Finite Group Databasebeta

← #44417249

Subgroups — #44417249

Order 29248.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×D4×D457C211yesmaximal, characteristic
2C4×D1828C211yesmaximal, characteristic, complemented
3D4×Dic457C211yesmaximal, characteristic, complemented
4#28410514C211yesmaximal, characteristic, complemented
5C4×C22⋊D457C212yesmaximal, complemented
6#28410512C212yesmaximal, complemented
7#28410510C211yesmaximal, characteristic, complemented
8#28410509C211yesmaximal, characteristic, complemented
9C2×#20300718C212yesmaximal, complemented
10C22⋊C4×D457C212yesmaximal, complemented
11C4×D4×C457C211yesmaximal, characteristic, complemented
12C23×D457C2212yes—
13C2×D1828C2211yescharacteristic
14C2×C22⋊D457C2212yes—
15D4×D457C418yescomplemented
16C22×Dic457C2212yescomplemented
17C2×C4×D457C2211yescharacteristic
18C2×C4×D457C2212yescomplemented
19C2×C4×D457C2212yescomplemented
20C4⋊Dic457C2211yescharacteristic, complemented
21#20300720C2211yescharacteristic, complemented
22#20300720C2211yescharacteristic, complemented
23C22⋊Dic457C2212yescomplemented
24#20300718C2211yescharacteristic
25#20300718C2212yes—
26#20300718C2211yescharacteristic
27#20300718C2212yescomplemented
28#20300718C2212yescomplemented
29C4×Dic457C2211yescharacteristic, complemented
30C4×Dic457C2212yescomplemented
31C2×D4×C457C2211yescharacteristic
32C22×C4×C457C2212yescomplemented
33C4⋊C4×C457C2211yescharacteristic, complemented
34C22⋊C4×C457C2212yescomplemented
35C42×C457C2211yescharacteristic, complemented
36C22×D457—42no—
37C22×D457—42no—
38C22×D457C2×C418yescomplemented
39C22×D457C2311yescharacteristic
40C22×D457C2312yes—
41D1828C2×C414yescomplemented
42C22⋊D457C2×C418yescomplemented
43C2×Dic457—42no—
44C2×Dic457C2311yescharacteristic
45C2×Dic457C2312yes—
46C2×Dic457C2311yescharacteristic
47C2×Dic457C2311yescharacteristic
48C4×D457—42no—
49C4×D457—42no—
50C4×D457C2×C414yescomplemented
51C23×C457C2312yes—
52D4×C457C2×C414yescomplemented
53C2×C4×C457—42no—
54C2×C4×C457C2311yescharacteristic
55C2×C4×C457C2311yescharacteristic
56C2×C4×C457C2312yes—
57C2×C4×C457C2311yescharacteristic
58C22×C457—22no—
59C22×C457—22no—
60C22×C457C22×C414yes—
61C22×C457C2411yescharacteristic
62C2×D457—22no—
63C2×D457—22no—
64C2×D457—21no—
65C2×D457—21no—
66C2×D457—48no—
67C2×D457C22×C412yes—
68C2×D457C22×C414yes—
69C4×C457—21no—
70C4×C457—22no—
71C4×C457—21no—
72C4×C457C22×C412yes—
73Dic457—21no—
74Dic457—22no—
75Dic457—21no—
76Dic457C22×C412yes—
77C2×C457—24no—
78C2×C457C23×C411yescharacteristic
79C2×C457H(5,𝔽2)11yescharacteristic
80C2×C457H(5,𝔽2)11yescharacteristic
81D457—22no—
82D457—24no—
83C457#51811yescharacteristic, complemented, Sylow
84#518—4571nomaximal, Sylow
85C22×D4—4571no—
86C4×D4—4571no—
87C4×D4—4572no—
88C4×D4—4571no—
89C4×D4—4572no—
90C4×D4—4571no—
91C4×D4D45711yescharacteristic, complemented
92#117—4571no—
93#117—4571no—
