Finite Group Databasebeta

← #15689689

Subgroups — #15689689

Order 3008.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10625350C211yesmaximal, characteristic, complemented
2C2×D4×D47C211yesmaximal, characteristic, complemented
3#13094020C212yesmaximal, complemented
4#13094010C212yesmaximal, complemented
5#13093999C211yesmaximal, characteristic, complemented
6#13093998C211yesmaximal, characteristic, complemented
7#13093995C211yesmaximal, characteristic, complemented
8#13093994C212yesmaximal, complemented
9#13093992C212yesmaximal, complemented
10#13093982C211yesmaximal, characteristic, complemented
11#121×C47C211yesmaximal, characteristic, complemented
12C23×D47C2212yes—
13C2×D4×C47C2211yescharacteristic
14C2×D4×C47C2212yescomplemented
15C22×C4×C47C2211yescharacteristic, complemented
16C2×C22⋊D47C2211yescharacteristic
17C2×C22⋊D47C2212yes—
18C2×C22⋊D47C2211yescharacteristic, complemented
19C2×C22⋊D47C2212yescomplemented
20C2×C22⋊D47C2212yescomplemented
21D4×D47—24no—
22#10625350—24no—
23C2×D188C2211yescharacteristic
24C2×D188C2211yescharacteristic
25C2×D188C2212yescomplemented
26C2×C4×D47C2211yescharacteristic
27C2×C4×D47C2211yescharacteristic, complemented
28C2×Dic94C2211yescharacteristic, complemented
29C4⋊C4×C47C2211yescharacteristic, complemented
30C22⋊C4×C47C2212yescomplemented
31C22⋊Dic47C2212yescomplemented
32(C2×D47)⋊C4C2212yes—
33(C2×D47)⋊C4C2212yescomplemented
34(C2×D47)⋊C4C2212yescomplemented
35C4⋊Dic47C2211yescharacteristic, complemented
36C4×Dic47C2212yescomplemented
37C23×C47C2312yes—
38C23×C47C2311yescharacteristic
39C22×D47—24no—
40C22×D47—42no—
41C22×D47—42no—
42C22×D47C2312yes—
43C22×D47C2311yescharacteristic
44C22×D47C2311yescharacteristic
45D4×C47—22no—
46D4×C47—42no—
47C2×C4×C47—22no—
48C2×C4×C47C2312yes—
49C2×C4×C47C2311yescharacteristic
50C2×C4×C47C2311yescharacteristic
51C22⋊D47—22no—
52C22⋊D47—22no—
53C22⋊D47—24no—
54C22⋊D47—42no—
55C22⋊D47—42no—
56C2×Dic47C2312yes—
57C2×Dic47C2311yescharacteristic
58C2×Dic47C2311yescharacteristic
59D188—22no—
60D188—22no—
61D188—42no—
62C4×D47—22no—
63C4×D47D414yescomplemented
64Dic94—22no—
65C22×C47—21no—
66C22×C47—22no—
67C22×C47—21no—
68C22×C47—22no—
69C22×C47—21no—
70C22×C47—22no—
71C22×C47C2411yescharacteristic
72C2×D47—21no—
73C2×D47—21no—
74C2×D47—21no—
75C2×D47—22no—
76C2×D47—21no—
77C2×D47—22no—
78C2×D47—21no—
79C2×D47—22no—
80C2×D47—48no—
81C2×D47C2×D412yes—
82C4×C47—21no—
83C4×C47—22no—
84C4×C47C2×D412yes—
85Dic47—21no—
86Dic47—22no—
87Dic47C2×D412yes—
88C2×C47—42no—
89C2×C47—41no—
90C2×C47C22×D411yescharacteristic
91C2×C47H(5,𝔽2)11yescharacteristic
92C2×C47H(5,𝔽2)11yescharacteristic
93D47—22no—
94D47—41no—
95D47—42no—
96#535—471nomaximal, Sylow
97C47#53511yescharacteristic, complemented, Sylow
98C2×#41—471no—
99C22×D4—471no—
