Finite Group Databasebeta

← SL(2,ℤ/4)⋊Dic3 #10593239

Subgroups — SL(2,ℤ/4)⋊Dic3 #10593239

Order 576.

234 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 41 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×Dic3×A4C211yesmaximal, characteristic
2C2×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C3×SL(2,ℤ/4)C211yesmaximal, characteristic
4SL(2,ℤ/4)⋊C4—31nomaximal
5#4950—31nomaximal
6C22×C3×A4C2211yescharacteristic
7Dic3×A4—21no—
8C3⋊SL(2,ℤ/4)—21no—
9C3×SL(2,ℤ/4)C412yescomplemented
10Dic3⋊Dic3—41nomaximal
11C23×Dic3D311yescharacteristic
12C2×C4×A4—31no—
13C2×SL(2,ℤ/4)—31no—
14C2×SL(2,ℤ/4)—61no—
15C2×SL(2,ℤ/4)D311yescharacteristic
16C2×C3×C22⋊C4—31no—
17C2×#217—31no—
18C2×C4⋊Dic3—31no—
19C2×C4⋊Dic3—31no—
20C3⋊#95—31no—
21C3⋊#95—31no—
22C2×C3×A4C2×C411yescharacteristic
23C2×C3×A4D411yescharacteristic
24C2×C3×A4Q811yescharacteristic
25C2×C3⋊Dic3—41no—
26C2×C3×Dic3—41no—
27C2×C3×Dic3—41no—
28#385—91noSylow
29C24×C3C2×D311yescharacteristic
30C22×A4—21no—
31C22×A4C2×D311yescharacteristic
32C22×C3×C4—31no—
33C22×C3×C4—31no—
34C22×Dic3—21no—
35C22×Dic3—31no—
36C22×Dic3—31no—
37C22×Dic3—31no—
38C22×Dic3—31no—
39C22×Dic3—61no—
40C4×A4—61no—
41SL(2,ℤ/4)—62no—
42SL(2,ℤ/4)—61no—
43SL(2,ℤ/4)Dic312yescomplemented
44C3×C22⋊C4—32no—
45C3×C22⋊C4—32no—
46#217—61no—
47#217—61no—
48C4⋊Dic3—62no—
49C4⋊Dic3—61no—
50C4⋊Dic3—61no—
51Dic3⋊C4—121no—
52C22×C32—41no—
53C3×A4C4⋊C411yescharacteristic, complemented
54C3⋊Dic3—81no—
55C3×Dic3—42no—
56C3×Dic3—81no—
57C23×C4—31no—
58C2×C4⋊C4—91no—
59C2×C4⋊C4—91no—
60C2×C22⋊C4—31no—
61C2×C22⋊C4—91no—
62#95—91no—
63#95—91no—
64C23×C3—31no—
65C23×C3—31no—
66C23×C3—31no—
67C23×C3—31no—
68C23×C3Dic611yescharacteristic
69C23×C3C4×D311yescharacteristic
70C23×C3#6711yescharacteristic
71C2×A4—21no—
72C2×A4—21no—
73C2×A4—21no—
74C2×A4Dic611yescharacteristic
75C2×A4D1211yescharacteristic
76C2×A4C2×Dic311yescharacteristic
77C2×C3×C4—32no—
78C2×C3×C4—32no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—121no—
84C2×Dic3—32no—
85C2×Dic3—31no—
86C2×Dic3—41no—
87C2×Dic3—61no—
88C2×Dic3—61no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93C2×Dic3—61no—
94C2×Dic3—61no—
95C2×Dic3—61no—
96C2×Dic3—121no—
97C2×Dic3—241no—
98C2×Dic3S411yescharacteristic
99C2×C32—41no—
100C2×C32—41no—
101C2×C32—41no—
102C24D3211yescharacteristic
103C22×C4—31no—
104C22×C4—31no—
105C22×C4—61no—
106C22×C4—91no—
107C22×C4—91no—
108C22×C4—91no—
109C22×C4—91no—
110C22×C4—181no—
111C4⋊C4—181no—
112C4⋊C4—182no—
113C4⋊C4—181no—
114C22⋊C4—32no—
115C22⋊C4—32no—
116C22⋊C4—181no—
117C22⋊C4—181no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—31no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—31no—
124C22×C3—31no—
125C22×C3—31no—
126C22×C3—31no—
127C22×C3—41no—
128C22×C3—61no—
129C22×C3—81no—
130C22×C3Dic3⋊C411yescharacteristic, complemented
131C22×C3C2×S411yescharacteristic
132A4—21no—
133A4C4⋊Dic311yescharacteristic, complemented
134C3×C4—62no—
135C3×C4—62no—
136C3×C4—241no—
137Dic3—21no—
138Dic3—42no—
139Dic3—61no—
140Dic3—121no—
141Dic3—121no—
142Dic3—241no—
143Dic3—242no—
144C32—41noSylow
145C23—31no—
146C23—31no—
147C23—31no—
148C23—31no—
149C23D3×Dic311yescharacteristic
150C23#62611yescharacteristic
151C23#62711yescharacteristic
152C2×C4—32no—
153C2×C4—32no—
154C2×C4—31no—
155C2×C4—61no—
156C2×C4—61no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—92no—
160C2×C4—91no—
161C2×C4—181no—
162C2×C4—181no—
163C2×C4—181no—
164C2×C4—181no—
165C2×C4—181no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—181no—
170C2×C3—31no—
171C2×C3—31no—
172C2×C3—31no—
173C2×C3—31no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—41no—
177C2×C3—81no—
178C2×C3—81no—
179C2×C3—81no—
180C2×C3A4⋊Q811yescharacteristic
181C2×C3C4×S411yescharacteristic
182C2×C3GL(2,ℤ/4)11yescharacteristic
183C22—31no—
184C22—31no—
185C22—31no—
186C22—31no—
187C22—31no—
188C22—31no—
189C22—31no—
190C22—31no—
191C22—31no—
192C22—61no—
193C22Dic3⋊Dic311yescharacteristic, complemented
194C22D3×S411yescharacteristic
195C4—62no—
196C4—62no—
197C4—61no—
198C4—181no—
199C4—361no—
200C4—361no—
201C3—41no—
202C3—81no—
203C3SL(2,ℤ/4)⋊C411yescharacteristic, complemented
204C2—31no—
205C2—31no—
206C2—31no—
207C2—31no—
208C2#6420411yescharacteristic
209C2Dic3×S411yescharacteristic
210C2#6421011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D3×S4
commutatorC2×C3×A4C2×C4
Fitting, socleC24×C3C2×D3
prime radical, cosocleC22×C3×A4C22
hypocenterC3×A4C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
9. C3×SL(2,ℤ/4)C4semidirect
43. SL(2,ℤ/4)Dic3semidirect
53. C3×A4C4⋊C4semidirect
130. C22×C3Dic3⋊C4semidirect
133. A4C4⋊Dic3semidirect
193. C22Dic3⋊Dic3semidirect
203. C3SL(2,ℤ/4)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×A42
C2×C3⋊SL(2,ℤ/4)2
C2×C3×SL(2,ℤ/4)2
SL(2,ℤ/4)⋊C43
#49503
Dic3⋊Dic34