Finite Group Databasebeta

← (#560⋊C3)⋊D3 #11921057

Subgroups — (#560⋊C3)⋊D3 #11921057

Order 1152.

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

normal subgroups only

This group has 282 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×#560⋊C3C211yesmaximal, characteristic, complemented
2#10593631C211yesmaximal, characteristic, complemented
3C3⋊#4626C211yesmaximal, characteristic, complemented
4#4626⋊C2—33nomaximal
5#71947—31nomaximal
6#64269—41nomaximal
7C3×#127⋊C3C2211yescharacteristic
8C3×#126⋊C3—21no—
9C3⋊#857—21no—
10C3×#560D311yescharacteristic, complemented
11#560⋊C3D313yescomplemented
12#857⋊C2—33no—
13#5077—31no—
14#5053—31no—
15#5032—31no—
16#4626—33no—
17#4545—31no—
18#4539—31no—
19#4536—31no—
20C22×C3×A4—41no—
21C2×C3⋊S4—41no—
22C3⋊SL(2,ℤ/4)—41no—
23C3×C42⋊C3D411yescharacteristic, complemented
24#2200—91noSylow
25#1004—31no—
26GL(2,ℤ/4)—123no—
27C3×#127C2×D311yescharacteristic
28C3×#126—21no—
29C3×#123—31no—
30C3×#121—61no—
31C3×#120—31no—
32#953—61no—
33#932—61no—
34#929—61no—
35#127⋊C3C2×D313yes—
36#126⋊C3—23no—
37#857—63no—
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—
47#638—161no—
48#560C3⋊D311yescharacteristic, complemented
49#458—91no—
50B(4,𝔽2)—91no—
51#453—91no—
52#353—91no—
53#352—91no—
54AΣL(1,𝔽16)—91no—
55C24×C3S411yescharacteristic
56C22×A4—43no—
57C2×S4—123no—
58C2×C3×D4—31no—
59C2×C3×D4—31no—
60C2×C3×D4—61no—
61C22×C3×C4—31no—
62C2×#67—61no—
63C2×#67—61no—
64C2×#67—121no—
65#237—121no—
66D3×D4—121no—
67#235—61no—
68SL(2,ℤ/4)—123no—
69C3×C4⋊C4—61no—
70C3×C22⋊C4—31no—
71C3×C22⋊C4—31no—
72C3×C22⋊C4—61no—
73C3×C42#6711yescharacteristic, complemented
74#217—61no—
75#217—61no—
76#217—121no—
77#214—121no—
78#213—121no—
79(C2×D3)⋊C4—121no—
80Dic3⋊C4—121no—
81#208—61no—
82C42⋊C3#6713yescomplemented
83C22×C32—161no—
84C2×C3⋊D3—161no—
85C3×A4—41no—
86C3⋊Dic3—161no—
87H(5,𝔽2)—91no—
88AGL(1,ℤ/8)—181no—
89#127C2×C3⋊D311yescharacteristic
90#126—21no—
91#123—31no—
92#123—181no—
93#121—61no—
94#120—31no—
95#120—181no—
96#104—181no—
97#100—91no—
98#99—91no—
99#99—91no—
100#99—181no—
101#99—181no—
102C23×C3—21no—
103C23×C3—31no—
104C23×C3—121no—
105C23×C3C2×S411yescharacteristic
106C22×D3—61no—
107C22×D3—61no—
108C2×A4—43no—
109C2×A4—83no—
110S4—243no—
111C3×D4—121no—
112C3×D4—121no—
113C3×D4—241no—
114C2×C3×C4—31no—
115C2×C3×C4—61no—
116C2×C3×C4—121no—
117#67—121no—
118#67—121no—
119#67—121no—
120#67—241no—
121#67—241no—
122#67—483no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127D12—61no—
128C4×D3—121no—
129Dic6—61no—
130C3⋊C8—121no—
131C2×C32—161no—
132C2×C32—321no—
133C3⋊D3—321no—
134C24C3⋊S411yescharacteristic
135#41—181no—
136#41—361no—
137C2×D4—31no—
138C2×D4—31no—
139C2×D4—61no—
140C2×D4—181no—
141C2×D4—181no—
142C2×D4—361no—
143C2×D4—361no—
144C22×C4—31no—
145SD16—361no—
146D8—361no—
147M16—181no—
148C4⋊C4—61no—
149C4⋊C4—361no—
150C22⋊C4—31no—
151C22⋊C4—31no—
152C22⋊C4—61no—
153C22⋊C4—181no—
154C22⋊C4—181no—
155C22⋊C4—361no—
156C22⋊C4—361no—
157C42#63811yescharacteristic, complemented
158C22×C3—41no—
159C22×C3—61no—
160C22×C3—61no—
161C22×C3—121no—
162C22×C3—121no—
163C22×C3—121no—
164C22×C3—163no—
165C22×C3GL(2,ℤ/4)11yescharacteristic
166C2×D3—121no—
167C2×D3—241no—
168C2×D3—241no—
169C2×D3—483no—
170A4—43no—
171C3×C4—61no—
172C3×C4—121no—
173Dic3—121no—
174Dic3—241no—
175Dic3—241no—
176Dic3—483no—
177C32—161noSylow
178C23—21no—
179C23—31no—
180C23—121no—
181C23—181no—
182C23—181no—
183C23C2×C3⋊S411yescharacteristic
184Q8—181no—
185D4—121no—
186D4—121no—
187D4—181no—
188D4—241no—
189D4—361no—
190D4—361no—
191D4—361no—
192D4—721no—
193D4—721no—
194C2×C4—31no—
195C2×C4—61no—
196C2×C4—121no—
197C2×C4—181no—
198C2×C4—181no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C8—361no—
203C2×C3—31no—
204C2×C3—41no—
205C2×C3—81no—
206C2×C3—121no—
207C2×C3—163no—
208C2×C3—323no—
209D3—241no—
210D3—963no—
211C22—41no—
212C22—61no—
213C22—61no—
214C22—121no—
215C22—121no—
216C22—121no—
217C22—361no—
218C22—721no—
219C22—721no—
220C22#6426911yescharacteristic
221C4—61no—
222C4—121no—
223C4—361no—
224C4—721no—
225C4—721no—
226C3—163no—
227C3#4626⋊C211yescharacteristic, complemented
228C2—31no—
229C2—41no—
230C2—81no—
231C2—121no—
232C2—721no—
subgroupG/H
center, hypercenterC1G
commutator, cosocleC3×#127⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#560D3
socleC22×C3GL(2,ℤ/4)
hypocenterC3×C42⋊C3D4
LCSG ▷ C3×#127⋊C3 ▷ C3×C42⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#560⋊C3C2semidirect
2. #10593631C2semidirect
3. C3⋊#4626C2semidirect
10. C3×#560D3semidirect
11. #560⋊C3D3semidirect
23. C3×C42⋊C3D4semidirect
48. #560C3⋊D3semidirect
73. C3×C42#67semidirect
82. C42⋊C3#67semidirect
157. C42#638semidirect
227. C3#4626⋊C2semidirect

Maximal subgroups

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

subgroupindex
C3×#560⋊C32
#105936312
C3⋊#46262
#4626⋊C23
#719473
#642694