Finite Group Databasebeta

← #11777927

Subgroups — #11777927

Order 1152.

258 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593835C212yesmaximal
2Q16×C3⋊Dic3C211yesmaximal, characteristic
3Q8⋊#622C212yesmaximal
4#10590170C211yesmaximal, characteristic
5#10590168C211yesmaximal, characteristic
6C2×C32×Q16C411yescharacteristic
7Q8×C3⋊Dic3C2212yes—
8#63779—22no—
9#63777—22no—
10C4⋊#622C2212yes—
11C4×#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63662C412yes—
14#63645C411yescharacteristic
15C8×C3⋊Dic3C2211yescharacteristic
16Dic3×Q16—62no—
17C2×C32×Q8C2×C412yes—
18C2×#622—22no—
19C2×#622—21no—
20C2×#622D412yes—
21C32×Q16—22no—
22C2×C32×C8C2×C411yescharacteristic
23C4⋊(C3⋊Dic3)—22no—
24C4⋊(C3⋊Dic3)C2×C412yes—
25C4×C3⋊Dic3—22no—
26C4×C3⋊Dic3C2311yescharacteristic
27C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
28#1593—91nomaximal, Sylow
29C2×C3×Q16—22no—
30Q8×Dic3—64no—
31#835—64no—
32#818—62no—
33C8×Dic3—62no—
34C32×Q8—22no—
35C32×Q8—22no—
36C2×C32×C4—22no—
37C2×C32×C4C22×C411yescharacteristic
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3C2×D411yescharacteristic
40C2×C3⋊Dic3#4111yescharacteristic
41#622—22no—
42#622—41no—
43#622—42no—
44C32×C8M1612yes—
45C3⋊(C3⋊C8)—21no—
46#446—92no—
47C4×Q16—91no—
48#334—91no—
49Q8⋊C8—92no—
50#322—91no—
51C2×C3×Q8—24no—
52C3×Q16—28no—
53C2×C3×C8—22no—
54C4⋊Dic3—64no—
55C4⋊Dic3—124no—
56C4×Dic3—62no—
57C4×Dic3—124no—
58C2×C3⋊C8—62no—
59C22×C32C4×D411yescharacteristic
60C32×C4—42no—
61C32×C4C2×M1611yescharacteristic
62C32×C4#13111yescharacteristic
63C3⋊Dic3—21no—
64C3⋊Dic3—42no—
65C3⋊Dic3#13712yes—
66C2×Q16#15711yescharacteristic
67C4×Q8—92no—
68#107—91no—
69C4⋊C8—92no—
70C4⋊C8—182no—
71#103—92no—
72#97—182no—
73C4×C8—91no—
74C4×C8—91no—
75C4×C8—91no—
76C3×Q8—28no—
77C3×Q8—44no—
78C2×C3×C4—22no—
79C2×C3×C4—44no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C2×Dic3—124no—
83C3×C8—24no—
84C3⋊C8—122no—
85C2×C32#43611yescharacteristic
86C2×C32#44111yescharacteristic
87C2×C32#44411yescharacteristic
88C2×Q8C2×#15712yes—
89Q16—22no—
90C2×C8—92no—
91C2×C8—91no—
92C2×C8—181no—
93C2×C8—182no—
94C2×C8C2×#15711yescharacteristic
95C4⋊C4—92no—
96C4⋊C4—182no—
97C42—91no—
98C42—182no—
99C22×C3—22no—
100C3×C4—22no—
101C3×C4—22no—
102C3×C4—48no—
103Dic3—64no—
104Dic3—122no—
105Dic3—244no—
106C32#159311yescharacteristic, complemented, Sylow
107Q8—22no—
108Q8—22no—
109C2×C4—22no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—182no—
113C2×C4C22×#15711yescharacteristic
114C8—182no—
115C8—181no—
116C8—362no—
117C8—361no—
118C8#379212yes—
119C2×C3—22no—
120C2×C3—22no—
121C2×C3—22no—
122C22D4×#15711yescharacteristic
123C4—42no—
124C4—92no—
125C4—181no—
126C4—362no—
127C4#6428711yescharacteristic
128C4C2×#379211yescharacteristic
129C3—22no—
130C2#1059378611yescharacteristic
131C2#1059378811yescharacteristic
132C2#1059382111yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×Q16C4
socle, prime radicalC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenterC2×Q16#157
hypocenterC32#1593
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
106. C32#1593semidirect

Maximal subgroups

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

subgroupindex
#105938352
Q16×C3⋊Dic32
Q8⋊#6222
#105901702
#105901682
#15939