Finite Group Databasebeta

← #11922840

Subgroups — #11922840

Order 1152.

676 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 83 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×C42×A4C211yesmaximal, characteristic, complemented
2#10593647C213yesmaximal
3#10593645C213yesmaximal, complemented
4#85291—33nomaximal
5#82078—31nomaximal
6C22×C3⋊S4C2211yescharacteristic
7C2×C3×C4×A4C2213yes—
8C2×C3⋊SL(2,ℤ/4)C2213yes—
9#64085—41nomaximal
10C22×C3×C42D311yescharacteristic, complemented
11C2×#876—31no—
12C42×A4D313yescomplemented
13(C2×S4)⋊C4—39no—
14SL(2,ℤ/4)⋊C4—39no—
15#5213—33no—
16#5210—33no—
17#4940—33no—
18#4937—31no—
19#4933—33no—
20C22×C3×A4C2311yescharacteristic
21C2×C3⋊S4—23no—
22C3×C4×A4—23no—
23C3⋊SL(2,ℤ/4)—23no—
24C32×C42—41no—
25#3752—43no—
26#3750—43no—
27#2852—91noSylow
28C22×S4—33no—
29C23×C3×C4C2×D313yes—
30C22×#67—31no—
31C2×C4×A4C2×D319yes—
32C2×SL(2,ℤ/4)—39no—
33C2×C3×C42—31no—
34C2×C3×C42—33no—
35C2×#217—33no—
36C2×(C2×D3)⋊C4—33no—
37C2×(C2×D3)⋊C4—33no—
38C2×Dic3⋊C4—33no—
39C2×Dic3⋊C4—33no—
40#876—63no—
41#876—61no—
42#876—123no—
43C3⋊#95—33no—
44C3⋊#95—33no—
45C3⋊#95—33no—
46C3⋊#95—33no—
47C22×C3⋊D3—41no—
48C2×C3×A4#4113yes—
49C3⋊S4—41no—
50C2×C32×C4—43no—
51C2×C3⋊Dic3—43no—
52C2×#126—91no—
53C22×C42C3⋊D311yescharacteristic, complemented
54#388—93no—
55#387—93no—
56#386—93no—
57#385—93no—
58#383—91no—
59C24×C3C22×D311yescharacteristic
60C23×D3—31no—
61C22×A4C22×D313yes—
62C2×S4—69no—
63C22×C3×C4—23no—
64C22×C3×C4—33no—
65C22×C3×C4—33no—
66C22×C3×C4—63no—
67C2×#67—63no—
68C2×#67—63no—
69C22×Dic3—31no—
70C22×Dic3—33no—
71C22×Dic3—33no—
72C4×A4—29no—
73SL(2,ℤ/4)—69no—
74C3×C42—33no—
75C3×C42—43no—
76C3×C42—61no—
77C3×C42S411yescharacteristic, complemented
78#217—63no—
79#217—63no—
80(C2×D3)⋊C4—63no—
81(C2×D3)⋊C4—66no—
82(C2×D3)⋊C4—63no—
83(C2×D3)⋊C4—129no—
84Dic3⋊C4—63no—
85Dic3⋊C4—66no—
86Dic3⋊C4—63no—
87Dic3⋊C4—129no—
88C22×C32—41no—
89C2×C3⋊D3—83no—
90C3×A4#12611yescharacteristic, complemented
91C32×C4—83no—
92C3⋊Dic3—83no—
93C22×D4—91no—
94C23×C4C2×C3⋊D313yes—
95#126—183no—
96#126—181no—
97C2×C4⋊C4—93no—
98C2×C4⋊C4—93no—
99C2×C22⋊C4—93no—
100C2×C22⋊C4—93no—
101C2×C22⋊C4—93no—
102C2×C42—31no—
103C2×C42—33no—
104#95—93no—
105#95—93no—
106#95—93no—
107#95—93no—
108C23×C3—31no—
109C23×C3—33no—
110C23×C3#23513yes—
111C22×D3—63no—
112C22×D3—63no—
113C22×D3—61no—
114C22×D3—123no—
115C2×A4#23519yes—
116S4—123no—
117C2×C3×C4—36no—
118C2×C3×C4—33no—
119C2×C3×C4—49no—
