Finite Group Databasebeta

← #11797389

Subgroups — #11797389

Order 1152.

270 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 52 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
1M16×C3⋊Dic3C211yesmaximal, characteristic
2#10590201C212yesmaximal
3#10590179C212yesmaximal, complemented
4#10590178C212yesmaximal, complemented
5C2×C32×M16C411yescharacteristic
6C2×C4×C3⋊Dic3C411yescharacteristic
7C2×#3748C2211yescharacteristic
8#63773C2214yes—
9#63642C411yescharacteristic
10#63642C2211yescharacteristic
11C8×C3⋊Dic3C411yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13Dic3×M16—62no—
14C22×C32×C4C2×C411yescharacteristic
15C22×C3⋊Dic3—21no—
16C32×M16—22no—
17C2×C32×C8C2×C411yescharacteristic
18C2×C32×C8C2×C411yescharacteristic
19C4×C3⋊Dic3—21no—
20C4×C3⋊Dic3C2×C411yescharacteristic
21C4×C3⋊Dic3C2×C411yescharacteristic
22#3748—22no—
23C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25#3708—24no—
26#2165—91nomaximal, Sylow
27C2×C3×M16—22no—
28C2×C4×Dic3—62no—
29C2×#208—62no—
30#815—62no—
31#815—62no—
32C8×Dic3—62no—
33C8×Dic3—62no—
34C23×C32M1611yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4M1611yescharacteristic
38C2×C32×C4C22×C411yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—42no—
42C32×C8—21no—
43C32×C8M1612yes—
44C3⋊(C3⋊C8)—21no—
45C3⋊(C3⋊C8)#4112yes—
46C4×M16—91no—
47#364—92no—
48#349—92no—
49#347—92no—
50C22×C3×C4—22no—
51C22×Dic3—64no—
52C3×M16—28no—
53C2×C3×C8—22no—
54C2×C3×C8—22no—
55C4×Dic3—62no—
56C4×Dic3—62no—
57C4×Dic3—64no—
58#208—68no—
59C2×C3⋊C8—62no—
60C2×C3⋊C8—62no—
61C22×C32—21no—
62C22×C32—41no—
63C22×C32C2×M1611yescharacteristic
64C32×C4—21no—
65C32×C4#11711yescharacteristic
66C32×C4C2×M1611yescharacteristic
67C3⋊Dic3—22no—
68C3⋊Dic3—41no—
69C2×M16—91no—
70C2×M16#15711yescharacteristic
71C2×C42—91no—
72M32—94no—
73#97—91no—
74#97—91no—
75C4×C8—91no—
76C4×C8—91no—
77C23×C3—22no—
78C2×C3×C4—24no—
79C2×C3×C4—24no—
80C2×C3×C4—22no—
81C2×C3×C4—22no—
82C2×Dic3—64no—
83C2×Dic3—64no—
84C2×Dic3—128no—
85C3×C8—24no—
86C3×C8—24no—
87C3⋊C8—64no—
88C3⋊C8—64no—
89C2×C32—21no—
90C2×C32—41no—
91C2×C32#43211yescharacteristic
92C22×C4—181no—
93C22×C4C2×#15711yescharacteristic
94M16—22no—
95M16—182no—
96C2×C8—91no—
97C2×C8—91no—
98C2×C8C2×#15711yescharacteristic
99C2×C8C2×#15711yescharacteristic
100C42—91no—
101C42—91no—
102C42—181no—
103C16—184no—
104C22×C3—24no—
105C22×C3—22no—
106C22×C3—44no—
107C3×C4—24no—
108C3×C4—22no—
109C3×C4—22no—
110Dic3—68no—
111Dic3—124no—
112C32#216511yescharacteristic, complemented, Sylow
113C23#378811yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—181no—
117C2×C4—181no—
118C2×C4—362no—
119C2×C4#378811yescharacteristic
120C2×C4C22×#15711yescharacteristic
121C8—21no—
122C8—92no—
123C8—181no—
124C8#379212yes—
125C2×C3—24no—
126C2×C3—22no—
127C2×C3—44no—
128C22—21no—
129C22—41no—
130C22C2×#378811yescharacteristic
131C4—21no—
132C4—182no—
133C4—361no—
134C4#6428611yescharacteristic
135C4C2×#379211yescharacteristic
136C3—22no—
137C2—21no—
138C2—41no—
139C2#1059380611yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC2×C32#432
prime radicalC23×C32M16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×M16#157
hypocenterC32#2165
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10590179C2semidirect
4. #10590178C2semidirect
112. C32#2165semidirect

Maximal subgroups

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

subgroupindex
M16×C3⋊Dic32
#105902012
#105901792
#105901782
#21659