94C2×C22⋊C4—4572no—
95C2×C22⋊C4—4572no—
96C24—4572no—
97C2×D4—4572no—
98C2×D4—4578no—
99C2×D4—4571no—
100C2×D4C2×D45711yescharacteristic
101C22×C4—4572no—
102C22×C4—4572no—
103C22×C4—4572no—
104C22×C4—4571no—
105C22×C4C2×D45712yescomplemented
106C4⋊C4—4571no—
107C4⋊C4—4571no—
108C4⋊C4—4571no—
109C4⋊C4C2×D45711yescharacteristic, complemented
110C22⋊C4—4572no—
111C22⋊C4—4572no—
112C22⋊C4—4571no—
113C22⋊C4—4571no—
114C22⋊C4—4572no—
115C22⋊C4—4572no—
116C22⋊C4C2×D45712yescomplemented
117C42—4571no—
118C42—4572no—
119C42C2×D45711yescharacteristic, complemented
120C23—18282no—
121C23—18282no—
122C23—4578no—
123C23—4571no—
124C23—4572no—
125C23C22×D45712yes—
126D4—4578no—
127D4—4574no—
128D4C4×D45714yescomplemented
129C2×C4—42no—
130C2×C4—18282no—
131C2×C4—18282no—
132C2×C4—18282no—
133C2×C4—4571no—
134C2×C4—4572no—
135C2×C4—4571no—
136C2×C4—4571no—
137C2×C4—4574no—
138C2×C4C22×D45712yes—
139C2×C4C22×D45711yescharacteristic
140C2×C4C22×D45711yescharacteristic
141C2×C4C22×D45711yescharacteristic
142C22—22no—
143C22—22no—
144C22—18288no—
145C22—9142no—
146C22—9141no—
147C22—9142no—
148C22—9141no—
149C22—4572no—
150C22—4574no—
151C22C2×C4×D45714yes—
152C22C23×D45711yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—9141no—
157C4—9142no—
158C4—9141no—
159C4—4572no—
160C4C2×C4×D45712yes—
161C2—24no—
162C2—9142no—
163C2—9144no—
164C2C22×C4×D45711yescharacteristic
165C2#2841059711yescharacteristic
166C2#2841059811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D457
commutatorC2×C457C23×C4
FittingC4×D4×C457C2
socle, cosocleC22×C457C24
prime radicalC2×D4×D457C2
hypercenterC4×D4D457
hypocenterC457#518
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1828C2semidirect
3. D4×Dic457C2semidirect
4. #28410514C2semidirect
5. C4×C22⋊D457C2semidirect
6. #28410512C2semidirect
7. #28410510C2semidirect
8. #28410509C2semidirect
9. C2×#20300718C2semidirect
10. C22⋊C4×D457C2semidirect
11. C4×D4×C457C2semidirect
15. D4×D457C4semidirect
16. C22×Dic457C22semidirect
18. C2×C4×D457C22semidirect
19. C2×C4×D457C22semidirect
20. C4⋊Dic457C22semidirect
21. #20300720C22semidirect
22. #20300720C22semidirect
23. C22⋊Dic457C22semidirect
27. #20300718C22semidirect
28. #20300718C22semidirect
29. C4×Dic457C22semidirect
30. C4×Dic457C22semidirect
32. C22×C4×C457C22semidirect
33. C4⋊C4×C457C22semidirect
34. C22⋊C4×C457C22semidirect
35. C42×C457C22semidirect
38. C22×D457C2×C4semidirect
41. D1828C2×C4semidirect
42. C22⋊D457C2×C4semidirect
50. C4×D457C2×C4semidirect
52. D4×C457C2×C4semidirect
83. C457#518semidirect
91. C4×D4D457semidirect
105. C22×C4C2×D457semidirect
109. C4⋊C4C2×D457semidirect
116. C22⋊C4C2×D457semidirect
119. C42C2×D457semidirect
128. D4C4×D457semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4572
C4×D18282
D4×Dic4572
#284105142
C4×C22⋊D4572
#284105122
#284105102
#284105092
C2×#203007182
C22⋊C4×D4572
C4×D4×C4572
#518457