Finite Group Databasebeta

← #11772537

Subgroups — #11772537

Order 1152.

242 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 48 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
3#10592559C211yesmaximal, characteristic
4#64283—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#64101—21no—
7#63773—21no—
8#63771C412yescomplemented
9#63770—21no—
10#63765C412yescomplemented
11#63764—21no—
12C32×#106C411yescharacteristic
13#63644C411yescharacteristic
14#63634—21no—
15#4860—62no—
16C2×C4×C3⋊D3D411yescharacteristic
17#3792—41no—
18#3788—22no—
19#3787—41no—
20C2×C32×C8C2×C411yescharacteristic
21C32×C4⋊C4—21no—
22#3752—41no—
23C4⋊(C3⋊Dic3)—21no—
24C4×C3⋊Dic3—41no—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1389—91nomaximal, Sylow
32C2×D3×C8—62no—
33#892—64no—
34C3×#106—22no—
35#817—62no—
36#807—64no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×C32×C4—41no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3D811yescharacteristic
42C4×C3⋊D3C22⋊C411yescharacteristic
43C4×C3⋊D3C4⋊C411yescharacteristic
44C4×C3⋊D3SD1611yescharacteristic
45C4×C3⋊D3Q1611yescharacteristic
46#622—42no—
47C32×C8C4211yescharacteristic
48C32×C8C4⋊C411yescharacteristic
49C3⋊(C3⋊C8)C22⋊C411yescharacteristic
50C3⋊(C3⋊C8)C4⋊C411yescharacteristic
51C2×M32—91no—
52C2×#108—91no—
53#427—91no—
54C2×C4×D3—62no—
55C2×C3×C8—22no—
56C3×C4⋊C4—24no—
57(C2×D3)⋊C4—124no—
58C4⋊Dic3—64no—
59C4×Dic3—124no—
60C2×C3⋊C8—62no—
61D3×C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65C22×C32#10211yescharacteristic
66C2×C3⋊D3—41no—
67C2×C3⋊D3#10311yescharacteristic
68C2×C3⋊D3#10611yescharacteristic
69C32×C4—81no—
70C32×C4#9511yescharacteristic
71C32×C4#10311yescharacteristic
72C3⋊Dic3—81no—
73C3⋊Dic3#10211yescharacteristic
74C3⋊Dic3#10711yescharacteristic
75C2×M16—181no—
76C22×C8—91no—
77#117—181no—
78M32—92no—
79M32—181no—
80C2×C16—181no—
81#108—92no—
82#108—181no—
83#107—181no—
84#106—91no—
85#106#15711yescharacteristic
86C22×D3—62no—
87C2×C3×C4—22no—
88C2×C3×C4—44no—
89C2×Dic3—62no—
90C2×Dic3—124no—
91C4×D3—62no—
92C4×D3—62no—
93C4×D3—62no—
94C4×D3—62no—
95C3×C8—22no—
96C3×C8—22no—
97C3⋊C8—62no—
98C3⋊C8—62no—
99C2×C32—21no—
100C2×C32#34011yescharacteristic
101C3⋊D3—21no—
102C3⋊D3—21no—
103C22×C4—91no—
104M16—182no—
105M16—361no—
106C2×C8—91no—
107C2×C8—91no—
108C2×C8—91no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—361no—
112C2×C8C2×#15711yescharacteristic
113C4⋊C4—21no—
114C4⋊C4—181no—
115C22⋊C4—361no—
116C42—361no—
117C16—182no—
118C22×C3—22no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—124no—
122C3×C4—22no—
123C3×C4—22no—
124C3×C4—84no—
125Dic3—62no—
126Dic3—62no—
127Dic3—244no—
128C32#138911yescharacteristic, complemented, Sylow
129C23—91no—
130C2×C4—41no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—361no—
137C2×C4C22⋊#15711yescharacteristic
138C8—91no—
139C8—91no—
140C8—362no—
141C8C4×#15711yescharacteristic
142C8C4⋊#15711yescharacteristic
143C2×C3—24no—
144C2×C3—22no—
145D3—122no—
146D3—122no—
147C22—91no—
148C22—91no—
149C22—361no—
150C22#6378211yescharacteristic
151C4—81no—
152C4—91no—
153C4—91no—
154C4—721no—
155C4#6378111yescharacteristic
156C4#6378411yescharacteristic
157C3—22no—
158C2—21no—
159C2—181no—
160C2—181no—
161C2#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#1389
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
8. #63771C4semidirect
10. #63765C4semidirect
128. C32#1389semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105937622
#105925592
#13899