Finite Group Databasebeta

← #83582⋊C3 #11921303

Subgroups — #83582⋊C3 #11921303

Order 1152.

271 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 271 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C3×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
2C4⋊(C3⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
3C3⋊C8×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4#83582C311yesmaximal, characteristic, complemented
5#3391⋊C3—31nomaximal
6C2×C3×#41⋊C3—21no—
7C2×C3⋊(#41⋊C3)—21no—
8C3×C4×SL(2,𝔽3)C2211yescharacteristic
9C3×#807—41nomaximal
10C3×#550C2×C311yescharacteristic
11#5577C2×C311yescharacteristic
12C4⋊(#41⋊C3)—21no—
13C4⋊(#41⋊C3)—31no—
14C4⋊(#41⋊C3)D311yescharacteristic, complemented
15#5073—31no—
16#5072—31no—
17Q8×C3⋊C8C2×C311yescharacteristic
18#5015—31no—
19C4×#213—31no—
20C8×SL(2,𝔽3)—31no—
21C3×#41⋊C3—41no—
22C2×C3×SL(2,𝔽3)D411yescharacteristic
23C3⋊(#41⋊C3)—41no—
24C32×C4⋊C4—41no—
25C3×C4⋊Dic3—41no—
26C2×C3×C3⋊C8—41no—
27#3391—31noSylow
28C2×C3×#41—21no—
29C2×#239—21no—
30C2×#41⋊C3—22no—
31C2×#41⋊C3—21no—
32C2×#41⋊C3—61no—
33C3×#127—31no—
34C3×#121—61no—
35C3×C4×Q8C22×C311yescharacteristic
36C3×C4×D4—31no—
37C2×#213—32no—
38C2×#213—31no—
39#895—61no—
40#874—31no—
41C4×D12—31no—
42C4×SL(2,𝔽3)—21no—
43C4×SL(2,𝔽3)C2×D311yescharacteristic
44C3×#107—121no—
45#832—31no—
46#809—31no—
47#807A411yescharacteristic
48C4⋊(C3⋊C8)—31no—
49C4×C3⋊C8—31no—
50C2×C32×C4—41no—
51C2×C32×C4—81no—
52C2×C3×Dic3—81no—
53C3×SL(2,𝔽3)D811yescharacteristic, complemented
54C3×C3⋊C8—42no—
55#550—31no—
56#550C3×D311yescharacteristic
57#493—91no—
58#459—91no—
59#459—91no—
60C8×Q8—31no—
61C4×D8—91no—
62C3×#41—41no—
63C3×#41—121no—
64C2×C3×Q8C3×D411yescharacteristic
65C2×C3×D4—31no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C22×C3×C4—61no—
69#239—41no—
70#239—121no—
71C2×D12—31no—
72C2×D12—61no—
73C2×D12—61no—
74C2×C4×D3—61no—
75#41⋊C3—42no—
76#41⋊C3—41no—
77#41⋊C3—121no—
78C2×SL(2,𝔽3)—21no—
79C2×SL(2,𝔽3)#6711yescharacteristic
80C2×C3×C8—121no—
81C3×C4⋊C4—31no—
82C3×C4⋊C4—41no—
83C3×C4⋊C4—81no—
84C3×C4⋊C4—121no—
85C3×C4⋊C4C2×A411yescharacteristic
86C3×C22⋊C4—61no—
87C3×C42—31no—
88#213—62no—
89#213—122no—
90(C2×D3)⋊C4—61no—
91C4⋊Dic3C2×A411yescharacteristic
92C2×C3⋊C8—31no—
93C2×C3⋊C8C2×A411yescharacteristic
94C22×C32—41no—
95C32×C4—41no—
96C32×C4—41no—
97C32×C4—161no—
98C3×Dic3—161no—
99C2×#41—21no—
100C2×#41—61no—
101C2×D8—91no—
102C2×D8—92no—
103#127—31no—
104#127—91no—
105#121—61no—
106#121—181no—
107C4×Q8C2×C3×D311yescharacteristic
108C4×D4—31no—
109C4×D4—91no—
110#107—31no—
111C4⋊C8—91no—
112#102—91no—
113#102—91no—
114C4×C8—91no—
115C23×C3—61no—
116C22×D3—61no—
117C3×Q8—31no—
118C3×Q8C3×D811yescharacteristic
119C3×D4—61no—
120C3×D4—61no—
121C3×D4—121no—
122C3×D4—121no—
123C3×D4—241no—
124C2×C3×C4—21no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—41no—
128C2×C3×C4—81no—
129C2×C3×C4—82no—
130C2×C3×C4—81no—
