Finite Group Databasebeta

← #10591633

Subgroups — #10591633

Order 576.

251 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 251 conjugacy classes of subgroups — too many to draw. Only its 68 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
1Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#216C212yesmaximal
3#63873C211yesmaximal, characteristic
4#63572C211yesmaximal, characteristic
5#63566C212yesmaximal
6#5182—32nomaximal
7C2×C32×Q8C2211yescharacteristic
8C2×C3×Dic6C2212yes—
9C4⋊(C3⋊Dic3)—21no—
10C4⋊(C3⋊Dic3)C2211yescharacteristic
11C4×C3⋊Dic3—21no—
12C4×C3⋊Dic3C2211yescharacteristic
13C3×#216—24no—
14C2×C3×C3⋊C8C2212yes—
15#3724—21no—
16#3724—21no—
17C2×C3×Q16—32no—
18Q8×Dic3—32no—
19Q8×Dic3—61no—
20#944—32no—
21C2×#216D312yes—
22#835—32no—
23#816—32no—
24Dic3⋊C8—32no—
25C32×Q8—21no—
26C32×Q8D412yes—
27C2×C32×C4—21no—
28C2×C32×C4C2311yescharacteristic
29C2×C3⋊Dic3—21no—
30C2×C3⋊Dic3D411yescharacteristic
31C2×C3⋊Dic3D411yescharacteristic
32C2×C3×Dic3—22no—
33C3×Dic6—22no—
34C3×Dic6—22no—
35C3×C3⋊C8—22no—
36#462—91noSylow
37C2×C3×Q8—21no—
38C2×C3×Q8—32no—
39C2×C3×Q8C2×D312yes—
40C2×Dic6C2×D312yes—
41C3×Q16—64no—
42C2×C3×C8—32no—
43#216—24no—
44C4⋊Dic3—32no—
45C4⋊Dic3—61no—
46C4⋊Dic3—62no—
47C4⋊Dic3—62no—
48Dic3⋊C4—62no—
49Dic3⋊C4—62no—
50C4×Dic3—32no—
51C4×Dic3—61no—
52C4×Dic3—62no—
53C4×Dic3—62no—
54C2×C3⋊C8C2×D312yes—
55C22×C32C2×D411yescharacteristic
56C32×C4—22no—
57C32×C4C2×D411yescharacteristic
58C32×C4#4111yescharacteristic
59C3⋊Dic3—21no—
60C3⋊Dic3—41no—
61C3⋊Dic3Q1612yescomplemented
62C3×Dic3—42no—
63C2×Q16—32no—
64C4⋊Q8—91no—
65C4×Q8—91no—
66C4⋊C8—91no—
67#103—92no—
68C3×Q8—22no—
69C3×Q8—22no—
70C3×Q8—22no—
71C3×Q8—62no—
72C3×Q8—62no—
73C3×Q8#6714yes—
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×C3×C4—21no—
77C2×C3×C4—62no—
78C2×C3×C4C22×D312yes—
79C2×Dic3—22no—
80C2×Dic3—32no—
81C2×Dic3—32no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86Dic6—22no—
87Dic6—22no—
88C3×C8—62no—
89C3⋊C8—22no—
90C2×C32#12111yescharacteristic
91C2×C32C2×Q1611yescharacteristic
92C2×C32#13711yescharacteristic
93C2×Q8—32no—
94C2×Q8D3211yescharacteristic
95Q16—64no—
96C2×C8—32no—
97C4⋊C4—91no—
98C4⋊C4—181no—
99C4⋊C4—181no—
100C4⋊C4—181no—
101C42—91no—
102C42—181no—
103C22×C3—21no—
104C22×C3D3×D412yes—
105C3×C4—24no—
106C3×C4—24no—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—122no—
110C3×C4#23712yes—
111C3×C4C2×#6712yes—
112Dic3—34no—
113Dic3—42no—
114Dic3—62no—
115Dic3—62no—
116Dic3—121no—
117Dic3—122no—
118Dic3—122no—
119C32#46211yescharacteristic, complemented, Sylow
120Q8—21no—
121Q8—62no—
122Q8—62no—
123Q8#62512yes—
124C2×C4—21no—
125C2×C4—62no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—181no—
129C2×C4C2×D3211yescharacteristic
130C8—62no—
131C2×C3—21no—
132C2×C3—21no—
133C2×C3—21no—
134C2×C3D3×Q1612yes—
135C2×C3#91812yes—
136C2×C3#93912yes—
137C22#381111yescharacteristic
138C4—22no—
139C4—92no—
140C4—122no—
141C4—181no—
142C4—361no—
143C4#380511yescharacteristic
144C4C2×#62511yescharacteristic
145C3—21no—
146C3#518212yescomplemented
147C2#6394411yescharacteristic
148C2#6394511yescharacteristic
149C2#6398011yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#462
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
61. C3⋊Dic3Q16semidirect
119. C32#462semidirect
146. C3#5182semidirect

Maximal subgroups

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

subgroupindex
Q8×C3⋊Dic32
C2×C3×#2162
#638732
#635722
#635662
#51823