Finite Group Databasebeta

← #83580⋊C3 #11921305

Subgroups — #83580⋊C3 #11921305

Order 1152.

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

normal subgroups only

This group has 283 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
2SL(2,𝔽3)×D12C211yesmaximal, characteristic, complemented
3C3⋊C8×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4#83580C311yesmaximal, characteristic, complemented
5#3358⋊C3—31nomaximal
6C2×C3×#41⋊C3—21no—
7C2×D3×SL(2,𝔽3)—21no—
8C3×C4×SL(2,𝔽3)C2211yescharacteristic
9C3×#809—41nomaximal
10C3×#550C2×C311yescharacteristic, complemented
11Q8×D12C2×C311yescharacteristic
12C4⋊(#41⋊C3)—21no—
13C4⋊(#41⋊C3)D311yescharacteristic, complemented
14D4×SL(2,𝔽3)—31no—
15#5072—31no—
16#5070—31no—
17Q8×C3⋊C8C2×C311yescharacteristic, complemented
18C4×#213—31no—
19#5007—31no—
20C8×SL(2,𝔽3)—31no—
21C2×C3×D12—41no—
22C3×#41⋊C3—41no—
23C2×C3×SL(2,𝔽3)D411yescharacteristic
24D3×SL(2,𝔽3)—41no—
25C32×C4⋊C4—41no—
26C2×C3×C3⋊C8—41no—
27#3358—31noSylow
28C2×C3×#41—21no—
29C2×D3×Q8—21no—
30C2×#41⋊C3—22no—
31C2×#41⋊C3—21no—
32C22×SL(2,𝔽3)—61no—
33C3×#127—31no—
34C3×#121—61no—
35C3×C4×Q8C22×C311yescharacteristic
36C3×C4×D4—31no—
37C2×#213—31no—
38#897—61no—
39C4×D12—31no—
40#869—31no—
41C4×SL(2,𝔽3)—21no—
42C4×SL(2,𝔽3)C2×D311yescharacteristic
43C3×#102—121no—
44#832—32no—
45#832—31no—
46#809A411yescharacteristic
47#807—31no—
48C4⋊(C3⋊C8)—31no—
49C4×C3⋊C8—31no—
50C22×C3×D3—81no—
51C2×C32×C4—41no—
52C2×C32×C4—81no—
53C3×D12—42no—
54C3×D12—81no—
55C3×SL(2,𝔽3)D811yescharacteristic, complemented
56C3×C3⋊C8—81no—
57#550C3×D311yescharacteristic, complemented
58D4×Q8—31no—
59#486—91no—
60#474—91no—
61#459—91no—
62C8×Q8—31no—
63C4×D8—91no—
64C3×#41—41no—
65C3×#41—121no—
66C2×C3×Q8C3×D411yescharacteristic
67C2×C3×D4—31no—
68C2×C3×D4—61no—
69C2×C3×D4—61no—
70C2×C3×D4—121no—
71C22×C3×C4—61no—
72D3×Q8—41no—
73D3×Q8—121no—
74C2×D12C2×A411yescharacteristic
75C2×C4×D3—61no—
76C2×Dic6—61no—
77#41⋊C3—42no—
78#41⋊C3—41no—
79C2×SL(2,𝔽3)—21no—
80C2×SL(2,𝔽3)—121no—
81C2×SL(2,𝔽3)#6711yescharacteristic
82C2×C3×C8—121no—
83C3×C4⋊C4—31no—
84C3×C4⋊C4—41no—
85C3×C4⋊C4—81no—
86C3×C4⋊C4C2×A411yescharacteristic
87C3×C22⋊C4—61no—
88C3×C42—31no—
89#213—62no—
90(C2×D3)⋊C4—61no—
91C4⋊Dic3—31no—
92C4⋊Dic3—61no—
93C2×C3⋊C8—31no—
94C2×C3⋊C8C2×A411yescharacteristic
95C22×C32—41no—
96C2×C3×D3—82no—
97C2×C3×D3—161no—
98C2×C3×D3—161no—
99C32×C4—41no—
100C32×C4—41no—
101C32×C4—161no—
102C2×#41—21no—
103C22×Q8—61no—
104C2×D8—91no—
105C4⋊Q8—91no—
106#127—31no—
107C22⋊Q8—181no—
108#121—61no—
109C4×Q8C2×C3×D311yescharacteristic
110C4×D4—31no—
111C4×D4—91no—
112#107—91no—
113C4⋊C8—91no—
114#102—31no—
115#102—91no—
116#102—92no—
117C4×C8—91no—
118C23×C3—61no—
119C23×C3—241no—
120C22×D3—21no—
121C3×Q8—31no—
122C3×Q8C3×D811yescharacteristic
123C3×D4—61no—
124C3×D4—61no—
125C3×D4—122no—
126C3×D4—121no—
127C3×D4—121no—
