Finite Group Databasebeta

← #20242425

Subgroups — #20242425

Order 6016.

246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689439C212yesmaximal, complemented
2#15689062C211yesmaximal, characteristic, complemented
3#15688857C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#537C211yesmaximal, characteristic
6C2×C4⋊Dic47C2211yescharacteristic
7#13093955—22no—
8#13093945—22no—
9C22⋊(C47⋊C8)C2212yes—
10C47⋊#95—21no—
11C47⋊#95—21no—
12C47⋊#95C2211yescharacteristic
13C2×#41×C47—21no—
14C22⋊Q8×C47—22no—
15#121×C47—22no—
16#121×C47—21no—
17#121×C47C2212yes—
18C2×C4⋊C4×C47C2211yescharacteristic
19#41×C47—42no—
20#41×C47—42no—
21C2×Q8×C47—21no—
22C2×D4×C47—21no—
23C2×D4×C47—22no—
24C2×D4×C47—21no—
25C2×D4×C47D412yes—
26C22×C4×C47—22no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—22no—
34C4⋊C4×C47D412yes—
35C22⋊C4×C47—22no—
36C22⋊C4×C47—22no—
37C4⋊Dic47—22no—
38C2×C47⋊C8—22no—
39C23×C47—22no—
40C23×C47C2×D411yescharacteristic
41Q8×C47—42no—
42D4×C47—42no—
43D4×C47—42no—
44D4×C47—42no—
45D4×C47—42no—
46D4×C47—81no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—44no—
53C2×C4×C47—41no—
54C2×C4×C47SD1612yes—
55C2×C4×C47C2×D412yes—
56C2×Dic47—41no—
57C2×Dic47—41no—
58C2×Dic47—42no—
59C2×Dic47—41no—
60C2×Dic47—41no—
61C47⋊C8—42no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47—42no—
65C22×C47—42no—
66C22×C47—42no—
67C22×C47#12011yescharacteristic
68C22×C47C2×SD1611yescharacteristic
69C22×C47AGL(1,ℤ/8)11yescharacteristic
70C4×C47—22no—
71C4×C47—22no—
72C4×C47—42no—
73C4×C47—41no—
74Dic47—81no—
75Dic47—81no—
76#1616—471nomaximal, Sylow
77C2×C47—21no—
78C2×C47—21no—
79C2×C47—82no—
80C2×C47#45011yescharacteristic
81C2×C47#45411yescharacteristic
82C2×C47#45811yescharacteristic
83#537D4711yescharacteristic
84#481—472no—
85#400—471no—
86#327—472no—
87#324—471no—
88C47#161611yescharacteristic, complemented, Sylow
89C2×#41—21no—
90C22⋊Q8—22no—
91#121—22no—
92#121—21no—
93#121C2×D4712yes—
94C2×C4⋊C4—471no—
95C2×C4⋊C4C2×D4711yescharacteristic
96#106—942no—
97#102—942no—
98C22⋊C8—472no—
99#95—471no—
100#95—941no—
101#95—941no—
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4C22⋊D4712yes—
109C22×C4—22no—
110C22×C4—941no—
111C22×C4—941no—
112C22×C4C22⋊D4711yescharacteristic
113C22×C4C22⋊D4711yescharacteristic
114C22×C4C22×D4711yescharacteristic
115C2×C8—942no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—942no—
119C4⋊C4C22⋊D4712yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×C22⋊D4711yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—1881no—
138C2×C4—1881no—
139C2×C4—1882no—
140C2×C4—1881no—
141C2×C4—1881no—
142C2×C4#1062533512yes—
143C2×C4C2×C22⋊D4712yes—
144C8—1882no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#1309399311yescharacteristic
151C22C2×#1062533511yescharacteristic
152C22#1309405011yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—3761no—
158C4—3761no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2#1568927411yescharacteristic
163C2#1568929611yescharacteristic
164C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#537C2
socleC22×C47#120
hypercenter#537D47
hypocenterC47#1616
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #15689439C2semidirect
2. #15689062C2semidirect
3. #15688857C2semidirect
4. #15688849C2semidirect
88. C47#1616semidirect