Finite Group Databasebeta

← #11772445

Subgroups — #11772445

Order 1152.

246 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 55 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×#63773C211yesmaximal, characteristic
2#10591138C212yesmaximal
3C22×C3⋊(C3⋊C8)C2211yescharacteristic
4C3×#926—22no—
5#63773—22no—
6C2×#3708C412yescomplemented
7#63576—22no—
8#63574C414yescomplemented
9#4998—62no—
10C22×C32×C4D411yescharacteristic
11C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
12C2×C3⋊(C3⋊C8)C2×C412yes—
13C2×C3⋊(C3⋊C8)D412yes—
14C2×C3⋊(C3⋊C8)Q811yescharacteristic
15C3×#217—42no—
16C3×C4⋊Dic3—24no—
17C3×C4×Dic3—42no—
18#3708—22no—
19#1384—91nomaximal, Sylow
20C3×#117—62no—
21#926—22no—
22C22×C3⋊C8—62no—
23#808—64no—
24#807—64no—
25C23×C32D811yescharacteristic
26C2×C32×C4C22⋊C412yes—
27C2×C32×C4C4⋊C411yescharacteristic
28C2×C32×C4SD1612yes—
29C2×C32×C4Q1611yescharacteristic
30C2×C3×Dic3—44no—
31C3⋊(C3⋊C8)C4211yescharacteristic
32C3⋊(C3⋊C8)C22⋊C411yescharacteristic
33C3⋊(C3⋊C8)C4⋊C412yes—
34C2×M32—91no—
35#427—92no—
36C22×C3×C4—22no—
37C3×C4⋊C4—64no—
38C3×C22⋊C4—122no—
39C3×C42—122no—
40#217—42no—
41C4⋊Dic3—24no—
42C4×Dic3—42no—
43C2×C3⋊C8—62no—
44C2×C3⋊C8—62no—
45C2×C3⋊C8—62no—
46C2×C3⋊C8—62no—
47C2×C3⋊C8—62no—
48C2×C3⋊C8—62no—
49C22×C32—41no—
50C22×C32#10212yes—
51C22×C32#10711yescharacteristic
52C32×C4#9511yescharacteristic
53C32×C4#10312yes—
54C32×C4#10611yescharacteristic
55C3×Dic3—84no—
56C22×C8—91no—
57#117—62no—
58M32—182no—
59C2×C16—92no—
60#107—182no—
61#106—94no—
62C23×C3—22no—
63C2×C3×C4—22no—
64C2×C3×C4—22no—
65C2×C3×C4—22no—
66C2×C3×C4—22no—
67C2×C3×C4—22no—
68C2×C3×C4—22no—
69C2×C3×C4—124no—
70C2×Dic3—44no—
71C3⋊C8—62no—
72C3⋊C8—62no—
73C3⋊C8—62no—
74C3⋊C8—62no—
75C2×C32—22no—
76C2×C32—21no—
77C2×C32#34011yescharacteristic
78C22×C4GO+(4,𝔽2)11yescharacteristic
79C2×C8—92no—
80C2×C8—92no—
81C2×C8—91no—
82C2×C8—91no—
83C4⋊C4—64no—
84C22⋊C4—122no—
85C42—122no—
86C16—182no—
87C22×C3—22no—
88C22×C3—22no—
89C22×C3—22no—
90C22×C3—44no—
91C3×C4—22no—
92C3×C4—22no—
93C3×C4—22no—
94C3×C4—22no—
95C3×C4—244no—
96Dic3—84no—
97C32#138411yescharacteristic, complemented, Sylow
98C23#377411yescharacteristic
99C2×C4—124no—
100C2×C4D32⋊C412yes—
101C2×C4#377311yescharacteristic
102C2×C4#377512yes—
103C2×C4#377611yescharacteristic
104C8—91no—
105C8—91no—
106C8—92no—
107C2×C3—24no—
108C2×C3—22no—
109C2×C3—42no—
110C2×C3—42no—
111C22—41no—
112C22#6373912yes—
113C22#6374311yescharacteristic
114C4—244no—
115C4#6373711yescharacteristic
116C4#6374012yes—
117C4#6374211yescharacteristic
118C3—22no—
119C2—22no—
120C2—21no—
121C2#1059007511yescharacteristic
subgroupG/H
centerC4#63742
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#340
prime radicalC23×C32D8
cosocleC22×C3⋊(C3⋊C8)C22
hypocenterC32#1384
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C2×#3708C4semidirect
8. #63574C4semidirect
97. C32#1384semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
#105911382
#13849