Finite Group Databasebeta

← C2×#911 #5755

Subgroups — C2×#911 #5755

Order 192.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 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×#237C211yesmaximal, characteristic, complemented
2C2×D3×D4C211yesmaximal, characteristic, complemented
3C2×C3×D8C211yesmaximal, characteristic, complemented
4C2×#214C211yesmaximal, characteristic, complemented
5C2×#213C211yesmaximal, characteristic, complemented
6#911C218yesmaximal, direct product factor
7C2×#204C211yesmaximal, characteristic, complemented
8C2×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)—31nomaximal, Sylow
10C23×D3—21no—
11C2×C3×D4C2211yescharacteristic
12C2×C3×D4C2211yescharacteristic, complemented
13C2×#67—21no—
14C2×#67—21no—
15C22×Dic3—21no—
16#237—22no—
17#237C2214yescomplemented
18D3×D4—22no—
19D3×D4C2214yescomplemented
20C2×D12C2211yescharacteristic
21C2×C4×D3C2211yescharacteristic
22C2×Dic6C2211yescharacteristic, complemented
23C3×D8C2214yescomplemented
24C2×C3×C8C2211yescharacteristic, complemented
25#214C2214yescomplemented
26#213C2214yescomplemented
27C2×C3⋊C8C2211yescharacteristic, complemented
28#204C2214yescomplemented
29ΓL(1,𝔽25)C2214yescomplemented
30C2×#41—31no—
31C22×D4—31no—
32AGL(1,ℤ/8)—38no—
33C2×SD16—31no—
34C2×SD16—31no—
35C2×D8—31no—
36C2×D8D311yescharacteristic, complemented
37C2×M16—31no—
38C23×C3—21no—
39C23×C3—21no—
40C22×D3—21no—
41C22×D3—24no—
42C22×D3—44no—
43C22×D3D411yescharacteristic
44C3×D4—21no—
45C3×D4—21no—
46C3×D4C2312yes—
47C3×D4C2312yescomplemented
48C2×C3×C4C2311yescharacteristic
49#67—24no—
50#67—24no—
51C2×Dic3—21no—
52C2×Dic3—24no—
53C2×Dic3D411yescharacteristic
54D12—21no—
55D12C2312yes—
56C4×D3D412yes—
57C4×D3C2312yes—
58Dic6—21no—
59Dic6C2312yescomplemented
60C3×C8C2312yescomplemented
61C3⋊C8C2312yescomplemented
62C24—61no—
63#41—34no—
64#41—62no—
65C2×Q8—31no—
66C2×D4—34no—
67C2×D4—31no—
68C2×D4—62no—
69C2×D4—61no—
70C2×D4—61no—
71C2×D4C2×D311yescharacteristic
72C2×D4C2×D311yescharacteristic, complemented
73C22×C4—31no—
74C22×C4—61no—
75SD16—34no—
76SD16—34no—
77D8—34no—
78D8C2×D314yescomplemented
79M16—34no—
80C2×C8—31no—
81C2×C8C2×D311yescharacteristic, complemented
82C22×C3—22no—
83C22×C3—22no—
84C22×C3—42no—
85C22×C3—42no—
86C22×C3C2×D411yescharacteristic
87C2×D3—22no—
88C2×D3—22no—
89C2×D3—48no—
90C2×D3—42no—
91C2×D3C2×D412yes—
92C3×C4C2×D411yescharacteristic
93C3×C4C2411yescharacteristic
94Dic3—22no—
95Dic3C2×D412yes—
96C23—21no—
97C23—21no—
98C23—31no—
99C23—64no—
100C23—61no—
101C23—124no—
102Q8—32no—
103Q8—61no—
104D4—21no—
105D4—21no—
106D4—32no—
107D4—64no—
108D4—64no—
109D4—61no—
110D4C22×D312yes—
111D4C22×D312yescomplemented
112C2×C4—31no—
113C2×C4—32no—
114C2×C4—32no—
115C2×C4—64no—
116C2×C4—61no—
117C2×C4C22×D311yescharacteristic
118C8—32no—
119C8C22×D312yescomplemented
120C2×C3—42no—
121C2×C3—42no—
122C2×C3AGL(1,ℤ/8)12yescomplemented
123C2×C3C22×D411yescharacteristic
124D3—22no—
125D3—42no—
126C22—22no—
127C22—22no—
128C22—32no—
129C22—42no—
130C22—42no—
131C22—62no—
132C22—62no—
133C22—128no—
134C22—122no—
135C22D3×D411yescharacteristic
136C4—32no—
137C4—62no—
138C4D3×D411yescharacteristic
139C4C23×D311yescharacteristic
140C3C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
141C2—42no—
142C2—42no—
143C2—62no—
144C2—122no—
145C2#91112yesdirect product factor
146C2C2×D3×D411yescharacteristic
subgroupG/H
centerC22D3×D4
commutator, cosocleC3×C4C24
FrattiniC4C23×D3
FittingC2×C3×D8C2
socleC22×C3C2×D4
hypercenterC2×D8D3
hypocenterC3C2×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#237C2semidirect
2. C2×D3×D4C2semidirect
3. C2×C3×D8C2semidirect
4. C2×#214C2semidirect
5. C2×#213C2semidirect
6. #911C2direct (N × H)
7. C2×#204C2semidirect
8. C2×ΓL(1,𝔽25)C2semidirect
12. C2×C3×D4C22semidirect
17. #237C22semidirect
19. D3×D4C22semidirect
22. C2×Dic6C22semidirect
23. C3×D8C22semidirect
24. C2×C3×C8C22semidirect
25. #214C22semidirect
26. #213C22semidirect
27. C2×C3⋊C8C22semidirect
28. #204C22semidirect
29. ΓL(1,𝔽25)C22semidirect
36. C2×D8D3semidirect
47. C3×D4C23semidirect
59. Dic6C23semidirect
60. C3×C8C23semidirect
61. C3⋊C8C23semidirect
72. C2×D4C2×D3semidirect
78. D8C2×D3semidirect
81. C2×C8C2×D3semidirect
111. D4C22×D3semidirect
119. C8C22×D3semidirect
122. C2×C3AGL(1,ℤ/8)semidirect
140. C3C2×AGL(1,ℤ/8)semidirect
145. C2#911direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#2372
C2×D3×D42
C2×C3×D82
C2×#2142
C2×#2132
#9112
C2×#2042
C2×ΓL(1,𝔽25)2
C2×AGL(1,ℤ/8)3