Finite Group Databasebeta

← #11921065

Subgroups — #11921065

Order 1152.

382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 91 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
2C4⋊(C3⋊SL(2,ℤ/4))C212yesmaximal
3#73110—33nomaximal
4#71970—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C2×C3⋊SL(2,ℤ/4)—22no—
7C3×C8×A4C412yescomplemented
8#63644—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4D313yes—
11C4⋊SL(2,ℤ/4)—36no—
12#5212—32no—
13C2×#817—31no—
14C2×#817—31no—
15#4551—32no—
16C22×C3×A4D411yescharacteristic
17C3×C4×A4C2×C411yescharacteristic
18C3×C4×A4Q811yescharacteristic
19C3⋊SL(2,ℤ/4)—42no—
20C2×C32×C8—41no—
21C4⋊(C3⋊Dic3)—42no—
22#1807—91noSylow
23C23×C3×C4C2×D311yescharacteristic
24C2×C4×A4C2×D313yes—
25C2×SL(2,ℤ/4)—66no—
26C22×C3×C8—31no—
27C22×C3×C8—32no—
28C22×C3×C8—31no—
29C22×C3×C8Dic312yescomplemented
30C2×#217—62no—
31C2×C4⋊Dic3—32no—
32C2×C4⋊Dic3—32no—
33C8×A4Dic316yescomplemented
34C3⋊#95—62no—
35#817—62no—
36#817—61no—
37#817—61no—
38#817—123no—
39C2×C3×A4C4⋊C411yescharacteristic
40C2×C3×A4SD1612yes—
41C2×C32×C4—41no—
42C2×C3⋊Dic3—82no—
43C32×C8—42no—
44C23×C8C3⋊D311yescharacteristic
45C2×#106—91no—
46C2×#106—91no—
47#380—92no—
48#340—92no—
49C24×C3D1211yescharacteristic
50C22×A4D1213yes—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4Dic611yescharacteristic
56C22×C3×C4C2×Dic311yescharacteristic
57C22×Dic3—62no—
58C22×Dic3—62no—
59C4×A4Dic613yes—
60C4×A4C2×Dic313yes—
61SL(2,ℤ/4)—126no—
62C2×C3×C8—31no—
63C2×C3×C8—32no—
64C2×C3×C8—32no—
65C2×C3×C8—32no—
66C2×C3×C8—43no—
67C2×C3×C8—61no—
68C2×C3×C8S411yescharacteristic
69#217—122no—
70#217—122no—
71C4⋊Dic3—62no—
72C4⋊Dic3—62no—
73C4⋊Dic3—62no—
74C4⋊Dic3—62no—
75C4⋊Dic3—126no—
76C22×C32—41no—
77C3×A4#10611yescharacteristic, complemented
78C32×C4—41no—
79C32×C4—41no—
80C3⋊Dic3—162no—
81C23×C4C2×C3⋊D311yescharacteristic
82C22×C8—31no—
83C22×C8—31no—
84C22×C8—32no—
85C22×C8C3⋊Dic312yescomplemented
86C2×C4⋊C4—92no—
87C2×C4⋊C4—92no—
88C2×C22⋊C4—182no—
89#106—182no—
90#106—181no—
91#106—181no—
92#95—182no—
93C23×C3—31no—
94C23×C3—32no—
95C23×C3—31no—
96C23×C3#20412yes—
97C23×C3C4⋊Dic311yescharacteristic
98C2×A4#20416yes—
99C2×A4C4⋊Dic313yes—
100C2×C3×C4—31no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—43no—
108C2×C3×C4—61no—
109C2×C3×C4C2×S411yescharacteristic
110C2×Dic3—122no—
111C2×Dic3—122no—
112C2×Dic3—122no—
113C2×Dic3—122no—
114C2×Dic3—122no—
115C2×Dic3—122no—
116C2×Dic3—246no—
117C3×C8—32no—
118C3×C8—46no—
119C3×C8SL(2,ℤ/4)12yescomplemented
120C2×C32—42no—
121C2×C32—41no—
122C24C4⋊(C3⋊D3)11yescharacteristic
123C22×C4—31no—
124C22×C4—31no—
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—182no—
128C22×C4—182no—
129C22×C4#63411yescharacteristic
130C22×C4C2×C3⋊Dic311yescharacteristic
131C2×C8—31no—
132C2×C8—32no—
133C2×C8—32no—
134C2×C8—32no—
135C2×C8—61no—
136C2×C8C3⋊S411yescharacteristic
137C4⋊C4—182no—
138C4⋊C4—182no—
139C4⋊C4—182no—
140C4⋊C4—182no—
141C22⋊C4—362no—
142C22⋊C4—362no—
143C22×C3—32no—
144C22×C3—31no—
145C22×C3—32no—
146C22×C3—32no—
147C22×C3—31no—
148C22×C3—31no—
149C22×C3—43no—
150C22×C3—61no—
151C22×C3#81711yescharacteristic, complemented
152C22×C3C4⋊S411yescharacteristic
153A4#81713yescomplemented
154C3×C4—31no—
155C3×C4—31no—
156C3×C4—43no—
157C3×C4—43no—
158C3×C4A4⋊Q811yescharacteristic
159C3×C4C2×SL(2,ℤ/4)11yescharacteristic
160Dic3—242no—
161Dic3—242no—
162Dic3—486no—
163C32—41noSylow
164C23—31no—
165C23—32no—
166C23—31no—
167C23#374412yes—
168C23C4⋊(C3⋊Dic3)11yescharacteristic
169C2×C4—31no—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—31no—
174C2×C4—31no—
175C2×C4—31no—
176C2×C4—61no—
177C2×C4—362no—
178C2×C4—362no—
179C2×C4—362no—
180C2×C4—362no—
181C2×C4—362no—
182C2×C4—362no—
183C2×C4C2×C3⋊S411yescharacteristic
184C8—32no—
185C8C3⋊SL(2,ℤ/4)12yescomplemented
186C2×C3—32no—
187C2×C3—31no—
188C2×C3—31no—
189C2×C3—46no—
190C2×C3—43no—
191C2×C3#540112yes—
192C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
193C22—32no—
194C22—31no—
195C22—32no—
196C22—32no—
197C22—31no—
198C22—31no—
199C22—61no—
200C22#6364411yescharacteristic, complemented
201C22C4⋊(C3⋊S4)11yescharacteristic
202C4—31no—
203C4—31no—
204C4—722no—
205C4—722no—
206C4#6425911yescharacteristic
207C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
208C3—43no—
209C3#7311011yescharacteristic, complemented
210C2—32no—
211C2—31no—
212C2—31no—
213C2#1059363512yes—
214C2C4⋊(C3⋊SL(2,ℤ/4))11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3D12
prime radicalC22×C3×A4D4
cosocleC2×C3×C4×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#106
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
7. C3×C8×A4C4semidirect
29. C22×C3×C8Dic3semidirect
33. C8×A4Dic3semidirect
77. C3×A4#106semidirect
85. C22×C8C3⋊Dic3semidirect
119. C3×C8SL(2,ℤ/4)semidirect
151. C22×C3#817semidirect
153. A4#817semidirect
185. C8C3⋊SL(2,ℤ/4)semidirect
200. C22#63644semidirect
209. C3#73110semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C4⋊(C3⋊SL(2,ℤ/4))2
#731103
#719703
#636444