Finite Group Databasebeta

← #16854621

Subgroups — #16854621

Order 3968.

458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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
1#14521816C212yesmaximal, complemented
2#14521171C214yesmaximal, complemented
3#14521166C214yesmaximal, complemented
4#14521098C211yesmaximal, characteristic, complemented
5C2×#11758425C212yesmaximal, complemented
6M16×Dic31C211yesmaximal, characteristic, complemented
7C31×#575C211yesmaximal, characteristic
8C2×#41×C31C2212yes—
9C31×#137C414yescomplemented
10C31×AGL(1,ℤ/8)C414yescomplemented
11C31×#135C2214yes—
12C2×M16×C31C2211yescharacteristic
13#11758525—24no—
14#11758525C2218yescomplemented
15C2×C4×Dic31C2211yescharacteristic
16C2×#92474—24no—
17C2×#92474C2212yes—
18C2×#92474C2211yescharacteristic
19#11758425C2214yescomplemented
20#11758425C2214yescomplemented
21#11758407C2214yescomplemented
22#11758403C2212yescomplemented
23C8×Dic31C2212yescomplemented
24#41×C31—22no—
25#41×C31—22no—
26#41×C31C2×C414yes—
27#41×C31C2314yes—
28C2×Q8×C31C2×C412yes—
29C2×D4×C31—22no—
30C2×D4×C31C2×C412yes—
31C22×C4×C31—22no—
32C22×C4×C31C2311yescharacteristic
33C22×Dic31—21no—
34Q16×C31C2×C414yescomplemented
35SD16×C31C2×C418yescomplemented
36D8×C31C2×C414yescomplemented
37M16×C31C2×C414yes—
38C2×C8×C31C2312yes—
39C4×Dic31—21no—
40C4×Dic31C2311yescharacteristic
41C4×Dic31C2311yescharacteristic
42#92474—22no—
43#92474—28no—
44#92474D414yes—
45#92474C2314yes—
46C2×C31⋊C8—22no—
47C2×C31⋊C8—28no—
48C2×C31⋊C8C2312yes—
49C23×C31—22no—
50C23×C31#4111yescharacteristic
51Q8×C31—22no—
52Q8×C31C22×C414yes—
53D4×C31—24no—
54D4×C31—24no—
55D4×C31—22no—
56D4×C31C22×C414yes—
57C2×C4×C31—22no—
58C2×C4×C31—24no—
59C2×C4×C31—24no—
60C2×C4×C31C22×C412yes—
61C2×C4×C31C2×D412yes—
62C2×C4×C31#4111yescharacteristic
63C2×C4×C31C2411yescharacteristic
64C2×Dic31—21no—
65C2×Dic31—21no—
66C2×Dic31—42no—
67C8×C31C22×C414yes—
68C31⋊C8—24no—
69C31⋊C8C2×D414yes—
70#2956—311nomaximal, Sylow
71C22×C31—24no—
72C22×C31—41no—
73C22×C31—82no—
74C22×C31C4×D412yes—
75C22×C31C2×#4111yescharacteristic
76C4×C31—24no—
77C4×C31C4×D412yes—
78C4×C31C23×C411yescharacteristic
79C4×C31C22×D411yescharacteristic
80Dic31—22no—
81Dic31—41no—
82#575D3111yescharacteristic
83#568—312no—
84#444—314no—
85#443—314no—
86#430—311no—
87C2×#104—312no—
88C4×M16—311no—
89C2×C31—21no—
90C2×C31—22no—
91C2×C31—44no—
92C2×C31C2×C4×D411yescharacteristic
93C2×#41C2×D3112yes—
94#137Dic3114yescomplemented
95AGL(1,ℤ/8)Dic3114yescomplemented
96#135C2×D3114yes—
97#131—318no—
98#131—624no—
99C2×M16—311no—
100C2×M16—312no—
101C2×M16—624no—
102C2×M16C2×D3111yescharacteristic
103C2×C42—311no—
104#108—314no—
105#104—314no—
106#104—314no—
107#97—312no—
108C4×C8—312no—
109C31#295611yescharacteristic, complemented, Sylow
110#41—22no—
111#41—22no—
112#41C2×Dic3114yes—
113#41C22×D3114yes—
114C2×Q8C2×Dic3112yes—
115C2×D4—22no—
116C2×D4C2×Dic3112yes—
117C22×C4—22no—
118C22×C4—621no—
119C22×C4C22×D3111yescharacteristic
120Q16C2×Dic3114yescomplemented
121SD16C2×Dic3118yescomplemented
122D8C2×Dic3114yescomplemented
123M16—314no—
124M16—314no—
125M16—628no—
126M16—622no—
127M16C2×Dic3114yes—
128C2×C8—312no—
129C2×C8—628no—
130C2×C8—622no—
131C2×C8C22×D3112yes—
132C42—311no—
133C42—311no—
134C42—621no—
135C23—22no—
136C23#9249711yescharacteristic
137Q8—22no—
138Q8C22×Dic3114yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic3114yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—621no—
147C2×C4—621no—
148C2×C4—1242no—
149C2×C4D4×D3112yes—
150C2×C4#9249711yescharacteristic
151C2×C4C22×Dic3112yes—
152C2×C4C23×D3111yescharacteristic
153C8—314no—
154C8—624no—
155C8C22×Dic3114yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic3112yes—
160C22C2×#9249711yescharacteristic
161C4—24no—
162C4—622no—
163C4—1241no—
164C4D4×Dic3112yes—
165C4C2×D4×D3111yescharacteristic
166C4C23×Dic3111yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic3111yescharacteristic
subgroupG/H
centerC4C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#575C2
socleC2×C31C2×C4×D4
cosocleC2×C4×C31C24
hypercenter#575D31
hypocenterC31#2956
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14521816C2semidirect
2. #14521171C2semidirect
3. #14521166C2semidirect
4. #14521098C2semidirect
5. C2×#11758425C2semidirect
6. M16×Dic31C2semidirect
9. C31×#137C4semidirect
10. C31×AGL(1,ℤ/8)C4semidirect
14. #11758525C22semidirect
19. #11758425C22semidirect
20. #11758425C22semidirect
21. #11758407C22semidirect
22. #11758403C22semidirect
23. C8×Dic31C22semidirect
34. Q16×C31C2×C4semidirect
35. SD16×C31C2×C4semidirect
36. D8×C31C2×C4semidirect
94. #137Dic31semidirect
95. AGL(1,ℤ/8)Dic31semidirect
109. C31#2956semidirect
120. Q16C2×Dic31semidirect
121. SD16C2×Dic31semidirect
122. D8C2×Dic31semidirect

Maximal subgroups

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

subgroupindex
#145218162
#145211712
#145211662
#145210982
C2×#117584252
M16×Dic312
C31×#5752
#295631