Finite Group Databasebeta

← #11772423

Subgroups — #11772423

Order 1152.

266 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 50 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#10593771C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic
4#64283—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6C4⋊C4×C3⋊D3—21no—
7#63773—21no—
8#63771—21no—
9#63770C412yescomplemented
10#63765—21no—
11#63764C412yescomplemented
12C32×#106C411yescharacteristic
13#63644C411yescharacteristic
14#63635—21no—
15D3×#106—62no—
16C2×C4×C3⋊D3—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18#3792—41no—
19#3788—22no—
20#3787—41no—
21C2×C32×C8C2×C411yescharacteristic
22C32×C4⋊C4—21no—
23C4⋊(C3⋊Dic3)—21no—
24#3750—41no—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1383—91nomaximal, Sylow
32C2×D3×C8—62no—
33D3×C4⋊C4—64no—
34C3×#106—22no—
35#817—62no—
36#808—64no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×C32×C4—41no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3D811yescharacteristic
42C4×C3⋊D3—82no—
43C4×C3⋊D3C22⋊C411yescharacteristic
44C4×C3⋊D3C4⋊C411yescharacteristic
45C4×C3⋊D3SD1611yescharacteristic
46C4×C3⋊D3Q1611yescharacteristic
47#622—42no—
48C32×C8C4211yescharacteristic
49C32×C8C4⋊C411yescharacteristic
50C3⋊(C3⋊C8)C22⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C2×M32—91no—
53C2×#108—91no—
54C2×#106—91no—
55C2×C4×D3—62no—
56C2×C4×D3—124no—
57C2×C3×C8—22no—
58C3×C4⋊C4—24no—
59C4⋊Dic3—64no—
60Dic3⋊C4—124no—
61C2×C3⋊C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65D3×C8—62no—
66C22×C32#10211yescharacteristic
67C2×C3⋊D3—22no—
68C2×C3⋊D3#10311yescharacteristic
69C2×C3⋊D3#10611yescharacteristic
70C32×C4—81no—
71C32×C4#9511yescharacteristic
72C32×C4#10311yescharacteristic
73C3⋊Dic3—81no—
74C3⋊Dic3#10211yescharacteristic
75C3⋊Dic3#10711yescharacteristic
76C2×M16—181no—
77C22×C8—91no—
78C2×C4⋊C4—181no—
79M32—181no—
80M32—181no—
81C2×C16—92no—
82#108—92no—
83#108—181no—
84#106—91no—
85#106—181no—
86#106#15711yescharacteristic
87C22×D3—62no—
88C2×C3×C4—22no—
89C2×C3×C4—44no—
90C2×Dic3—62no—
91C2×Dic3—124no—
92C4×D3—62no—
93C4×D3—62no—
94C4×D3—62no—
95C4×D3—62no—
96C4×D3—248no—
97C3×C8—22no—
98C3×C8—22no—
99C3⋊C8—62no—
100C3⋊C8—62no—
101C2×C32—21no—
102C2×C32#34011yescharacteristic
103C3⋊D3—21no—
104C3⋊D3#36512yes—
105C22×C4—91no—
106C22×C4—361no—
107M16—182no—
108M16—361no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—361no—
115C2×C8C2×#15711yescharacteristic
116C4⋊C4—21no—
117C4⋊C4—181no—
118C4⋊C4—361no—
119C16—182no—
120C22×C3—22no—
121C2×D3—62no—
122C2×D3—62no—
123C2×D3—68no—
124C3×C4—22no—
125C3×C4—22no—
126C3×C4—84no—
127Dic3—62no—
128Dic3—62no—
129Dic3—244no—
130C32#138311yescharacteristic, complemented, Sylow
131C23—91no—
132C2×C4—41no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—361no—
139C2×C4—722no—
140C2×C4C22⋊#15711yescharacteristic
141C8—91no—
142C8—91no—
143C8—362no—
144C8C4×#15711yescharacteristic
145C8C4⋊#15711yescharacteristic
146C2×C3—24no—
147C2×C3—22no—
148D3—64no—
149D3—64no—
150C22—91no—
151C22—91no—
152C22—182no—
153C22#6378211yescharacteristic
154C4—81no—
155C4—91no—
156C4—91no—
157C4—721no—
158C4#6378111yescharacteristic
159C4#6378411yescharacteristic
160C3—22no—
161C2—21no—
162C2—92no—
163C2—181no—
164C2#1059016311yescharacteristic
subgroupG/H
centerC2#10590163
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#106C4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenter#106#157
hypocenterC32#1383
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
9. #63770C4semidirect
11. #63764C4semidirect
130. C32#1383semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105937622
C3⋊D3×#1062
#13839