Finite Group Databasebeta

← #11921058

Subgroups — #11921058

Order 1152.

298 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 29 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
1C3×#5450C211yesmaximal, characteristic, complemented
2#10593630C211yesmaximal, characteristic, complemented
3C3⋊#4625C211yesmaximal, characteristic, complemented
4#4625⋊C2—33nomaximal
5#71950—31nomaximal
6C3⋊#1020—21no—
7#64269—41nomaximal
8C3×#120⋊C3—21no—
9C3×#120⋊C3C2211yescharacteristic
10C3×H(3,𝔽4)D311yescharacteristic, complemented
11#5450D313yescomplemented
12#1020⋊C2—33no—
13#5061—31no—
14#5032—31no—
15#5032—31no—
16#4625—33no—
17#4541—31no—
18#4536—31no—
19#4536—31no—
20C3×C22⋊A4D411yescharacteristic, complemented
21C22×C3×A4—41no—
22C2×C3⋊S4—41no—
23C3⋊SL(2,ℤ/4)—41no—
24#2199—91noSylow
25#1020—63no—
26#1004—31no—
27GL(2,ℤ/4)—123no—
28C3×#124—31no—
29C3×#124—61no—
30C3×#120—21no—
31C3×#120—31no—
32C3×#120C2×D311yescharacteristic
33#953—61no—
34#953—61no—
35#942—61no—
36#120⋊C3—23no—
37#120⋊C3C2×D313yes—
38#834—31no—
39#834—31no—
40#833—31no—
41#806—61no—
42#806—61no—
43#805—61no—
44C2×C3×A4—41no—
45C2×C3×A4—81no—
46C3⋊S4—81no—
47C3⋊S4—161no—
48#638—161no—
49H(3,𝔽4)C3⋊D311yescharacteristic, complemented
50B(4,𝔽2)—91no—
51B(4,𝔽2)—91no—
52#455—91no—
53#354—91no—
54AΣL(1,𝔽16)—91no—
55AΣL(1,𝔽16)—91no—
56C24×C3#6711yescharacteristic, complemented
57C24×C3S411yescharacteristic, complemented
58C22⋊A4#6713yescomplemented
59C22×A4—43no—
60C2×S4—123no—
61C2×C3×Q8—31no—
62C2×C3×D4—31no—
63C2×C3×D4—61no—
64C2×#67—61no—
65C2×#67—61no—
66C2×#67—121no—
67C2×#67—121no—
68#237—121no—
69D3×D4—121no—
70#235—61no—
71SL(2,ℤ/4)—123no—
72C3×C22⋊C4—31no—
73C3×C22⋊C4—31no—
74C3×C22⋊C4—61no—
75C3×C22⋊C4—61no—
76C3×C42—31no—
77#217—61no—
78#217—61no—
79#217—121no—
80#217—121no—
81#216—121no—
82#215—121no—
83#208—61no—
84C22×C32—161no—
85C2×C3⋊D3—161no—
86C3×A4—41no—
87C3×A4—161no—
88C3⋊Dic3—161no—
89H(5,𝔽2)—91no—
90#137—181no—
91#124—31no—
92#124—61no—
93#120—21no—
94#120—31no—
95#120—181no—
96#120—181no—
97#120C2×C3⋊D311yescharacteristic
98#104—181no—
99#100—91no—
100#99—91no—
101#99—91no—
102#99—181no—
103#99—181no—
104C23×C3—21no—
105C23×C3—31no—
106C23×C3—121no—
107C23×C3—121no—
108C23×C3C2×S411yescharacteristic
109C22×D3—61no—
110C22×D3—61no—
111C2×A4—43no—
112C2×A4—83no—
113S4—243no—
114S4—483no—
115C3×Q8—121no—
116C3×D4—121no—
117C3×D4—241no—
118C2×C3×C4—31no—
119C2×C3×C4—61no—
120#67—121no—
121#67—121no—
122#67—121no—
123#67—241no—
124#67—241no—
125#67—241no—
126#67—241no—
127#67—483no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—121no—
