Finite Group Databasebeta

← #44529849

Subgroups — #44529849

Order 31168.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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×#21441262C211yesmaximal, characteristic, complemented
2#41×D487C211yesmaximal, characteristic, complemented
3#29510247C212yesmaximal, complemented
4#29510246C211yesmaximal, characteristic, complemented
5#29510243C211yesmaximal, characteristic, complemented
6#29510242C212yesmaximal, complemented
7#29510240C211yesmaximal, characteristic, complemented
8#29510238C212yesmaximal, complemented
9#29510236C212yesmaximal, complemented
10M16×D487C211yesmaximal, characteristic, complemented
11#137×C487C211yesmaximal, characteristic, complemented
12#21441262—21no—
13#21441262—21no—
14#21441262C2212yes—
15#21441262C2212yescomplemented
16#21441262C2211yescharacteristic, complemented
17#21441261—21no—
18#21441261C2211yescharacteristic
19#21441260—21no—
20#21441260C2211yescharacteristic, complemented
21Q8×D487C2211yescharacteristic, complemented
22C2×D1948—21no—
23C2×D1948C2211yescharacteristic, complemented
24D4×D487—21no—
25D4×D487C2211yescharacteristic, complemented
26C2×C4×D487—21no—
27C2×C4×D487—21no—
28C2×C4×D487C2211yescharacteristic
29#21441251C2212yescomplemented
30#21441250C2212yescomplemented
31#21441248C2212yescomplemented
32#21441248C2212yescomplemented
33D3896C2212yescomplemented
34#21441246C2212yescomplemented
35#21441245C2211yescharacteristic, complemented
36#21441244C2212yescomplemented
37C8×D487C2212yescomplemented
38#41×C487C2211yescharacteristic
39C2×Q8×C487C2211yescharacteristic, complemented
40Q16×C487C2212yescomplemented
41SD16×C487C2212yescomplemented
42M16×C487C2211yescharacteristic, complemented
43C22×D487—21no—
44C22×D487—21no—
45C22×D487D411yescharacteristic
46Dic974—21no—
47Dic974C2311yescharacteristic
48D1948—21no—
49D1948—22no—
50D1948—22no—
51D1948—21no—
52D1948C2312yes—
53D1948C2311yescharacteristic
54C22⋊D487—21no—
55C22⋊D487—21no—
56C22⋊D487—21no—
57C2×Dic487—21no—
58C2×Dic487D411yescharacteristic
59C4×D487—21no—
60C4×D487—21no—
61C4×D487—21no—
62C4×D487—22no—
63C4×D487—22no—
64C4×D487D411yescharacteristic
65C4×D487D411yescharacteristic
66C4×D487C2311yescharacteristic
67C4×D487C2311yescharacteristic
68C487⋊C8C2312yes—
69Q8×C487—21no—
70Q8×C487C2312yes—
71Q8×C487C2311yescharacteristic
72D4×C487—21no—
73D4×C487C2311yescharacteristic
74C2×C4×C487—21no—
75C2×C4×C487—21no—
76C2×C4×C487C2311yescharacteristic
77C8×C487C2312yes—
78C22×C487—21no—
79C22×C487C2×D411yescharacteristic
80C2×D487—21no—
81C2×D487—22no—
82C2×D487—41no—
83C2×D487—42no—
84C2×D487—42no—
85C2×D487C2×D411yescharacteristic
86C2×D487C2×D411yescharacteristic
87C4×C487—21no—
88C4×C487—22no—
89C4×C487C2×D411yescharacteristic
90C4×C487C2411yescharacteristic
91Dic487—21no—
92Dic487C2×D411yescharacteristic
93Dic487C2×D411yescharacteristic
94C2×C487—21no—
95C2×C487—41no—
96C2×C487C22×D411yescharacteristic
97D487—21no—
98D487—21no—
99D487—41no—
100D487—42no—
101C487#57511yescharacteristic, complemented, Sylow
102#575—4871nomaximal, Sylow
103C2×#41—4871no—
104C2×#41—4871no—
105#137—4871no—
106#137—4872no—
