Finite Group Databasebeta

← #20242519

Subgroups — #20242519

Order 6016.

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

normal subgroups only

This group has 214 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#15689834C211yesmaximal, characteristic
2#15689415C211yesmaximal, characteristic, complemented
3#15689410C211yesmaximal, characteristic
4#15688872C211yesmaximal, characteristic, complemented
5#15688855C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic
7C47×#494C211yesmaximal, characteristic, complemented
8#13094015—21no—
9#13094004—21no—
10#13094000—22no—
11C4×Dic94C2211yescharacteristic
12C4×D188C2211yescharacteristic
13#13093986—21no—
14C4⋊C4×D47—21no—
15#13093957—21no—
16#13093955—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093947—21no—
20#13093944—21no—
21C2×Q16×C47—22no—
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊Q8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×Q8×C47D412yes—
27C2×D188D411yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47—22no—
30C2×Dic94D411yescharacteristic
31Q16×C47—44no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C42×C47C2311yescharacteristic
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—21no—
40C4⋊Dic47—22no—
41C4⋊Dic47D411yescharacteristic
42C4⋊Dic47D411yescharacteristic
43Dic47⋊C4—22no—
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C22×D47—21no—
49Q8×C47—42no—
50Q8×C47—42no—
51C2×C4×C47—22no—
52C2×C4×C47—41no—
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—21no—
57C2×Dic47—21no—
58C2×Dic47—21no—
59D188—21no—
60D188Q1612yescomplemented
61C4×D47—41no—
62C4×D47—41no—
63C4×D47—82no—
64Dic94—21no—
65Dic94—21no—
66C8×C47—22no—
67C47⋊C8—41no—
68C47⋊C8—41no—
69C22×C47#12011yescharacteristic
70C2×D47—22no—
71C2×D47—41no—
72C2×D47—41no—
73C4×C47—21no—
74C4×C47—42no—
75C4×C47—81no—
76C4×C47C2×Q1611yescharacteristic
77C4×C47#13511yescharacteristic
78C4×C47#13711yescharacteristic
79C4×C47#13711yescharacteristic
80Dic47—41no—
81Dic47—41no—
82Dic47—41no—
83#1632—471nomaximal, Sylow
84C2×C47#45111yescharacteristic
85C2×C47#45211yescharacteristic
86C2×C47#45311yescharacteristic
87D47—42no—
88#554—471no—
89#494D4711yescharacteristic, complemented
90#477—471no—
91#476—471no—
92#333—471no—
93Q8⋊C8—471no—
94D4⋊C8—471no—
95C47#163211yescharacteristic, complemented, Sylow
96C2×Q16—22no—
97C4⋊Q8C2×D4711yescharacteristic
98C4⋊Q8C2×D4711yescharacteristic
99#125—941no—
100C22⋊Q8—941no—
101C22⋊Q8—942no—
102C4×Q8—471no—
103C4×D4—471no—
104C4×D4—941no—
105C2×C4⋊C4—941no—
106#107—941no—
107#106—941no—
108C4⋊C8—471no—
109C4⋊C8—471no—
110#103—941no—
111#102—941no—
112C4×C8C2×D4711yescharacteristic
113C2×Q8—21no—
114C2×Q8—471no—
115C2×Q8C22⋊D4712yes—
116C2×D4—471no—
117C22×C4—942no—
118C22×C4—941no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—941no—
122C2×C8—941no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—471no—
128C4⋊C4—471no—
129C4⋊C4—942no—
130C4⋊C4—942no—
131C4⋊C4—941no—
132C22⋊C4—942no—
133C22⋊C4—941no—
134C42—941no—
135C42C22×D4711yescharacteristic
136C23—941no—
137Q8—42no—
138Q8—42no—
139Q8—941no—
140Q8—941no—
141D4—472no—
142D4—941no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—941no—
146C2×C4—941no—
147C2×C4—941no—
148C2×C4—3762no—
149C2×C4—1881no—
150C2×C4—1881no—
151C2×C4D4×D4711yescharacteristic
152C2×C4D4×D4711yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—22no—
155C8—1881no—
156C8—1881no—
157C22—942no—
158C22—1881no—
159C22—1881no—
160C22#1309399211yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—1881no—
165C4—1881no—
166C4—1881no—
167C4Q16×D4711yescharacteristic
168C4#1309404711yescharacteristic
169C4#1309405611yescharacteristic
170C4#1309405611yescharacteristic
171C2—1882no—
172C2#1568927711yescharacteristic
173C2#1568928411yescharacteristic
174C2#1568929011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#494C2
socleC22×C47#120
hypercenter#494D47
hypocenterC47#1632
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #15689415C2semidirect
4. #15688872C2semidirect
5. #15688855C2semidirect
7. C47×#494C2semidirect
60. D188Q16semidirect
89. #494D47semidirect
95. C47#1632semidirect