Finite Group Databasebeta

← C3⋊#67998 #11920134

Subgroups — C3⋊#67998 #11920134

Order 1152.

190 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 29 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×#379⋊C3C211yesmaximal, characteristic
2#67998—33nomaximal
3#67622—31nomaximal
4C2×C3×C22⋊A4C411yescharacteristic
5C3⋊(A4⋊C8)—41nomaximal
6C3×#379D311yescharacteristic
7#379⋊C3D313yes—
8#4525—31no—
9#4525—31no—
10C3×C22⋊A4C811yescharacteristic, complemented
11C3×C4×A4—41no—
12#1316—91noSylow
13C25×C3Dic311yescharacteristic
14C2×C22⋊A4Dic313yes—
15C2×C3×C22⋊C4—31no—
16C2×C3×C22⋊C4—31no—
17A4⋊C8—123no—
18#830—61no—
19#830—61no—
20C2×C3×A4—41no—
21C2×C3×A4—161no—
22C3⋊(C3⋊C8)—161no—
23#379C3⋊D311yescharacteristic
24#323—91no—
25#323—91no—
26C24×C3—31no—
27C24×C3—31no—
28C24×C3—121no—
29C24×C3—121no—
30C24×C3C3⋊C811yescharacteristic, complemented
31C22⋊A4C3⋊C813yescomplemented
32C22×C3×C4—31no—
33C22×C3×C4S411yescharacteristic
34C4×A4—43no—
35C3×C22⋊C4—121no—
36C3×C22⋊C4—121no—
37C2×C3⋊C8—121no—
38C2×C3⋊C8—121no—
39C3×A4—41no—
40C3×A4—161no—
41C32×C4—161no—
42C25C3⋊Dic311yescharacteristic
43C2×C22⋊C4—31no—
44C2×C22⋊C4—31no—
45C22⋊C8—181no—
46C22⋊C8—181no—
47C23×C3—31no—
48C23×C3—31no—
49C23×C3—41no—
50C23×C3—61no—
51C23×C3—61no—
52C23×C3—121no—
53C23×C3—121no—
54C23×C3—121no—
55C23×C3—121no—
56C23×C3—122no—
57C23×C3—121no—
58C23×C3—121no—
59C23×C3—121no—
60C23×C3—122no—
61C23×C3SL(2,ℤ/4)11yescharacteristic
62C2×A4—43no—
63C2×A4—163no—
64C2×C3×C4—61no—
65C2×C3×C4—61no—
66C2×C3×C4—121no—
67C3⋊C8—241no—
68C3⋊C8—241no—
69C3⋊C8—483no—
70C2×C32—161no—
71C24—31no—
72C24—31no—
73C24—121no—
74C24—121no—
75C24C3⋊(C3⋊C8)11yescharacteristic, complemented
76C22×C4—31no—
77C22×C4C3⋊S411yescharacteristic
78C2×C8—361no—
79C2×C8—361no—
80C22⋊C4—121no—
81C22⋊C4—121no—
82C22×C3—31no—
83C22×C3—31no—
84C22×C3—41no—
85C22×C3—61no—
86C22×C3—61no—
87C22×C3—121no—
88C22×C3—121no—
89C22×C3—122no—
90C22×C3—121no—
91C22×C3—121no—
92C22×C3—121no—
93C22×C3—121no—
94C22×C3—122no—
95C22×C3—121no—
96C22×C3A4⋊C811yescharacteristic
97A4—43no—
98A4—163no—
99C3×C4—41no—
100C3×C4—121no—
101C3×C4—163no—
102C32—161noSylow
103C23—31no—
104C23—31no—
105C23—41no—
106C23—61no—
107C23—61no—
108C23—121no—
109C23—121no—
110C23—121no—
111C23—121no—
112C23—122no—
113C23—121no—
114C23—121no—
115C23—121no—
116C23—122no—
117C23C3⋊SL(2,ℤ/4)11yescharacteristic
118C2×C4—61no—
119C2×C4—61no—
120C2×C4—121no—
121C8—721no—
122C8—721no—
123C2×C3—31no—
124C2×C3—31no—
125C2×C3—121no—
126C2×C3—121no—
127C2×C3—163no—
128C2×C3#462511yescharacteristic
129C22—31no—
130C22—31no—
131C22—41no—
132C22—61no—
133C22—61no—
134C22—121no—
135C22—121no—
136C22—122no—
137C22—121no—
138C22—121no—
139C22—121no—
140C22—121no—
141C22—122no—
142C22—121no—
143C22C3⋊(A4⋊C8)11yescharacteristic
144C4—41no—
145C4—121no—
146C3—163no—
147C3#6799811yescharacteristic, complemented
148C2—31no—
149C2—31no—
150C2—121no—
151C2—121no—
152C2C3⋊#462511yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#4625
commutator, hypocenterC3×C22⋊A4C8
FrattiniC22×C4C3⋊S4
FittingC3×#379D3
socleC23×C3SL(2,ℤ/4)
prime radicalC2×C3×C22⋊A4C4
cosocleC3×#379⋊C3C2
LCSG ▷ C3×C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
10. C3×C22⋊A4C8semidirect
30. C24×C3C3⋊C8semidirect
31. C22⋊A4C3⋊C8semidirect
75. C24C3⋊(C3⋊C8)semidirect
147. C3#67998semidirect

Maximal subgroups

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

subgroupindex
C3×#379⋊C32
#679983
#676223
C3⋊(A4⋊C8)4