Finite Group Databasebeta

← #15689684

Subgroups — #15689684

Order 3008.

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

normal subgroups only

This group has 346 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
1C22×D188C211yesmaximal, characteristic, complemented
2C2×D4×D47C211yesmaximal, characteristic, complemented
3#13094009C212yesmaximal, complemented
4#13094007C211yesmaximal, characteristic, complemented
5#13093999C212yesmaximal, complemented
6#13093997C212yesmaximal, complemented
7#13093994C212yesmaximal, complemented
8#13093994C211yesmaximal, characteristic, complemented
9#13093992C211yesmaximal, characteristic, complemented
10C22⋊C4×D47C211yesmaximal, characteristic, complemented
11#123×C47C211yesmaximal, characteristic, complemented
12C23×D47C2211yescharacteristic
13C23×D47C2211yescharacteristic, complemented
14C23×D47C2211yescharacteristic, complemented
15C2×D4×C47C2211yescharacteristic
16C22×C4×C47C2211yescharacteristic, complemented
17C2×C22⋊D47C2211yescharacteristic
18C2×C22⋊D47C2211yescharacteristic, complemented
19C2×C22⋊D47C2212yescomplemented
20D4×D47—24no—
21C2×D188—24no—
22C2×D188C2212yes—
23C2×D188C2212yescomplemented
24C2×D188C2211yescharacteristic, complemented
25C2×D188C2212yescomplemented
26C2×C4×D47C2211yescharacteristic, complemented
27C2×C4×D47C2212yescomplemented
28C4⋊C4×C47C2212yescomplemented
29C22⋊C4×C47C2211yescharacteristic, complemented
30C22⋊C4×C47C2212yescomplemented
31C22⋊Dic47C2211yescharacteristic, complemented
32(C2×D47)⋊C4C2212yescomplemented
33(C2×D47)⋊C4C2212yescomplemented
34(C2×D47)⋊C4C2212yescomplemented
35(C2×D47)⋊C4C2212yescomplemented
36Dic47⋊C4C2212yescomplemented
37C23×C47C2311yescharacteristic
38C23×C47C2311yescharacteristic
39C22×D47—22no—
40C22×D47—22no—
41C22×D47—42no—
42C22×D47—42no—
43C22×D47—42no—
44C22×D47D414yescomplemented
45C22×D47C2312yes—
46C22×D47C2311yescharacteristic
47C22×D47C2311yescharacteristic
48C22×D47C2311yescharacteristic
49D4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47C2312yes—
52C2×C4×C47C2312yes—
53C2×C4×C47C2311yescharacteristic
54C22⋊D47—22no—
55C22⋊D47—22no—
56C22⋊D47—42no—
57C2×Dic47C2311yescharacteristic
58C2×Dic47C2312yes—
59D188—24no—
60D188—24no—
61D188—22no—
62D188—42no—
63C4×D47—22no—
64C4×D47—42no—
65C22×C47—22no—
66C22×C47—21no—
67C22×C47—22no—
68C22×C47C2×D412yes—
69C22×C47C2411yescharacteristic
70C2×D47—22no—
71C2×D47—22no—
72C2×D47—22no—
73C2×D47—21no—
74C2×D47—22no—
75C2×D47—22no—
76C2×D47—22no—
77C2×D47—44no—
78C2×D47—44no—
79C2×D47—44no—
80C2×D47C2×D412yes—
81C2×D47C2×D412yes—
82C4×C47—21no—
83C4×C47—22no—
84C4×C47—22no—
85Dic47—21no—
86Dic47—22no—
87C2×C47—22no—
88C2×C47—41no—
89C2×C47C22×D411yescharacteristic
90C2×C47H(5,𝔽2)12yes—
91D47—22no—
92D47—22no—
93D47—42no—
94D47—41no—
95#534—471nomaximal, Sylow
96C47#53411yescharacteristic, complemented, Sylow
97C22×D4—471no—
98C22×D4—471no—
