Finite Group Databasebeta

← #11800035

Subgroups — #11800035

Order 1152.

161 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 32 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#10593547C211yesmaximal, characteristic
2#10593449C211yesmaximal, characteristic
3#10593266C211yesmaximal, characteristic
4#10593170C212yesmaximal, complemented
5#10593169C212yesmaximal, complemented
6#64283—21no—
7C2×#3788C2211yescharacteristic
8C2×#3776C2211yescharacteristic
9#64218C2212yes—
10#63865—21no—
11#63748—21no—
12#63748C2212yes—
13#63742C2211yescharacteristic
14#63740—21no—
15C2×C4×C3⋊D3D411yescharacteristic
16C2×#627—21no—
17#3792—22no—
18C2×#622D411yescharacteristic
19C2×#622C2311yescharacteristic
20#3788—22no—
21#3788—41no—
22#3787—41no—
23#3776—22no—
24#3771—22no—
25C3×Dic3⋊C4—41no—
26#3724—21no—
27#3722—41no—
28#2239—91nomaximal, Sylow
29#896—121no—
30C22×C3⋊D3SD1611yescharacteristic
31C2×C32×C4SD1611yescharacteristic
32C2×C3⋊Dic3C2×D411yescharacteristic
33C4×C3⋊D3—21no—
34C4×C3⋊D3—21no—
35C2×C3×Dic3—41no—
36C2×C3×Dic3—41no—
37#627—41no—
38#627—41no—
39#622—21no—
40#622—42no—
41#622#4112yes—
42#470—91no—
43#430—91no—
44#365—92no—
45#362—92no—
46#349—91no—
47C2×C4×D3—121no—
48C2×Dic6—121no—
49C3×C4⋊C4—121no—
50(C2×D3)⋊C4—121no—
51(C2×D3)⋊C4—121no—
52Dic3⋊C4—41no—
53Dic3⋊C4—121no—
54C22×C32C2×SD1611yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—41no—
57C32×C4—21no—
58C3⋊Dic3#12311yescharacteristic
59C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
60C3×Dic3—81no—
61C3×Dic3—81no—
62C2×Q16—91no—
63C2×M16—91no—
64C2×M16—181no—
65C22⋊Q8—181no—
66M32—92no—
67#108—92no—
68#108—181no—
69#106—91no—
70#103—181no—
71C22×D3—121no—
72C2×C3×C4—41no—
73C2×C3×C4—121no—
74C2×C3×C4—121no—
75C2×Dic3—41no—
76C2×Dic3—41no—
77C2×Dic3—121no—
78C4×D3—241no—
79C4×D3—241no—
80Dic6—241no—
81Dic6—241no—
82C2×C32—21no—
83C2×C32#48111yescharacteristic
84C3⋊D3—41no—
85C2×Q8—181no—
86C22×C4—91no—
87Q16—182no—
88M16—182no—
89M16—182no—
90M16—361no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—361no—
94C4⋊C4—121no—
95C4⋊C4—181no—
96C22⋊C4—361no—
97C16—182no—
98C22×C3—41no—
99C2×D3—122no—
100C2×D3—241no—
101C2×D3—241no—
102C3×C4—81no—
103C3×C4—241no—
104C3×C4—241no—
105Dic3—81no—
106Dic3—81no—
107Dic3—121no—
108Dic3—121no—
109C32#223911yescharacteristic, complemented, Sylow
110C23—91no—
111Q8—361no—
112Q8—361no—
113C2×C4—91no—
114C2×C4—121no—
115C2×C4—121no—
116C2×C4—181no—
117C2×C4—181no—
118C2×C4AΓL(1,𝔽9)11yescharacteristic
119C8—92no—
120C8—181no—
121C8—362no—
122C2×C3—41no—
123C2×C3—41no—
124C2×C3—41no—
125D3—242no—
126C22—181no—
127C22—361no—
128C22C2×AΓL(1,𝔽9)11yescharacteristic
129C4—21no—
130C4—91no—
131C4—91no—
132C4—241no—
133C4—241no—
134C3—41no—
135C2—21no—
136C2—361no—
137C2#1059641211yescharacteristic
subgroupG/H
centerC2#10596412
commutator, cosocleC2×#622C23
FrattiniC22C2×AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#481
prime radicalC22×C3⋊D3SD16
hypercenterC2×C4AΓL(1,𝔽9)
hypocenterC32#2239
LCSG ▷ C2×#622 ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593170C2semidirect
5. #10593169C2semidirect
109. C32#2239semidirect

Maximal subgroups

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

subgroupindex
#105935472
#105934492
#105932662
#105931702
#105931692
#22399