Finite Group Databasebeta

← #74298⋊C3 #11921152

Subgroups — #74298⋊C3 #11921152

Order 1152.

305 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 305 conjugacy classes of subgroups — too many to draw. Only its 37 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)C211yesmaximal, characteristic
2C3×#383⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
4#74298C311yesmaximal, characteristic, complemented
5#2380⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊(#127⋊C3)C412yescomplemented
9C2×#874C2×C311yescharacteristic
10C2×#127⋊C3—31no—
11C3×#383C2×C311yescharacteristic, complemented
12#4937C2×C311yescharacteristic, complemented
13#4665—31no—
14#4665—31no—
15#4665—31no—
16#4665—31no—
17#383⋊C3—21no—
18#383⋊C3—31no—
19#383⋊C3D311yescharacteristic, complemented
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24#2380—31noSylow
25C22×D12—31no—
26C22×D12—31no—
27C22×C4×D3—31no—
28C22×C4×D3A411yescharacteristic
29C2×C4×A4—121no—
30C2×C3×C42C22×C311yescharacteristic
31C2×(C2×D3)⋊C4—31no—
32C2×(C2×D3)⋊C4—31no—
33C2×(C2×D3)⋊C4—31no—
34C2×(C2×D3)⋊C4—31no—
35#874—32no—
36#874C3×C412yescomplemented
37#127⋊C3—32no—
38C2×C42⋊C3—21no—
39C2×C42⋊C3C2×D311yescharacteristic
40C3×#95—31no—
41C3×#95—31no—
42C3⋊#95—31no—
43C3⋊#95—31no—
44C2×C3×A4—41no—
45D3×A4—42no—
46C3×C4×D3—161no—
47C2×#127—31no—
48#386—91no—
49#386—91no—
50#386—91no—
51#386—91no—
52#383—31no—
53#383C3×D311yescharacteristic, complemented
54C23×D3—31no—
55C23×D3C2×A411yescharacteristic
56C22×A4—121no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4C2×A411yescharacteristic
60C22×Dic3—31no—
61C22×Dic3C2×A411yescharacteristic
62C2×D12—32no—
63C2×D12—32no—
64C2×D12—32no—
65C2×D12—32no—
66C2×D12—121no—
67C2×D12—121no—
68C2×D12—121no—
69C2×D12—121no—
70C2×C4×D3—121no—
71C2×C4×D3—121no—
72C2×C4×D3—121no—
73C2×C4×D3—121no—
74C4×A4—41no—
75C4×A4—81no—
76C4×A4—121no—
77C3×C42—31no—
78C3×C42C2×C3×C411yescharacteristic, complemented
79(C2×D3)⋊C4—121no—
80(C2×D3)⋊C4—121no—
81(C2×D3)⋊C4—121no—
82(C2×D3)⋊C4—121no—
83C42⋊C3—21no—
84C42⋊C3C4×D311yescharacteristic, complemented
85C2×C3×D3—161no—
86C3×A4—41no—
87C32×C4—161no—
88C3×Dic3—161no—
89C22×D4—91no—
90C22×D4—91no—
91C23×C4—31no—
92C23×C4—91no—
93#127—32no—
94#127—92no—
95C2×C22⋊C4—91no—
96C2×C22⋊C4—91no—
97C2×C22⋊C4—91no—
98C2×C22⋊C4—91no—
99C2×C42C2×C3×D311yescharacteristic
100#95—31no—
101#95—31no—
102#95—91no—
103#95—91no—
104C23×C3C22×A411yescharacteristic
105C22×D3—32no—
106C22×D3—61no—
107C22×D3—61no—
108C22×D3—61no—
109C22×D3—61no—
110C22×D3—61no—
111C22×D3—61no—
112C22×D3—61no—
113C22×D3—61no—
114C22×D3C4×A412yes—
115C2×A4—41no—
116C2×A4—81no—
117C2×A4—122no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—61no—
125C2×C3×C4—61no—
126C2×C3×C4—481no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131D12—122no—
132D12—122no—
133D12—122no—
134D12—122no—
135C4×D3—41no—
136C4×D3—121no—
137C4×D3—124no—
138C2×C32—161no—
139C3×D3—162no—
140C24—31no—
141C24—91no—
142C2×D4—92no—
143C2×D4—92no—
144C2×D4—92no—
145C2×D4—92no—
146C2×D4—361no—
147C2×D4—361no—
148C2×D4—361no—
149C2×D4—361no—
150C22×C4—31no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—91no—
154C22×C4—361no—
155C22×C4—361no—
156C22×C4—361no—
157C22×C4—361no—
158C22×C4D3×A411yescharacteristic
159C22⋊C4—361no—
160C22⋊C4—361no—
161C22⋊C4—361no—
162C22⋊C4—361no—
163C42—31no—
164C42C3×C4×D311yescharacteristic, complemented
165C22×C3—31no—
166C22×C3—31no—
167C22×C3—481no—
168C22×C3C2×C4×A411yescharacteristic
169C2×D3—41no—
170C2×D3—62no—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—62no—
174C2×D3—121no—
175C2×D3—121no—
176C2×D3—121no—
177C2×D3—121no—
178C2×D3—121no—
179A4—41no—
180A4—81no—
181C3×C4—41no—
182C3×C4—61no—
183C3×C4—61no—
184C3×C4—121no—
185C3×C4—161no—
186C3×C4—321no—
187C3×C4—481no—
188Dic3—41no—
189Dic3—121no—
190C32—161noSylow
191C23—32no—
192C23—92no—
193C23—181no—
194C23—181no—
195C23—181no—
196C23—181no—
197C23—181no—
198C23—181no—
199C23—181no—
200C23—181no—
201C23C2×D3×A411yescharacteristic
202D4—362no—
203D4—362no—
204D4—362no—
205D4—362no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—61no—
209C2×C4—61no—
210C2×C4—61no—
211C2×C4—61no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—121no—
215C2×C4—181no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—361no—
220C2×C4—364no—
221C2×C3—31no—
222C2×C3—31no—
223C2×C3—161no—
224C2×C3—321no—
225C2×C3—482no—
226C2×C3#560⋊C311yescharacteristic
227D3—42no—
228D3—122no—
229C22—31no—
230C22—31no—
231C22—121no—
232C22—182no—
233C22—182no—
234C22—182no—
235C22—182no—
236C22—361no—
237C22—361no—
238C22—361no—
239C22—361no—
240C22—361no—
241C22C4×D3×A411yescharacteristic
242C4—41no—
243C4—61no—
244C4—61no—
245C4—121no—
246C4—121no—
247C4—361no—
248C3—161no—
249C3—321no—
250C3#2380⋊C311yescharacteristic, complemented
251C2—31no—
252C2—31no—
253C2—122no—
254C2—362no—
255C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×#383C2×C3
socleC23×C3C22×A4
prime radicalC2×C3⋊(#127⋊C3)C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#383⋊C3C2semidirect
3. C3⋊(#383⋊C3)C2semidirect
4. #74298C3semidirect
8. C3⋊(#127⋊C3)C4semidirect
11. C3×#383C2×C3semidirect
12. #4937C2×C3semidirect
19. #383⋊C3D3semidirect
23. C3×C42⋊C3C2×C4semidirect
36. #874C3×C4semidirect
53. #383C3×D3semidirect
78. C3×C42C2×C3×C4semidirect
84. C42⋊C3C4×D3semidirect
164. C42C3×C4×D3semidirect
250. C3#2380⋊C3semidirect

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×#383⋊C32
C3⋊(#383⋊C3)2
#742983
#2380⋊C33
C4×D3×A44