Finite Group Databasebeta

← #20242522

Subgroups — #20242522

Order 6016.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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#15689502C211yesmaximal, characteristic, complemented
2#15689418C211yesmaximal, characteristic, complemented
3#15689413C211yesmaximal, characteristic
4#15688872C211yesmaximal, characteristic, complemented
5Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic
7C47×#554C211yesmaximal, characteristic
8C2×#10625337—22no—
9#13094024C2211yescharacteristic
10#13093957—21no—
11#13093955—21no—
12C4⋊(C47⋊C8)C2211yescharacteristic
13C4⋊(C47⋊C8)C2211yescharacteristic
14#13093948—21no—
15#13093945—21no—
16C4×C47⋊C8C2211yescharacteristic
17C4⋊Q8×C47C2211yescharacteristic
18#125×C47—21no—
19C22⋊Q8×C47—21no—
20C22⋊Q8×C47—22no—
21C4×Q8×C47C2211yescharacteristic
22C4×D4×C47—21no—
23C4×D4×C47C2211yescharacteristic
24C2×C4⋊C4×C47—21no—
25C2×Q8×C47D411yescharacteristic
26C2×Q8×C47D412yes—
27C2×D4×C47D411yescharacteristic
28C22×C4×C47—22no—
29C22×C4×C47—21no—
30C2×Dic94—21no—
31C4⋊C4×C47—22no—
32C4⋊C4×C47—22no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47—22no—
39C22⋊C4×C47—21no—
40C42×C47—21no—
41C42×C47C2311yescharacteristic
42#10625337—44no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49Q8×C47—21no—
50Q8×C47—21no—
51Q8×C47—42no—
52D4×C47—21no—
53D4×C47Q1612yescomplemented
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—82no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—41no—
65Dic94—42no—
66C47⋊C8—22no—
67C47⋊C8—41no—
68C47⋊C8—41no—
69C22×C47—22no—
70C22×C47—41no—
71C22×C47—41no—
72C22×C47#12011yescharacteristic
73C4×C47—21no—
74C4×C47—41no—
75C4×C47—41no—
76C4×C47—41no—
77C4×C47—42no—
78C4×C47C2×Q1611yescharacteristic
79C4×C47#13511yescharacteristic
80C4×C47#13711yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—81no—
83#1632—471nomaximal, Sylow
84C2×C47—42no—
85C2×C47#45111yescharacteristic
86C2×C47#45211yescharacteristic
87C2×C47#45311yescharacteristic
88#554D4711yescharacteristic
89#494—471no—
90#477—471no—
91#476—471no—
92#333—471no—
93Q8⋊C8—471no—
94D4⋊C8—471no—
95C47#163211yescharacteristic, complemented, Sylow
96C2×Q16—942no—
97C4⋊Q8—471no—
98C4⋊Q8C2×D4711yescharacteristic
99#125—21no—
100C22⋊Q8—21no—
101C22⋊Q8—22no—
102C4×Q8C2×D4711yescharacteristic
103C4×D4—21no—
104C4×D4C2×D4711yescharacteristic
105C2×C4⋊C4—21no—
106#107—941no—
107#106—941no—
108C4⋊C8—471no—
109C4⋊C8—471no—
110#103—941no—
111#102—941no—
112C4×C8—471no—
113C2×Q8—941no—
114C2×Q8C22⋊D4711yescharacteristic
115C2×Q8C22⋊D4712yes—
116C2×D4C22⋊D4711yescharacteristic
117C22×C4—22no—
118C22×C4—21no—
119Q16—1884no—
120C2×C8—941no—
121C2×C8—941no—
122C2×C8—941no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4C22⋊D4711yescharacteristic
131C4⋊C4C22⋊D4711yescharacteristic
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—21no—
135C42C22×D4711yescharacteristic
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—1882no—
141D4—21no—
142D4#1062533712yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—1881no—
151C2×C4C2×C22⋊D4711yescharacteristic
152C2×C4C2×C22⋊D4711yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—942no—
155C8—1881no—
156C8—1881no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1309399311yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—41no—
165C4—42no—
166C4—3761no—
167C4C2×#1062533711yescharacteristic
168C4#1309404411yescharacteristic
169C4#1309405411yescharacteristic
170C4#1309405511yescharacteristic
171C2—42no—
172C2#1568927911yescharacteristic
173C2#1568928511yescharacteristic
174C2#1568929111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#554C2
socleC22×C47#120
hypercenter#554D47
hypocenterC47#1632
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #15689502C2semidirect
2. #15689418C2semidirect
4. #15688872C2semidirect
5. Q8⋊(C47⋊C8)C2semidirect
53. D4×C47Q16semidirect
95. C47#1632semidirect
142. D4#10625337semidirect