Finite Group Databasebeta

← #4822

Subgroups — #4822

Order 192.

168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 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#1009C211yesmaximal, characteristic, complemented
2#949C211yesmaximal, characteristic, complemented
3#908C211yesmaximal, characteristic, complemented
4#874C211yesmaximal, characteristic, complemented
5C3×#104C211yesmaximal, characteristic, complemented
6#823C211yesmaximal, characteristic, complemented
7#805C211yesmaximal, characteristic, complemented
8#453—31nomaximal, Sylow
9C3×#41C2211yescharacteristic
10#239—21no—
11D3×D4—22no—
12D3×D4—21no—
13#235—21no—
14#235C2211yescharacteristic
15C2×D12—21no—
16C2×D12—22no—
17C2×D12C2211yescharacteristic
18C2×D12C2211yescharacteristic, complemented
19C3×M16C2211yescharacteristic, complemented
20C3×C42C2211yescharacteristic, complemented
21#215—21no—
22#213—21no—
23#208C2211yescharacteristic, complemented
24D24—21no—
25#204—21no—
26H(5,𝔽2)—31no—
27AGL(1,ℤ/8)—31no—
28AGL(1,ℤ/8)—31no—
29#127—31no—
30#104—31no—
31#104D311yescharacteristic, complemented
32#100—31no—
33C22×D3—22no—
34C22×D3—21no—
35C22×D3D412yes—
36C3×Q8D411yescharacteristic, complemented
37C3×D4—21no—
38C3×D4D411yescharacteristic, complemented
39C2×C3×C4—21no—
40C2×C3×C4—21no—
41C2×C3×C4C2311yescharacteristic
42#67—22no—
43#67—21no—
44D12—22no—
45D12—21no—
46D12—21no—
47D12—21no—
48D12—21no—
49D12—44no—
50D12D411yescharacteristic, complemented
51C4×D3—22no—
52C4×D3—21no—
53Dic6D411yescharacteristic, complemented
54C3×C8—21no—
55C3⋊C8—21no—
56#41—31no—
57#41—61no—
58#41—61no—
59#41C2×D311yescharacteristic
60C2×D4—31no—
61C2×D4—31no—
62C2×D4—61no—
63C2×D4—62no—
64C2×D4—62no—
65C2×D4—61no—
66SD16—61no—
67SD16—61no—
68D8—61no—
69D8—61no—
70M16—31no—
71M16C2×D311yescharacteristic, complemented
72C42C2×D311yescharacteristic, complemented
73C22×C3—21no—
74C22×C3C2×D411yescharacteristic
75C2×D3—22no—
76C2×D3—21no—
77C2×D3—42no—
78C2×D3—42no—
79C2×D3—41no—
80C2×D3—82no—
81C3×C4—22no—
82C3×C4—21no—
83C3×C4C2×D411yescharacteristic
84C3×C4C2×D411yescharacteristic
85Dic3—21no—
86C23—32no—
87C23—62no—
88C23—61no—
89Q8—31no—
90Q8D1211yescharacteristic, complemented
91D4—21no—
92D4—31no—
93D4—62no—
94D4—62no—
95D4—61no—
96D4—61no—
97D4—61no—
98D4—61no—
99D4—61no—
100D4—124no—
101D4D1211yescharacteristic, complemented
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—62no—
105C2×C4—61no—
106C2×C4C22×D311yescharacteristic
107C8—21no—
108C8—61no—
109C2×C3—21no—
110C2×C3—41no—
111C2×C3#12011yescharacteristic
112D3—42no—
113D3—41no—
114D3—81no—
115C22—21no—
116C22—61no—
117C22—62no—
118C22—122no—
119C22—122no—
120C22—121no—
121C22—242no—
122C22D3×D411yescharacteristic
123C4—22no—
124C4—21no—
125C4—61no—
126C4C2×D1211yescharacteristic
127C4D3×D411yescharacteristic
128C3#45311yescharacteristic, complemented, Sylow
129C2—21no—
130C2—41no—
131C2—122no—
132C2—121no—
133C2—241no—
134C2#88211yescharacteristic
subgroupG/H
centerC2#882
commutator, cosocleC2×C3×C4C23
FrattiniC2×C4C22×D3
FittingC3×#104C2
socleC2×C3#120
hypercenter#104D3
hypocenterC3#453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #1009C2semidirect
2. #949C2semidirect
3. #908C2semidirect
4. #874C2semidirect
5. C3×#104C2semidirect
6. #823C2semidirect
7. #805C2semidirect
18. C2×D12C22semidirect
19. C3×M16C22semidirect
20. C3×C42C22semidirect
23. #208C22semidirect
31. #104D3semidirect
36. C3×Q8D4semidirect
38. C3×D4D4semidirect
50. D12D4semidirect
53. Dic6D4semidirect
71. M16C2×D3semidirect
72. C42C2×D3semidirect
90. Q8D12semidirect
101. D4D12semidirect
128. C3#453semidirect

Maximal subgroups

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

subgroupindex
#10092
#9492
#9082
#8742
C3×#1042
#8232
#8052
#4533