Finite Group Databasebeta

← C3×#5401 #10593587

Subgroups — C3×#5401 #10593587

Order 576.

152 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 30 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×C4⋊S4C211yesmaximal, characteristic
2C3×A4⋊Q8C211yesmaximal, characteristic, complemented
3C3×C8×A4C211yesmaximal, characteristic, complemented
4#5401C311yesmaximal, characteristic, direct product factor
5C3×#465—31nomaximal
6C2×C3×S4—21no—
7C3×C4×A4C2211yescharacteristic
8C3×SL(2,ℤ/4)—21no—
9C3×#204—41nomaximal
10C4⋊S4C2×C311yescharacteristic
11A4⋊Q8C2×C311yescharacteristic, complemented
12C2×C3×SD16—31no—
13C22×C3×C8D311yescharacteristic, complemented
14C3×C22⋊Q8—31no—
15C3×#121—31no—
16C8×A4—21no—
17C8×A4C2×C311yescharacteristic, complemented
18C3×#106—31no—
19C3×#103—31no—
20C3×#102—31no—
21C2×C3×A4D411yescharacteristic
22C3×S4—41no—
23C3×D12—41no—
24C3×Dic6—41no—
25C32×C8—41no—
26#465—31noSylow
27C2×S4—21no—
28C2×C3×Q8—31no—
29C2×C3×D4—31no—
30C2×C3×D4—61no—
31C22×C3×C4C2×D311yescharacteristic
32C4×A4—21no—
33C4×A4C22×C311yescharacteristic
34SL(2,ℤ/4)—21no—
35C3×SD16—61no—
36C3×SD16—61no—
37C2×C3×C8—31no—
38C2×C3×C8—31no—
39C3×C4⋊C4—31no—
40C3×C4⋊C4—31no—
41C3×C4⋊C4—61no—
42C3×C22⋊C4—61no—
43C3×C22⋊C4—61no—
44#204—41no—
45C2×C3×D3—81no—
46C3×A4SD1611yescharacteristic, complemented
47C32×C4—41no—
48C3×Dic3—81no—
49C2×SD16—31no—
50C22×C8C3×D311yescharacteristic, complemented
51C22⋊Q8—31no—
52#121—31no—
53#106—31no—
54#103—31no—
55#102—31no—
56C23×C3—61no—
57C23×C3D1211yescharacteristic
58C2×A4—21no—
59C2×A4C3×D411yescharacteristic
60S4—41no—
61C3×Q8—61no—
62C3×Q8—61no—
63C3×D4—61no—
64C3×D4—61no—
65C3×D4—121no—
66C3×D4—121no—
67C2×C3×C4—31no—
68C2×C3×C4—31no—
69C2×C3×C4—61no—
70C2×C3×C4—61no—
71C2×C3×C4—61no—
72D12—41no—
73Dic6—41no—
74C3×C8—31no—
75C3×C8—41no—
76C3×C8—81no—
77C3×C8S411yescharacteristic, complemented
78C2×C32—41no—
79C3×D3—161no—
80C2×Q8—31no—
81C2×D4—31no—
82C2×D4—61no—
83C22×C4C2×C3×D311yescharacteristic
84SD16—61no—
85SD16—61no—
86C2×C8—31no—
87C2×C8—31no—
88C4⋊C4—31no—
89C4⋊C4—31no—
90C4⋊C4—61no—
91C22⋊C4—61no—
92C22⋊C4—61no—
93C22×C3—31no—
94C22×C3—31no—
95C22×C3—121no—
96C22×C3—121no—
97C22×C3—121no—
98C22×C3#20411yescharacteristic, complemented
99C2×D3—81no—
100A4—21no—
101A4C3×SD1611yescharacteristic, complemented
102C3×C4—31no—
103C3×C4—41no—
104C3×C4—81no—
105C3×C4—121no—
106C3×C4—121no—
107C3×C4—121no—
108C3×C4C2×S411yescharacteristic
109Dic3—81no—
110C32—41noSylow
111C23—61no—
112C23C3×D1211yescharacteristic
113Q8—61no—
114Q8—61no—
115D4—61no—
116D4—61no—
117D4—121no—
118D4—121no—
119C2×C4—31no—
120C2×C4—31no—
121C2×C4—61no—
122C2×C4—61no—
123C2×C4—61no—
124C8—31no—
125C8C3×S411yescharacteristic, complemented
126C2×C3—31no—
127C2×C3—31no—
128C2×C3—41no—
129C2×C3—81no—
130C2×C3—241no—
131C2×C3C4⋊S411yescharacteristic
132D3—161no—
133C22—31no—
134C22—31no—
135C22—121no—
136C22—121no—
137C22—121no—
138C22C3×#20411yescharacteristic, complemented
139C4—31no—
140C4—121no—
141C4—121no—
142C4—121no—
143C4C2×C3×S411yescharacteristic
144C3—41no—
145C3—81no—
146C3#540111yescharacteristic, direct product factor
147C2—31no—
148C2—31no—
149C2—241no—
150C2C3×C4⋊S411yescharacteristic
subgroupG/H
centerC2×C3C4⋊S4
commutator, cosocleC4×A4C22×C3
FrattiniC4C2×C3×S4
FittingC22×C3×C8D3
socleC23×C3D12
prime radicalC3×C4⋊S4C2
hypercenterC3×C8S4
hypocenterA4C3×SD16
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

Complements

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

NH ≅ G/Ntype
2. C3×A4⋊Q8C2semidirect
3. C3×C8×A4C2semidirect
4. #5401C3direct (N × H)
11. A4⋊Q8C2×C3semidirect
13. C22×C3×C8D3semidirect
17. C8×A4C2×C3semidirect
46. C3×A4SD16semidirect
50. C22×C8C3×D3semidirect
77. C3×C8S4semidirect
98. C22×C3#204semidirect
101. A4C3×SD16semidirect
125. C8C3×S4semidirect
138. C22C3×#204semidirect
146. C3#5401direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4⋊S42
C3×A4⋊Q82
C3×C8×A42
#54013
C3×#4653
C3×#2044