Finite Group Databasebeta

← #20242520

Subgroups — #20242520

Order 6016.

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

normal subgroups only

This group has 214 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#15689830C211yesmaximal, characteristic
2#15689502C211yesmaximal, characteristic, complemented
3#15689415C211yesmaximal, characteristic, complemented
4#15688871C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic
7C47×#476C211yesmaximal, characteristic
8C2×#10625337—22no—
9#13094024C2211yescharacteristic
10#13094015—21no—
11#13094003—21no—
12#13094001—22no—
13C4×Dic94C2211yescharacteristic
14D4×Dic47—21no—
15C2×C4⋊Dic47—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093947—21no—
19C4×C47⋊C8C2211yescharacteristic
20C4⋊Q8×C47C2211yescharacteristic
21C4×D4×C47C2211yescharacteristic
22#106×C47—21no—
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C22×Dic47—22no—
29C2×Dic94D411yescharacteristic
30C2×Dic94D412yes—
31C2×C8×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47D411yescharacteristic
35C22⋊C4×C47—21no—
36C42×C47C2311yescharacteristic
37C22⋊Dic47—22no—
38#10625337—44no—
39C4⋊Dic47—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47D411yescharacteristic
43Dic47⋊C4—22no—
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49Q8×C47—42no—
50D4×C47—21no—
51D4×C47Q1612yescomplemented
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×Dic47—21no—
60C2×Dic47—21no—
61C2×Dic47—22no—
62C2×Dic47—82no—
63Dic94—21no—
64Dic94—21no—
65Dic94—42no—
66C8×C47—41no—
67C47⋊C8—22no—
68C47⋊C8—41no—
69C22×C47—22no—
70C22×C47—41no—
71C22×C47—41no—
72C22×C47#12011yescharacteristic
73C4×C47—21no—
74C4×C47—41no—
75C4×C47—81no—
76C4×C47C2×Q1611yescharacteristic
77C4×C47#13511yescharacteristic
78C4×C47#13711yescharacteristic
79C4×C47#13711yescharacteristic
80Dic47—41no—
81Dic47—42no—
82Dic47—41no—
83#1632—471nomaximal, Sylow
84C2×C47—42no—
85C2×C47#45111yescharacteristic
86C2×C47#45211yescharacteristic
87C2×C47#45311yescharacteristic
88#554—471no—
89#494—471no—
90#477—471no—
91#476D4711yescharacteristic
92#333—471no—
93Q8⋊C8—471no—
94D4⋊C8—471no—
95C47#163211yescharacteristic, complemented, Sylow
96C2×Q16—942no—
97C4⋊Q8—471no—
98C4⋊Q8C2×D4711yescharacteristic
99#125—941no—
100C22⋊Q8—942no—
101C22⋊Q8—941no—
102C4×Q8—471no—
103C4×D4—941no—
104C4×D4C2×D4711yescharacteristic
105C2×C4⋊C4—941no—
106#107—941no—
107#106—21no—
108C4⋊C8—471no—
109C4⋊C8C2×D4711yescharacteristic
110#103—941no—
111#102—21no—
112C4×C8—471no—
113C2×Q8—21no—
114C2×Q8—471no—
115C2×Q8—472no—
116C2×D4C22⋊D4711yescharacteristic
117C22×C4—21no—
118C22×C4—942no—
119Q16—1884no—
120C2×C8—21no—
121C2×C8—941no—
122C2×C8—941no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—471no—
126C4⋊C4—942no—
127C4⋊C4—942no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4C22⋊D4711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—942no—
134C42—941no—
135C42C22×D4711yescharacteristic
136C23—21no—
137Q8—42no—
138Q8—941no—
139Q8—941no—
140Q8—1882no—
141D4—21no—
142D4#1062533712yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—941no—
148C2×C4—941no—
149C2×C4—942no—
150C2×C4—3762no—
151C2×C4D4×D4711yescharacteristic
152C2×C4D4×D4711yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—41no—
155C8—942no—
156C8—1881no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1309399211yescharacteristic
161C4—21no—
162C4—41no—
163C4—81no—
164C4—1881no—
165C4—1881no—
166C4—1882no—
167C4C2×#1062533711yescharacteristic
168C4#1309404511yescharacteristic
169C4#1309405311yescharacteristic
170C4#1309405411yescharacteristic
171C2—42no—
172C2#1568927811yescharacteristic
173C2#1568928211yescharacteristic
174C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#476C2
socleC22×C47#120
hypercenter#476D47
hypocenterC47#1632
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689502C2semidirect
3. #15689415C2semidirect
4. #15688871C2semidirect
5. #15688853C2semidirect
51. D4×C47Q16semidirect
95. C47#1632semidirect
142. D4#10625337semidirect