Finite Group Databasebeta

← #74317⋊C3 #11921154

Subgroups — #74317⋊C3 #11921154

Order 1152.

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

normal subgroups only

This group has 283 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×D3×C42⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#126⋊C3)C211yesmaximal, characteristic, complemented
3C3×#383⋊C3C211yesmaximal, characteristic, complemented
4#74317C311yesmaximal, characteristic, complemented
5#2852⋊C3—31nomaximal
6A4×D12—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8D3×C42⋊C3—21no—
9C3⋊(#126⋊C3)—21no—
10C2×#876C2×C311yescharacteristic, complemented
11C2×C42×D3C2×C311yescharacteristic, complemented
12C2×#126⋊C3—31no—
13C22×C42⋊C3—31no—
14C3×#383C2×C311yescharacteristic, complemented
15#4670—31no—
16#4668—31no—
17#4665—31no—
18#4653—31no—
19#383⋊C3—21no—
20#383⋊C3D311yescharacteristic, complemented
21C2×D3×A4—41no—
22C2×D3×A4—41no—
23C3×C4×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2852—31noSylow
26C22×D12A411yescharacteristic
27C22×C4×D3—31no—
28D4×A4—121no—
29C2×C3×C42C22×C311yescharacteristic
30C2×(C2×D3)⋊C4—31no—
31C2×(C2×D3)⋊C4—31no—
32C2×(C2×D3)⋊C4—31no—
33C2×C4⋊Dic3—31no—
34C2×Dic3⋊C4—31no—
35C2×C4×Dic3—31no—
36#876—21no—
37#876—61no—
38C42×D3—21no—
39C42×D3—61no—
40#126⋊C3—61no—
41C2×C42⋊C3—21no—
42C2×C42⋊C3—61no—
43C2×C42⋊C3C2×D311yescharacteristic
44C3×#95—31no—
45C3×#95—31no—
46C3⋊#95—31no—
47C3⋊#95—31no—
48C2×C3×A4—41no—
49D3×A4—81no—
50D3×A4—81no—
51C3×D12—161no—
52C2×#126—31no—
53C22×C42—31no—
54#388—91no—
55#387—91no—
56#386—91no—
57#385—91no—
58#383C3×D311yescharacteristic, complemented
59C23×D3C2×A411yescharacteristic
60C23×D3C2×A411yescharacteristic
61C22×A4—121no—
62C22×A4—121no—
63C22×C3×C4—31no—
64C22×C3×C4—31no—
65C22×C3×C4C2×A411yescharacteristic
66C22×Dic3—31no—
67C22×Dic3—31no—
68C2×D12—61no—
69C2×D12—61no—
70C2×C4×D3—62no—
71C2×C4×D3—61no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C4×A4—41no—
76C4×A4—81no—
77C3×C42—31no—
78C3×C42C3×D411yescharacteristic, complemented
79(C2×D3)⋊C4—62no—
80(C2×D3)⋊C4—61no—
81(C2×D3)⋊C4—61no—
82(C2×D3)⋊C4—61no—
83(C2×D3)⋊C4—61no—
84C4⋊Dic3—62no—
85Dic3⋊C4—61no—
86Dic3⋊C4—61no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C42⋊C3—21no—
90C42⋊C3D1211yescharacteristic, complemented
91C2×C3×D3—161no—
92C2×C3×D3—161no—
93C3×A4—41no—
94C32×C4—161no—
95C22×D4—31no—
96C23×C4—91no—
97#126—61no—
98#126—181no—
99C2×C4⋊C4—91no—
100C2×C4⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—91no—
103C2×C22⋊C4—91no—
104C2×C42—61no—
105C2×C42—91no—
106C2×C42—181no—
107C2×C42C2×C3×D311yescharacteristic
108#95—31no—
109#95—31no—
110#95—91no—
111#95—91no—
112C23×C3C22×A411yescharacteristic
113C22×D3—21no—
114C22×D3—21no—
115C22×D3—31no—
116C22×D3—31no—
117C22×D3—61no—
118C22×D3—61no—
119C22×D3—61no—
120C2×A4—41no—
121C2×A4—81no—
122C2×A4—241no—
123C2×A4—241no—
