Finite Group Databasebeta

← #11795941

Subgroups — #11795941

Order 1152.

290 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593762C212yesmaximal
2#10592388C211yesmaximal, characteristic
3#10590179C212yesmaximal, complemented
4#10590149C212yesmaximal, complemented
5C2×#3743C411yescharacteristic
6C2×C8×C3⋊D3C2211yescharacteristic
7#64081C411yescharacteristic
8#63773C2214yes—
9#63765C414yescomplemented
10#63764C414yescomplemented
11C32×C4×C8C411yescharacteristic
12#63642C2211yescharacteristic
13C8×C3⋊Dic3C411yescharacteristic
14#63630C2211yescharacteristic
15#4689—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C32×C8C2×C411yescharacteristic
18C2×C32×C8C2×C411yescharacteristic
19C32×C42C2×C411yescharacteristic
20#3752—21no—
21#3750—21no—
22C4×C3⋊Dic3C2×C411yescharacteristic
23C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25#3743—22no—
26C8×C3⋊D3C2×C412yes—
27C8×C3⋊D3C2×C412yes—
28#3708C2×C418yes—
29#2110—91nomaximal, Sylow
30C2×ΓL(1,𝔽25)—62no—
31C2×D3×C8—62no—
32#872—62no—
33C3×C4×C8—22no—
34#815—62no—
35C8×Dic3—62no—
36#803—62no—
37C22×C3⋊D3M1611yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4C22×C411yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3M1611yescharacteristic
42C4×C3⋊D3C4212yes—
43C4×C3⋊D3M1612yes—
44C32×C8—21no—
45C32×C8C4211yescharacteristic
46C32×C8C4211yescharacteristic
47C3⋊(C3⋊C8)—21no—
48C3⋊(C3⋊C8)C22×C412yes—
49C2×M32—92no—
50#405—91no—
51#347—92no—
52#347—92no—
53C2×C4×D3—62no—
54C2×C3×C8—22no—
55C2×C3×C8—22no—
56C3×C42—22no—
57(C2×D3)⋊C4—64no—
58Dic3⋊C4—64no—
59C4×Dic3—62no—
60C2×C3⋊C8—62no—
61C2×C3⋊C8—62no—
62ΓL(1,𝔽25)—68no—
63D3×C8—64no—
64D3×C8—64no—
65C22×C32C2×M1611yescharacteristic
66C2×C3⋊D3—41no—
67C2×C3⋊D3#9712yes—
68C32×C4—41no—
69C32×C4C2×C4211yescharacteristic
70C32×C4C2×M1611yescharacteristic
71C3⋊Dic3—41no—
72C3⋊Dic3#9712yes—
73C2×M16—91no—
74C22×C8—91no—
75#117—91no—
76M32—94no—
77M32—94no—
78C2×C16—94no—
79#97—91no—
80#97—91no—
81C4×C8—91no—
82C4×C8#15711yescharacteristic
83C22×D3—62no—
84C2×C3×C4—24no—
85C2×C3×C4—22no—
86C2×Dic3—62no—
87C2×Dic3—64no—
88C4×D3—64no—
89C4×D3—64no—
90C3×C8—24no—
91C3×C8—22no—
92C3×C8—22no—
93C3⋊C8—64no—
94C3⋊C8—64no—
95C2×C32—21no—
96C2×C32C2×#9711yescharacteristic
97C3⋊D3—22no—
98C22×C4—91no—
99M16—182no—
100C2×C8—91no—
101C2×C8—92no—
102C2×C8—92no—
103C2×C8—91no—
104C2×C8C2×#15711yescharacteristic
105C2×C8C2×#15711yescharacteristic
106C4⋊C4—181no—
107C22⋊C4—181no—
108C42—91no—
109C42C2×#15711yescharacteristic
110C16—98no—
111C22×C3—22no—
112C2×D3—64no—
113C2×D3—124no—
114C3×C4—22no—
115C3×C4—22no—
116C3×C4—44no—
117Dic3—64no—
118Dic3—124no—
119C32#211011yescharacteristic, complemented, Sylow
120C23—91no—
121C2×C4—21no—
122C2×C4—91no—
123C2×C4—92no—
124C2×C4—92no—
125C2×C4—181no—
126C2×C4C22×#15711yescharacteristic
127C8—21no—
128C8—92no—
129C8—181no—
130C8C4×#15711yescharacteristic
131C8C4×#15711yescharacteristic
132C2×C3—24no—
133C2×C3—22no—
134D3—124no—
135C22—92no—
136C22—361no—
137C22#6428311yescharacteristic
138C4—41no—
139C4—92no—
140C4—361no—
141C4#6428311yescharacteristic
142C4C2×C4×#15711yescharacteristic
143C3—22no—
144C2—21no—
145C2—182no—
146C2#1059372311yescharacteristic
subgroupG/H
centerC8C4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC2×C32C2×#97
prime radicalC22×C3⋊D3M16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4×C8#157
hypocenterC32#2110
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10590179C2semidirect
4. #10590149C2semidirect
9. #63765C4semidirect
10. #63764C4semidirect
119. C32#2110semidirect

Maximal subgroups

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

subgroupindex
#105937622
#105923882
#105901792
#105901492
#21109