Finite Group Databasebeta

← #11771908

Subgroups — #11771908

Order 1152.

218 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592586C211yesmaximal, characteristic
2#10590185C211yesmaximal, characteristic
3#10590176C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×#3746C411yescharacteristic
6C2×C8×C3⋊D3C2211yescharacteristic
7#64106—21no—
8C2×#3708—21no—
9C32×#107C411yescharacteristic
10#63637—21no—
11#4887—62no—
12C2×C4×C3⋊D3D411yescharacteristic
13C2×#634—21no—
14C2×#622—41no—
15#3788—22no—
16#3788—41no—
17C2×C32×C8C2×C411yescharacteristic
18C32×C4⋊C4—21no—
19#3752—41no—
20C4⋊(C3⋊Dic3)—41no—
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3746—41no—
23C8×C3⋊D3—41no—
24#3708—41no—
25#1350—91nomaximal, Sylow
26C2×Dic12—62no—
27C2×D3×C8—62no—
28#897—64no—
29C3×#107—22no—
30#810—64no—
31C22×C3⋊D3SD1611yescharacteristic
32C2×C32×C4—41no—
33C2×C32×C4C22⋊C411yescharacteristic
34C2×C3⋊Dic3—41no—
35C2×C3⋊Dic3D811yescharacteristic
36C4×C3⋊D3—21no—
37C4×C3⋊D3—21no—
38#634—41no—
39#634—41no—
40#622—42no—
41C32×C8—21no—
42C3⋊(C3⋊C8)—21no—
43#467—91no—
44C22⋊C16—91no—
45#341—91no—
46C2×C4×D3—62no—
47C2×Dic6—64no—
48C2×C3×C8—22no—
49C3×C4⋊C4—24no—
50(C2×D3)⋊C4—124no—
51C4⋊Dic3—124no—
52C2×C3⋊C8—62no—
53Dic12—124no—
54D3×C8—124no—
55C22×C32#10211yescharacteristic
56C2×C3⋊D3—21no—
57C2×C3⋊D3—21no—
58C2×C3⋊D3—21no—
59C32×C4—81no—
60C32×C4#9911yescharacteristic
61C32×C4#10411yescharacteristic
62C3⋊Dic3—21no—
63C3⋊Dic3—81no—
64C2×Q16—91no—
65C2×M16—181no—
66C22×C8—91no—
67C22⋊Q8—181no—
68C2×C16—181no—
69#107#15711yescharacteristic
70#103—181no—
71C22×D3—62no—
72C2×C3×C4—22no—
73C2×C3×C4—44no—
74C2×Dic3—62no—
75C2×Dic3—124no—
76C4×D3—122no—
77C4×D3—122no—
78Dic6—124no—
79Dic6—124no—
80C3×C8—24no—
81C3⋊C8—122no—
82C2×C32#32711yescharacteristic
83C2×C32#35911yescharacteristic
84C2×C32#36211yescharacteristic
85C3⋊D3—41no—
86C2×Q8—181no—
87C22×C4—91no—
88Q16—361no—
89M16—182no—
90M16—361no—
91C2×C8—91no—
92C2×C8—361no—
93C2×C8—361no—
94C2×C8C2×#15711yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—361no—
97C22⋊C4—361no—
98C16—361no—
99C22×C3—22no—
100C2×D3—64no—
101C2×D3—122no—
102C2×D3—122no—
103C3×C4—22no—
104C3×C4—22no—
105C3×C4—84no—
106Dic3—122no—
107Dic3—244no—
108C32#135011yescharacteristic, complemented, Sylow
109C23—91no—
110Q8—361no—
111Q8—361no—
112C2×C4—41no—
113C2×C4—91no—
114C2×C4—181no—
115C2×C4—181no—
116C2×C4—361no—
117C2×C4C22⋊#15711yescharacteristic
118C8—21no—
119C8—181no—
120C8—362no—
121C2×C3—22no—
122C2×C3—22no—
123C2×C3—22no—
124D3—124no—
125C22—181no—
126C22—181no—
127C22—181no—
128C22#6378211yescharacteristic
129C4—81no—
130C4—181no—
131C4—721no—
132C4#6377411yescharacteristic
133C4#6378511yescharacteristic
134C3—22no—
135C2—361no—
136C2#1059015711yescharacteristic
137C2#1059019411yescharacteristic
138C2#1059019911yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC32×#107C4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenter#107#157
hypocenterC32#1350
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
108. C32#1350semidirect

Maximal subgroups

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

subgroupindex
#105925862
#105901852
#105901762
#13509