Finite Group Databasebeta

← #20242543

Subgroups — #20242543

Order 6016.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689848C211yesmaximal, characteristic
2#15689415C211yesmaximal, characteristic
3#15689415C211yesmaximal, characteristic
4#15688869C211yesmaximal, characteristic
5#15688855C211yesmaximal, characteristic
6#15688855C211yesmaximal, characteristic
7C47×#487C211yesmaximal, characteristic
8#13094022—21no—
9#13094015—21no—
10#13094014—22no—
11Q8×Dic47—21no—
12C4×Dic94C2211yescharacteristic
13C4×Dic94C2211yescharacteristic
14#13093989—21no—
15#13093957—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093947—21no—
20#13093947—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#103×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Dic94D411yescharacteristic
28C2×Dic94D411yescharacteristic
29C2×C8×C47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47D412yes—
34C42×C47C2311yescharacteristic
35C4⋊Dic47—22no—
36C4⋊Dic47D411yescharacteristic
37C4⋊Dic47D411yescharacteristic
38Dic47⋊C4—22no—
39Dic47⋊C4—22no—
40Dic47⋊C4—21no—
41Dic47⋊C4—21no—
42C4×Dic47—22no—
43C4×Dic47—21no—
44C4×Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47Q8×C47—42no—
48Q8×C47—41no—
49Q8×C47—41no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×Dic47—21no—
56C2×Dic47—21no—
57C2×Dic47—21no—
58C2×Dic47—21no—
59Dic94—21no—
60Dic94—21no—
61Dic94—21no—
62Dic94Q1612yes—
63C8×C47—41no—
64C47⋊C8—41no—
65C47⋊C8—41no—
66C22×C47#12011yescharacteristic
67C4×C47—21no—
68C4×C47—42no—
69C4×C47—81no—
70C4×C47C2×Q1611yescharacteristic
71C4×C47#13511yescharacteristic
72C4×C47#13711yescharacteristic
73C4×C47#13711yescharacteristic
74Dic47—22no—
75Dic47—41no—
76Dic47—41no—
77Dic47—41no—
78#1636—471nomaximal, Sylow
79C2×C47#45111yescharacteristic
80C2×C47#45211yescharacteristic
81C2×C47#45411yescharacteristic
82#557—471no—
83#487D4711yescharacteristic
84#477—471no—
85#477—471no—
86#332—471no—
87Q8⋊C8—471no—
88Q8⋊C8—471no—
89C47#163611yescharacteristic, complemented, Sylow
90C4⋊Q8—941no—
91C4⋊Q8C2×D4711yescharacteristic
92C4⋊Q8C2×D4711yescharacteristic
93#125—941no—
94#125—942no—
95C4×Q8—471no—
96C4×Q8—471no—
97C4×Q8—941no—
98C4×Q8—941no—
99#107—941no—
100#107—941no—
101C4⋊C8—471no—
102C4⋊C8—471no—
103#103—22no—
104#103—941no—
105#103—941no—
106C4×C8C2×D4711yescharacteristic
107C2×Q8—21no—
108C2×Q8—21no—
109C2×Q8—471no—
110C2×Q8—471no—
111C2×C8—21no—
112C2×C8—941no—
113C2×C8—941no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—471no—
118C4⋊C4—471no—
119C4⋊C4—942no—
120C4⋊C4—942no—
121C4⋊C4—942no—
122C4⋊C4—941no—
123C4⋊C4—941no—
124C4⋊C4C22⋊D4712yes—
125C42—942no—
126C42—941no—
127C42—941no—
128C42C22×D4711yescharacteristic
129Q8—42no—
130Q8—41no—
131Q8—41no—
132Q8—472no—
133Q8—941no—
134Q8—941no—
135Q8—941no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—941no—
139C2×C4—941no—
140C2×C4—941no—
141C2×C4—941no—
142C2×C4D4×D4711yescharacteristic
143C2×C4D4×D4711yescharacteristic
144C2×C4C2×C22⋊D4711yescharacteristic
145C8—41no—
146C8—1881no—
147C8—1881no—
148C22#1309399211yescharacteristic
149C4—21no—
150C4—42no—
151C4—81no—
152C4—942no—
153C4—1881no—
154C4—1881no—
155C4—1881no—
156C4Q16×D4711yescharacteristic
157C4#1309404511yescharacteristic
158C4#1309405311yescharacteristic
159C4#1309405611yescharacteristic
160C2#1568927711yescharacteristic
161C2#1568928211yescharacteristic
162C2#1568929511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#487C2
socleC22×C47#120
hypercenter#487D47
hypocenterC47#1636
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
89. C47#1636semidirect