107#137D48711yescharacteristic, complemented
108AGL(1,ℤ/8)—4871no—
109AGL(1,ℤ/8)—4872no—
110AGL(1,ℤ/8)—4871no—
111#135—4872no—
112#135—4872no—
113C2×M16—4871no—
114#41—9741no—
115#41—9741no—
116#41—9741no—
117#41—9741no—
118#41—4871no—
119#41—4872no—
120#41—4872no—
121#41—4871no—
122#41—4871no—
123#41C2×D48711yescharacteristic
124C2×Q8—4871no—
125C2×Q8C2×D48711yescharacteristic, complemented
126C2×D4—9741no—
127C2×D4—9741no—
128C2×D4—4871no—
129C2×D4—4871no—
130C22×C4—9741no—
131C22×C4—9741no—
132C22×C4—4871no—
133Q16—4872no—
134Q16C2×D48712yescomplemented
135SD16—4872no—
136SD16—4872no—
137SD16—4872no—
138SD16C2×D48712yescomplemented
139D8—4872no—
140D8—4872no—
141M16—4871no—
142M16—4872no—
143M16C2×D48711yescharacteristic, complemented
144C2×C8—4872no—
145C23—9741no—
146C23—9741no—
147C23—4871no—
148Q8—21no—
149Q8—9741no—
150Q8—4871no—
151Q8C22×D48711yescharacteristic
152Q8C22×D48712yes—
153D4—21no—
154D4—9741no—
155D4—9742no—
156D4—9742no—
157D4—9741no—
158D4—9741no—
159D4—9741no—
160D4—9741no—
161D4—4872no—
162D4—4871no—
163D4C22×D48711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—9741no—
167C2×C4—9741no—
168C2×C4—9742no—
169C2×C4—9742no—
170C2×C4—9741no—
171C2×C4—9741no—
172C2×C4—4871no—
173C2×C4—4871no—
174C2×C4—4871no—
175C2×C4—4871no—
176C2×C4—4871no—
177C2×C4C22×D48711yescharacteristic
178C8—4872no—
179C8C22×D48712yes—
180C22—21no—
181C22—19482no—
182C22—19481no—
183C22—19482no—
184C22—9742no—
185C22—9741no—
186C22—4871no—
187C22—4871no—
188C22D4×D48711yescharacteristic
189C4—21no—
190C4—22no—
191C4—9741no—
192C4—4871no—
193C4—4871no—
194C4D4×D48711yescharacteristic
195C4C23×D48711yescharacteristic
196C2—21no—
197C2—41no—
198C2—19482no—
199C2—19481no—
200C2—9741no—
201C2—9741no—
202C2C2×D4×D48711yescharacteristic
subgroupG/H
centerC2C2×D4×D487
commutator, cosocleC4×C487C24
FrattiniC4C23×D487
Fitting#137×C487C2
socleC2×C487C22×D4
hypercenter#137D487
hypocenterC487#575
LCSG ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#21441262C2semidirect
2. #41×D487C2semidirect
3. #29510247C2semidirect
4. #29510246C2semidirect
5. #29510243C2semidirect
6. #29510242C2semidirect
7. #29510240C2semidirect
8. #29510238C2semidirect
9. #29510236C2semidirect
10. M16×D487C2semidirect
11. #137×C487C2semidirect
15. #21441262C22semidirect
16. #21441262C22semidirect
20. #21441260C22semidirect
21. Q8×D487C22semidirect
23. C2×D1948C22semidirect
25. D4×D487C22semidirect
29. #21441251C22semidirect
30. #21441250C22semidirect
31. #21441248C22semidirect
32. #21441248C22semidirect
33. D3896C22semidirect
34. #21441246C22semidirect
35. #21441245C22semidirect
36. #21441244C22semidirect
37. C8×D487C22semidirect
39. C2×Q8×C487C22semidirect
40. Q16×C487C22semidirect
41. SD16×C487C22semidirect
42. M16×C487C22semidirect
101. C487#575semidirect
107. #137D487semidirect
125. C2×Q8C2×D487semidirect
134. Q16C2×D487semidirect
138. SD16C2×D487semidirect
143. M16C2×D487semidirect

Maximal subgroups

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

subgroupindex
C2×#214412622
#41×D4872
#295102472
#295102462
#295102432
#295102422
#295102402
#295102382
#295102362
M16×D4872
#137×C4872
#575487