Finite Group Databasebeta

← A4×#126⋊C3 #11922557

Subgroups — A4×#126⋊C3 #11922557

Order 1152.

204 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 25 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
1A4×C42⋊C3C211yesmaximal, characteristic, complemented
2#85646C312yesmaximal, complemented
3A4×#126C311yesmaximal, characteristic, complemented
4C22×#126⋊C3C311yesmaximal, characteristic, complemented
5C2×A42—41nomaximal
6C3×#126⋊C3—41nomaximal
7C22⋊(C42⋊C3)C2×C312yescomplemented
8C2×#126⋊C3—31no—
9C2×#126⋊C3—31no—
10A4×C4⋊C4—31no—
11A4×C22⋊C4—31no—
12C42×A4C2×C311yescharacteristic, complemented
13C22×C42⋊C3C2×C311yescharacteristic, complemented
14A42—41no—
15C3×C42⋊C3—41no—
16C22×#126C3211yescharacteristic, complemented, Sylow
17C2×C22⋊A4—42no—
18C23×A4—41no—
19C23×A4A411yescharacteristic
20C2×C4×A4—31no—
21C2×C4×A4—31no—
22C3×#126—41no—
23#126⋊C3—31no—
24#126⋊C3—42no—
25#126⋊C3—122no—
26#126⋊C3A411yescharacteristic, direct product factor
27C2×C42⋊C3—31no—
28C2×C3×A4—161no—
29C2×C3×A4—161no—
30C2×#126—31no—
31C2×#126—31no—
32C2×#126—91no—
33C2×#126—91no—
34C22×C4⋊C4—31no—
35C22×C22⋊C4—31no—
36C22×C42C2×C3211yescharacteristic, complemented
37C22⋊A4—42no—
38C22×A4—41no—
39C22×A4—61no—
40C22×A4—121no—
41C22×A4—121no—
42C22×A4C2×A411yescharacteristic
43C4×A4—61no—
44C4×A4—61no—
45C3×C4⋊C4—121no—
46C3×C22⋊C4—121no—
47C3×C42—41no—
48C42⋊C3—42no—
49C42⋊C3—122no—
50C42⋊C3C2×A411yescharacteristic, complemented
51C3×A4—161no—
52C3×A4—161no—
53C25C3×A411yescharacteristic
54C23×C4—31no—
55C23×C4—31no—
56#126—32no—
57#126—31no—
58#126—92no—
59#126—91no—
60#126—91no—
61#126—92no—
62#126C3×A411yescharacteristic, complemented
63C2×C4⋊C4—91no—
64C2×C4⋊C4—91no—
65C2×C4⋊C4—92no—
66C2×C22⋊C4—91no—
67C2×C22⋊C4—91no—
68C2×C22⋊C4—91no—
69C2×C22⋊C4—91no—
70C2×C42—31no—
71C2×C42—91no—
72C23×C3—41no—
73C23×C3—161no—
74C2×A4—31no—
75C2×A4—41no—
76C2×A4—41no—
77C2×A4—121no—
78C2×A4—121no—
79C2×A4—162no—
80C2×A4—162no—
81C2×A4—482no—
82C2×C3×C4—121no—
83C2×C3×C4—121no—
84C2×C32—641no—
85C24—31no—
86C24—31no—
87C24—61no—
88C24—181no—
89C24C2×C3×A411yescharacteristic
90C22×C4—61no—
91C22×C4—61no—
92C22×C4—91no—
93C22×C4—91no—
94C22×C4—91no—
95C22×C4—91no—
96C22×C4—181no—
97C22×C4—181no—
98C4⋊C4—31no—
99C4⋊C4—91no—
100C4⋊C4—92no—
101C4⋊C4—92no—
102C22⋊C4—31no—
103C22⋊C4—91no—
104C22⋊C4—91no—
105C22⋊C4—92no—
106C22⋊C4—91no—
107C42—32no—
108C42—91no—
109C42C2×C3×A411yescharacteristic, complemented
110C22×C3—41no—
111C22×C3—161no—
112C22×C3—241no—
113C22×C3—481no—
114C22×C3—481no—
115A4—41no—
116A4—162no—
117A4—162no—
118A4—482no—
119A4#126⋊C311yescharacteristic, direct product factor
120C3×C4—241no—
121C3×C4—241no—
122C32—641noSylow
123C23—31no—
124C23—31no—
125C23—31no—
126C23—41no—
127C23—91no—
128C23—122no—
129C23—181no—
130C23—181no—
131C23—181no—
132C23—181no—
133C23—361no—
134C23A4211yescharacteristic
135C2×C4—31no—
136C2×C4—31no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—181no—
140C2×C4—181no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4—181no—
144C2×C4—181no—
145C2×C4—181no—
146C2×C4—181no—
147C2×C3—121no—
148C2×C3—161no—
149C2×C3—161no—
150C2×C3—481no—
151C2×C3—481no—
152C2×C3—642no—
153C22—32no—
154C22—61no—
155C22—91no—
156C22—91no—
157C22—91no—
158C22—121no—
159C22—121no—
160C22—181no—
161C22—361no—
162C22—361no—
163C22C3×#126⋊C311yescharacteristic, complemented
164C22C2×A4211yescharacteristic
165C4—61no—
166C4—61no—
167C4—181no—
168C4—181no—
169C3—41no—
170C3—161no—
171C3—642no—
172C2—31no—
173C2—31no—
174C2—41no—
175C2—91no—
176C2—121no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C42C2×C32
FrattiniC22C2×A42
FittingC22×#126C32
socleC24C2×C3×A4
LCSG ▷ C22×C42
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×C42⋊C3C2semidirect
2. #85646C3semidirect
3. A4×#126C3semidirect
4. C22×#126⋊C3C3semidirect
7. C22⋊(C42⋊C3)C2×C3semidirect
12. C42×A4C2×C3semidirect
13. C22×C42⋊C3C2×C3semidirect
16. C22×#126C32semidirect
26. #126⋊C3A4direct (N × H)
36. C22×C42C2×C32semidirect
50. C42⋊C3C2×A4semidirect
62. #126C3×A4semidirect
109. C42C2×C3×A4semidirect
119. A4#126⋊C3direct (N × H)
163. C22C3×#126⋊C3semidirect

Maximal subgroups

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

subgroupindex
A4×C42⋊C32
#856463
A4×#1263
C22×#126⋊C33
C2×A424
C3×#126⋊C34