Finite Group Databasebeta

← #44529611

Subgroups — #44529611

Order 31168.

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×D1948C211yesmaximal, characteristic, complemented
2C2×D4×D487C211yesmaximal, characteristic, complemented
3#29510200C212yesmaximal, complemented
4#29510198C211yesmaximal, characteristic, complemented
5#29510190C212yesmaximal, complemented
6#29510188C212yesmaximal, complemented
7#29510185C211yesmaximal, characteristic, complemented
8#29510185C212yesmaximal, complemented
9#29510183C211yesmaximal, characteristic, complemented
10C22⋊C4×D487C211yesmaximal, characteristic, complemented
11#123×C487C211yesmaximal, characteristic, complemented
12C23×D487C2211yescharacteristic
13C23×D487C2211yescharacteristic, complemented
14C23×D487C2211yescharacteristic, complemented
15C2×D1948—24no—
16C2×D1948C2212yes—
17C2×D1948C2212yescomplemented
18C2×D1948C2211yescharacteristic, complemented
19C2×D1948C2212yescomplemented
20C2×C22⋊D487C2211yescharacteristic
21C2×C22⋊D487C2211yescharacteristic, complemented
22C2×C22⋊D487C2212yescomplemented
23D4×D487—24no—
24C2×C4×D487C2211yescharacteristic, complemented
25C2×C4×D487C2212yescomplemented
26Dic487⋊C4C2212yescomplemented
27C22⋊Dic487C2211yescharacteristic, complemented
28(C2×D487)⋊C4C2212yescomplemented
29(C2×D487)⋊C4C2212yescomplemented
30(C2×D487)⋊C4C2212yescomplemented
31(C2×D487)⋊C4C2212yescomplemented
32C2×D4×C487C2211yescharacteristic
33C22×C4×C487C2211yescharacteristic, complemented
34C4⋊C4×C487C2212yescomplemented
35C22⋊C4×C487C2211yescharacteristic, complemented
36C22⋊C4×C487C2212yescomplemented
37C22×D487—22no—
38C22×D487—22no—
39C22×D487—42no—
40C22×D487—42no—
41C22×D487—42no—
42C22×D487D414yescomplemented
43C22×D487C2311yescharacteristic
44C22×D487C2312yes—
45C22×D487C2311yescharacteristic
46C22×D487C2311yescharacteristic
47D1948—22no—
48D1948—24no—
49D1948—24no—
50D1948—42no—
51C22⋊D487—22no—
52C22⋊D487—22no—
53C22⋊D487—42no—
54C2×Dic487C2312yes—
55C2×Dic487C2311yescharacteristic
56C4×D487—22no—
57C4×D487—42no—
58C23×C487C2311yescharacteristic
59C23×C487C2311yescharacteristic
60D4×C487—22no—
61C2×C4×C487—22no—
62C2×C4×C487C2312yes—
63C2×C4×C487C2312yes—
64C2×C4×C487C2311yescharacteristic
65C22×C487—22no—
66C22×C487—21no—
67C22×C487—22no—
68C22×C487C2×D412yes—
69C22×C487C2411yescharacteristic
70C2×D487—22no—
71C2×D487—22no—
72C2×D487—21no—
73C2×D487—22no—
74C2×D487—22no—
75C2×D487—22no—
76C2×D487—22no—
77C2×D487—44no—
78C2×D487—44no—
79C2×D487—44no—
80C2×D487C2×D412yes—
81C2×D487C2×D412yes—
82C4×C487—22no—
83C4×C487—21no—
84C4×C487—22no—
85Dic487—21no—
86Dic487—22no—
87C2×C487—22no—
88C2×C487—41no—
89C2×C487C22×D411yescharacteristic
90C2×C487H(5,𝔽2)12yes—
91D487—22no—
92D487—22no—
93D487—41no—
94D487—42no—
95C487#53411yescharacteristic, complemented, Sylow
96#534—4871nomaximal, Sylow
97C22×D4—4871no—
98C22×D4—4871no—
99#123—4871no—
100#123—4872no—
101#123D48711yescharacteristic, complemented
102#121—4872no—
103#121—4872no—
