Finite Group Databasebeta

← C3×#68000 #11920121

Subgroups — C3×#68000 #11920121

Order 1152.

150 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 20 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
1C3×#392⋊C3C211yesmaximal, characteristic
2#68000C311yesmaximal, characteristic, direct product factor
3C3×#1343—31nomaximal
4C3×A4⋊C8—41nomaximal
5C3×#95⋊C3C411yescharacteristic, complemented
6C3×#392D311yescharacteristic
7#392⋊C3—21no—
8#392⋊C3C2×C311yescharacteristic
9C3×#342—31no—
10C3×#323—31no—
11C3×C4×A4—41no—
12#1343—31noSylow
13C22×C3×D4—31no—
14C2×C3×C22⋊C4—31no—
15C2×C3×C22⋊C4—61no—
16A4⋊C8—41no—
17C3×C22⋊C8—61no—
18C3×#95Dic311yescharacteristic
19#95⋊C3—21no—
20#95⋊C3C3×C411yescharacteristic, complemented
21C2×C3×A4—41no—
22C3×C3⋊C8—161no—
23#392C3×D311yescharacteristic
24#342—31no—
25#323—31no—
26C24×C3—31no—
27C2×C3×D4—121no—
28C2×C3×D4—121no—
29C2×C3×D4—121no—
30C22×C3×C4—31no—
31C22×C3×C4—121no—
32C22×C3×C4S411yescharacteristic
33C4×A4—41no—
34C4×A4—81no—
35C2×C3×C8—121no—
36C3×C22⋊C4—62no—
37C3×C22⋊C4—121no—
38C3×C22⋊C4—121no—
39C3×A4—41no—
40C32×C4—161no—
41C22×D4—31no—
42C2×C22⋊C4—31no—
43C2×C22⋊C4—61no—
44C22⋊C8—61no—
45#95C3×Dic311yescharacteristic
46C23×C3—31no—
47C23×C3—31no—
48C23×C3—61no—
49C23×C3—61no—
50C23×C3—121no—
51C23×C3—121no—
52C23×C3SL(2,ℤ/4)11yescharacteristic
53C2×A4—41no—
54C2×A4—81no—
55C3×D4—121no—
56C3×D4—121no—
57C3×D4—122no—
58C2×C3×C4—61no—
59C2×C3×C4—61no—
60C2×C3×C4—121no—
61C2×C3×C4—122no—
62C2×C3×C4—241no—
63C2×C3×C4—241no—
64C3×C8—241no—
65C3⋊C8—161no—
66C2×C32—161no—
67C24—31no—
68C2×D4—121no—
69C2×D4—121no—
70C2×D4—121no—
71C22×C4—31no—
72C22×C4—121no—
73C22×C4C3×S411yescharacteristic
74C2×C8—121no—
75C22⋊C4—62no—
76C22⋊C4—121no—
77C22⋊C4—121no—
78C22×C3—31no—
79C22×C3—31no—
80C22×C3—61no—
81C22×C3—61no—
82C22×C3—121no—
83C22×C3—121no—
84C22×C3—121no—
85C22×C3—121no—
86C22×C3—241no—
87C22×C3GU(2,𝔽3)11yescharacteristic
88A4—41no—
89A4—81no—
90C3×C4—41no—
91C3×C4—121no—
92C3×C4—161no—
93C3×C4—242no—
94C3×C4—321no—
95C32—161noSylow
96C23—31no—
97C23—31no—
98C23—61no—
99C23—61no—
100C23—121no—
101C23—121no—
102C23C3×SL(2,ℤ/4)11yescharacteristic
103D4—121no—
104D4—121no—
105D4—122no—
106C2×C4—61no—
107C2×C4—61no—
108C2×C4—121no—
109C2×C4—122no—
110C2×C4—241no—
111C2×C4—241no—
112C8—241no—
113C2×C3—31no—
114C2×C3—31no—
115C2×C3—121no—
116C2×C3—121no—
117C2×C3—161no—
118C2×C3—321no—
119C2×C3#462611yescharacteristic
120C22—31no—
121C22—31no—
122C22—61no—
123C22—61no—
124C22—121no—
125C22—121no—
126C22—121no—
127C22—121no—
128C22—241no—
129C22C3×GU(2,𝔽3)11yescharacteristic
130C4—41no—
131C4—121no—
132C4—242no—
133C3—161no—
134C3—321no—
135C3#6800011yescharacteristic, direct product factor
136C2—31no—
137C2—31no—
138C2—121no—
139C2—121no—
140C2C3×#462611yescharacteristic
subgroupG/H
center, hypercenterC2×C3#4626
commutator, hypocenter#95⋊C3C3×C4
FrattiniC22×C4C3×S4
FittingC3×#392D3
socleC23×C3SL(2,ℤ/4)
prime radicalC3×#392⋊C3C2
cosocle#392⋊C3C2×C3
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. #68000C3direct (N × H)
5. C3×#95⋊C3C4semidirect
20. #95⋊C3C3×C4semidirect
135. C3#68000direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#392⋊C32
#680003
C3×#13433
C3×A4⋊C84