Finite Group Databasebeta

← #74374⋊C3 #11921162

Subgroups — #74374⋊C3 #11921162

Order 1152.

241 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 31 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
1C2×C3⋊(#126⋊C3)C212yesmaximal, complemented
2C3×#384⋊C3C211yesmaximal, characteristic, complemented
3#74374C311yesmaximal, characteristic, complemented
4#2823⋊C3—31nomaximal
5A4×D12—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3⋊(#126⋊C3)—22no—
8C2×#876C2×C312yescomplemented
9C2×#126⋊C3—32no—
10C3×#384C2×C311yescharacteristic, complemented
11#4994—32no—
12#4991—31no—
13#4981—31no—
14#384⋊C3—21no—
15#384⋊C3D311yescharacteristic, complemented
16C2×D3×A4—42no—
17C3×C4×A4—41no—
18C3×C42⋊C3D411yescharacteristic, complemented
19#2823—31noSylow
20C22×D12A411yescharacteristic
21D4×A4—121no—
22C2×C3×C4⋊C4—31no—
23C2×C3×C4⋊C4—31no—
24C2×C3×C42C22×C311yescharacteristic
25C2×(C2×D3)⋊C4—32no—
26C2×(C2×D3)⋊C4—32no—
27C2×C4⋊Dic3—31no—
28C2×Dic3⋊C4—32no—
29#876—22no—
30#876—62no—
31#126⋊C3—62no—
32C2×C42⋊C3—21no—
33C2×C42⋊C3C2×D311yescharacteristic
34C3⋊#95—31no—
35C3⋊#95—31no—
36C2×C3×A4—41no—
37D3×A4—82no—
38C3×D12—161no—
39C2×#126—32no—
40#398—91no—
41#396—92no—
42#394—91no—
43#384C3×D311yescharacteristic, complemented
44C23×D3C2×A412yes—
45C22×A4—122no—
46C22×C3×C4—31no—
47C22×C3×C4—31no—
48C22×C3×C4C2×A411yescharacteristic
49C22×Dic3—32no—
50C2×D12—121no—
51C4×A4—41no—
52C4×A4—81no—
53C3×C4⋊C4—121no—
54C3×C4⋊C4—121no—
55C3×C42—31no—
56C3×C42C3×D411yescharacteristic, complemented
57(C2×D3)⋊C4—62no—
58(C2×D3)⋊C4—62no—
59(C2×D3)⋊C4—122no—
60C4⋊Dic3—121no—
61Dic3⋊C4—62no—
62Dic3⋊C4—62no—
63C42⋊C3—21no—
64C42⋊C3D1211yescharacteristic, complemented
65C2×C3×D3—162no—
66C3×A4—41no—
67C32×C4—161no—
68C22×D4—31no—
69#126—62no—
70#126—182no—
71C2×C4⋊C4—31no—
72C2×C4⋊C4—31no—
73C2×C4⋊C4—92no—
74C2×C4⋊C4—91no—
75C2×C22⋊C4—92no—
76C2×C22⋊C4—92no—
77C2×C42C2×C3×D311yescharacteristic
78#95—91no—
79#95—91no—
80C23×C3C22×A411yescharacteristic
81C22×D3—22no—
82C22×D3—62no—
83C22×D3—62no—
84C2×A4—41no—
85C2×A4—81no—
86C2×A4—242no—
87C3×D4—481no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—61no—
91C2×C3×C4—61no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—62no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98D12—41no—
99D12—121no—
100C2×C32—161no—
101C3×D3—322no—
102C24—32no—
103C2×D4—361no—
104C22×C4—31no—
105C22×C4—31no—
106C22×C4—92no—
107C22×C4D3×A411yescharacteristic
108C4⋊C4—121no—
109C4⋊C4—121no—
110C4⋊C4—182no—
111C4⋊C4—182no—
112C4⋊C4—361no—
113C22⋊C4—182no—
114C22⋊C4—182no—
115C22⋊C4—362no—
116C42—31no—
117C42C3×D1211yescharacteristic, complemented
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—482no—
121C22×C3D4×A411yescharacteristic
122C2×D3—42no—
123C2×D3—122no—
124C2×D3—122no—
125A4—41no—
126A4—81no—
127C3×C4—41no—
128C3×C4—61no—
129C3×C4—61no—
130C3×C4—121no—
131C3×C4—161no—
132C3×C4—321no—
133Dic3—122no—
134C32—161noSylow
135C23—62no—
136C23—182no—
137C23—182no—
138C23C2×D3×A411yescharacteristic
139D4—121no—
140D4—361no—
141C2×C4—31no—
142C2×C4—31no—
143C2×C4—61no—
144C2×C4—61no—
145C2×C4—61no—
146C2×C4—62no—
147C2×C4—61no—
148C2×C4—182no—
149C2×C4—182no—
150C2×C4—182no—
151C2×C3—31no—
152C2×C3—31no—
153C2×C3—161no—
154C2×C3—321no—
155C2×C3—962no—
156C2×C3#560⋊C311yescharacteristic
157D3—82no—
158C22—31no—
159C22—31no—
160C22—122no—
161C22—362no—
162C22—362no—
163C22A4×D1211yescharacteristic
164C4—41no—
165C4—61no—
166C4—61no—
167C4—121no—
168C4—362no—
169C3—161no—
170C3—321no—
171C3#2823⋊C311yescharacteristic, complemented
172C2—31no—
173C2—31no—
174C2—242no—
175C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#384C2×C3
socleC23×C3C22×A4
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(#126⋊C3)C2semidirect
2. C3×#384⋊C3C2semidirect
3. #74374C3semidirect
8. C2×#876C2×C3semidirect
10. C3×#384C2×C3semidirect
15. #384⋊C3D3semidirect
18. C3×C42⋊C3D4semidirect
43. #384C3×D3semidirect
56. C3×C42C3×D4semidirect
64. C42⋊C3D12semidirect
117. C42C3×D12semidirect
171. C3#2823⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#126⋊C3)2
C3×#384⋊C32
#743743
#2823⋊C33
A4×D124