104#120—4871no—
105#120—4872no—
106#120—4871no—
107C2×C22⋊C4—4871no—
108C24—4871no—
109C24—4871no—
110C24—4871no—
111C2×D4—9744no—
112C2×D4—9744no—
113C2×D4—4872no—
114C2×D4—4871no—
115C2×D4—4871no—
116C2×D4—4872no—
117C2×D4—4872no—
118C2×D4—4871no—
119C2×D4—4872no—
120C2×D4C2×D48711yescharacteristic
121C22×C4—4872no—
122C22×C4—4871no—
123C22×C4C2×D48711yescharacteristic, complemented
124C4⋊C4—4872no—
125C4⋊C4C2×D48712yescomplemented
126C22⋊C4—4871no—
127C22⋊C4—4872no—
128C22⋊C4—4872no—
129C22⋊C4—4872no—
130C22⋊C4—4872no—
131C22⋊C4C2×D48711yescharacteristic, complemented
132C22⋊C4C2×D48712yescomplemented
133C23—19482no—
134C23—19482no—
135C23—19482no—
136C23—9742no—
137C23—9742no—
138C23—4874no—
139C23—4872no—
140C23—4871no—
141C23—4871no—
142C23—4871no—
143C23C22×D48711yescharacteristic
144C23C22×D48711yescharacteristic
145D4—22no—
146D4—19482no—
147D4—19482no—
148D4—9744no—
149D4—9744no—
150D4—9742no—
151D4—9742no—
152D4—9742no—
153C2×C4—22no—
154C2×C4—19482no—
155C2×C4—9742no—
156C2×C4—4872no—
157C2×C4—4871no—
158C2×C4C22×D48712yes—
159C2×C4C22×D48711yescharacteristic
160C2×C4C22×D48712yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—19484no—
165C22—19484no—
166C22—19484no—
167C22—9742no—
168C22—9741no—
169C22—9742no—
170C22—9742no—
171C22—9742no—
172C22—9742no—
173C22—9742no—
174C22—4872no—
175C22—4872no—
176C22D4×D48712yes—
177C22C23×D48711yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—9741no—
182C4—9742no—
183C2—22no—
184C2—41no—
185C2—19482no—
186C2—19481no—
187C2—9742no—
188C2—9742no—
189C2C2×D4×D48711yescharacteristic
190C2#2951026112yes—
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
Fitting#123×C487C2
hypercenter#123D487
hypocenterC487#534
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D1948C2semidirect
2. C2×D4×D487C2semidirect
3. #29510200C2semidirect
4. #29510198C2semidirect
5. #29510190C2semidirect
6. #29510188C2semidirect
7. #29510185C2semidirect
8. #29510185C2semidirect
9. #29510183C2semidirect
10. C22⋊C4×D487C2semidirect
11. #123×C487C2semidirect
13. C23×D487C22semidirect
14. C23×D487C22semidirect
17. C2×D1948C22semidirect
18. C2×D1948C22semidirect
19. C2×D1948C22semidirect
21. C2×C22⋊D487C22semidirect
22. C2×C22⋊D487C22semidirect
24. C2×C4×D487C22semidirect
25. C2×C4×D487C22semidirect
26. Dic487⋊C4C22semidirect
27. C22⋊Dic487C22semidirect
28. (C2×D487)⋊C4C22semidirect
29. (C2×D487)⋊C4C22semidirect
30. (C2×D487)⋊C4C22semidirect
31. (C2×D487)⋊C4C22semidirect
33. C22×C4×C487C22semidirect
34. C4⋊C4×C487C22semidirect
35. C22⋊C4×C487C22semidirect
36. C22⋊C4×C487C22semidirect
42. C22×D487D4semidirect
95. C487#534semidirect
101. #123D487semidirect
123. C22×C4C2×D487semidirect
125. C4⋊C4C2×D487semidirect
131. C22⋊C4C2×D487semidirect
132. C22⋊C4C2×D487semidirect

Maximal subgroups

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

subgroupindex
C22×D19482
C2×D4×D4872
#295102002
#295101982
#295101902
#295101882
#295101852
#295101832
C22⋊C4×D4872
#123×C4872
#534487