Finite Group Databasebeta

← #73430⋊C3 #11921140

Subgroups — #73430⋊C3 #11921140

Order 1152.

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

normal subgroups only

This group has 218 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×#376⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(#396⋊C3)C212yesmaximal, complemented
3#73430C311yesmaximal, characteristic, complemented
4#2644⋊C3—31nomaximal
5A4×D12—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C3×#376C2×C311yescharacteristic, complemented
8#4939—31no—
9#4928—31no—
10#4676C2×C312yescomplemented
11#4675—32no—
12#396⋊C3—32no—
13#376⋊C3—21no—
14#376⋊C3D311yescharacteristic, complemented
15C2×D3×A4—42no—
16C3×C4×A4—41no—
17#2644—31noSylow
18C22×D12A411yescharacteristic
19D4×A4—121no—
20C2×C3×C42—31no—
21C2×(C2×D3)⋊C4—32no—
22C2×(C2×D3)⋊C4—32no—
23C2×C4⋊Dic3—31no—
24C2×Dic3⋊C4—32no—
25C3×#95—31no—
26C3×#95C22×C311yescharacteristic
27C3⋊#95—32no—
28#95⋊C3—21no—
29#95⋊C3C2×D311yescharacteristic
30C2×C3×A4—41no—
31D3×A4—82no—
32C3×D12—161no—
33#397—92no—
34#396—32no—
35#390—91no—
36#389—91no—
37#376C3×D311yescharacteristic, complemented
38C23×D3C2×A412yes—
39C22×A4—122no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×C3×C4C2×A411yescharacteristic
43C22×Dic3—32no—
44C2×D12—61no—
45C2×D12—61no—
46C4×A4—41no—
47C4×A4—81no—
48C3×C42—61no—
49C3×C42—61no—
50(C2×D3)⋊C4—122no—
51(C2×D3)⋊C4—122no—
52C4⋊Dic3—61no—
53C4⋊Dic3—61no—
54Dic3⋊C4—122no—
55C2×C3×D3—162no—
56C3×A4—41no—
57C32×C4—161no—
58C22×D4—31no—
59C2×C4⋊C4—91no—
60C2×C4⋊C4—92no—
61C2×C22⋊C4—92no—
62C2×C22⋊C4—92no—
63C2×C42—31no—
64#95—31no—
65#95—92no—
66#95C2×C3×D311yescharacteristic
67C23×C3C22×A411yescharacteristic
68C22×D3—22no—
69C22×D3—62no—
70C22×D3—62no—
71C2×A4—41no—
72C2×A4—81no—
73C2×A4—242no—
74C3×D4—481no—
75C2×C3×C4—31no—
76C2×C3×C4—31no—
77C2×C3×C4—61no—
78C2×C3×C4—61no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86D12—41no—
87D12—121no—
88C2×C32—161no—
89C3×D3—322no—
90C24—32no—
91C2×D4—181no—
92C2×D4—181no—
93C22×C4—31no—
94C22×C4—31no—
95C22×C4—92no—
96C22×C4D3×A411yescharacteristic
97C4⋊C4—181no—
98C4⋊C4—181no—
99C4⋊C4—362no—
100C22⋊C4—362no—
101C22⋊C4—362no—
102C42—61no—
103C42—61no—
104C22×C3—31no—
105C22×C3—31no—
106C22×C3—482no—
107C22×C32−1+4⋊C311yescharacteristic
108C2×D3—42no—
109C2×D3—122no—
110C2×D3—122no—
111A4—41no—
112A4—81no—
113C3×C4—31no—
114C3×C4—121no—
115C3×C4—121no—
116C3×C4—161no—
117C3×C4—321no—
118C3×C4#126⋊C311yescharacteristic
119Dic3—122no—
120C32—161noSylow
121C23—62no—
122C23—182no—
123C23—182no—
124C23C2×D3×A411yescharacteristic
125D4—121no—
126D4—361no—
127C2×C4—31no—
128C2×C4—31no—
129C2×C4—61no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—61no—
133C2×C4—61no—
134C2×C4—61no—
135C2×C4—182no—
136C2×C4—182no—
137C2×C4—182no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—161no—
141C2×C3—321no—
142C2×C3—962no—
143C2×C3C2×#126⋊C311yescharacteristic
144D3—82no—
145C22—31no—
146C22—31no—
147C22—122no—
148C22—362no—
149C22—362no—
150C22#1010⋊C311yescharacteristic
151C4—31no—
152C4—121no—
153C4—121no—
154C4—362no—
155C4C3⋊(#126⋊C3)11yescharacteristic
156C3—161no—
157C3—321no—
158C3#2644⋊C311yescharacteristic, complemented
159C2—31no—
160C2—31no—
161C2—242no—
162C2C2×C3⋊(#126⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#126⋊C3)
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#376C2×C3
socleC23×C3C22×A4
hypercenterC4C3⋊(#126⋊C3)
LCSG ▷ C3×#95
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C3×#376⋊C3C2semidirect
2. C3⋊(#396⋊C3)C2semidirect
3. #73430C3semidirect
7. C3×#376C2×C3semidirect
10. #4676C2×C3semidirect
14. #376⋊C3D3semidirect
37. #376C3×D3semidirect
158. C3#2644⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#376⋊C32
C3⋊(#396⋊C3)2
#734303
#2644⋊C33
A4×D124