Finite Group Databasebeta

← #15689767

Subgroups — #15689767

Order 3008.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#10625352C211yesmaximal, characteristic, complemented
2#13094011C211yesmaximal, characteristic, complemented
3#13094005C212yesmaximal, complemented
4#13094003C211yesmaximal, characteristic, complemented
5#13093996C212yesmaximal, complemented
6#13093995C211yesmaximal, characteristic, complemented
7#13093993C212yesmaximal, complemented
8D4×Dic47C211yesmaximal, characteristic, complemented
9C4×C22⋊D47C211yesmaximal, characteristic, complemented
10C2×C22⋊Dic47C212yesmaximal, complemented
11C22×D4×C47C211yesmaximal, characteristic, complemented
12C24×C47C2212yes—
13C2×D4×C47—24no—
14C2×D4×C47C2211yescharacteristic
15C2×D4×C47C2212yes—
16C2×D4×C47C2211yescharacteristic
17C22×C4×C47C2211yescharacteristic
18C2×C22⋊D47C2211yescharacteristic
19C2×C22⋊D47C2212yescomplemented
20C2×C22⋊D47C2212yescomplemented
21C22×Dic47C2212yescomplemented
22C22×Dic47C2212yescomplemented
23#10625352—24no—
24C2×C4×D47C2211yescharacteristic, complemented
25C2×Dic94C2211yescharacteristic, complemented
26C22⋊Dic47C2211yescharacteristic
27C22⋊Dic47C2212yes—
28C22⋊Dic47C2212yescomplemented
29C22⋊Dic47C2212yescomplemented
30C22⋊Dic47C2212yescomplemented
31C22⋊Dic47C2212yescomplemented
32(C2×D47)⋊C4C2211yescharacteristic, complemented
33C4⋊Dic47C2211yescharacteristic, complemented
34Dic47⋊C4C2211yescharacteristic, complemented
35Dic47⋊C4C2212yescomplemented
36C4×Dic47C2211yescharacteristic, complemented
37C23×C47—24no—
38C23×C47—24no—
39C23×C47—42no—
40C23×C47C2312yes—
41C23×C47C2312yes—
42C23×C47C2311yescharacteristic
43C22×D47C2311yescharacteristic
44D4×C47—24no—
45D4×C47—22no—
46D4×C47D414yescomplemented
47C2×C4×C47—22no—
48C2×C4×C47C2311yescharacteristic
49C2×C4×C47C2311yescharacteristic
50C22⋊D47—24no—
51C22⋊D47—22no—
52C22⋊D47—42no—
53C2×Dic47—24no—
54C2×Dic47—42no—
55C2×Dic47C2311yescharacteristic
56C2×Dic47C2311yescharacteristic
57C2×Dic47C2312yes—
58C2×Dic47C2312yes—
59C2×Dic47C2311yescharacteristic
60C4×D47—22no—
61Dic94—22no—
62C22×C47—21no—
63C22×C47—22no—
64C22×C47—22no—
65C22×C47—21no—
66C22×C47—22no—
67C22×C47—22no—
68C22×C47—22no—
69C22×C47—48no—
70C22×C47C2×D414yes—
71C22×C47#4112yescomplemented
72C22×C47C2411yescharacteristic
73C2×D47—21no—
74C2×D47—21no—
75C2×D47—21no—
76C4×C47—21no—
77C4×C47C2×D412yes—
78Dic47—22no—
79Dic47—21no—
80Dic47—21no—
81Dic47—21no—
82Dic47—22no—
83C2×C47—22no—
84C2×C47—24no—
85C2×C47—42no—
86C2×C47C22×D411yescharacteristic
87C2×C47C2×#4111yescharacteristic
88C2×C47H(5,𝔽2)11yescharacteristic
89D47—41no—
90#546—471nomaximal, Sylow
91C47#54611yescharacteristic, complemented, Sylow
92C2×#41—471no—
93C22×D4D4711yescharacteristic, complemented
