Finite Group Databasebeta

← #44529558

Subgroups — #44529558

Order 31168.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4×D487C211yesmaximal, characteristic, complemented
3#29510198C211yesmaximal, characteristic, complemented
4#29510193C212yesmaximal, complemented
5#29510188C212yesmaximal, complemented
6#29510185C211yesmaximal, characteristic, complemented
7#29510183C211yesmaximal, characteristic, complemented
8#29510177C212yesmaximal, complemented
9(C22⋊D487)⋊C4C212yesmaximal, complemented
10#29510171C211yesmaximal, characteristic, complemented
11#123×C487C211yesmaximal, characteristic, complemented
12C23×D487C2211yescharacteristic
13#21441260—24no—
14C2×Dic974C2211yescharacteristic, complemented
15C2×D1948C2212yes—
16C2×C22⋊D487C2212yes—
17C2×C22⋊D487C2211yescharacteristic
18C2×C22⋊D487C2211yescharacteristic, complemented
19C22×Dic487C2211yescharacteristic
20C22×Dic487C2211yescharacteristic, complemented
21C2×C4×D487—24no—
22C2×C4×D487C2212yes—
23C2×C4×D487C2212yes—
24C2×C4×D487C2211yescharacteristic, complemented
25Dic487⋊C4C2212yescomplemented
26Dic487⋊C4C2212yescomplemented
27C22⋊Dic487C2211yescharacteristic
28(C2×D487)⋊C4C2212yes—
29(C2×D487)⋊C4C2212yes—
30(C2×D487)⋊C4C2212yescomplemented
31C4×Dic487C2212yescomplemented
32C2×D4×C487C2211yescharacteristic
33C22×C4×C487C2211yescharacteristic
34C4⋊C4×C487C2212yescomplemented
35C22⋊C4×C487C2211yescharacteristic
36C22⋊C4×C487C2212yescomplemented
37C22×D487—22no—
38C22×D487—24no—
39C22×D487C2311yescharacteristic
40C22×D487C2312yes—
41Dic974—22no—
42D1948—24no—
43C22⋊D487—22no—
44C22⋊D487—24no—
45C22⋊D487—22no—
46C2×Dic487—22no—
47C2×Dic487D414yescomplemented
48C2×Dic487C2312yes—
49C2×Dic487C2311yescharacteristic
50C2×Dic487C2311yescharacteristic
51C2×Dic487C2311yescharacteristic
52C4×D487—24no—
53C4×D487—24no—
54C4×D487—22no—
55C23×C487C2311yescharacteristic
56C23×C487C2311yescharacteristic
57D4×C487—22no—
58C2×C4×C487—22no—
59C2×C4×C487C2312yes—
60C2×C4×C487C2312yes—
61C2×C4×C487C2311yescharacteristic
62C22×C487—22no—
63C22×C487—21no—
64C22×C487—22no—
65C22×C487C2×D412yes—
66C22×C487C2411yescharacteristic
67C2×D487—28no—
68C2×D487—22no—
69C2×D487—22no—
70C2×D487—21no—
71C2×D487—22no—
72C2×D487#4114yescomplemented
73C4×C487—22no—
74C4×C487—21no—
75C4×C487—22no—
76Dic487—21no—
77Dic487—22no—
78Dic487C2×D412yes—
79Dic487C2×D412yes—
80C2×C487—22no—
81C2×C487—41no—
82C2×C487C22×D411yescharacteristic
83C2×C487C2×#4112yes—
84D487—24no—
85D487—41no—
86C487#52511yescharacteristic, complemented, Sylow
87#525—4871nomaximal, Sylow
88C2×#41—4871no—
89C23×C4—4871no—
90#123—4871no—
91#123D48711yescharacteristic, complemented
92C22⋊Q8—4872no—
93#121—4872no—
94#120—4871no—
95#120—4871no—
96C4×D4—4872no—
97C4×D4—4872no—
98#117—4871no—
99C24—4871no—
100#41—9744no—
101C2×Q8—4871no—
102C2×D4—4872no—
103C2×D4—4871no—
104C2×D4—4871no—
105C2×D4—4872no—
106C2×D4C2×D48711yescharacteristic
107C22×C4—9744no—
108C22×C4—4871no—
109C22×C4—4872no—
110C22×C4—4871no—
111C22×C4—4872no—
112C22×C4—4871no—
113C22×C4C2×D48711yescharacteristic
114C4⋊C4—4872no—
115C4⋊C4—4872no—
116C4⋊C4C2×D48712yescomplemented
117C22⋊C4—4871no—
118C22⋊C4—4872no—
119C22⋊C4—4872no—
120C22⋊C4—4872no—
121C22⋊C4C2×D48711yescharacteristic
122C22⋊C4C2×D48712yescomplemented
123C42—4872no—
124C23—9744no—
125C23—9742no—
126C23—4871no—
127C23—4872no—
128C23C22×D48711yescharacteristic
129C23C22×D48711yescharacteristic
130Q8—9742no—
131D4—22no—
132D4—9744no—
133D4—9744no—
134D4—9742no—
135D4—9742no—
136C2×C4—22no—
137C2×C4—9744no—
138C2×C4—9744no—
139C2×C4—9742no—
140C2×C4—9742no—
141C2×C4—4872no—
142C2×C4—4871no—
143C2×C4—4874no—
144C2×C4—4871no—
145C2×C4—4871no—
146C2×C4C22×D48712yes—
147C2×C4C22×D48711yescharacteristic
148C2×C4C22×D48712yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—9748no—
153C22—9741no—
154C22—9742no—
155C22—9742no—
156C22—9742no—
157C22—4874no—
158C22D4×D48712yes—
159C22C23×D48711yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—9741no—
164C4—9742no—
165C4—4872no—
166C4—4872no—
167C2—22no—
168C2—41no—
169C2—19481no—
170C2—9744no—
171C2C2×D4×D48711yescharacteristic
172C2#41×D48712yes—
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
Fitting#123×C487C2
hypercenter#123D487
hypocenterC487#525
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#21441260C2semidirect
2. C22×C4×D487C2semidirect
3. #29510198C2semidirect
4. #29510193C2semidirect
5. #29510188C2semidirect
6. #29510185C2semidirect
7. #29510183C2semidirect
8. #29510177C2semidirect
9. (C22⋊D487)⋊C4C2semidirect
10. #29510171C2semidirect
11. #123×C487C2semidirect
14. C2×Dic974C22semidirect
18. C2×C22⋊D487C22semidirect
20. C22×Dic487C22semidirect
24. C2×C4×D487C22semidirect
25. Dic487⋊C4C22semidirect
26. Dic487⋊C4C22semidirect
30. (C2×D487)⋊C4C22semidirect
31. C4×Dic487C22semidirect
34. C4⋊C4×C487C22semidirect
36. C22⋊C4×C487C22semidirect
47. C2×Dic487D4semidirect
72. C2×D487#41semidirect
86. C487#525semidirect
91. #123D487semidirect
116. C4⋊C4C2×D487semidirect
122. 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×C4×D4872
#295101982
#295101932
#295101882
#295101852
#295101832
#295101772
(C22⋊D487)⋊C42
#295101712
#123×C4872
#525487