99#123—471no—
100#123—472no—
101#123D4711yescharacteristic, complemented
102#121—472no—
103#121—472no—
104#120—471no—
105#120—472no—
106#120—471no—
107C2×C22⋊C4—471no—
108C24—471no—
109C24—471no—
110C24—471no—
111C2×D4—471no—
112C2×D4—471no—
113C2×D4—472no—
114C2×D4—472no—
115C2×D4—471no—
116C2×D4—472no—
117C2×D4—472no—
118C2×D4—944no—
119C2×D4—944no—
120C2×D4C2×D4711yescharacteristic
121C22×C4—471no—
122C22×C4—472no—
123C22×C4C2×D4711yescharacteristic, complemented
124C4⋊C4—472no—
125C4⋊C4C2×D4712yescomplemented
126C22⋊C4—471no—
127C22⋊C4—472no—
128C22⋊C4—472no—
129C22⋊C4—472no—
130C22⋊C4—472no—
131C22⋊C4C2×D4711yescharacteristic, complemented
132C22⋊C4C2×D4712yescomplemented
133C23—471no—
134C23—471no—
135C23—474no—
136C23—472no—
137C23—471no—
138C23—942no—
139C23—942no—
140C23—1882no—
141C23—1882no—
142C23—1882no—
143C23C22×D4711yescharacteristic
144C23C22×D4711yescharacteristic
145D4—22no—
146D4—944no—
147D4—944no—
148D4—942no—
149D4—942no—
150D4—942no—
151D4—1882no—
152D4—1882no—
153C2×C4—22no—
154C2×C4—472no—
155C2×C4—471no—
156C2×C4—942no—
157C2×C4—1882no—
158C2×C4C22×D4712yes—
159C2×C4C22×D4711yescharacteristic
160C2×C4C22×D4712yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—472no—
165C22—472no—
166C22—942no—
167C22—942no—
168C22—942no—
169C22—941no—
170C22—942no—
171C22—942no—
172C22—942no—
173C22—1884no—
174C22—1884no—
175C22—1884no—
176C22D4×D4712yes—
177C22C23×D4711yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—941no—
182C4—942no—
183C2—22no—
184C2—41no—
185C2—942no—
186C2—942no—
187C2—1882no—
188C2—1881no—
189C2C2×D4×D4711yescharacteristic
190C2#1309407012yes—
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#123×C47C2
hypercenter#123D47
hypocenterC47#534
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D188C2semidirect
2. C2×D4×D47C2semidirect
3. #13094009C2semidirect
4. #13094007C2semidirect
5. #13093999C2semidirect
6. #13093997C2semidirect
7. #13093994C2semidirect
8. #13093994C2semidirect
9. #13093992C2semidirect
10. C22⋊C4×D47C2semidirect
11. #123×C47C2semidirect
13. C23×D47C22semidirect
14. C23×D47C22semidirect
16. C22×C4×C47C22semidirect
18. C2×C22⋊D47C22semidirect
19. C2×C22⋊D47C22semidirect
23. C2×D188C22semidirect
24. C2×D188C22semidirect
25. C2×D188C22semidirect
26. C2×C4×D47C22semidirect
27. C2×C4×D47C22semidirect
28. C4⋊C4×C47C22semidirect
29. C22⋊C4×C47C22semidirect
30. C22⋊C4×C47C22semidirect
31. C22⋊Dic47C22semidirect
32. (C2×D47)⋊C4C22semidirect
33. (C2×D47)⋊C4C22semidirect
34. (C2×D47)⋊C4C22semidirect
35. (C2×D47)⋊C4C22semidirect
36. Dic47⋊C4C22semidirect
44. C22×D47D4semidirect
96. C47#534semidirect
101. #123D47semidirect
123. C22×C4C2×D47semidirect
125. C4⋊C4C2×D47semidirect
131. C22⋊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
C22×D1882
C2×D4×D472
#130940092
#130940072
#130939992
#130939972
#130939942
#130939922
C22⋊C4×D472
#123×C472
#53447