94#124—471no—
95#123—472no—
96C22⋊Q8—471no—
97#121—471no—
98#121—472no—
99#120—472no—
100C4×D4—471no—
101C4×D4—471no—
102C2×C22⋊C4—472no—
103C24C2×D4712yes—
104#41—944no—
105C2×Q8—471no—
106C2×D4—24no—
107C2×D4—471no—
108C2×D4—472no—
109C2×D4—472no—
110C2×D4C2×D4712yes—
111C2×D4C2×D4711yescharacteristic
112C2×D4C2×D4711yescharacteristic
113C22×C4—472no—
114C22×C4—472no—
115C22×C4—471no—
116C22×C4C2×D4711yescharacteristic
117C4⋊C4—471no—
118C4⋊C4—472no—
119C4⋊C4—471no—
120C22⋊C4—471no—
121C22⋊C4—472no—
122C22⋊C4—472no—
123C22⋊C4—472no—
124C22⋊C4—472no—
125C22⋊C4—472no—
126C22⋊C4—471no—
127C42—471no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—471no—
132C23C22×D4712yes—
133C23C22×D4711yescharacteristic
134C23C22×D4712yes—
135Q8—942no—
136D4—24no—
137D4—22no—
138D4—942no—
139D4—944no—
140D4—1882no—
141D4C22⋊D4714yescomplemented
142C2×C4—22no—
143C2×C4—471no—
144C2×C4—471no—
145C2×C4—472no—
146C2×C4—471no—
147C2×C4—472no—
148C2×C4—944no—
149C2×C4—942no—
150C2×C4—1882no—
151C2×C4C22×D4711yescharacteristic
152C2×C4C22×D4711yescharacteristic
153C22—21no—
154C22—22no—
155C22—22no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—941no—
162C22—941no—
163C22—941no—
164C22#1062535212yescomplemented
165C22C2×C22⋊D4714yes—
166C22C23×D4711yescharacteristic
167C4—21no—
168C4—941no—
169C4—942no—
170C4—941no—
171C4—941no—
172C4—942no—
173C4C2×C22⋊D4712yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—1881no—
178C2C22×C22⋊D4711yescharacteristic
179C2C2×#1062535211yescharacteristic
180C2#1309406911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
FittingC22×D4×C47C2
hypercenterC22×D4D47
hypocenterC47#546
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10625352C2semidirect
2. #13094011C2semidirect
3. #13094005C2semidirect
4. #13094003C2semidirect
5. #13093996C2semidirect
6. #13093995C2semidirect
7. #13093993C2semidirect
8. D4×Dic47C2semidirect
9. C4×C22⋊D47C2semidirect
10. C2×C22⋊Dic47C2semidirect
11. C22×D4×C47C2semidirect
19. C2×C22⋊D47C22semidirect
20. C2×C22⋊D47C22semidirect
21. C22×Dic47C22semidirect
22. C22×Dic47C22semidirect
24. C2×C4×D47C22semidirect
25. C2×Dic94C22semidirect
28. C22⋊Dic47C22semidirect
29. C22⋊Dic47C22semidirect
30. C22⋊Dic47C22semidirect
31. C22⋊Dic47C22semidirect
32. (C2×D47)⋊C4C22semidirect
33. C4⋊Dic47C22semidirect
34. Dic47⋊C4C22semidirect
35. Dic47⋊C4C22semidirect
36. C4×Dic47C22semidirect
46. D4×C47D4semidirect
71. C22×C47#41semidirect
91. C47#546semidirect
93. C22×D4D47semidirect
141. D4C22⋊D47semidirect
164. C22#10625352semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106253522
#130940112
#130940052
#130940032
#130939962
#130939952
#130939932
D4×Dic472
C4×C22⋊D472
C2×C22⋊Dic472
C22×D4×C472
#54647