Finite Group Databasebeta

← #11776880

Subgroups — #11776880

Order 1152.

310 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#3787C211yesmaximal, characteristic
2#10590340C212yesmaximal
3#10590041C214yesmaximal, complemented
4C2×#3787C412yes—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712—22no—
7C4×#622C411yescharacteristic
8C4×#622C411yescharacteristic
9C4×#622C2212yes—
10C3×C4⋊(C3⋊C8)—22no—
11#63572C2214yes—
12#4837—62no—
13C2×C4×C3⋊D3C2×C411yescharacteristic
14C2×C4×C3⋊D3D411yescharacteristic
15C2×C4×C3⋊D3Q811yescharacteristic
16C2×#622C2×C412yes—
17C2×#622C2×C412yes—
18#3787—24no—
19C32×C42D411yescharacteristic
20C4×C3⋊Dic3C2×C411yescharacteristic
21C4×C3⋊Dic3Q811yescharacteristic
22C4×C3⋊Dic3C2311yescharacteristic
23C2×C3×C3⋊C8—24no—
24#3712—44no—
25#1566—91nomaximal, Sylow
26C2×ΓL(1,𝔽25)—64no—
27C42×D3—62no—
28C3×C4⋊C8—62no—
29Dic3⋊C8—64no—
30C4⋊(C3⋊C8)—22no—
31C22×C3⋊D3C4⋊C411yescharacteristic
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4C4⋊C411yescharacteristic
34C2×C32×C4C2×D411yescharacteristic
35C2×C3⋊Dic3C4⋊C411yescharacteristic
36C2×C3⋊Dic3C22×C411yescharacteristic
37C2×C3⋊Dic3C2×Q811yescharacteristic
38C4×C3⋊D3—22no—
39C4×C3⋊D3—22no—
40C4×C3⋊D3SD1614yes—
41#622—22no—
42#622M1614yescomplemented
43C3×C3⋊C8—44no—
44#423—92no—
45C2×C4×C8—91no—
46#334—94no—
47C2×C4×D3—62no—
48C2×C4×D3—62no—
49C2×C4×D3—62no—
50C2×C3×C8—64no—
51C3×C42—22no—
52C4×Dic3—62no—
53C4×Dic3—62no—
54C4×Dic3—62no—
55C2×C3⋊C8—24no—
56ΓL(1,𝔽25)—128no—
57C22×C32C2×C4⋊C411yescharacteristic
58C2×C3⋊D3—21no—
59C2×C3⋊D3—21no—
60C2×C3⋊D3#10612yes—
61C32×C4—21no—
62C32×C4#10812yes—
63C32×C4C2×SD1612yes—
64C3⋊Dic3—21no—
65C3⋊Dic3#10612yes—
66C3⋊Dic3C2×M1612yes—
67C2×M16—182no—
68C22×C8—92no—
69C2×C42—91no—
70C4⋊C8—62no—
71C4⋊C8—94no—
72C4×C8—91no—
73C4×C8—91no—
74C4×C8—92no—
75C22×D3—62no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×Dic3—62no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C4×D3—64no—
83C4×D3—64no—
84C4×D3—124no—
85C4×D3—124no—
86C3×C8—124no—
87C3⋊C8—44no—
88C2×C32#42311yescharacteristic
89C2×C32C2×#10611yescharacteristic
90C2×C32C2×#10811yescharacteristic
91C3⋊D3—22no—
92C22×C4—91no—
93C22×C4—91no—
94C22×C4—91no—
95M16—364no—
96C2×C8—64no—
97C2×C8—92no—
98C2×C8—92no—
99C2×C8—184no—
100C42—91no—
101C42—91no—
102C42—91no—
103C42GO+(4,𝔽2)11yescharacteristic
104C22×C3—22no—
105C2×D3—64no—
106C2×D3—122no—
107C2×D3—122no—
108C3×C4—22no—
109C3×C4—22no—
110C3×C4—24no—
111C3×C4—42no—
112Dic3—64no—
113Dic3—64no—
114Dic3—122no—
115C32#156611yescharacteristic, complemented, Sylow
116C23—91no—
117C2×C4—91no—
118C2×C4—91no—
119C2×C4—94no—
120C2×C4—91no—
121C2×C4—182no—
122C2×C4—182no—
123C2×C4#377311yescharacteristic
124C2×C4#377311yescharacteristic
125C2×C4C2×GO+(4,𝔽2)11yescharacteristic
126C8—94no—
127C8—124no—
128C8—182no—
129C2×C3—22no—
130C2×C3—22no—
131C2×C3—22no—
132D3—124no—
133C22—92no—
134C22—181no—
135C22—181no—
136C22C2×#377311yescharacteristic
137C4—21no—
138C4—92no—
139C4—92no—
140C4—181no—
141C4#6373312yes—
142C4#6422712yes—
143C3—22no—
144C2—182no—
145C2#1059332811yescharacteristic
146C2C2×#6373311yescharacteristic
147C2#1059338711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1566
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10590041C2semidirect
42. #622M16semidirect
115. C32#1566semidirect

Maximal subgroups

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

subgroupindex
C4×#37872
#105903402
#105900412
#15669