131C2×C3×C4—121no—
132C2×C3×C4—121no—
133C2×C3×C4—241no—
134C2×C3×C4C22×A411yescharacteristic
135C2×Dic3—21no—
136D12—61no—
137D12—61no—
138D12—121no—
139D12—121no—
140D12—241no—
141C4×D3—121no—
142C4×D3—121no—
143SL(2,𝔽3)—21no—
144SL(2,𝔽3)#21311yescharacteristic, complemented
145C3×C8—122no—
146C3⋊C8—61no—
147C3⋊C8#41⋊C312yescomplemented
148C2×C32—41no—
149C2×C32—41no—
150C2×C32—41no—
151#41—41no—
152#41—121no—
153#41—121no—
154#41—361no—
155C2×Q8C3×#6711yescharacteristic
156C2×D4—31no—
157C2×D4—61no—
158C2×D4—61no—
159C2×D4—91no—
160C2×D4—181no—
161C2×D4—181no—
162C22×C4—61no—
163C22×C4—181no—
164D8—182no—
165D8—362no—
166C2×C8—31no—
167C2×C8—91no—
168C4⋊C4—31no—
169C4⋊C4—31no—
170C4⋊C4D3×A411yescharacteristic
171C22⋊C4—61no—
172C22⋊C4—181no—
173C42—31no—
174C22×C3—41no—
175C22×C3—81no—
176C22×C3—121no—
177C22×C3—121no—
178C22×C3—121no—
179C22×C3D4×A411yescharacteristic
180C2×D3—121no—
181C2×D3—121no—
182C2×D3—121no—
183C3×C4—31no—
184C3×C4—31no—
185C3×C4—41no—
186C3×C4—41no—
187C3×C4—41no—
188C3×C4—61no—
189C3×C4—81no—
190C3×C4—81no—
191C3×C4—161no—
192C3×C4—162no—
193C3×C4—481no—
194C3×C4C2×#41⋊C311yescharacteristic
195C3×C4#99411yescharacteristic
196Dic3—41no—
197C32—41noSylow
198C23—61no—
199C23—181no—
200Q8—31no—
201Q8C3×#21311yescharacteristic
202D4—61no—
203D4—61no—
204D4—121no—
205D4—121no—
206D4—181no—
207D4—181no—
208D4—241no—
209D4—361no—
210D4—361no—
211D4—721no—
212C2×C4—21no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—61no—
216C2×C4—121no—
217C2×C4—121no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4C2×D3×A411yescharacteristic
221C8—32no—
222C8—181no—
223C2×C3—41no—
224C2×C3—41no—
225C2×C3—41no—
226C2×C3—81no—
227C2×C3—81no—
228C2×C3—81no—
229C2×C3—241no—
230C2×C3C4⋊(#41⋊C3)11yescharacteristic
231C2×C3A4×D811yescharacteristic
232C2×C3#576⋊C311yescharacteristic
233D3—241no—
234C22—121no—
235C22—121no—
236C22—121no—
237C22—361no—
238C22—361no—
239C22—361no—
240C22A4×#6711yescharacteristic
241C4—31no—
242C4—31no—
243C4—41no—
244C4—61no—
245C4—121no—
246C4C3⋊#99411yescharacteristic
247C4D3×#41⋊C311yescharacteristic
248C3—41no—
249C3—81no—
250C3#3391⋊C311yescharacteristic, complemented
251C2—241no—
252C2—721no—
253C2A4×#21311yescharacteristic
254C2#5834⋊C311yescharacteristic
255C2#5835⋊C311yescharacteristic
subgroupG/H
centerC22A4×#67
commutator, cosocleC3×C4×Q8C22×C3
FrattiniC2×C4C2×D3×A4
FittingC3×#550C2×C3
socleC22×C3D4×A4
hypercenterC4⋊C4D3×A4
hypocenterC3×Q8C3×D8
LCSG ▷ C3×C4×Q8 ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×C4⋊(#41⋊C3)C2semidirect
2. C4⋊(C3⋊(#41⋊C3))C2semidirect
3. C3⋊C8×SL(2,𝔽3)C2semidirect
4. #83582C3semidirect
14. C4⋊(#41⋊C3)D3semidirect
53. C3×SL(2,𝔽3)D8semidirect
144. SL(2,𝔽3)#213semidirect
147. C3⋊C8#41⋊C3semidirect
250. C3#3391⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4⋊(#41⋊C3)2
C4⋊(C3⋊(#41⋊C3))2
C3⋊C8×SL(2,𝔽3)2
#835823
#3391⋊C33
C3×#8074