Finite Group Databasebeta

← #4898

Subgroups — #4898

Order 192.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#909C211yesmaximal, characteristic, complemented
2#908C211yesmaximal, characteristic
3C2×#204C211yesmaximal, characteristic, complemented
4#901C211yesmaximal, characteristic, complemented
5C3×#108C211yesmaximal, characteristic, complemented
6#824C211yesmaximal, characteristic, complemented
7#823C211yesmaximal, characteristic, complemented
8#471—31nomaximal, Sylow
9#235C2211yescharacteristic
10C2×D12C2211yescharacteristic
11C2×Dic6C2211yescharacteristic
12C3×M16C2211yescharacteristic
13C3×M16C2211yescharacteristic
14C2×C3×C8C2211yescharacteristic
15#208C2211yescharacteristic
16Dic12—21no—
17D24—21no—
18#204—21no—
19#204—21no—
20#204—21no—
21#204—21no—
22ΓL(1,𝔽25)—21no—
23D3×C8—21no—
24#137—31no—
25AGL(1,ℤ/8)—31no—
26C2×SD16—31no—
27#131—31no—
28#108D311yescharacteristic, complemented
29#101—31no—
30#100—31no—
31C22×D3—21no—
32C2×C3×C4C2311yescharacteristic
33#67—21no—
34C2×Dic3—21no—
35D12—21no—
36D12—21no—
37D12D411yescharacteristic
38C4×D3—21no—
39Dic6—21no—
40Dic6—21no—
41Dic6D411yescharacteristic
42C3×C8—21no—
43C3×C8—21no—
44C3×C8D411yescharacteristic
45C3×C8D411yescharacteristic
46C3⋊C8—21no—
47#41—31no—
48C2×Q8—31no—
49C2×D4—31no—
50Q16—61no—
51SD16—61no—
52SD16—61no—
53SD16—61no—
54SD16—61no—
55D8—61no—
56M16—31no—
57M16—61no—
58M16C2×D311yescharacteristic
59M16C2×D311yescharacteristic
60C2×C8—61no—
61C2×C8C2×D311yescharacteristic
62C22×C3#4111yescharacteristic
63C2×D3—21no—
64C2×D3—41no—
65C2×D3—81no—
66C3×C4C2×D411yescharacteristic
67C3×C4C2×D411yescharacteristic
68Dic3—21no—
69Dic3—41no—
70C23—61no—
71Q8—31no—
72Q8—61no—
73Q8—61no—
74D4—31no—
75D4—61no—
76D4—61no—
77D4—61no—
78C2×C4—61no—
79C2×C4—61no—
80C2×C4C22×D311yescharacteristic
81C8—21no—
82C8—21no—
83C8—61no—
84C8D1211yescharacteristic
85C8D1211yescharacteristic
86C2×C3—21no—
87C2×C3#12111yescharacteristic
88D3—41no—
89D3—81no—
90C22—61no—
91C22—121no—
92C22—241no—
93C22#23911yescharacteristic
94C4—61no—
95C4—121no—
96C4C2×D1211yescharacteristic
97C4D3×D411yescharacteristic
98C3#47111yescharacteristic, complemented, Sylow
99C2—21no—
100C2—121no—
101C2—241no—
102C2#89511yescharacteristic
subgroupG/H
centerC2#895
commutator, cosocleC2×C3×C4C23
FrattiniC2×C4C22×D3
FittingC3×#108C2
socleC2×C3#121
prime radical#908C2
hypercenter#108D3
hypocenterC3#471
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #909C2semidirect
3. C2×#204C2semidirect
4. #901C2semidirect
5. C3×#108C2semidirect
6. #824C2semidirect
7. #823C2semidirect
28. #108D3semidirect
98. C3#471semidirect

Maximal subgroups

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

subgroupindex
#9092
#9082
C2×#2042
#9012
C3×#1082
#8242
#8232
#4713