Finite Group Databasebeta

← #10591628

Subgroups — #10591628

Order 576.

278 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 70 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
2C2×C3×#216C212yesmaximal
3#63873C211yesmaximal, characteristic
4C2×#3719C212yesmaximal
5#63553C211yesmaximal, characteristic
6#5183—32nomaximal
7C2×C32×Q8C2211yescharacteristic
8C2×#634C2211yescharacteristic
9C2×C3×Dic6C2212yes—
10#3750—22no—
11C4×C3⋊Dic3C2211yescharacteristic
12C3×#216—24no—
13C2×C3×C3⋊C8C2212yes—
14#3724—22no—
15#3719—24no—
16C2×C3×Q16—32no—
17#944—32no—
18#944—32no—
19#944—61no—
20C2×#216—32no—
21C2×#216D312yes—
22C2×Dic12—32no—
23C8×Dic3—32no—
24C32×Q8—22no—
25C2×C32×C4—21no—
26C2×C32×C4C2311yescharacteristic
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3D412yes—
29#634—22no—
30C2×C3×Dic3—22no—
31C3×Dic6—22no—
32C3×Dic6—22no—
33C3×C3⋊C8D414yes—
34#494—91noSylow
35C2×C3×Q8—21no—
36C2×C3×Q8—32no—
37C2×C3×Q8C2×D312yes—
38C2×Dic6—32no—
39C2×Dic6—61no—
40C2×Dic6C2×D312yes—
41C3×Q16—64no—
42C2×C3×C8—32no—
43#216—24no—
44#216—64no—
45Dic3⋊C4—64no—
46Dic3⋊C4—64no—
47Dic3⋊C4—64no—
48C4×Dic3—32no—
49C4×Dic3—61no—
50C2×C3⋊C8C2×D312yes—
51Dic12—64no—
52C22×C32C2×D411yescharacteristic
53C32×C4—41no—
54C32×C4C2×D412yes—
55C3⋊Dic3—41no—
56C3⋊Dic3Q1614yescomplemented
57C3×Dic3—42no—
58C2×Q16—32no—
59C2×Q16—92no—
60C4⋊Q8—91no—
61C4⋊Q8—91no—
62C4×C8—91no—
63C3×Q8—22no—
64C3×Q8—22no—
65C3×Q8—42no—
66C3×Q8—62no—
67C3×Q8—62no—
68C2×C3×C4—22no—
69C2×C3×C4—22no—
70C2×C3×C4—21no—
71C2×C3×C4—62no—
72C2×C3×C4C22×D312yes—
73C2×Dic3—22no—
74C2×Dic3—34no—
75C2×Dic3—62no—
76C2×Dic3—62no—
77C2×Dic3—62no—
78Dic6—22no—
79Dic6—22no—
80Dic6—62no—
81Dic6—62no—
82Dic6—122no—
83C3×C8—34no—
84C3⋊C8#6714yes—
85C2×C32#12711yescharacteristic
86C2×C32C2×Q1612yes—
87C2×Q8—32no—
88C2×Q8—91no—
89C2×Q8D3211yescharacteristic
90Q16—64no—
91Q16—184no—
92C2×C8—32no—
93C4⋊C4—182no—
94C4⋊C4—182no—
95C42—91no—
96C22×C3—21no—
97C22×C3D3×D412yes—
98C3×C4—22no—
99C3×C4—42no—
100C3×C4—42no—
101C3×C4—122no—
102C3×C4D3×D412yes—
103C3×C4C2×#6712yes—
104Dic3—38no—
105Dic3—42no—
106Dic3—64no—
107Dic3—122no—
108Dic3—122no—
109C32#49411yescharacteristic, complemented, Sylow
110Q8—22no—
111Q8—62no—
112Q8—62no—
113Q8—182no—
114C2×C4—21no—
115C2×C4—62no—
116C2×C4—92no—
117C2×C4—181no—
118C2×C4C2×D3211yescharacteristic
119C8—34no—
120C2×C3—22no—
121C2×C3—21no—
122C2×C3D3×Q1614yes—
123C2×C3#94012yes—
124C22#381111yescharacteristic
125C4—41no—
126C4—94no—
127C4—122no—
128C4—361no—
129C4D3×#6712yes—
130C3—21no—
131C3#518312yescomplemented
132C2#6394412yes—
133C2#6397911yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#494
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
56. C3⋊Dic3Q16semidirect
109. C32#494semidirect
131. C3#5183semidirect

Maximal subgroups

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

subgroupindex
#641532
C2×C3×#2162
#638732
C2×#37192
#635532
#51833