Finite Group Databasebeta

← C4⋊(C3⋊(#127⋊C3)) #11921121

Subgroups — C4⋊(C3⋊(#127⋊C3)) #11921121

Order 1152.

513 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 513 conjugacy classes of subgroups — too many to draw. Only its 33 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⋊(#127⋊C3)C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3#73318C311yesmaximal, characteristic, complemented
4C4⋊(#127⋊C3)—31nomaximal
5A4×D12—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3⋊(#127⋊C3)—22no—
8C2×#874—32no—
9C2×#874—31no—
10C2×#874—31no—
11C2×#874C2×C312yescomplemented
12C2×#127⋊C3—32no—
13C3×C43C2×C311yescharacteristic, complemented
14C4×C42⋊C3—21no—
15C4×C42⋊C3D311yescharacteristic, complemented
16C2×D3×A4—42no—
17C3×C4×A4—41no—
18C3×C42⋊C3D411yescharacteristic, complemented
19#2867—31noSylow
20C22×D12—32no—
21C22×D12—32no—
22C22×D12—32no—
23C22×D12—32no—
24C22×D12—31no—
25C22×D12A411yescharacteristic
26D4×A4—121no—
27C2×C3×C42—31no—
28C2×C3×C42—31no—
29C2×C3×C42C22×C311yescharacteristic
30#874—22no—
31#874—62no—
32#874—62no—
33#874—68no—
34#874—62no—
35#874—62no—
36#874—62no—
37#127⋊C3—62no—
38C2×C42⋊C3—21no—
39C2×C42⋊C3C2×D311yescharacteristic
40C2×C3×A4—41no—
41D3×A4—82no—
42C3×D12—161no—
43C2×#127—32no—
44C2×#127—91no—
45C2×#127—92no—
46C2×#127—91no—
47C43C3×D311yescharacteristic, complemented
48C23×D3—32no—
49C23×D3C2×A412yes—
50C22×A4—122no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4C2×A411yescharacteristic
54C2×D12—61no—
55C2×D12—62no—
56C2×D12—62no—
57C2×D12—62no—
58C2×D12—62no—
59C2×D12—64no—
60C2×D12—64no—
61C2×D12—64no—
62C2×D12—64no—
63C2×D12—68no—
64C2×D12—64no—
65C2×D12—68no—
66C2×D12—64no—
67C2×D12—62no—
68C2×D12—61no—
69C2×D12—61no—
70C2×D12—62no—
71C2×D12—61no—
72C4×A4—41no—
73C4×A4—81no—
74C3×C42—31no—
75C3×C42—34no—
76C3×C42—32no—
77C3×C42—32no—
78C3×C42C3×D411yescharacteristic, complemented
79C42⋊C3—21no—
80C42⋊C3D1211yescharacteristic, complemented
81C2×C3×D3—162no—
82C3×A4—41no—
83C32×C4—161no—
84C22×D4—31no—
85C22×D4—92no—
86C22×D4—92no—
87C22×D4—92no—
88C22×D4—92no—
89C22×D4—91no—
90#127—62no—
91#127—182no—
92#127—182no—
93#127—188no—
94#127—182no—
95#127—182no—
96#127—182no—
97C2×C42—31no—
98C2×C42—31no—
99C2×C42C2×C3×D311yescharacteristic
100C23×C3C22×A411yescharacteristic
101C22×D3—22no—
102C22×D3—62no—
103C22×D3—64no—
104C22×D3—62no—
105C22×D3—62no—
106C22×D3—64no—
107C22×D3—62no—
108C22×D3—62no—
109C2×A4—41no—
110C2×A4—81no—
111C2×A4—242no—
112C3×D4—481no—
113C2×C3×C4—32no—
114C2×C3×C4—34no—
115C2×C3×C4—32no—
116C2×C3×C4—32no—
117C2×C3×C4—31no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—31no—
121D12—41no—
122D12—121no—