124C3×D4—481no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—61no—
128C2×C3×C4—61no—
129C2×C3×C4—61no—
130C2×C3×C4—61no—
131C2×C3×C4—61no—
132C2×C3×C4—61no—
133C2×Dic3—32no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139D12—41no—
140D12—121no—
141C4×D3—62no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—62no—
145C2×C32—161no—
146C3×D3—321no—
147C3×D3—321no—
148C24—31no—
149C24—31no—
150C2×D4—181no—
151C2×D4—181no—
152C22×C4—31no—
153C22×C4—31no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—181no—
157C22×C4—181no—
158C22×C4—182no—
159C22×C4—181no—
160C22×C4—181no—
161C22×C4D3×A411yescharacteristic
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4—182no—
165C22⋊C4—181no—
166C22⋊C4—181no—
167C22⋊C4—182no—
168C22⋊C4—181no—
169C22⋊C4—181no—
170C42—31no—
171C42—181no—
172C42—181no—
173C42C3×D1211yescharacteristic, complemented
174C22×C3—31no—
175C22×C3—31no—
176C22×C3—481no—
177C22×C3—481no—
178C22×C3D4×A411yescharacteristic
179C2×D3—31no—
180C2×D3—41no—
181C2×D3—61no—
182C2×D3—61no—
183C2×D3—61no—
184C2×D3—61no—
185C2×D3—121no—
186C2×D3—121no—
187C2×D3#126⋊C311yescharacteristic, complemented
188A4—41no—
189A4—81no—
190C3×C4—41no—
191C3×C4—61no—
192C3×C4—61no—
193C3×C4—121no—
194C3×C4—161no—
195C3×C4—321no—
196Dic3—62no—
197Dic3—121no—
198C32—161noSylow
199C23—61no—
200C23—61no—
201C23—91no—
202C23—91no—
203C23—181no—
204C23—181no—
205C23—181no—
206C23C2×D3×A411yescharacteristic
207D4—121no—
208D4—361no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—61no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—61no—
215C2×C4—61no—
216C2×C4—61no—
217C2×C4—92no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—182no—
221C2×C4—182no—
222C2×C4—181no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C3—31no—
228C2×C3—31no—
229C2×C3—161no—
230C2×C3—321no—
231C2×C3—961no—
232C2×C3—961no—
233C2×C3C2×#126⋊C311yescharacteristic
234D3—21no—
235D3—61no—
236D3—81no—
237C22—31no—
238C22—31no—
239C22—31no—
240C22—91no—
241C22—121no—
242C22—181no—
243C22—181no—
244C22—181no—
245C22—181no—
246C22—361no—
247C22—361no—
248C22A4×D1211yescharacteristic
249C4—41no—
250C4—61no—
251C4—61no—
252C4—121no—
253C4—182no—
254C4—361no—
255C3—161no—
256C3—321no—
257C3#2852⋊C311yescharacteristic, complemented
258C2—31no—
259C2—31no—
260C2—61no—
261C2—181no—
262C2—241no—
263C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#383C2×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×D3×C42⋊C3C2semidirect
2. C2×C3⋊(#126⋊C3)C2semidirect
3. C3×#383⋊C3C2semidirect
4. #74317C3semidirect
10. C2×#876C2×C3semidirect
11. C2×C42×D3C2×C3semidirect
14. C3×#383C2×C3semidirect
20. #383⋊C3D3semidirect
24. C3×C42⋊C3D4semidirect
58. #383C3×D3semidirect
78. C3×C42C3×D4semidirect
90. C42⋊C3D12semidirect
173. C42C3×D12semidirect
187. C2×D3#126⋊C3semidirect
257. C3#2852⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C42⋊C32
C2×C3⋊(#126⋊C3)2
C3×#383⋊C32
#743173
#2852⋊C33
A4×D124