Finite Group Databasebeta

← #20242715

Subgroups — #20242715

Order 6016.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C47⋊#564C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic
3#15689491C211yesmaximal, characteristic
4#15688865C211yesmaximal, characteristic
5#15688864C211yesmaximal, characteristic
6#15688864C211yesmaximal, characteristic
7C47×#501C211yesmaximal, characteristic
8#13094016C2211yescharacteristic
9#13094016C2211yescharacteristic
10#13094015—21no—
11#13094015—21no—
12#13094014—21no—
13#13094014—21no—
14#13094014—21no—
15#13094014—21no—
16#13093957—21no—
17#13093955—21no—
18#13093948—21no—
19#13093948—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#125×C47C2211yescharacteristic
24#107×C47—21no—
25#106×C47—21no—
26#97×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×C8×C47—21no—
29C4⋊C4×C47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47D411yescharacteristic
34C4⋊C4×C47D411yescharacteristic
35C42×C47C2311yescharacteristic
36C4⋊Dic47—21no—
37C4⋊Dic47—21no—
38C4⋊Dic47D411yescharacteristic
39C4⋊Dic47D411yescharacteristic
40C4⋊Dic47D411yescharacteristic
41C4⋊Dic47D411yescharacteristic
42Dic47⋊C4—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50C4×Dic47—21no—
51C4×Dic47—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54Q8×C47—42no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C8×C47—22no—
66C47⋊C8—22no—
67C47⋊C8—41no—
68C22×C47#12011yescharacteristic
69C4×C47—21no—
70C4×C47—21no—
71C4×C47—21no—
72C4×C47—41no—
73C4×C47—41no—
74C4×C47—81no—
75Dic47—41no—
76Dic47—41no—
77Dic47—41no—
78Dic47—41no—
79#1663—471nomaximal, Sylow
80C2×C47#45411yescharacteristic
81C2×C47#45611yescharacteristic
82C2×C47#45611yescharacteristic
83#564—471no—
84#501—471no—
85#501D4711yescharacteristic
86#491—471no—
87#330—471no—
88#330—471no—
89#330—471no—
90C47#166311yescharacteristic, complemented, Sylow
91C4⋊Q8C2×D4711yescharacteristic
92#125—471no—
93#125—471no—
94#125—941no—
95#125—941no—
96#125—941no—
97#125—941no—
98#125—941no—
99#125—941no—
100#125C2×D4711yescharacteristic
101#107—21no—
102#107—941no—
103#106—21no—
104#106—941no—
105#103—941no—
106#103—941no—
107#97—471no—
108#97—471no—
109#97C2×D4711yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—941no—
113C2×C8—941no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—471no—
119C4⋊C4—471no—
120C4⋊C4—471no—
121C4⋊C4—471no—
122C4⋊C4—941no—
123C4⋊C4—941no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4—941no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C4⋊C4C22⋊D4711yescharacteristic
133C4⋊C4C22⋊D4711yescharacteristic
134C42—941no—
135C42—941no—
136C42C22×D4711yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—941no—
142C2×C4—941no—
143C2×C4—941no—
144C2×C4—941no—
145C2×C4D4×D4711yescharacteristic
146C2×C4D4×D4711yescharacteristic
147C2×C4C2×C22⋊D4711yescharacteristic
148C8—22no—
149C8—942no—
150C8—1881no—
151C22#1309399211yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—1881no—
159C4—1881no—
160C4—1881no—
161C4—1881no—
162C2#1568929411yescharacteristic
163C2#1568930411yescharacteristic
164C2#1568930511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#501C2
socleC22×C47#120
hypercenter#501D47
hypocenterC47#1663
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
90. C47#1663semidirect