Finite Group Databasebeta

← C3⋊#10596770 #13181787

Subgroups — C3⋊#10596770 #13181787

Order 1728.

151 conjugacy classes of subgroups; only the 9 normal subgroups are shown.

normal subgroups only

This group has 151 conjugacy classes of subgroups — too many to draw. Only its 9 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×A4⋊S4C211yesmaximal, characteristic
2#10596770—31nomaximal
3C3×A42C411yescharacteristic, complemented
4C3×#1020—61no—
5A4⋊S4D311yescharacteristic
6C3×GL(2,ℤ/4)—61no—
7C3×C3⋊S4—81no—
8#4536—91nomaximal
9C3×C22⋊A4—21no—
10C22×C3×A4—21no—
11C2×C3×S4—61no—
12A42—41no—
13A42—41no—
14A42Dic311yescharacteristic, complemented
15C3×SL(2,ℤ/4)—61no—
16C32×A4—81no—
17C3⋊#157—161nomaximal
18#1020—61no—
19GL(2,ℤ/4)—61no—
20C3×#120—91no—
21#834—91no—
22#833—91no—
23C2×C3×A4—61no—
24C3⋊S4—81no—
25C3×S4—121no—
26C3×S4—242no—
27C3×S4—241no—
28C3×#67—241no—
29AΣL(1,𝔽16)—271noSylow
30C3×C3⋊D3—161no—
31C24×C3#15711yescharacteristic, complemented
32C22⋊A4—21no—
33C22⋊A4—41no—
34C22×A4—21no—
35C22×A4—41no—
36C2×S4—61no—
37C2×C3×D4—91no—
38C2×C3×D4—181no—
39SL(2,ℤ/4)—61no—
40C3×C22⋊C4—91no—
41C3×C22⋊C4—181no—
42#217—181no—
43#208—181no—
44C22×C32—81no—
45C2×C3×D3—241no—
46C3×A4—21no—
47C3×A4—81no—
48C3×A4—82no—
49C3×A4—161no—
50C3×A4—162no—
51C3×A4—161no—
52C3×A4—241no—
53#157—481no—
54C3×Dic3—241no—
55#120—91no—
56#100—271no—
57#99—271no—
58C33—161noSylow
59C23×C3—61no—
60C23×C3—91no—
61C23×C3—91no—
62C2×A4—61no—
63C2×A4—121no—
64S4—121no—
65S4—242no—
66S4—241no—
67C3×D4—361no—
68C3×D4—361no—
69C3×D4—361no—
70C2×C3×C4—91no—
71C2×C3×C4—181no—
72#67—241no—
73C2×Dic3—361no—
74C3⋊C8—361no—
75C2×C32—241no—
76C3⋊D3—161no—
77C3×D3—481no—
78C3×D3—961no—
79C24C3⋊#15711yescharacteristic, complemented
80C2×D4—91no—
81C2×D4—181no—
82M16—541no—
83C22⋊C4—91no—
84C22⋊C4—181no—
85C22⋊C4—541no—
86C22×C3—21no—
87C22×C3—61no—
88C22×C3—81no—
89C22×C3—91no—
90C22×C3—161no—
91C22×C3—181no—
92C22×C3—181no—
93C22×C3—361no—
94C2×D3—241no—
95A4—21no—
96A4—41no—
97A4—82no—
98A4—162no—
99A4—241no—
100A4—481no—
101C3×C4—181no—
102C3×C4—361no—
103Dic3—241no—
104Dic3—721no—
105C32—81no—
106C32—161no—
107C32—321no—
108C32—641no—
109C32—641no—
110C23—61no—
111C23—91no—
112C23—91no—
113D4—361no—
114D4—361no—
115D4—361no—
116C2×C4—91no—
117C2×C4—181no—
118C2×C4—1081no—
119C8—1081no—
120C2×C3—61no—
121C2×C3—91no—
122C2×C3—241no—
123C2×C3—361no—
124C2×C3—481no—
125D3—481no—
126D3—961no—
127C22—21no—
128C22—61no—
129C22—91no—
130C22—181no—
131C22—181no—
132C22—361no—
133C4—181no—
134C4—361no—
135C4—2161no—
136C3—81no—
137C3—161no—
138C3—321no—
139C3—641no—
140C3#1059677011yescharacteristic, complemented
141C2—61no—
142C2—91no—
143C2—361no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterC3×A42C4
Fitting, socleC24×C3#157
prime radical, cosocleC3×A4⋊S4C2
LCSG ▷ C3×A42
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×A42C4semidirect
14. A42Dic3semidirect
31. C24×C3#157semidirect
79. C24C3⋊#157semidirect
140. C3#10596770semidirect

Maximal subgroups

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

subgroupindex
C3×A4⋊S42
#105967703
#45369
C3⋊#15716