Finite Group Databasebeta

← #11771608

Subgroups — #11771608

Order 1152.

242 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 38 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
1D8×C3⋊Dic3C211yesmaximal, characteristic
2#10590175C211yesmaximal, characteristic, complemented
3#10590170C211yesmaximal, characteristic, complemented
4C2×C32×D8C411yescharacteristic
5D4×C3⋊Dic3—21no—
6C4⋊#622—21no—
7C2×#3708—21no—
8#63659—21no—
9#63645C411yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11Dic3×D8—62no—
12C2×C32×D4—21no—
13C22×C3⋊Dic3—41no—
14C2×#622—41no—
15C32×D8—21no—
16C32×D8C812yescomplemented
17C2×C32×C8C2×C411yescharacteristic
18#3757—41no—
19C4⋊(C3⋊Dic3)—21no—
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3708—22no—
23#1333—91nomaximal, Sylow
24C2×C3×D8—22no—
25D4×Dic3—64no—
26#832—64no—
27#818—62no—
28C8×Dic3—62no—
29C23×C32—41no—
30C32×D4—22no—
31C32×D4—41no—
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C3⋊Dic3—41no—
34C2×C3⋊Dic3—82no—
35C2×C3⋊Dic3D811yescharacteristic
36C2×C3⋊Dic3SD1611yescharacteristic
37#622—81no—
38C32×C8C2×C811yescharacteristic
39C32×C8M1611yescharacteristic
40C3⋊(C3⋊C8)—21no—
41C4×D8—91no—
42#346—91no—
43#334—91no—
44C2×C3×D4—24no—
45C22×Dic3—124no—
46C3×D8—24no—
47C3×D8—24no—
48C2×C3×C8—22no—
49#217—124no—
50C4⋊Dic3—64no—
51C4×Dic3—62no—
52C2×C3⋊C8—62no—
53C22×C32—42no—
54C22×C32—81no—
55C22×C32—81no—
56C22×C32#10211yescharacteristic
57C32×C4C22⋊C811yescharacteristic
58C32×C4#10411yescharacteristic
59C3⋊Dic3—21no—
60C3⋊Dic3—21no—
61C3⋊Dic3—81no—
62C2×D8#15711yescharacteristic
63C4×D4—181no—
64C2×C16—181no—
65#107—91no—
66C4⋊C8—181no—
67#102—181no—
68C4×C8—91no—
69C23×C3—44no—
70C3×D4—28no—
71C3×D4—44no—
72C2×C3×C4—22no—
73C2×Dic3—62no—
74C2×Dic3—62no—
75C2×Dic3—124no—
76C2×Dic3—248no—
77C3×C8—22no—
78C3×C8—22no—
79C3⋊C8—122no—
80C2×C32—82no—
81C2×C32D4⋊C811yescharacteristic
82C2×C32#36011yescharacteristic
83C2×C32#36111yescharacteristic
84C2×D4—21no—
85C22×C4—361no—
86D8—21no—
87D8#62212yescomplemented
88C2×C8—91no—
89C2×C8—361no—
90C2×C8C2×#15711yescharacteristic
91C4⋊C4—181no—
92C22⋊C4—361no—
93C42—91no—
94C16—182no—
95C22×C3—22no—
96C22×C3—48no—
97C22×C3—84no—
98C22×C3—84no—
99C3×C4—22no—
100C3×C4—22no—
101Dic3—64no—
102Dic3—122no—
103Dic3—244no—
104C32#133311yescharacteristic, complemented, Sylow
105C23—41no—
106D4—22no—
107D4—41no—
108C2×C4—91no—
109C2×C4—91no—
110C2×C4—361no—
111C2×C4—722no—
112C2×C4C22⋊#15711yescharacteristic
113C8—181no—
114C8—721no—
115C8C2×#62211yescharacteristic
116C8#379211yescharacteristic
117C2×C3—22no—
118C2×C3—22no—
119C2×C3—22no—
120C2×C3—88no—
121C22—42no—
122C22—81no—
123C22—81no—
124C22#6378211yescharacteristic
125C4—181no—
126C4—181no—
127C4—721no—
128C4#6378311yescharacteristic
129C4C22⋊#62211yescharacteristic
130C3—22no—
131C2—82no—
132C2#1059019211yescharacteristic
133C2#1059019511yescharacteristic
134C2D4⋊#62211yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
Fitting, prime radicalC2×C32×D8C4
socleC22×C32#102
cosocleC8×C3⋊Dic3C22
hypercenterC2×D8#157
hypocenterC32#1333
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590175C2semidirect
3. #10590170C2semidirect
16. C32×D8C8semidirect
87. D8#622semidirect
104. C32#1333semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
#105901752
#105901702
#13339