Finite Group Databasebeta

← #83104⋊C3 #11921291

Subgroups — #83104⋊C3 #11921291

Order 1152.

267 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 32 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
3Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
4#83104C311yesmaximal, characteristic, complemented
5C4⋊(#126⋊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#4990—31no—
16#4976—31no—
17#4957—31no—
18#4945—31no—
19C42×Dic3C2×C311yescharacteristic, complemented
20C4×C42⋊C3—31no—
21C22×C3×A4—41no—
22C2×D3×A4—41no—
23Dic3×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2860—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×Dic3⋊C4—31no—
37C2×Dic3⋊C4—31no—
38C2×C4×Dic3—31no—
39C2×C4×Dic3—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—32no—
48C2×C3×A4—41no—
49C2×C3×A4—81no—
50D3×A4—81no—
51C3×#67—161no—
52C2×#126—31no—
53C2×#126C3×D311yescharacteristic, complemented
54#390—91no—
55#389—91no—
56#388—91no—
57#388—91no—
58C43—31no—
59C24×C3C2×A411yescharacteristic
60C23×D3C2×A411yescharacteristic
61C22×A4—41no—
62C22×A4—81no—
63C22×A4—121no—
64C22×C3×C4—31no—
65C22×C3×C4—31no—
66C2×#67—61no—
67C2×#67—61no—
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—62no—
79(C2×D3)⋊C4—62no—
80(C2×D3)⋊C4—61no—
81(C2×D3)⋊C4—61no—
82Dic3⋊C4—61no—
83Dic3⋊C4—61no—
84Dic3⋊C4—61no—
85Dic3⋊C4—61no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88C4×Dic3—62no—
89C42⋊C3—21no—
90C42⋊C3#6711yescharacteristic, complemented
91C22×C32—161no—
92C2×C3×D3—161no—
93C3×A4—41no—
94C3×Dic3—161no—
95C22×D4—31no—
96#126—21no—
97#126—61no—
98#126—61no—
99#126—181no—
100C2×C4⋊C4—31no—
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×C42—91no—
108C2×C42—91no—
109C2×C42C2×C3×D311yescharacteristic
110#95—92no—
111C23×C3—21no—
112C23×C3—61no—
113C23×C3—61no—
114C23×C3C22×A411yescharacteristic
115C22×D3—21no—
116C22×D3—61no—
117C22×D3—61no—
118C2×A4—41no—
119C2×A4—81no—
120C2×A4—82no—
121C2×A4—81no—
122C2×A4—241no—
123C3×D4—481no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—61no—
127C2×C3×C4—61no—
128C2×C3×C4—61no—
129C2×C3×C4—61no—
130C2×C3×C4—61no—
131#67—41no—
132#67—121no—
133C2×Dic3—31no—
134C2×Dic3—31no—
135C2×Dic3—32no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×C32—161no—
142C2×C32—321no—
143C3×D3—321no—
144C24—31no—
145C24D3×A411yescharacteristic
146C2×D4—181no—
147C2×D4—181no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—91no—
152C22×C4—91no—
153C4⋊C4—61no—
154C4⋊C4—61no—
155C4⋊C4—181no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C22⋊C4—61no—
160C22⋊C4—61no—
161C22⋊C4—181no—
162C22⋊C4—181no—
163C22⋊C4—182no—
164C22⋊C4—182no—
165C42—31no—
166C42—181no—
167C42—181no—
168C42—182no—
169C42C3×#6711yescharacteristic, complemented
170C22×C3—31no—
171C22×C3—31no—
172C22×C3—41no—
173C22×C3—121no—
174C22×C3—121no—
175C22×C3—161no—
176C22×C3—321no—
177C22×C3—481no—
178C22×C3D4×A411yescharacteristic
179C2×D3—41no—
180C2×D3—121no—
181C2×D3—121no—
182A4—41no—
183A4—81no—
184C3×C4—61no—
185C3×C4—61no—
186C3×C4—121no—
187C3×C4—481no—
188Dic3—31no—
189Dic3—62no—
190Dic3—121no—
191Dic3#126⋊C311yescharacteristic, complemented
192C32—161noSylow
193C23—21no—
194C23—61no—
195C23—61no—
196C23—61no—
197C23—181no—
198C23—181no—
199C23C2×D3×A411yescharacteristic
200D4—121no—
201D4—361no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—61no—
205C2×C4—61no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—92no—
212C2×C4—181no—
213C2×C4—181no—
214C2×C4—181no—
215C2×C4—181no—
216C2×C4—181no—
217C2×C3—31no—
218C2×C3—31no—
219C2×C3—81no—
220C2×C3—161no—
221C2×C3—321no—
222C2×C3—322no—
223C2×C3—321no—
224C2×C3—961no—
225C2×C3C2×#126⋊C311yescharacteristic
226D3—81no—
227C22—31no—
228C22—31no—
229C22—41no—
230C22—121no—
231C22—121no—
232C22—121no—
233C22—361no—
234C22—361no—
235C22A4×#6711yescharacteristic
236C4—31no—
237C4—61no—
238C4—61no—
239C4—91no—
240C4—121no—
241C4—182no—
242C4—361no—
243C3—161no—
244C3—321no—
245C3C4⋊(#126⋊C3)11yescharacteristic, complemented
246C2—31no—
247C2—31no—
248C2—81no—
249C2—241no—
250C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
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. Dic3×C42⋊C3C2semidirect
4. #83104C3semidirect
10. C2×C3×#126C2×C3semidirect
11. C2×#876C2×C3semidirect
14. C2×#126⋊C3D3semidirect
19. C42×Dic3C2×C3semidirect
24. C3×C42⋊C3D4semidirect
53. C2×#126C3×D3semidirect
77. C3×C42C3×D4semidirect
90. C42⋊C3#67semidirect
169. C42C3×#67semidirect
191. Dic3#126⋊C3semidirect
245. C3C4⋊(#126⋊C3)semidirect

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
Dic3×C42⋊C32
#831043
C4⋊(#126⋊C3)3
A4×#674