Finite Group Databasebeta

← #11920990

Subgroups — #11920990

Order 1152.

242 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C8×C3⋊S4C211yesmaximal, characteristic
2C3×A4×C16C211yesmaximal, characteristic, complemented
3C3⋊(A4⋊C16)C211yesmaximal, characteristic, complemented
4#73034—33nomaximal
5#71407—31nomaximal
6C4×C3⋊S4C411yescharacteristic
7C3×C8×A4C2211yescharacteristic
8C3⋊(A4⋊C8)C411yescharacteristic
9#63625—41nomaximal
10C8×S4—33no—
11C22×C3×C16D311yescharacteristic, complemented
12C8×#67—31no—
13C2×#798—31no—
14A4×C16D313yescomplemented
15A4⋊C16—33no—
16#4549—31no—
17(C2×D3)⋊C16—31no—
18#4502—31no—
19Dic3⋊C16—31no—
20C2×C3⋊S4C811yescharacteristic
21C3×C4×A4C2×C411yescharacteristic
22C3⋊SL(2,ℤ/4)C811yescharacteristic
23C8×C3⋊D3—41no—
24C32×C16—41no—
25C3⋊(C3⋊C16)—41no—
26#2168—91noSylow
27C4×S4—33no—
28C22×C3×C8C2×D311yescharacteristic
29C4×#67—31no—
30C2×D3×C8—31no—
31C8×A4C2×D313yes—
32A4⋊C8—33no—
33C2×C3×C16—31no—
34C2×C3×C16—31no—
35#830—31no—
36(C2×D3)⋊C8—31no—
37Dic3⋊C8—31no—
38C8×Dic3—31no—
39C2×C3⋊C16—31no—
40C2×C3⋊C16—31no—
41#798—61no—
42#798—61no—
43#798—123no—
44C2×C3×A4C2×C811yescharacteristic
45C3⋊S4—21no—
46C4×C3⋊D3—41no—
47C32×C8—41no—
48C3⋊(C3⋊C8)—41no—
49C2×M32—91no—
50C22×C16C3⋊D311yescharacteristic, complemented
51C8×D4—91no—
52C4⋊C16—91no—
53C22⋊C16—91no—
54C22⋊C16—91no—
55#346—91no—
56C2×S4—33no—
57C22×C3×C4C4×D311yescharacteristic
58C2×#67—31no—
59C2×C4×D3—31no—
60C4×A4C4×D313yes—
61SL(2,ℤ/4)—33no—
62C2×C3×C8—31no—
63C2×C3×C8—31no—
64#217—31no—
65(C2×D3)⋊C4—31no—
66Dic3⋊C4—31no—
67C4×Dic3—31no—
68C2×C3⋊C8—31no—
69C2×C3⋊C8—31no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—123no—
73C3×C16—31no—
74C3×C16—43no—
75C3×C16S411yescharacteristic, complemented
76C3⋊C16—61no—
77C3⋊C16—61no—
78C3⋊C16—123no—
79C2×C3⋊D3—41no—
80C3×A4M3211yescharacteristic, complemented
81C32×C4—41no—
82C3⋊Dic3—41no—
83C22×C8—91no—
84C22×C8C2×C3⋊D311yescharacteristic
85C4×D4—91no—
86M32—181no—
87M32—181no—
88C2×C16—31no—
89C2×C16—31no—
90C2×C16—91no—
91C2×C16—91no—
92C4⋊C8—91no—
93C22⋊C8—91no—
94C22⋊C8—91no—
95C4×C8—91no—
96C23×C3D3×C811yescharacteristic
97C22×D3—31no—
98C2×A4D3×C813yes—
99S4—63no—
100C2×C3×C4—31no—
101C2×C3×C4—31no—
102#67—61no—
103#67—61no—
104C2×Dic3—31no—
105C2×Dic3—31no—
106C2×Dic3—31no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—123no—
110C3×C8—31no—
111C3×C8—43no—
112C3×C8C2×S411yescharacteristic
113C3⋊C8—61no—
114C3⋊C8—61no—
115C3⋊C8—123no—
116C2×C32—41no—
117C3⋊D3—81no—
118C2×D4—91no—
119C22×C4—91no—
120C22×C4C4×C3⋊D311yescharacteristic
121C2×C8—31no—
122C2×C8—31no—
123C2×C8—91no—
124C2×C8—91no—
125C2×C8—181no—
126C2×C8—181no—
127C4⋊C4—91no—
128C22⋊C4—91no—
129C22⋊C4—91no—
130C42—91no—
131C16—31no—
132C16—181no—
133C16—181no—
134C16C3⋊S411yescharacteristic, complemented
135C22×C3—31no—
136C22×C3—31no—
137C22×C3#79811yescharacteristic, complemented
138C2×D3—61no—
139C2×D3—61no—
140C2×D3—61no—
141C2×D3—123no—
142A4#79813yescomplemented
143C3×C4—31no—
144C3×C4—43no—
145C3×C4C4×S411yescharacteristic
146Dic3—61no—
147Dic3—61no—
148Dic3—61no—
149Dic3—123no—
150C32—41noSylow
151C23—91no—
152C23C8×C3⋊D311yescharacteristic
153D4—181no—
154D4—181no—
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—181no—
161C2×C4—181no—
162C8—31no—
163C8—181no—
164C8—181no—
165C8C2×C3⋊S411yescharacteristic
166C2×C3—31no—
167C2×C3—31no—
168C2×C3—43no—
169C2×C3C8×S411yescharacteristic
170D3—121no—
171D3—243no—
172C22—31no—
173C22—31no—
174C22—181no—
175C22—181no—
176C22—181no—
177C22#6362511yescharacteristic, complemented
178C4—31no—
179C4—181no—
180C4—181no—
181C4—181no—
182C4C4×C3⋊S411yescharacteristic
183C3—43no—
184C3#7303411yescharacteristic, complemented
185C2—31no—
186C2—31no—
187C2—361no—
188C2C8×C3⋊S411yescharacteristic
subgroupG/H
center, FrattiniC8C2×C3⋊S4
commutatorC2×C3×A4C2×C8
FittingC22×C3×C16D3
socleC23×C3D3×C8
prime radicalC2×C3⋊S4C8
cosocleC3×C8×A4C22
hypercenterC16C3⋊S4
hypocenterC3×A4M32
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
2. C3×A4×C16C2semidirect
3. C3⋊(A4⋊C16)C2semidirect
11. C22×C3×C16D3semidirect
14. A4×C16D3semidirect
50. C22×C16C3⋊D3semidirect
75. C3×C16S4semidirect
80. C3×A4M32semidirect
134. C16C3⋊S4semidirect
137. C22×C3#798semidirect
142. A4#798semidirect
177. C22#63625semidirect
184. C3#73034semidirect

Maximal subgroups

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

subgroupindex
C8×C3⋊S42
C3×A4×C162
C3⋊(A4⋊C16)2
#730343
#714073
#636254