128C3×D4—241no—
129C3×D4—241no—
130C2×C3×C4—21no—
131C2×C3×C4—31no—
132C2×C3×C4—31no—
133C2×C3×C4—41no—
134C2×C3×C4—81no—
135C2×C3×C4—82no—
136C2×C3×C4—81no—
137C2×C3×C4—121no—
138C2×C3×C4—121no—
139C2×C3×C4C22×A411yescharacteristic
140C2×Dic3—61no—
141D12—21no—
142D12#41⋊C312yescomplemented
143C4×D3—121no—
144C4×D3—121no—
145Dic6—121no—
146Dic6—121no—
147SL(2,𝔽3)—21no—
148SL(2,𝔽3)#21311yescharacteristic, complemented
149C3×C8—241no—
150C3⋊C8—21no—
151C3⋊C8—61no—
152C2×C32—41no—
153C2×C32—41no—
154C2×C32—41no—
155C3×D3—162no—
156#41—41no—
157#41—121no—
158C2×Q8—121no—
159C2×Q8—181no—
160C2×Q8—361no—
161C2×Q8C3×#6711yescharacteristic
162C2×D4—31no—
163C2×D4—31no—
164C2×D4—61no—
165C2×D4—61no—
166C22×C4—61no—
167C22×C4—181no—
168D8—182no—
169C2×C8—31no—
170C2×C8—91no—
171C4⋊C4—31no—
172C4⋊C4—91no—
173C4⋊C4—181no—
174C4⋊C4D3×A411yescharacteristic
175C22⋊C4—61no—
176C22⋊C4—181no—
177C42—31no—
178C22×C3—41no—
179C22×C3—81no—
180C22×C3—121no—
181C22×C3—121no—
182C22×C3—121no—
183C22×C3—242no—
184C22×C3—481no—
185C22×C3—481no—
186C22×C3D4×A411yescharacteristic
187C2×D3—22no—
188C2×D3—41no—
189C2×D3—41no—
190C3×C4—31no—
191C3×C4—31no—
192C3×C4—41no—
193C3×C4—41no—
194C3×C4—41no—
195C3×C4—61no—
196C3×C4—81no—
197C3×C4—81no—
198C3×C4—161no—
199C3×C4—162no—
200C3×C4C2×#41⋊C311yescharacteristic
201C3×C42−1+4⋊C311yescharacteristic
202Dic3—121no—
203C32—41noSylow
204C23—61no—
205C23—61no—
206Q8—31no—
207Q8—361no—
208Q8—361no—
209Q8C3×#21311yescharacteristic
210D4—32no—
211D4—61no—
212D4—61no—
213D4—61no—
214D4—121no—
215D4—121no—
216D4—241no—
217C2×C4—21no—
218C2×C4—31no—
219C2×C4—31no—
220C2×C4—121no—
221C2×C4—121no—
222C2×C4—181no—
223C2×C4—361no—
224C2×C4—361no—
225C2×C4C2×D3×A411yescharacteristic
226C8—61no—
227C8—181no—
228C2×C3—41no—
229C2×C3—41no—
230C2×C3—41no—
231C2×C3—81no—
232C2×C3—81no—
233C2×C3—81no—
234C2×C3—241no—
235C2×C3—482no—
236C2×C3#548⋊C311yescharacteristic
237C2×C3A4×D811yescharacteristic
238C2×C3#577⋊C311yescharacteristic
239D3—42no—
240C22—62no—
241C22—121no—
242C22—121no—
243C22—121no—
244C22—121no—
245C22—121no—
246C22A4×#6711yescharacteristic
247C4—31no—
248C4—31no—
249C4—41no—
250C4—61no—
251C4—361no—
252C4D3×#41⋊C311yescharacteristic
253C4#1010⋊C311yescharacteristic
254C3—41no—
255C3—81no—
256C3#3358⋊C311yescharacteristic, complemented
257C2—122no—
258C2—241no—
259C2A4×#21311yescharacteristic
260C2#5831⋊C311yescharacteristic
261C2#5836⋊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. SL(2,𝔽3)×D12C2semidirect
3. C3⋊C8×SL(2,𝔽3)C2semidirect
4. #83580C3semidirect
10. C3×#550C2×C3semidirect
13. C4⋊(#41⋊C3)D3semidirect
17. Q8×C3⋊C8C2×C3semidirect
55. C3×SL(2,𝔽3)D8semidirect
57. #550C3×D3semidirect
142. D12#41⋊C3semidirect
148. SL(2,𝔽3)#213semidirect
256. C3#3358⋊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
SL(2,𝔽3)×D122
C3⋊C8×SL(2,𝔽3)2
#835803
#3358⋊C33
C3×#8094