Finite Group Databasebeta

← #74259⋊C3 #11921151

Subgroups — #74259⋊C3 #11921151

Order 1152.

261 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 261 conjugacy classes of subgroups — too many to draw. Only its 38 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
3Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
4#74259C311yesmaximal, characteristic, complemented
5C4×#126⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊(#126⋊C3)C412yescomplemented
9C2×#876C2×C311yescharacteristic
10C2×#126⋊C3—31no—
11C3×#383C2×C311yescharacteristic, complemented
12C42×Dic3C2×C311yescharacteristic, complemented
13#4669—31no—
14#4666—31no—
15#4652—31no—
16#4649—31no—
17#383⋊C3—21no—
18#383⋊C3D311yescharacteristic, complemented
19C4×C42⋊C3—31no—
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C4×#126—31noSylow
25C22×C4×D3A411yescharacteristic
26C2×C4×A4—121no—
27C2×C3×C42C22×C311yescharacteristic
28C2×(C2×D3)⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×Dic3⋊C4—31no—
31C2×Dic3⋊C4—31no—
32C2×C4×Dic3—31no—
33C2×C4×Dic3—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#388—91no—
49#387—91no—
50#383C3×D311yescharacteristic, complemented
51C4×C4⋊C4—91no—
52C4×C22⋊C4—91no—
53C43—31no—
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—61no—
63C2×C4×D3—61no—
64C4×A4—41no—
65C4×A4—81no—
66C4×A4—121no—
67C3×C42—31no—
68C3×C42C2×C3×C411yescharacteristic, complemented
69(C2×D3)⋊C4—32no—
70(C2×D3)⋊C4—32no—
71(C2×D3)⋊C4—62no—
72Dic3⋊C4—32no—
73Dic3⋊C4—32no—
74Dic3⋊C4—62no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—62no—
80C42⋊C3—21no—
81C42⋊C3C4×D311yescharacteristic, complemented
82C2×C3×D3—161no—
83C3×A4—41no—
84C32×C4—161no—
85C3×Dic3—161no—
86C23×C4—31no—
87#126—32no—
88#126—92no—
89C2×C4⋊C4—91no—
90C2×C4⋊C4—91no—
91C2×C22⋊C4—91no—
92C2×C22⋊C4—91no—
93C2×C42—91no—
94C2×C42—91no—
95C2×C42—91no—
96C2×C42C2×C3×D311yescharacteristic
97#95—31no—
98#95—31no—
99#95—91no—
100#95—91no—
101C23×C3C22×A411yescharacteristic
102C22×D3—61no—
103C22×D3—61no—
104C22×D3C4×A412yes—
105C2×A4—41no—
106C2×A4—81no—
107C2×A4—122no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—61no—
111C2×C3×C4—61no—
112C2×C3×C4—61no—
113C2×C3×C4—61no—
114C2×C3×C4—61no—
115C2×C3×C4—61no—
116C2×C3×C4—481no—
117C2×Dic3—31no—
118C2×Dic3—31no—
119C2×Dic3—32no—
120C2×Dic3—32no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C4×D3—41no—
126C4×D3—121no—
127C2×C32—161no—
128C3×D3—162no—
129C24—31no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—181no—
136C22×C4—181no—
137C22×C4D3×A411yescharacteristic
138C4⋊C4—92no—
139C4⋊C4—92no—
140C4⋊C4—182no—
141C22⋊C4—92no—
142C22⋊C4—92no—
143C22⋊C4—182no—
144C42—31no—
145C42—181no—
146C42—181no—
147C42—182no—
148C42—181no—
149C42—181no—
150C42C3×C4×D311yescharacteristic, complemented
151C22×C3—31no—
152C22×C3—31no—
153C22×C3—481no—
154C22×C3C2×C4×A411yescharacteristic
155C2×D3—41no—
156C2×D3—62no—
157C2×D3—121no—
158A4—41no—
159A4—81no—
160C3×C4—41no—
161C3×C4—61no—
162C3×C4—61no—
163C3×C4—121no—
164C3×C4—161no—
165C3×C4—321no—
166C3×C4—481no—
167Dic3—31no—
168Dic3—62no—
169Dic3—62no—
170Dic3#126⋊C311yescharacteristic, complemented
171C32—161noSylow
172C23—32no—
173C23—181no—
174C23—181no—
175C23C2×D3×A411yescharacteristic
176C2×C4—31no—
177C2×C4—31no—
178C2×C4—61no—
179C2×C4—61no—
180C2×C4—61no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—92no—
187C2×C4—92no—
188C2×C4—121no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—361no—
194C2×C3—31no—
195C2×C3—31no—
196C2×C3—161no—
197C2×C3—321no—
198C2×C3—482no—
199C2×C3C2×#126⋊C311yescharacteristic
200D3—42no—
201C22—31no—
202C22—31no—
203C22—121no—
204C22—182no—
205C22—361no—
206C22C4×D3×A411yescharacteristic
207C4—31no—
208C4—41no—
209C4—61no—
210C4—61no—
211C4—91no—
212C4—121no—
213C4—182no—
214C4—182no—
215C3—161no—
216C3—321no—
217C3C4×#126⋊C311yescharacteristic, complemented
218C2—31no—
219C2—31no—
220C2—122no—
221C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
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. Dic3×C42⋊C3C2semidirect
4. #74259C3semidirect
8. C3⋊(#126⋊C3)C4semidirect
11. C3×#383C2×C3semidirect
12. C42×Dic3C2×C3semidirect
18. #383⋊C3D3semidirect
23. C3×C42⋊C3C2×C4semidirect
36. #876C3×C4semidirect
50. #383C3×D3semidirect
68. C3×C42C2×C3×C4semidirect
81. C42⋊C3C4×D3semidirect
150. C42C3×C4×D3semidirect
170. Dic3#126⋊C3semidirect
217. C3C4×#126⋊C3semidirect

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
Dic3×C42⋊C32
#742593
C4×#126⋊C33
C4×D3×A44