123D12—124no—
124D12—124no—
125D12—128no—
126D12—124no—
127D12—124no—
128D12—128no—
129D12—121no—
130D12—122no—
131D12—121no—
132C2×C32—161no—
133C3×D3—322no—
134C24—32no—
135C24—92no—
136C2×D4—181no—
137C2×D4—182no—
138C2×D4—182no—
139C2×D4—182no—
140C2×D4—182no—
141C2×D4—184no—
142C2×D4—184no—
143C2×D4—184no—
144C2×D4—188no—
145C2×D4—184no—
146C2×D4—184no—
147C2×D4—188no—
148C2×D4—184no—
149C2×D4—181no—
150C2×D4—182no—
151C2×D4—182no—
152C2×D4—181no—
153C2×D4—181no—
154C22×C4—31no—
155C22×C4—31no—
156C22×C4D3×A411yescharacteristic
157C42—31no—
158C42—34no—
159C42—32no—
160C42—32no—
161C42C3×D1211yescharacteristic, complemented
162C22×C3—31no—
163C22×C3—31no—
164C22×C3—482no—
165C22×C3D4×A411yescharacteristic
166C2×D3—42no—
167C2×D3—122no—
168C2×D3—122no—
169C2×D3—122no—
170C2×D3—124no—
171C2×D3—122no—
172C2×D3—124no—
173C2×D3—122no—
174A4—41no—
175A4—81no—
176C3×C4—34no—
177C3×C4—32no—
178C3×C4—32no—
179C3×C4—31no—
180C3×C4—161no—
181C3×C4—321no—
182C3×C4#127⋊C311yescharacteristic, complemented
183C32—161noSylow
184C23—62no—
185C23—182no—
186C23—182no—
187C23—182no—
188C23—184no—
189C23—182no—
190C23—184no—
191C23—182no—
192C23C2×D3×A411yescharacteristic
193D4—121no—
194D4—361no—
195D4—364no—
196D4—364no—
197D4—368no—
198D4—364no—
199D4—364no—
200D4—368no—
201D4—361no—
202D4—362no—
203D4—361no—
204C2×C4—32no—
205C2×C4—34no—
206C2×C4—32no—
207C2×C4—32no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—31no—
212C2×C3—31no—
213C2×C3—31no—
214C2×C3—161no—
215C2×C3—321no—
216C2×C3—962no—
217C2×C3C2×#127⋊C311yescharacteristic
218D3—82no—
219D3—242no—
220C22—31no—
221C22—31no—
222C22—122no—
223C22—362no—
224C22—362no—
225C22—362no—
226C22—364no—
227C22—362no—
228C22—364no—
229C22—362no—
230C22A4×D1211yescharacteristic
231C4—32no—
232C4—32no—
233C4—34no—
234C4—31no—
235C4C3⋊(#127⋊C3)11yescharacteristic, complemented
236C3—161no—
237C3—321no—
238C3C4⋊(#127⋊C3)11yescharacteristic, complemented
239C2—31no—
240C2—31no—
241C2—242no—
242C2—722no—
243C2C2×C3⋊(#127⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#127⋊C3)
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
hypercenterC4C3⋊(#127⋊C3)
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(#127⋊C3)C2semidirect
2. C3×C4×C42⋊C3C2semidirect
3. #73318C3semidirect
11. C2×#874C2×C3semidirect
13. C3×C43C2×C3semidirect
15. C4×C42⋊C3D3semidirect
18. C3×C42⋊C3D4semidirect
47. C43C3×D3semidirect
78. C3×C42C3×D4semidirect
80. C42⋊C3D12semidirect
161. C42C3×D12semidirect
182. C3×C4#127⋊C3semidirect
235. C4C3⋊(#127⋊C3)semidirect
238. C3C4⋊(#127⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#127⋊C3)2
C3×C4×C42⋊C32
#733183
C4⋊(#127⋊C3)3
A4×D124