Finite Group Databasebeta

← #11921064

Subgroups — #11921064

Order 1152.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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)C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
4#73108—33nomaximal
5#71967—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)C412yes—
8C3×C8×A4C412yescomplemented
9C3⋊(A4⋊C8)C412yescomplemented
10#63642—41nomaximal
11C23×C3×C8D311yescharacteristic
12C2×C8×A4D313yes—
13C4×SL(2,ℤ/4)—33no—
14C2×A4⋊C8—33no—
15C4×#217—31no—
16C2×#830—31no—
17C2×#815—31no—
18C2×#815—31no—
19#4550—31no—
20#4550—31no—
21C22×C3×A4C2×C411yescharacteristic
22C3×C4×A4C2×C411yescharacteristic
23C3×C4×A4C2×C411yescharacteristic
24C3⋊SL(2,ℤ/4)—22no—
25C2×C32×C8—41no—
26C4×C3⋊Dic3—41no—
27C2×C3⋊(C3⋊C8)—41no—
28#1752—91noSylow
29C23×C3×C4C2×D311yescharacteristic
30C2×C4×A4C2×D313yes—
31C2×SL(2,ℤ/4)—36no—
32C22×C3×C8—31no—
33C22×C3×C8—32no—
34C22×C3×C8—31no—
35C22×C3×C8Dic312yescomplemented
36C2×#217—32no—
37C2×C4×Dic3—31no—
38C2×C4×Dic3—31no—
39C22×C3⋊C8—31no—
40C22×C3⋊C8—31no—
41C8×A4Dic316yescomplemented
42A4⋊C8—36no—
43C3⋊#95—32no—
44#830—32no—
45#830—32no—
46#815—62no—
47#815—61no—
48#815—61no—
49#815—123no—
50C2×C3×A4C4211yescharacteristic
51C2×C3×A4M1612yes—
52C2×C32×C4—41no—
53C2×C3⋊Dic3—42no—
54C32×C8—42no—
55C3⋊(C3⋊C8)—42no—
56C23×C8C3⋊D311yescharacteristic
57C2×C22⋊C8—91no—
58C2×#97—91no—
59C2×#97—91no—
60C4×C22⋊C4—91no—
61#336—91no—
62#336—91no—
63C24×C3C4×D311yescharacteristic
64C22×A4C4×D313yes—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4C4×D311yescharacteristic
70C22×C3×C4C2×Dic311yescharacteristic
71C22×Dic3—32no—
72C22×Dic3—32no—
73C4×A4C4×D313yes—
74C4×A4C2×Dic313yes—
75SL(2,ℤ/4)—66no—
76C2×C3×C8—31no—
77C2×C3×C8—32no—
78C2×C3×C8—32no—
79C2×C3×C8—32no—
80C2×C3×C8—43no—
81C2×C3×C8—61no—
82C2×C3×C8S411yescharacteristic
83#217—62no—
84#217—62no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C4×Dic3—123no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—61no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—123no—
97C22×C32—41no—
98C3×A4#9711yescharacteristic, complemented
99C32×C4—41no—
100C32×C4—41no—
101C3⋊Dic3—82no—
102C23×C4C2×C3⋊D311yescharacteristic
103C22×C8—31no—
104C22×C8—31no—
105C22×C8—32no—
106C22×C8—91no—
107C22×C8—91no—
108C22×C8C3⋊Dic312yescomplemented
109C2×C22⋊C4—92no—
110C2×C42—91no—
111C2×C42—91no—
112C22⋊C8—92no—
113C22⋊C8—92no—
114#97—182no—
115#97—181no—
116#97—181no—
117#95—92no—
118C23×C3—31no—
119C23×C3—32no—
120C23×C3—31no—
121C23×C3ΓL(1,𝔽25)12yes—
122C23×C3C4×Dic311yescharacteristic
123C2×A4ΓL(1,𝔽25)16yes—
124C2×A4C4×Dic313yes—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—43no—
133C2×C3×C4—61no—
134C2×C3×C4C2×S411yescharacteristic
