Finite Group Databasebeta

← #10591538

Subgroups — #10591538

Order 576.

230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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#64153C211yesmaximal, characteristic
2#63919C211yesmaximal, characteristic
3C3×#835C212yesmaximal
4#63567C212yesmaximal
5#63553C211yesmaximal, characteristic
6#4792—32nomaximal
7C2×C32×Q8C2211yescharacteristic
8C2×#634C2211yescharacteristic
9C2×#627—21no—
10#3750—21no—
11#3750—21no—
12C4×C3⋊Dic3C2211yescharacteristic
13C3×C4⋊Dic3C2212yes—
14C2×C3×C3⋊C8C2212yes—
15#3724—21no—
16#944—32no—
17#944—61no—
18#888—32no—
19C3×#103—32no—
20#835D312yes—
21#816—32no—
22C8×Dic3—32no—
23#810—32no—
24C32×Q8—22no—
25C2×C32×C4—21no—
26C2×C32×C4C2311yescharacteristic
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3D411yescharacteristic
29C2×C3⋊Dic3D411yescharacteristic
30#634—22no—
31C2×C3×Dic3—22no—
32#627—42no—
33C3×C3⋊C8—22no—
34#487—91noSylow
35C2×C3×Q8—21no—
36C2×C3×Q8C2×D312yes—
37C2×Dic6—32no—
38C2×Dic6—61no—
39C2×Dic6—62no—
40C2×C3×C8—32no—
41C3×C4⋊C4—32no—
42C4⋊Dic3C2×D312yes—
43Dic3⋊C4—62no—
44Dic3⋊C4—62no—
45Dic3⋊C4—62no—
46Dic3⋊C4—62no—
47Dic3⋊C4—62no—
48C4×Dic3—32no—
49C4×Dic3—61no—
50C2×C3⋊C8C2×D312yes—
51C22×C32C2×D411yescharacteristic
52C32×C4—41no—
53C32×C4#4112yes—
54C3⋊Dic3—41no—
55C3⋊Dic3SD1612yes—
56C3⋊Dic3Q1612yes—
57C3×Dic3—42no—
58C4⋊Q8—91no—
59C4⋊Q8—91no—
60#103—32no—
61#103—92no—
62C4×C8—91no—
63C3×Q8—22no—
64C3×Q8—22no—
65C3×Q8—42no—
66C2×C3×C4—22no—
67C2×C3×C4—22no—
68C2×C3×C4—21no—
69C2×C3×C4—62no—
70C2×C3×C4C22×D312yes—
71C2×Dic3—22no—
72C2×Dic3—32no—
73C2×Dic3—32no—
74C2×Dic3—61no—
75C2×Dic3—61no—
76C2×Dic3—62no—
77C2×Dic3—62no—
78Dic6—62no—
79Dic6—62no—
80Dic6—122no—
81Dic6—124no—
82C3×C8—62no—
83C3⋊C8—22no—
84C2×C32#12411yescharacteristic
85C2×C32C2×SD1611yescharacteristic
86C2×C32C2×Q1611yescharacteristic
87C2×Q8—91no—
88C2×Q8—181no—
89C2×Q8D3211yescharacteristic
90C2×C8—32no—
91C4⋊C4—32no—
92C4⋊C4—181no—
93C4⋊C4—181no—
94C4⋊C4—181no—
95C42—91no—
96C22×C3—21no—
97C22×C3D3×D412yes—
98C3×C4—22no—
99C3×C4—42no—
100C3×C4—42no—
101C3×C4—122no—
102C3×C4#23512yes—
103C3×C4#23712yes—
104Dic3—34no—
105Dic3—34no—
106Dic3—42no—
107Dic3—62no—
108Dic3—62no—
109Dic3—122no—
110Dic3—122no—
111C32#48711yescharacteristic, complemented, Sylow
112Q8—22no—
113Q8—182no—
114Q8—362no—
115C2×C4—21no—
116C2×C4—62no—
117C2×C4—91no—
118C2×C4—91no—
119C2×C4—181no—
120C2×C4C2×D3211yescharacteristic
121C8—62no—
122C2×C3—21no—
123C2×C3—21no—
124C2×C3—21no—
125C2×C3#88512yes—
126C2×C3D3×SD1612yes—
127C2×C3D3×Q1612yes—
128C22#381111yescharacteristic
129C4—41no—
130C4—92no—
131C4—92no—
132C4—122no—
133C4—361no—
134C4#380412yes—
135C3—21no—
136C3#479212yescomplemented
137C2#6394011yescharacteristic
138C2#6394411yescharacteristic
139C2#6395311yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
111. C32#487semidirect
136. C3#4792semidirect

Maximal subgroups

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

subgroupindex
#641532
#639192
C3×#8352
#635672
#635532
#47923