Finite Group Databasebeta

← #83119⋊C3 #11921293

Subgroups — #83119⋊C3 #11921293

Order 1152.

247 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 247 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#126⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#384⋊C3)C211yesmaximal, characteristic, complemented
4#83119C311yesmaximal, characteristic, complemented
5#2823⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#126⋊C3—21no—
8C2×C3×C42⋊C3C2211yescharacteristic
9C3⋊(#126⋊C3)—21no—
10C2×C3×#126C2×C311yescharacteristic, complemented
11C2×#876C2×C311yescharacteristic, complemented
12C2×#126⋊C3—21no—
13C2×#126⋊C3—31no—
14C2×#126⋊C3D311yescharacteristic, complemented
15#4994—31no—
16#4982—31no—
17#4961—31no—
18#4948—31no—
19#4935C2×C311yescharacteristic, complemented
20#384⋊C3—31no—
21C22×C3×A4—41no—
22C2×D3×A4—41no—
23Dic3×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2823—31noSylow
26C22×#67A411yescharacteristic
27D4×A4—121no—
28C3×#126—21no—
29C3×#126—61no—
30C2×C3×C4⋊C4—31no—
31C2×C3×C22⋊C4—31no—
32C2×C3×C42C22×C311yescharacteristic
33C2×#217—31no—
34C2×(C2×D3)⋊C4—31no—
35C2×(C2×D3)⋊C4—31no—
36C2×C4⋊Dic3—31no—
37C2×C4⋊Dic3—31no—
38C2×Dic3⋊C4—31no—
39C2×Dic3⋊C4—31no—
40#876—21no—
41#876—61no—
42#126⋊C3—22no—
43#126⋊C3—21no—
44#126⋊C3—61no—
45C2×C42⋊C3—21no—
46C2×C42⋊C3C2×D311yescharacteristic
47C3⋊#95—31no—
48C3⋊#95—31no—
49C2×C3×A4—41no—
50C2×C3×A4—81no—
51D3×A4—81no—
52C3×#67—161no—
53C2×#126—31no—
54C2×#126C3×D311yescharacteristic, complemented
55#398—91no—
56#396—91no—
57#396—91no—
58#394—91no—
59#384—31no—
60C24×C3C2×A411yescharacteristic
61C23×D3C2×A411yescharacteristic
62C22×A4—41no—
63C22×A4—81no—
64C22×A4—121no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C2×#67—121no—
68C22×Dic3—31no—
69C22×Dic3—31no—
70C22×Dic3C2×A411yescharacteristic
71C4×A4—121no—
72C3×C4⋊C4—61no—
73C3×C4⋊C4—61no—
74C3×C22⋊C4—61no—
75C3×C22⋊C4—61no—
76C3×C42—31no—
77C3×C42C3×D411yescharacteristic, complemented
78#217—121no—
79(C2×D3)⋊C4—61no—
80(C2×D3)⋊C4—61no—
81(C2×D3)⋊C4—121no—
82C4⋊Dic3—121no—
83C4⋊Dic3—121no—
84Dic3⋊C4—61no—
85Dic3⋊C4—61no—
86Dic3⋊C4—121no—
87C42⋊C3—21no—
88C42⋊C3#6711yescharacteristic, complemented
89C22×C32—161no—
90C2×C3×D3—161no—
91C3×A4—41no—
92C3×Dic3—161no—
93C22×D4—31no—
94#126—21no—
95#126—61no—
96#126—61no—
97#126—181no—
98C2×C4⋊C4—31no—
99C2×C4⋊C4—91no—
100C2×C4⋊C4—91no—
101C2×C4⋊C4—91no—
102C2×C4⋊C4—91no—
103C2×C22⋊C4—31no—
104C2×C22⋊C4—91no—
105C2×C22⋊C4—91no—
106C2×C22⋊C4—91no—
107C2×C42C2×C3×D311yescharacteristic
108#95—91no—
109#95—91no—
110C23×C3—21no—
111C23×C3—61no—
112C23×C3—61no—
113C23×C3C22×A411yescharacteristic
114C22×D3—21no—
115C22×D3—61no—
