Finite Group Databasebeta

← #11921060

Subgroups — #11921060

Order 1152.

266 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 75 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×C3×C8×A4C211yesmaximal, characteristic
2C3⋊(A4⋊C16)C212yesmaximal, complemented
3#73104—33nomaximal
4#71963—31nomaximal
5C2×C3×C4×A4C411yescharacteristic
6C3×C8×A4C411yescharacteristic
7C3×C8×A4C2211yescharacteristic
8#63639—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4D313yes—
11C2×#812—31no—
12C2×#812—31no—
13A4⋊C16—36no—
14#4549—32no—
15#4549—32no—
16C22×C3×A4C811yescharacteristic
17C3×C4×A4C811yescharacteristic
18C3×C4×A4C2×C411yescharacteristic
19C2×C32×C8—41no—
20C3⋊(C3⋊C16)—42no—
21#2112—91noSylow
22C23×C3×C4Dic311yescharacteristic
23C2×C4×A4Dic313yes—
24C22×C3×C8—31no—
25C22×C3×C8—31no—
26C22×C3×C8—31no—
27C22×C3×C8—31no—
28C22×C3×C8Dic311yescharacteristic
29C22×C3×C8C2×D311yescharacteristic
30C8×A4Dic313yes—
31C8×A4C2×D313yes—
32#812—61no—
33#812—61no—
34#812—61no—
35#812—61no—
36#812—123no—
37C2×C3⋊C16—32no—
38C2×C3⋊C16—32no—
39C2×C3×A4—21no—
40C2×C3×A4C2×C811yescharacteristic
41C2×C32×C4—41no—
42C32×C8—41no—
43C32×C8—41no—
44C23×C8C3⋊D311yescharacteristic
45C2×M32—91no—
46C2×M32—91no—
47C22⋊C16—92no—
48C22⋊C16—92no—
49C24×C3C3⋊C811yescharacteristic
50C22×A4C3⋊C813yes—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4C3⋊C811yescharacteristic
56C22×C3×C4C2×Dic311yescharacteristic
57C4×A4C3⋊C813yes—
58C4×A4C2×Dic313yes—
59C2×C3×C8—31no—
60C2×C3×C8—31no—
61C2×C3×C8—31no—
62C2×C3×C8—31no—
63C2×C3×C8—31no—
64C2×C3×C8—31no—
65C2×C3×C8—31no—
66C2×C3×C8—43no—
67C2×C3×C8—61no—
68C2×C3×C8S411yescharacteristic
69C3⋊C16—62no—
70C3⋊C16—62no—
71C3⋊C16—126no—
72C22×C32—41no—
73C3×A4M3211yescharacteristic, complemented
74C32×C4—41no—
75C32×C4—41no—
76C23×C4C3⋊Dic311yescharacteristic
77C22×C8—31no—
78C22×C8—31no—
79C22×C8—31no—
80C22×C8—31no—
81C22×C8C3⋊Dic311yescharacteristic
82C22×C8C2×C3⋊D311yescharacteristic
83M32—181no—
84M32—181no—
85M32—181no—
86M32—181no—
87C2×C16—92no—
88C2×C16—92no—
89C23×C3—21no—
90C23×C3—31no—
91C23×C3—31no—
92C23×C3—61no—
93C23×C3C2×C3⋊C811yescharacteristic
94C2×A4—23no—
95C2×A4C2×C3⋊C813yes—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—31no—
99C2×C3×C4—31no—
100C2×C3×C4—31no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—43no—
104C2×C3×C4—61no—
105C2×C3×C4SL(2,ℤ/4)11yescharacteristic
106C3×C8—31no—
107C3×C8—31no—
108C3×C8—43no—
109C3×C8—43no—
110C3×C8SL(2,ℤ/4)11yescharacteristic
111C3×C8C2×S411yescharacteristic
112C2×C32—41no—
113C2×C32—81no—
114C24C3⋊(C3⋊C8)11yescharacteristic
115C22×C4—31no—
116C22×C4—31no—
117C22×C4—31no—
118C22×C4—31no—
119C22×C4C3⋊(C3⋊C8)11yescharacteristic
120C22×C4C2×C3⋊Dic311yescharacteristic
121C2×C8—31no—
122C2×C8—31no—
123C2×C8—31no—
124C2×C8—31no—
125C2×C8—31no—
126C2×C8—31no—
127C2×C8—31no—
128C2×C8—61no—
129C2×C8C3⋊S411yescharacteristic
130C16—182no—
131C16—182no—
132C22×C3—31no—
133C22×C3—31no—
134C22×C3—32no—
135C22×C3—31no—
136C22×C3—43no—
137C22×C3—61no—
138C22×C3—61no—
139C22×C3—61no—
140C22×C3#81211yescharacteristic, complemented
141C22×C3A4⋊C811yescharacteristic
142A4#81213yescomplemented
143C3×C4—31no—
144C3×C4—31no—
145C3×C4—43no—
146C3×C4—43no—
147C3×C4A4⋊C811yescharacteristic
148C3×C4C2×SL(2,ℤ/4)11yescharacteristic
149C32—41noSylow
150C23—21no—
151C23—31no—
152C23—31no—
153C23—61no—
154C23C2×C3⋊(C3⋊C8)11yescharacteristic
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—31no—
162C2×C4—61no—
163C2×C4C3⋊SL(2,ℤ/4)11yescharacteristic
164C8—31no—
165C8—31no—
166C8C3⋊SL(2,ℤ/4)11yescharacteristic
167C8C2×C3⋊S411yescharacteristic
168C2×C3—21no—
169C2×C3—31no—
170C2×C3—31no—
171C2×C3—43no—
172C2×C3—61no—
173C2×C3—83no—
174C2×C3C2×A4⋊C811yescharacteristic
175C22—31no—
176C22—31no—
177C22—32no—
178C22—31no—
179C22—61no—
180C22—61no—
181C22—61no—
182C22#6363911yescharacteristic, complemented
183C22C3⋊(A4⋊C8)11yescharacteristic
184C4—31no—
185C4—31no—
186C4C3⋊(A4⋊C8)11yescharacteristic
187C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
188C3—43no—
189C3#7310411yescharacteristic, complemented
190C2—21no—
191C2—31no—
192C2—31no—
193C2—61no—
194C2C2×C3⋊(A4⋊C8)11yescharacteristic
subgroupG/H
center, FrattiniC8C2×C3⋊S4
commutatorC2×C3×A4C2×C8
FittingC23×C3×C8D3
socleC23×C3C2×C3⋊C8
prime radicalC22×C3×A4C8
cosocleC3×C8×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4M32
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C3⋊(A4⋊C16)C2semidirect
73. C3×A4M32semidirect
140. C22×C3#812semidirect
142. A4#812semidirect
182. C22#63639semidirect
189. C3#73104semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3⋊(A4⋊C16)2
#731043
#719633
#636394