Finite Group Databasebeta

← #44529615

Subgroups — #44529615

Order 31168.

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×#21441260C211yesmaximal, characteristic, complemented
2C22×C22⋊D487C211yesmaximal, characteristic, complemented
3#29510211C212yesmaximal, complemented
4#29510201C212yesmaximal, complemented
5#29510188C212yesmaximal, complemented
6#29510187C212yesmaximal, complemented
7#29510185C211yesmaximal, characteristic, complemented
8#29510184C211yesmaximal, characteristic, complemented
9#29510183C211yesmaximal, characteristic, complemented
10#29510171C211yesmaximal, characteristic, complemented
11#120×C487C211yesmaximal, characteristic, complemented
12C23×D487C2211yescharacteristic
13#21441260—24no—
14C2×Dic974C2211yescharacteristic, complemented
15C2×D1948C2212yescomplemented
16C2×C22⋊D487—24no—
17C2×C22⋊D487C2211yescharacteristic
18C2×C22⋊D487C2212yes—
19C2×C22⋊D487C2212yes—
20C2×C22⋊D487C2211yescharacteristic, complemented
21C2×C22⋊D487C2212yescomplemented
22C2×C22⋊D487C2212yescomplemented
23C22×Dic487C2211yescharacteristic
24C22×Dic487C2211yescharacteristic, complemented
25C2×C4×D487C2211yescharacteristic, complemented
26Dic487⋊C4C2212yescomplemented
27C22⋊Dic487C2211yescharacteristic
28C22⋊Dic487C2212yescomplemented
29(C2×D487)⋊C4C2212yescomplemented
30(C2×D487)⋊C4C2212yescomplemented
31C4×Dic487C2212yescomplemented
32C24×C487C2211yescharacteristic
33C2×D4×C487C2211yescharacteristic
34C2×D4×C487C2212yescomplemented
35C22⋊C4×C487C2211yescharacteristic
36C22⋊C4×C487C2212yescomplemented
37C22×D487—22no—
38C22×D487—42no—
39C22×D487C2312yes—
40C22×D487C2311yescharacteristic
41Dic974—22no—
42D1948—42no—
43C22⋊D487—22no—
44C22⋊D487—24no—
45C22⋊D487—24no—
46C22⋊D487—22no—
47C22⋊D487—42no—
48C22⋊D487—42no—
49C2×Dic487—22no—
50C2×Dic487D414yescomplemented
51C2×Dic487C2312yes—
52C2×Dic487C2311yescharacteristic
53C2×Dic487C2311yescharacteristic
54C2×Dic487C2311yescharacteristic
55C4×D487—22no—
56C23×C487—22no—
57C23×C487—42no—
58C23×C487C2312yes—
59C23×C487C2311yescharacteristic
60C23×C487C2311yescharacteristic
61D4×C487—22no—
62D4×C487—42no—
63C2×C4×C487C2312yes—
64C2×C4×C487C2311yescharacteristic
65C22×C487—22no—
66C22×C487—21no—
67C22×C487—22no—
68C22×C487—22no—
69C22×C487—22no—
70C22×C487—22no—
71C22×C487—44no—
72C22×C487C2×D412yes—
73C22×C487C2411yescharacteristic
74C2×D487—21no—
75C2×D487—22no—
76C2×D487—22no—
77C2×D487—22no—
78C2×D487—22no—
79C2×D487—44no—
80C4×C487—21no—
81C4×C487—22no—
82Dic487—21no—
83Dic487—22no—
84Dic487C2×D412yes—
85Dic487C2×D412yes—
86C2×C487—22no—
87C2×C487—41no—
88C2×C487—42no—
89C2×C487C22×D411yescharacteristic
90C2×C487H(5,𝔽2)12yes—
91D487—41no—
92D487—42no—
93C487#53511yescharacteristic, complemented, Sylow
94#535—4871nomaximal, Sylow
95C2×#41—4871no—
96C22×D4—4871no—
97#127—4872no—
98#124—4872no—
99#121—4872no—
100#121—4872no—
101#120—4871no—
102#120—4871no—
103#120—4871no—
104#120D48711yescharacteristic, complemented
105#117—4871no—
106C24—4871no—
107C24C2×D48711yescharacteristic
108#41—9744no—
109C2×Q8—4871no—
110C2×D4—9744no—
111C2×D4—4872no—
112C2×D4—4872no—
113C2×D4—4871no—
114C2×D4—4872no—
115C2×D4—4872no—
116C2×D4—4871no—
117C2×D4—4872no—
118C2×D4C2×D48711yescharacteristic
119C2×D4C2×D48712yescomplemented
120C22×C4—4871no—
121C22×C4—4871no—
122C22×C4—4871no—
123C4⋊C4—4872no—
124C22⋊C4—4871no—
125C22⋊C4—4872no—
126C22⋊C4—4872no—
127C22⋊C4—4872no—
128C22⋊C4C2×D48711yescharacteristic
129C22⋊C4C2×D48712yescomplemented
130C42—4872no—
131C23—22no—
132C23—42no—
133C23—19482no—
134C23—9742no—
135C23—4872no—
136C23—4871no—
137C23C22×D48712yes—
138C23C22×D48711yescharacteristic
139C23C22×D48711yescharacteristic
140Q8—9742no—
141D4—22no—
142D4—42no—
143D4—19482no—
144D4—19482no—
145D4—19482no—
146D4—9742no—
147D4—9744no—
148D4—9744no—
149D4—9742no—
150C2×C4—9742no—
151C2×C4—9742no—
152C2×C4—4872no—
153C2×C4—4871no—
154C2×C4—4874no—
155C2×C4—4871no—
156C2×C4—4871no—
157C2×C4C22×D48712yes—
158C2×C4C22×D48711yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—19484no—
167C22—9741no—
168C22—9742no—
169C22—9742no—
170C22—9742no—
171C22—9742no—
172C22D4×D48712yes—
173C22C23×D48711yescharacteristic
174C4—21no—
175C4—22no—
176C4—9741no—
177C4—9742no—
178C4—4872no—
179C4—4872no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—19482no—
184C2—19481no—
185C2C2×D4×D48711yescharacteristic
186C2#2951026012yes—
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
Fitting#120×C487C2
hypercenter#120D487
hypocenterC487#535
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#21441260C2semidirect
2. C22×C22⋊D487C2semidirect
3. #29510211C2semidirect
4. #29510201C2semidirect
5. #29510188C2semidirect
6. #29510187C2semidirect
7. #29510185C2semidirect
8. #29510184C2semidirect
9. #29510183C2semidirect
10. #29510171C2semidirect
11. #120×C487C2semidirect
14. C2×Dic974C22semidirect
15. C2×D1948C22semidirect
20. C2×C22⋊D487C22semidirect
21. C2×C22⋊D487C22semidirect
22. C2×C22⋊D487C22semidirect
24. C22×Dic487C22semidirect
25. C2×C4×D487C22semidirect
26. Dic487⋊C4C22semidirect
28. C22⋊Dic487C22semidirect
29. (C2×D487)⋊C4C22semidirect
30. (C2×D487)⋊C4C22semidirect
31. C4×Dic487C22semidirect
34. C2×D4×C487C22semidirect
36. C22⋊C4×C487C22semidirect
50. C2×Dic487D4semidirect
93. C487#535semidirect
104. #120D487semidirect
119. C2×D4C2×D487semidirect
129. C22⋊C4C2×D487semidirect

Maximal subgroups

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

subgroupindex
C2×#214412602
C22×C22⋊D4872
#295102112
#295102012
#295101882
#295101872
#295101852
#295101842
#295101832
#295101712
#120×C4872
#535487