Finite Group Databasebeta

← #11922838

Subgroups — #11922838

Order 1152.

1210 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 131 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×C4⋊(C3⋊S4)C216yesmaximal, complemented
2C3×C42×A4C211yesmaximal, characteristic, complemented
3#85289—33nomaximal
4#82081—31nomaximal
5C22×C3⋊S4C2214yes—
6C2×C3×C4×A4C2213yes—
7C4⋊(C3⋊S4)—212no—
8#64083—41nomaximal
9C2×C4⋊S4—318no—
10C22×C3×C42D311yescharacteristic, complemented
11C2×#930—36no—
12C2×#874—31no—
13C42×A4D313yescomplemented
14#4939—36no—
15#4935—31no—
16C22×C3×A4C2311yescharacteristic
17C2×C3⋊S4—212no—
18C2×C4⋊(C3⋊D3)—46no—
19C3×C4×A4D416yescomplemented
20C32×C42—41no—
21#2856—91noSylow
22C22×S4—312no—
23C23×C3×C4C2×D313yes—
24C22×#67—34no—
25C22×D12—36no—
26C2×C4×A4C2×D319yes—
27C4⋊S4—636no—
28C2×C3×C42—31no—
29C2×C3×C42—33no—
30#930—612no—
31#930—612no—
32C2×(C2×D3)⋊C4—312no—
33C2×C4⋊Dic3—36no—
34#874—63no—
35#874—61no—
36#874—123no—
37C22×C3⋊D3—44no—
38C2×C3×A4C2×D413yes—
39C3⋊S4—44no—
40C2×C32×C4—43no—
41C4⋊(C3⋊D3)—812no—
42C2×#127—91no—
43C2×#121—96no—
44C22×C42C3⋊D311yescharacteristic, complemented
45#390—96no—
46#384—91no—
47C24×C3C22×D311yescharacteristic
48C23×D3—34no—
49C22×A4C22×D313yes—
50C2×S4—636no—
51C22×C3×C4—33no—
52C22×C3×C4—33no—
53C22×C3×C4—36no—
54C22×C3×C4D1216yescomplemented
55C2×#67—612no—
56C2×#67—612no—
57C22×Dic3—34no—
58C2×D12—66no—
59C2×D12—612no—
60C2×D12—612no—
61C2×D12—66no—
62C2×D12—1218no—
63C4×A4D12118yescomplemented
64C3×C42—33no—
65C3×C42—43no—
66C3×C42—61no—
67C3×C42S411yescharacteristic, complemented
68(C2×D3)⋊C4—624no—
69C4⋊Dic3—612no—
70C22×C32—41no—
71C2×C3⋊D3—812no—
72C3×A4#12711yescharacteristic, complemented
73C32×C4—46no—
74C22×D4—96no—
75C22×D4—94no—
76C23×C4C2×C3⋊D313yes—
77#127—183no—
78#127—181no—
79#121—1812no—
80#121—1812no—
81C2×C4⋊C4—96no—
82C2×C22⋊C4—912no—
83C2×C42—31no—
84C2×C42—33no—
85C23×C3—31no—
86C23×C3—33no—
87C23×C3C2×D1213yes—
88C22×D3—612no—
89C22×D3—612no—
90C22×D3—64no—
91C22×D3—1212no—
92C2×A4C2×D1219yes—
93S4—1212no—
94C2×C3×C4—33no—
95C2×C3×C4—36no—
96C2×C3×C4—36no—
97C2×C3×C4—36no—
98C2×C3×C4—49no—
99C2×C3×C4—63no—
100C2×C3×C4C2×S413yes—
101#67—1212no—
102#67—124no—
103C2×Dic3—612no—
104D12—1212no—
105D12—1212no—
106D12—2436no—
107C2×C32—43no—
108C3⋊D3—164no—
109C24—94no—
110C24C22×C3⋊D311yescharacteristic
111C2×D4—1812no—
112C2×D4—186no—
113C2×D4—1812no—
114C2×D4—1812no—
115C2×D4—1812no—
116C2×D4—186no—
117C22×C4—33no—
118C22×C4—33no—
119C22×C4—36no—
120C22×C4—94no—
121C22×C4C4⋊(C3⋊D3)16yescomplemented
122C4⋊C4—1812no—
123C22⋊C4—1824no—
124C42—33no—
125C42—61no—
126C42C3⋊S411yescharacteristic, complemented
127C22×C3—33no—
128C22×C3—33no—
129C22×C3—33no—
130C22×C3—43no—
131C22×C3—61no—
132C22×C3#87411yescharacteristic, complemented
133C22×C3C22×S411yescharacteristic
134C2×D3—124no—
135C2×D3—1212no—
136C2×D3—1212no—
137C2×D3—2436no—
138A4#87413yescomplemented
139C3×C4—36no—
140C3×C4—418no—
141C3×C4C4⋊S416yescomplemented
142Dic3—124no—
143C32—41noSylow
144C23—31no—
145C23—33no—
146C23—1812no—
147C23—1812no—
148C23—184no—
149C23C2×C4⋊(C3⋊D3)13yes—
150D4—3612no—
151D4—3612no—
152D4—364no—
153D4—3612no—
154C2×C4—33no—
155C2×C4—36no—
156C2×C4—36no—
157C2×C4—36no—
158C2×C4—63no—
159C2×C4—1812no—
160C2×C4C2×C3⋊S413yes—
161C2×C3—31no—
162C2×C3—33no—
163C2×C3—49no—
164C2×C3C2×C4⋊S413yes—
165D3—244no—
166D3—4812no—
167C22—33no—
168C22—33no—
169C22—33no—
170C22—61no—
171C22—364no—
172C22—3612no—
173C22—3612no—
174C22#6408311yescharacteristic, complemented
175C22C22×C3⋊S411yescharacteristic
176C4—36no—
177C4—364no—
178C4C4⋊(C3⋊S4)16yescomplemented
179C3—43no—
180C3#8528911yescharacteristic, complemented
181C2—31no—
182C2—33no—
183C2—724no—
184C2C2×C4⋊(C3⋊S4)13yes—
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC22×C3×A4C23
FittingC22×C3×C42D3
socleC24×C3C22×D3
hypercenterC42C3⋊S4
hypocenterC3×A4#127
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊(C3⋊S4)C2semidirect
2. C3×C42×A4C2semidirect
10. C22×C3×C42D3semidirect
13. C42×A4D3semidirect
19. C3×C4×A4D4semidirect
44. C22×C42C3⋊D3semidirect
54. C22×C3×C4D12semidirect
63. C4×A4D12semidirect
67. C3×C42S4semidirect
72. C3×A4#127semidirect
121. C22×C4C4⋊(C3⋊D3)semidirect
126. C42C3⋊S4semidirect
132. C22×C3#874semidirect
138. A4#874semidirect
141. C3×C4C4⋊S4semidirect
174. C22#64083semidirect
178. C4C4⋊(C3⋊S4)semidirect
180. C3#85289semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C3×C42×A42
#852893
#820813
#640834