116C22×D3—61no—
117C2×A4—41no—
118C2×A4—81no—
119C2×A4—82no—
120C2×A4—81no—
121C2×A4—241no—
122C3×D4—481no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—61no—
126C2×C3×C4—61no—
127C2×C3×C4—61no—
128C2×C3×C4—61no—
129C2×C3×C4—61no—
130#67—41no—
131#67—121no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×C32—161no—
140C2×C32—321no—
141C3×D3—321no—
142C24—31no—
143C24D3×A411yescharacteristic
144C2×D4—361no—
145C22×C4—31no—
146C22×C4—31no—
147C22×C4—31no—
148C22×C4—91no—
149C22×C4—91no—
150C4⋊C4—61no—
151C4⋊C4—61no—
152C4⋊C4—181no—
153C4⋊C4—181no—
154C4⋊C4—361no—
155C4⋊C4—361no—
156C4⋊C4—361no—
157C22⋊C4—61no—
158C22⋊C4—61no—
159C22⋊C4—181no—
160C22⋊C4—181no—
161C22⋊C4—361no—
162C22⋊C4—361no—
163C42—31no—
164C42C3×#6711yescharacteristic, complemented
165C22×C3—31no—
166C22×C3—31no—
167C22×C3—41no—
168C22×C3—121no—
169C22×C3—121no—
170C22×C3—161no—
171C22×C3—321no—
172C22×C3—481no—
173C22×C3D4×A411yescharacteristic
174C2×D3—41no—
175C2×D3—121no—
176C2×D3—121no—
177A4—41no—
178A4—81no—
179C3×C4—61no—
180C3×C4—61no—
181C3×C4—121no—
182C3×C4—481no—
183Dic3—41no—
184Dic3—121no—
185Dic3—121no—
186C32—161noSylow
187C23—21no—
188C23—61no—
189C23—61no—
190C23—61no—
191C23—181no—
192C23—181no—
193C23C2×D3×A411yescharacteristic
194D4—121no—
195D4—361no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—61no—
203C2×C4—181no—
204C2×C4—181no—
205C2×C4—181no—
206C2×C4—181no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4—181no—
210C2×C3—31no—
211C2×C3—31no—
212C2×C3—81no—
213C2×C3—161no—
214C2×C3—321no—
215C2×C3—322no—
216C2×C3—321no—
217C2×C3—961no—
218C2×C3#560⋊C311yescharacteristic
219D3—81no—
220C22—31no—
221C22—31no—
222C22—41no—
223C22—121no—
224C22—121no—
225C22—121no—
226C22—361no—
227C22—361no—
228C22A4×#6711yescharacteristic
229C4—61no—
230C4—61no—
231C4—121no—
232C4—121no—
233C4—361no—
234C4—361no—
235C3—161no—
236C3—321no—
237C3#2823⋊C311yescharacteristic, complemented
238C2—31no—
239C2—31no—
240C2—81no—
241C2—241no—
242C2(#126⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2(#126⋊C3)⋊D3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC2×C3×#126C2×C3
socleC23×C3C22×A4
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#126⋊C3C2semidirect
2. C2×C3⋊(#126⋊C3)C2semidirect
3. C3⋊(#384⋊C3)C2semidirect
4. #83119C3semidirect
10. C2×C3×#126C2×C3semidirect
11. C2×#876C2×C3semidirect
14. C2×#126⋊C3D3semidirect
19. #4935C2×C3semidirect
24. C3×C42⋊C3D4semidirect
54. C2×#126C3×D3semidirect
77. C3×C42C3×D4semidirect
88. C42⋊C3#67semidirect
164. C42C3×#67semidirect
237. C3#2823⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#126⋊C32
C2×C3⋊(#126⋊C3)2
C3⋊(#384⋊C3)2
#831193
#2823⋊C33
A4×#674