Finite Group Databasebeta

← #74299⋊C3 #11921153

Subgroups — #74299⋊C3 #11921153

Order 1152.

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

normal subgroups only

This group has 241 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⋊(#126⋊C3)C211yesmaximal, characteristic
2C3×#383⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#384⋊C3)C211yesmaximal, characteristic, complemented
4#74299C311yesmaximal, characteristic, complemented
5(#126⋊C3)⋊C4—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊(#126⋊C3)C412yescomplemented
9C2×#876C2×C311yescharacteristic
10C2×#126⋊C3—31no—
11C3×#383C2×C311yescharacteristic, complemented
12#4935C2×C311yescharacteristic, complemented
13#4670—31no—
14#4668—31no—
15#4655—31no—
16#4647—31no—
17#384⋊C3—31no—
18#383⋊C3—21no—
19#383⋊C3D311yescharacteristic, complemented
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24#2383—31noSylow
25C22×C4×D3A411yescharacteristic
26C2×C4×A4—121no—
27C2×C3×C42C22×C311yescharacteristic
28C2×(C2×D3)⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×C4⋊Dic3—31no—
31C2×C4⋊Dic3—31no—
32C2×Dic3⋊C4—31no—
33C2×Dic3⋊C4—31no—
34C2×C4×Dic3—31no—
35#876—32no—
36#876C3×C412yescomplemented
37#126⋊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×#126—31no—
48#389—91no—
49#388—91no—
50#387—91no—
51#385—91no—
52#384—31no—
53#383C3×D311yescharacteristic, complemented
54C23×D3C2×A411yescharacteristic
55C22×A4—121no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4C2×A411yescharacteristic
59C22×Dic3—31no—
60C22×Dic3—31no—
61C22×Dic3C2×A411yescharacteristic
62C2×C4×D3—121no—
63C4×A4—41no—
64C4×A4—81no—
65C4×A4—121no—
66C3×C42—31no—
67C3×C42C2×C3×C411yescharacteristic, complemented
68(C2×D3)⋊C4—32no—
69(C2×D3)⋊C4—32no—
70(C2×D3)⋊C4—121no—
71C4⋊Dic3—121no—
72C4⋊Dic3—121no—
73Dic3⋊C4—32no—
74Dic3⋊C4—32no—
75Dic3⋊C4—121no—
76C4×Dic3—121no—
77C42⋊C3—21no—
78C42⋊C3C4×D311yescharacteristic, complemented
79C2×C3×D3—161no—
80C3×A4—41no—
81C32×C4—161no—
82C3×Dic3—161no—
83C23×C4—31no—
84#126—32no—
85#126—92no—
86C2×C4⋊C4—91no—
87C2×C4⋊C4—91no—
88C2×C4⋊C4—91no—
89C2×C4⋊C4—91no—
90C2×C22⋊C4—91no—
91C2×C22⋊C4—91no—
92C2×C42—91no—
93C2×C42C2×C3×D311yescharacteristic
94#95—31no—
95#95—31no—
96#95—91no—
97#95—91no—
98C23×C3C22×A411yescharacteristic
99C22×D3—61no—
100C22×D3—61no—
101C22×D3C4×A412yes—
102C2×A4—41no—
103C2×A4—81no—
104C2×A4—122no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—62no—
112C2×C3×C4—481no—
113C2×Dic3—32no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C4×D3—41no—
121C4×D3—121no—
122C2×C32—161no—
123C3×D3—162no—
124C24—31no—
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—31no—
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—361no—
131C22×C4D3×A411yescharacteristic
132C4⋊C4—92no—
133C4⋊C4—92no—
134C4⋊C4—361no—
135C4⋊C4—361no—
136C4⋊C4—361no—
137C22⋊C4—92no—
138C22⋊C4—92no—
139C22⋊C4—361no—
140C42—31no—
141C42—361no—
142C42C3×C4×D311yescharacteristic, complemented
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—481no—
146C22×C3C2×C4×A411yescharacteristic
147C2×D3—41no—
148C2×D3—62no—
149C2×D3—121no—
150A4—41no—
151A4—81no—
152C3×C4—41no—
153C3×C4—61no—
154C3×C4—61no—
155C3×C4—121no—
156C3×C4—161no—
157C3×C4—321no—
158C3×C4—481no—
159Dic3—41no—
160Dic3—62no—
161Dic3—121no—
162C32—161noSylow
163C23—32no—
164C23—181no—
165C23—181no—
166C23C2×D3×A411yescharacteristic
167C2×C4—31no—
168C2×C4—31no—
169C2×C4—61no—
170C2×C4—61no—
171C2×C4—61no—
172C2×C4—61no—
173C2×C4—62no—
174C2×C4—92no—
175C2×C4—121no—
176C2×C4—181no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4—361no—
183C2×C3—31no—
184C2×C3—31no—
185C2×C3—161no—
186C2×C3—321no—
187C2×C3—482no—
188C2×C3#560⋊C311yescharacteristic
189D3—42no—
190C22—31no—
191C22—31no—
192C22—121no—
193C22—182no—
194C22—361no—
195C22C4×D3×A411yescharacteristic
196C4—41no—
197C4—61no—
198C4—61no—
199C4—121no—
200C4—121no—
201C4—182no—
202C4—361no—
203C3—161no—
204C3—321no—
205C3(#126⋊C3)⋊C411yescharacteristic, complemented
206C2—31no—
207C2—31no—
208C2—122no—
209C2(#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⋊(#126⋊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⋊(#384⋊C3)C2semidirect
4. #74299C3semidirect
8. C3⋊(#126⋊C3)C4semidirect
11. C3×#383C2×C3semidirect
12. #4935C2×C3semidirect
19. #383⋊C3D3semidirect
23. C3×C42⋊C3C2×C4semidirect
36. #876C3×C4semidirect
53. #383C3×D3semidirect
67. C3×C42C2×C3×C4semidirect
78. C42⋊C3C4×D3semidirect
142. C42C3×C4×D3semidirect
205. C3(#126⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#126⋊C3)2
C3×#383⋊C32
C3⋊(#384⋊C3)2
#742993
(#126⋊C3)⋊C43
C4×D3×A44