120C2×C3×C4—63no—
121C2×C3×C4—63no—
122C2×C3×C4—63no—
123C2×C3×C4C2×S413yes—
124#67—123no—
125#67—121no—
126C2×Dic3—63no—
127C2×Dic3—63no—
128C2×Dic3—63no—
129C2×Dic3—63no—
130C2×Dic3—63no—
131C2×Dic3—63no—
132C2×Dic3—63no—
133C2×Dic3—129no—
134C2×C32—43no—
135C3⋊D3—161no—
136C24—91no—
137C24C22×C3⋊D311yescharacteristic
138C2×D4—183no—
139C2×D4—183no—
140C22×C4—23no—
141C22×C4—33no—
142C22×C4—33no—
143C22×C4—63no—
144C22×C4—91no—
145C22×C4—93no—
146C22×C4—93no—
147C4⋊C4—183no—
148C4⋊C4—186no—
149C4⋊C4—183no—
150C22⋊C4—183no—
151C22⋊C4—186no—
152C22⋊C4—183no—
153C22⋊C4—183no—
154C22⋊C4—183no—
155C42—33no—
156C42—61no—
157C42C3⋊S411yescharacteristic, complemented
158C22×C3—33no—
159C22×C3—33no—
160C22×C3—33no—
161C22×C3—43no—
162C22×C3—61no—
163C22×C3#87611yescharacteristic, complemented
164C22×C3C22×S411yescharacteristic
165C2×D3—121no—
166C2×D3—123no—
167C2×D3—123no—
168C2×D3—249no—
169A4#87613yescomplemented
170C3×C4—23no—
171C3×C4—63no—
172C3×C4—89no—
173Dic3—123no—
174Dic3—121no—
175Dic3—123no—
176Dic3—249no—
177C32—41noSylow
178C23—31no—
179C23—33no—
180C23—183no—
181C23—183no—
182C23—181no—
183C23#382813yes—
184D4—363no—
185D4—361no—
186C2×C4—36no—
187C2×C4—33no—
188C2×C4—63no—
189C2×C4—63no—
190C2×C4—63no—
191C2×C4—183no—
192C2×C4—183no—
193C2×C4—183no—
194C2×C4—183no—
195C2×C4—183no—
196C2×C4—183no—
197C2×C4—183no—
198C2×C4C2×C3⋊S413yes—
199C2×C3—31no—
200C2×C3—33no—
201C2×C3—49no—
202C2×C3#591213yes—
203D3—241no—
204D3—483no—
205C22—33no—
206C22—33no—
207C22—33no—
208C22—61no—
209C22—361no—
210C22—363no—
211C22—363no—
212C22#6408511yescharacteristic, complemented
213C22C22×C3⋊S411yescharacteristic
214C4—23no—
215C4—63no—
216C4—361no—
217C4—363no—
218C4—363no—
219C3—43no—
220C3#8529111yescharacteristic, complemented
221C2—31no—
222C2—33no—
223C2—721no—
224C2#1059657513yes—
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC22×C3×A4C23
FittingC22×C3×C42D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
hypercenterC42C3⋊S4
hypocenterC3×A4#126
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C3×C42×A4C2semidirect
3. #10593645C2semidirect
10. C22×C3×C42D3semidirect
12. C42×A4D3semidirect
53. C22×C42C3⋊D3semidirect
77. C3×C42S4semidirect
90. C3×A4#126semidirect
157. C42C3⋊S4semidirect
163. C22×C3#876semidirect
169. A4#876semidirect
212. C22#64085semidirect
220. C3#85291semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
#105936472
#105936452
#852913
#820783
#640854