131C2×Dic3—121no—
132D12—61no—
133C4×D3—121no—
134Dic6—61no—
135C3⋊C8—121no—
136C2×C32—161no—
137C2×C32—321no—
138C3⋊D3—321no—
139C24#63811yescharacteristic, complemented
140C24C3⋊S411yescharacteristic, complemented
141#41—181no—
142#41—361no—
143C2×Q8—31no—
144C2×D4—31no—
145C2×D4—61no—
146C2×D4—181no—
147C2×D4—181no—
148C2×D4—361no—
149C2×D4—361no—
150C2×D4—361no—
151Q16—361no—
152SD16—361no—
153M16—181no—
154C22⋊C4—31no—
155C22⋊C4—31no—
156C22⋊C4—61no—
157C22⋊C4—61no—
158C22⋊C4—181no—
159C22⋊C4—181no—
160C22⋊C4—361no—
161C22⋊C4—361no—
162C42—31no—
163C22×C3—41no—
164C22×C3—41no—
165C22×C3—61no—
166C22×C3—61no—
167C22×C3—121no—
168C22×C3—121no—
169C22×C3—121no—
170C22×C3—121no—
171C22×C3—163no—
172C22×C3GL(2,ℤ/4)11yescharacteristic
173C2×D3—121no—
174C2×D3—241no—
175C2×D3—241no—
176C2×D3—483no—
177A4—43no—
178A4—163no—
179C3×C4—61no—
180C3×C4—121no—
181Dic3—121no—
182Dic3—241no—
183Dic3—241no—
184Dic3—483no—
185C32—161noSylow
186C23—21no—
187C23—31no—
188C23—121no—
189C23—121no—
190C23—181no—
191C23—181no—
192C23C2×C3⋊S411yescharacteristic
193Q8—121no—
194Q8—181no—
195D4—121no—
196D4—181no—
197D4—241no—
198D4—361no—
199D4—361no—
200D4—361no—
201D4—721no—
202D4—721no—
203D4—721no—
204D4—721no—
205C2×C4—31no—
206C2×C4—61no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4—361no—
210C2×C4—361no—
211C2×C4—361no—
212C8—361no—
213C2×C3—31no—
214C2×C3—41no—
215C2×C3—81no—
216C2×C3—121no—
217C2×C3—163no—
218C2×C3—323no—
219D3—241no—
220D3—963no—
221C22—41no—
222C22—41no—
223C22—61no—
224C22—61no—
225C22—121no—
226C22—121no—
227C22—121no—
228C22—121no—
229C22—361no—
230C22—721no—
231C22—721no—
232C22#6426911yescharacteristic
233C4—61no—
234C4—121no—
235C4—361no—
236C4—721no—
237C4—721no—
238C3—163no—
239C3#4625⋊C211yescharacteristic, complemented
240C2—31no—
241C2—41no—
242C2—81no—
243C2—121no—
244C2—721no—
subgroupG/H
center, hypercenterC1G
commutator, cosocleC3×#120⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×H(3,𝔽4)D3
socleC22×C3GL(2,ℤ/4)
hypocenterC3×C22⋊A4D4
LCSG ▷ C3×#120⋊C3 ▷ C3×C22⋊A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#5450C2semidirect
2. #10593630C2semidirect
3. C3⋊#4625C2semidirect
10. C3×H(3,𝔽4)D3semidirect
11. #5450D3semidirect
20. C3×C22⋊A4D4semidirect
49. H(3,𝔽4)C3⋊D3semidirect
56. C24×C3#67semidirect
57. C24×C3S4semidirect
58. C22⋊A4#67semidirect
139. C24#638semidirect
140. C24C3⋊S4semidirect
239. C3#4625⋊C2semidirect

Maximal subgroups

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

subgroupindex
C3×#54502
#105936302
C3⋊#46252
#4625⋊C23
#719503
#642694