Finite Group Databasebeta

← #5039

Subgroups — #5039

Order 192.

130 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C3×#121C211yesmaximal, characteristic, complemented
2C2×#213C211yesmaximal, characteristic, complemented
3#930C211yesmaximal, characteristic, complemented
4C2×#208C211yesmaximal, characteristic, complemented
5#832C211yesmaximal, characteristic, complemented
6#809C211yesmaximal, characteristic, complemented
7#808C211yesmaximal, characteristic, complemented
8#469—31nomaximal, Sylow
9C2×C3×D4—21no—
10C2×C3×D4C2211yescharacteristic
11C22×C3×C4C2211yescharacteristic
12C2×#67—21no—
13C2×D12C2211yescharacteristic
14C3×C4⋊C4C2211yescharacteristic
15C3×C22⋊C4—21no—
16#213—22no—
17(C2×D3)⋊C4—21no—
18C4⋊Dic3C2211yescharacteristic
19#208—22no—
20C2×C3⋊C8C2211yescharacteristic
21C2×C3⋊C8C2211yescharacteristic
22C2×D8—31no—
23C2×M16—31no—
24#121—31no—
25#121D311yescharacteristic, complemented
26#106—31no—
27#102—31no—
28#102—31no—
29C23×C3—21no—
30C23×C3D411yescharacteristic
31C22×D3—21no—
32C3×D4—21no—
33C3×D4—21no—
34C3×D4—42no—
35C2×C3×C4—21no—
36C2×C3×C4—21no—
37C2×C3×C4—21no—
38C2×C3×C4D411yescharacteristic
39C2×C3×C4C2311yescharacteristic
40#67—42no—
41C2×Dic3—21no—
42D12—21no—
43D12—21no—
44C3⋊C8—21no—
45C3⋊C8D412yescomplemented
46C2×D4—21no—
47C2×D4—31no—
48C2×D4—61no—
49C2×D4C2×D311yescharacteristic
50C22×C4C2×D311yescharacteristic
51D8—62no—
52M16—62no—
53C2×C8—31no—
54C2×C8—31no—
55C4⋊C4—31no—
56C4⋊C4C2×D311yescharacteristic
57C22⋊C4—21no—
58C22⋊C4—61no—
59C22×C3—21no—
60C22×C3—21no—
61C22×C3—21no—
62C22×C3—41no—
63C22×C3—41no—
64C22×C3—41no—
65C22×C3C2×D411yescharacteristic
66C2×D3—41no—
67C2×D3—41no—
68C2×D3—41no—
69C3×C4—21no—
70C3×C4—41no—
71C3×C4C2×D411yescharacteristic
72C3×C4#4111yescharacteristic
73Dic3—41no—
74C23—21no—
75C23—61no—
76C23#6711yescharacteristic
77D4—21no—
78D4—21no—
79D4—42no—
80D4—61no—
81D4—61no—
82D4—122no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—61no—
87C2×C4#6711yescharacteristic
88C2×C4C22×D311yescharacteristic
89C8—32no—
90C8—61no—
91C2×C3—41no—
92C2×C3—81no—
93C2×C3#12111yescharacteristic
94C2×C3AGL(1,ℤ/8)11yescharacteristic
95C2×C3AGL(1,ℤ/8)11yescharacteristic
96D3—81no—
97C22—21no—
98C22—21no—
99C22—21no—
100C22—41no—
101C22—41no—
102C22—41no—
103C22—121no—
104C22—121no—
105C22—121no—
106C22C2×#6711yescharacteristic
107C4—21no—
108C4—41no—
109C4—121no—
110C4D3×D411yescharacteristic
111C4#23711yescharacteristic
112C3#46911yescharacteristic, complemented, Sylow
113C2—41no—
114C2—81no—
115C2—241no—
116C2#93211yescharacteristic
117C2#93911yescharacteristic
118C2#94911yescharacteristic
subgroupG/H
centerC22C2×#67
commutator, cosocleC2×C3×C4C23
FrattiniC2×C4C22×D3
FittingC3×#121C2
socleC22×C3C2×D4
hypercenter#121D3
hypocenterC3#469
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#121C2semidirect
2. C2×#213C2semidirect
3. #930C2semidirect
4. C2×#208C2semidirect
5. #832C2semidirect
6. #809C2semidirect
7. #808C2semidirect
25. #121D3semidirect
45. C3⋊C8D4semidirect
112. C3#469semidirect

Maximal subgroups

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

subgroupindex
C3×#1212
C2×#2132
#9302
C2×#2082
#8322
#8092
#8082
#4693