Finite Group Databasebeta

← #11772787

Subgroups — #11772787

Order 1152.

248 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 20 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#10592451C211yesmaximal, characteristic
2#10590220C211yesmaximal, characteristic, complemented
3#10590218C211yesmaximal, characteristic, complemented
4#64364C411yescharacteristic
5#64153C2211yescharacteristic
6#64118—21no—
7#63780—21no—
8#63779—21no—
9C32×#101C411yescharacteristic
10#63652—21no—
11#4752—62no—
12C2×C32×Q8C2×C411yescharacteristic
13#3832—41no—
14Q8×C3⋊D3—41no—
15#3828—21no—
16#3828—41no—
17C2×#634D411yescharacteristic
18#3792—41no—
19C2×#622—41no—
20C32×M16—21no—
21#3750—41no—
22C4×C3⋊Dic3D411yescharacteristic
23#3746—41no—
24#3744—41no—
25#1405—91nomaximal, Sylow
26#1007—62no—
27#944—62no—
28#909—64no—
29C3×#101—22no—
30#825—64no—
31C32×Q8—41no—
32C2×C32×C4—21no—
33C2×C32×C4C22⋊C411yescharacteristic
34#638—41no—
35C2×C3⋊Dic3—21no—
36C2×C3⋊Dic3—21no—
37C4⋊(C3⋊D3)—21no—
38C4⋊(C3⋊D3)—41no—
39C4×C3⋊D3—41no—
40C4×C3⋊D3—42no—
41#634—21no—
42#634—41no—
43#634—41no—
44#622—81no—
45#622—81no—
46C32×C8—41no—
47#456—91no—
48#356—91no—
49#333—91no—
50C2×C3×Q8—22no—
51#239—124no—
52D3×Q8—124no—
53#235—64no—
54#235—124no—
55C2×Dic6—62no—
56C3×M16—24no—
57Dic3⋊C4—124no—
58C4×Dic3—62no—
59Dic12—124no—
60#204—124no—
61C22×C32#9911yescharacteristic
62C2×C3⋊D3—41no—
63C32×C4—21no—
64C32×C4—41no—
65C3⋊Dic3—21no—
66C3⋊Dic3—21no—
67C3⋊Dic3—41no—
68C3⋊Dic3—41no—
692−1+4—91no—
70#137—181no—
71C4⋊Q8—91no—
72C4⋊C8—181no—
73#104—181no—
74#101—181no—
75#101#15711yescharacteristic
76C3×Q8—44no—
77C2×C3×C4—24no—
78C2×C3×C4—22no—
79#67—124no—
80C2×Dic3—122no—
81C2×Dic3—122no—
82D12—64no—
83D12—124no—
84C4×D3—124no—
85C4×D3—128no—
86Dic6—64no—
87Dic6—124no—
88Dic6—124no—
89C3×C8—44no—
90C2×C32—21no—
91C2×C32AΣL(1,𝔽16)11yescharacteristic
92C3⋊D3—81no—
93#41—181no—
94#41—361no—
95#41—361no—
96C2×Q8—91no—
97C2×Q8—361no—
98C2×Q8C2×#15711yescharacteristic
99Q16—361no—
100SD16—361no—
101M16—21no—
102M16—361no—
103C2×C8—361no—
104C4⋊C4—361no—
105C42—91no—
106C22×C3—22no—
107C2×D3—124no—
108C3×C4—24no—
109C3×C4—44no—
110Dic3—122no—
111Dic3—122no—
112Dic3—124no—
113Dic3—242no—
114C32#140511yescharacteristic, complemented, Sylow
115Q8—41no—
116Q8—181no—
117Q8—361no—
118Q8—361no—
119D4—181no—
120D4—361no—
121D4—361no—
122C2×C4—21no—
123C2×C4—181no—
124C2×C4—181no—
125C2×C4—361no—
126C2×C4—362no—
127C2×C4C22⋊#15711yescharacteristic
128C8—41no—
129C8—721no—
130C8—721no—
131C2×C3—22no—
132C2×C3—42no—
133D3—244no—
134C22—361no—
135C22#6377411yescharacteristic
136C4—21no—
137C4—41no—
138C4—181no—
139C4—181no—
140C4—361no—
141C4—361no—
142C3—22no—
143C2—21no—
144C2—721no—
145C2#1059015311yescharacteristic
subgroupG/H
centerC2#10590153
commutatorC2×C32×Q8C2×C4
FrattiniC2×Q8C2×#157
FittingC32×#101C4
socleC2×C32AΣL(1,𝔽16)
prime radical#64364C4
cosocle#64153C22
hypercenter#101#157
hypocenterC32#1405
LCSG ▷ C2×C32×Q8 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
2. #10590220C2semidirect
3. #10590218C2semidirect
114. C32#1405semidirect

Maximal subgroups

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

subgroupindex
#105924512
#105902202
#105902182
#14059