100#127—472no—
101#124—472no—
102#121—471no—
103#121—471no—
104#121—471no—
105#121D4711yescharacteristic, complemented
106#120—472no—
107#120—472no—
108#117—471no—
109C24—472no—
110#41—944no—
111C2×Q8—471no—
112C2×D4—471no—
113C2×D4—472no—
114C2×D4—471no—
115C2×D4—472no—
116C2×D4—472no—
117C2×D4—471no—
118C2×D4—471no—
119C2×D4—472no—
120C2×D4—944no—
121C2×D4C2×D4711yescharacteristic
122C2×D4C2×D4712yescomplemented
123C22×C4—471no—
124C22×C4—471no—
125C22×C4C2×D4711yescharacteristic, complemented
126C4⋊C4—471no—
127C4⋊C4C2×D4711yescharacteristic, complemented
128C22⋊C4—472no—
129C22⋊C4—472no—
130C22⋊C4—472no—
131C22⋊C4—472no—
132C22⋊C4C2×D4712yescomplemented
133C42—472no—
134C23—471no—
135C23—472no—
136C23—471no—
137C23—944no—
138C23—1882no—
139C23—1882no—
140C23C22×D4712yes—
141C23C22×D4711yescharacteristic
142Q8—942no—
143D4—22no—
144D4—42no—
145D4—942no—
146D4—944no—
147D4—942no—
148D4—942no—
149D4—942no—
150D4—1882no—
151D4—1882no—
152D4—1882no—
153C2×C4—22no—
154C2×C4—471no—
155C2×C4—474no—
156C2×C4—472no—
157C2×C4—471no—
158C2×C4—942no—
159C2×C4C22×D4712yes—
160C2×C4C22×D4711yescharacteristic
161C2×C4C22×D4711yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—472no—
169C22—941no—
170C22—941no—
171C22—941no—
172C22—942no—
173C22—941no—
174C22—942no—
175C22—941no—
176C22—942no—
177C22—1888no—
178C22C23×D4711yescharacteristic
179C4—21no—
180C4—22no—
181C4—472no—
182C4—941no—
183C4—942no—
184C4D4×D4712yes—
185C2—42no—
186C2—41no—
187C2—942no—
188C2—1882no—
189C2—1881no—
190C2C2×D4×D4711yescharacteristic
191C2#1309406911yescharacteristic
192C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#121×C47C2
hypercenter#121D47
hypocenterC47#535
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10625350C2semidirect
2. C2×D4×D47C2semidirect
3. #13094020C2semidirect
4. #13094010C2semidirect
5. #13093999C2semidirect
6. #13093998C2semidirect
7. #13093995C2semidirect
8. #13093994C2semidirect
9. #13093992C2semidirect
10. #13093982C2semidirect
11. #121×C47C2semidirect
14. C2×D4×C47C22semidirect
15. C22×C4×C47C22semidirect
18. C2×C22⋊D47C22semidirect
19. C2×C22⋊D47C22semidirect
20. C2×C22⋊D47C22semidirect
25. C2×D188C22semidirect
27. C2×C4×D47C22semidirect
28. C2×Dic94C22semidirect
29. C4⋊C4×C47C22semidirect
30. C22⋊C4×C47C22semidirect
31. C22⋊Dic47C22semidirect
33. (C2×D47)⋊C4C22semidirect
34. (C2×D47)⋊C4C22semidirect
35. C4⋊Dic47C22semidirect
36. C4×Dic47C22semidirect
63. C4×D47D4semidirect
97. C47#535semidirect
105. #121D47semidirect
122. C2×D4C2×D47semidirect
125. C22×C4C2×D47semidirect
127. C4⋊C4C2×D47semidirect
132. C22⋊C4C2×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#106253502
C2×D4×D472
#130940202
#130940102
#130939992
#130939982
#130939952
#130939942
#130939922
#130939822
#121×C472
#53547