Finite Group Databasebeta

← #11921066

Subgroups — #11921066

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#73111—33nomaximal
4#71971—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C2×C3⋊SL(2,ℤ/4)—22no—
7C3×C8×A4C412yescomplemented
8#63645—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4D313yes—
11C4⋊SL(2,ℤ/4)—36no—
12#5212—32no—
13C2×#818—31no—
14C2×#818—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#1808—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#818—62no—
36#818—61no—
37#818—61no—
38#818—123no—
39C2×C3×A4C4⋊C411yescharacteristic
40C2×C3×A4D811yescharacteristic
41C2×C3×A4Q1611yescharacteristic
42C2×C32×C4—41no—
43C2×C3⋊Dic3—82no—
44C32×C8—42no—
45C23×C8C3⋊D311yescharacteristic
46C2×#107—91no—
47C2×#107—91no—
48#380—92no—
49#340—92no—
50C24×C3D1211yescharacteristic
51C22×A4D1213yes—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C22×C3×C4Dic611yescharacteristic
57C22×C3×C4C2×Dic311yescharacteristic
58C22×Dic3—62no—
59C22×Dic3—62no—
60C4×A4Dic613yes—
61C4×A4C2×Dic313yes—
62SL(2,ℤ/4)—126no—
63C2×C3×C8—31no—
64C2×C3×C8—32no—
65C2×C3×C8—32no—
66C2×C3×C8—32no—
67C2×C3×C8—43no—
68C2×C3×C8—61no—
69C2×C3×C8S411yescharacteristic
70#217—122no—
71#217—122no—
72C4⋊Dic3—62no—
73C4⋊Dic3—62no—
74C4⋊Dic3—62no—
75C4⋊Dic3—62no—
76C4⋊Dic3—126no—
77C22×C32—41no—
78C3×A4#10711yescharacteristic, complemented
79C32×C4—41no—
80C32×C4—41no—
81C3⋊Dic3—162no—
82C23×C4C2×C3⋊D311yescharacteristic
83C22×C8—31no—
84C22×C8—31no—
85C22×C8—32no—
86C22×C8C3⋊Dic312yescomplemented
87C2×C4⋊C4—92no—
88C2×C4⋊C4—92no—
89C2×C22⋊C4—182no—
90#107—182no—
91#107—181no—
92#107—181no—
93#95—182no—
94C23×C3—31no—
95C23×C3—31no—
96C23×C3—31no—
97C23×C3—31no—
98C23×C3D2411yescharacteristic
99C23×C3Dic1211yescharacteristic
100C23×C3C4⋊Dic311yescharacteristic
101C2×A4D2413yes—
102C2×A4Dic1213yes—
103C2×A4C4⋊Dic313yes—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—43no—
112C2×C3×C4—61no—
113C2×C3×C4C2×S411yescharacteristic
114C2×Dic3—122no—
115C2×Dic3—122no—
116C2×Dic3—122no—
117C2×Dic3—122no—
118C2×Dic3—122no—
119C2×Dic3—122no—
120C2×Dic3—246no—
121C3×C8—32no—
122C3×C8—46no—
123C3×C8SL(2,ℤ/4)12yescomplemented
124C2×C32—41no—
125C2×C32—41no—
126C2×C32—41no—
127C24C4⋊(C3⋊D3)11yescharacteristic
128C22×C4—31no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—182no—
133C22×C4—182no—
134C22×C4#63411yescharacteristic
135C22×C4C2×C3⋊Dic311yescharacteristic
136C2×C8—31no—
137C2×C8—32no—
138C2×C8—32no—
139C2×C8—32no—
140C2×C8—61no—
141C2×C8C3⋊S411yescharacteristic
142C4⋊C4—182no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—182no—
146C22⋊C4—362no—
147C22⋊C4—362no—
148C22×C3—31no—
149C22×C3—31no—
150C22×C3—31no—
151C22×C3—31no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—31no—
156C22×C3—31no—
157C22×C3—43no—
158C22×C3—61no—
159C22×C3#81811yescharacteristic, complemented
160C22×C3C4⋊S411yescharacteristic
161A4#81813yescomplemented
162C3×C4—31no—
163C3×C4—31no—
164C3×C4—43no—
165C3×C4—43no—
166C3×C4A4⋊Q811yescharacteristic
167C3×C4C2×SL(2,ℤ/4)11yescharacteristic
168Dic3—242no—
169Dic3—242no—
170Dic3—486no—
171C32—41noSylow
172C23—31no—
173C23—31no—
174C23—31no—
175C23—31no—
176C23#374511yescharacteristic
177C23#374611yescharacteristic
178C23C4⋊(C3⋊Dic3)11yescharacteristic
179C2×C4—31no—
180C2×C4—31no—
181C2×C4—31no—
182C2×C4—31no—
183C2×C4—31no—
184C2×C4—31no—
185C2×C4—31no—
186C2×C4—61no—
187C2×C4—362no—
188C2×C4—362no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4—362no—
192C2×C4—362no—
193C2×C4C2×C3⋊S411yescharacteristic
194C8—32no—
195C8C3⋊SL(2,ℤ/4)12yescomplemented
196C2×C3—31no—
197C2×C3—31no—
198C2×C3—31no—
199C2×C3—31no—
200C2×C3—43no—
201C2×C3—43no—
202C2×C3—43no—
203C2×C3#539811yescharacteristic
204C2×C3#540211yescharacteristic
205C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
206C22—31no—
207C22—31no—
208C22—31no—
209C22—31no—
210C22—31no—
211C22—31no—
212C22—31no—
213C22—31no—
214C22—31no—
215C22—61no—
216C22#6364511yescharacteristic, complemented
217C22C4⋊(C3⋊S4)11yescharacteristic
218C4—31no—
219C4—31no—
220C4—722no—
221C4—722no—
222C4#6425911yescharacteristic
223C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
224C3—43no—
225C3#7311111yescharacteristic, complemented
226C2—31no—
227C2—31no—
228C2—31no—
229C2—31no—
230C2#1059363211yescharacteristic
231C2#1059363611yescharacteristic
232C2C4⋊(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#107
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
78. C3×A4#107semidirect
86. C22×C8C3⋊Dic3semidirect
123. C3×C8SL(2,ℤ/4)semidirect
159. C22×C3#818semidirect
161. A4#818semidirect
195. C8C3⋊SL(2,ℤ/4)semidirect
216. C22#63645semidirect
225. C3#73111semidirect

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
#731113
#719713
#636454