C22×C4—941no—
112C22×C4D18811yescharacteristic
113C22×C4D18811yescharacteristic
114C22×C4C22×D4711yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—472no—
118C4⋊C4—941no—
119C4⋊C4—942no—
120C22⋊C4—942no—
121C22⋊C4—942no—
122C23—942no—
123C23C2×D18811yescharacteristic
124Q8—1882no—
125D4—3761no—
126D4—1882no—
127D4—1882no—
128D4—1882no—
129D4—1882no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—942no—
136C2×C4—1884no—
137C2×C4—1881no—
138C2×C4—1881no—
139C2×C4—1882no—
140C2×C4—1881no—
141C2×C4—1881no—
142C2×C4#1062532512yes—
143C2×C4D4×D4712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—1882no—
148C22—1882no—
149C22—1882no—
150C22#1309399411yescharacteristic
151C22C2×#1062532511yescharacteristic
152C22#1309405211yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—3761no—
157C4—3761no—
158C4—1882no—
159C2—21no—
160C2—21no—
161C2—3762no—
162C2#1568927611yescharacteristic
163C2#1568929811yescharacteristic
164C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47#120
hypercenter#324D47
hypocenterC47#1616
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #15689442C2semidirect
3. #15689062C2semidirect
4. #15688858C2semidirect
5. C47×#324C2semidirect
87. #324D47semidirect
88. C47#1616semidirect