Finite Group Databasebeta

← #11772536

Subgroups — #11772536

Order 1152.

218 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 48 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×#63771C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3C3⋊D3×M32C211yesmaximal, characteristic
4#64286—21no—
5C2×#3788—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7#63771—21no—
8#63771C412yescomplemented
9#63769—21no—
10#63768C412yes—
11C32×M32C411yescharacteristic, complemented
12#63639C411yescharacteristic, complemented
13#63625—21no—
14C16×C3⋊D3—21no—
15D3×M32—62no—
16C2×C4×C3⋊D3D411yescharacteristic
17C22⋊#157—41no—
18C2×#622—41no—
19C4⋊#157—22no—
20C4×#157—41no—
21#3788—22no—
22#3788—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)Q811yescharacteristic
25C8×C3⋊D3C2×C411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3D411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C32×C16—21no—
30C3⋊(C3⋊C16)—21no—
31#1389—91nomaximal, Sylow
32C2×D3×C8—62no—
33C3×M32—22no—
34#812—62no—
35#798—64no—
36D3×C16—64no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×#157—42no—
39C2×C32×C4C4⋊C411yescharacteristic
40C2×C3⋊Dic3SD1611yescharacteristic
41C4×C3⋊D3C22⋊C411yescharacteristic
42C4×C3⋊D3C22⋊C411yescharacteristic
43C4×C3⋊D3D811yescharacteristic
44C4×C3⋊D3Q1611yescharacteristic
45#622—42no—
46C32×C8C4211yescharacteristic
47C32×C8C22⋊C411yescharacteristic
48C3⋊(C3⋊C8)C4⋊C411yescharacteristic
49C3⋊(C3⋊C8)C4⋊C411yescharacteristic
50C2×M32—91no—
51C2×#108—91no—
52#427—91no—
53C2×C4×D3—62no—
54C2×C3×C8—22no—
55C2×C3⋊C8—62no—
56D3×C8—62no—
57D3×C8—62no—
58D3×C8—62no—
59D3×C8—62no—
60C3×C16—24no—
61C3⋊C16—64no—
62C22×C32#10611yescharacteristic
63C2×C3⋊D3—41no—
64C2×C3⋊D3#10211yescharacteristic
65C2×C3⋊D3#10311yescharacteristic
66#157—82no—
67C32×C4#9511yescharacteristic
68C32×C4#10711yescharacteristic
69C3⋊Dic3#10211yescharacteristic
70C3⋊Dic3#10311yescharacteristic
71C2×M16—181no—
72C22×C8—91no—
73#117—181no—
74M32—91no—
75M32—181no—
76M32#15711yescharacteristic, complemented
77C2×C16—181no—
78#108—92no—
79#108—181no—
80#107—181no—
81#106—92no—
82C22×D3—62no—
83C2×C3×C4—22no—
84C2×Dic3—62no—
85C4×D3—62no—
86C4×D3—62no—
87C4×D3—62no—
88C4×D3—62no—
89C3×C8—22no—
90C3×C8—22no—
91C3⋊C8—62no—
92C3⋊C8—62no—
93C2×C32—21no—
94C2×C32#34011yescharacteristic
95C3⋊D3—21no—
96C3⋊D3—21no—
97C22×C4—91no—
98M16—182no—
99M16—361no—
100C2×C8—91no—
101C2×C8—91no—
102C2×C8—91no—
103C2×C8—91no—
104C2×C8—91no—
105C2×C8—361no—
106C2×C8C2×#15711yescharacteristic
107C4⋊C4—182no—
108C22⋊C4—361no—
109C42—361no—
110C16—21no—
111C16—181no—
112C22×C3—22no—
113C2×D3—62no—
114C2×D3—62no—
115C2×D3—124no—
116C3×C4—22no—
117C3×C4—22no—
118Dic3—62no—
119Dic3—62no—
120C32#138911yescharacteristic, complemented, Sylow
121C23—91no—
122C2×C4—91no—
123C2×C4—91no—
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—362no—
128C2×C4C4⋊#15711yescharacteristic
129C8—91no—
130C8—91no—
131C8—362no—
132C8C4×#15711yescharacteristic
133C8C22⋊#15711yescharacteristic
134C2×C3—22no—
135C2×C3—42no—
136D3—64no—
137D3—122no—
138C22—91no—
139C22—91no—
140C22—361no—
141C22#6376811yescharacteristic
142C4—91no—
143C4—91no—
144C4—722no—
145C4#6376911yescharacteristic
146C4#6378111yescharacteristic
147C3—22no—
148C2—21no—
149C2—181no—
150C2—181no—
151C2#1059018211yescharacteristic
subgroupG/H
centerC2#10590182
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×M32C4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenterM32#157
hypocenterC32#1389
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
8. #63771C4semidirect
11. C32×M32C4semidirect
12. #63639C4semidirect
76. M32#157semidirect
120. C32#1389semidirect

Maximal subgroups

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

subgroupindex
C2×#637712
#105937682
C3⋊D3×M322
#13899