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—126no—
142C3×C8—32no—
143C3×C8—46no—
144C3×C8SL(2,ℤ/4)12yescomplemented
145C3⋊C8—62no—
146C3⋊C8—62no—
147C3⋊C8—126no—
148C2×C32—42no—
149C2×C32—41no—
150C24C4×C3⋊D311yescharacteristic
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—31no—
154C22×C4—31no—
155C22×C4—92no—
156C22×C4—92no—
157C22×C4C4×C3⋊D311yescharacteristic
158C22×C4C2×C3⋊Dic311yescharacteristic
159C2×C8—31no—
160C2×C8—32no—
161C2×C8—32no—
162C2×C8—32no—
163C2×C8—61no—
164C2×C8—92no—
165C2×C8—92no—
166C2×C8—181no—
167C2×C8—181no—
168C2×C8—181no—
169C2×C8—181no—
170C2×C8C3⋊S411yescharacteristic
171C22⋊C4—182no—
172C22⋊C4—182no—
173C42—181no—
174C42—181no—
175C42—181no—
176C42—181no—
177C22×C3—32no—
178C22×C3—31no—
179C22×C3—32no—
180C22×C3—32no—
181C22×C3—31no—
182C22×C3—31no—
183C22×C3—43no—
184C22×C3—61no—
185C22×C3#81511yescharacteristic, complemented
186C22×C3C4×S411yescharacteristic
187A4#81513yescomplemented
188C3×C4—31no—
189C3×C4—31no—
190C3×C4—43no—
191C3×C4—43no—
192C3×C4C4×S411yescharacteristic
193C3×C4C2×SL(2,ℤ/4)11yescharacteristic
194Dic3—122no—
195Dic3—122no—
196Dic3—246no—
197C32—41noSylow
198C23—31no—
199C23—32no—
200C23—31no—
201C23#374312yes—
202C23C4×C3⋊Dic311yescharacteristic
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—61no—
211C2×C4—182no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—182no—
217C2×C4C2×C3⋊S411yescharacteristic
218C8—32no—
219C8—182no—
220C8—182no—
221C8C3⋊SL(2,ℤ/4)12yescomplemented
222C2×C3—32no—
223C2×C3—31no—
224C2×C3—31no—
225C2×C3—46no—
226C2×C3—43no—
227C2×C3#540012yes—
228C2×C3C4×SL(2,ℤ/4)11yescharacteristic
229C22—32no—
230C22—31no—
231C22—32no—
232C22—32no—
233C22—31no—
234C22—31no—
235C22—61no—
236C22#6364211yescharacteristic, complemented
237C22C4×C3⋊S411yescharacteristic
238C4—31no—
239C4—31no—
240C4—362no—
241C4—362no—
242C4C4×C3⋊S411yescharacteristic
243C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
244C3—43no—
245C3#7310811yescharacteristic, complemented
246C2—32no—
247C2—31no—
248C2—31no—
249C2#1059363412yes—
250C2C4×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×C3⋊S4
commutatorC2×C3×A4C42
FittingC23×C3×C8D3
socleC24×C3C4×D3
prime radicalC22×C3×A4C2×C4
cosocleC2×C3×C4×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#97
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
8. C3×C8×A4C4semidirect
9. C3⋊(A4⋊C8)C4semidirect
35. C22×C3×C8Dic3semidirect
41. C8×A4Dic3semidirect
98. C3×A4#97semidirect
108. C22×C8C3⋊Dic3semidirect
144. C3×C8SL(2,ℤ/4)semidirect
185. C22×C3#815semidirect
187. A4#815semidirect
221. C8C3⋊SL(2,ℤ/4)semidirect
236. C22#63642semidirect
245. C3#73108semidirect

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
C2×C3⋊(A4⋊C8)2
#731083
#719673
#636424