Finite Group Databasebeta

← #11771572

Subgroups — #11771572

Order 1152.

244 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 40 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#10590174C211yesmaximal, characteristic, complemented
3#10590171C211yesmaximal, 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#1331—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—81no—
35C2×C3⋊Dic3—81no—
36C2×C3⋊Dic3D811yescharacteristic
37C2×C3⋊Dic3SD1611yescharacteristic
38#622—81no—
39C32×C8C2×C811yescharacteristic
40C32×C8M1611yescharacteristic
41C3⋊(C3⋊C8)—21no—
42C4×D8—91no—
43C4×C16—91no—
44#335—91no—
45C2×C3×D4—24no—
46C22×Dic3—124no—
47C3×D8—24no—
48C3×D8—24no—
49C2×C3×C8—22no—
50#217—124no—
51C4⋊Dic3—64no—
52C4×Dic3—62no—
53C2×C3⋊C8—62no—
54C22×C32—42no—
55C22×C32—81no—
56C22×C32—81no—
57C22×C32#10211yescharacteristic
58C32×C4C22⋊C811yescharacteristic
59C32×C4#10411yescharacteristic
60C3⋊Dic3—21no—
61C3⋊Dic3—81no—
62C3⋊Dic3D1611yescharacteristic
63C3⋊Dic3SD3211yescharacteristic
64C2×D8#15711yescharacteristic
65C4×D4—181no—
66C2×C16—181no—
67#107—91no—
68C4⋊C8—181no—
69#102—181no—
70C4×C8—91no—
71C23×C3—44no—
72C3×D4—28no—
73C3×D4—44no—
74C2×C3×C4—22no—
75C2×Dic3—62no—
76C2×Dic3—62no—
77C2×Dic3—124no—
78C2×Dic3—244no—
79C2×Dic3—244no—
80C3×C8—22no—
81C3×C8—22no—
82C3⋊C8—122no—
83C2×C32—82no—
84C2×C32D4⋊C811yescharacteristic
85C2×C32#35711yescharacteristic
86C2×C32#35911yescharacteristic
87C2×D4—21no—
88C22×C4—361no—
89D8—21no—
90D8#62212yescomplemented
91C2×C8—91no—
92C2×C8—361no—
93C2×C8C2×#15711yescharacteristic
94C4⋊C4—181no—
95C22⋊C4—361no—
96C42—91no—
97C16—182no—
98C22×C3—22no—
99C22×C3—48no—
100C22×C3—84no—
101C22×C3—84no—
102C3×C4—22no—
103C3×C4—22no—
104Dic3—62no—
105Dic3—62no—
106Dic3—122no—
107Dic3—244no—
108C32#133111yescharacteristic, complemented, Sylow
109C23—41no—
110D4—22no—
111D4—41no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—361no—
115C2×C4—721no—
116C2×C4—721no—
117C2×C4C22⋊#15711yescharacteristic
118C8—181no—
119C8—721no—
120C8C2×#62211yescharacteristic
121C8#379211yescharacteristic
122C2×C3—22no—
123C2×C3—22no—
124C2×C3—22no—
125C2×C3—88no—
126C22—42no—
127C22—81no—
128C22—81no—
129C22#6378211yescharacteristic
130C4—91no—
131C4—91no—
132C4—181no—
133C4—721no—
134C4#6378311yescharacteristic
135C4C22⋊#62211yescharacteristic
136C3—22no—
137C2—82no—
138C2#1059019311yescharacteristic
139C2#1059019411yescharacteristic
140C2D4⋊#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#1331
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. #10590174C2semidirect
3. #10590171C2semidirect
16. C32×D8C8semidirect
90. D8#622semidirect
108. C32#1331semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
#105901742
#105901712
#13319