Finite Group Databasebeta

← C8×C3⋊(#41⋊C3) #11921207

Subgroups — C8×C3⋊(#41⋊C3) #11921207

Order 1152.

277 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C4×C3⋊(#41⋊C3)C211yesmaximal, characteristic
2C3×C8×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C3⋊C8×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4C8×#239C311yesmaximal, characteristic, complemented
5C8×#41⋊C3—31nomaximal
6C2×C3⋊(#41⋊C3)C411yescharacteristic
7C3×C4×SL(2,𝔽3)C2211yescharacteristic
8Dic3×SL(2,𝔽3)C411yescharacteristic
9C3×C8×Dic3—41nomaximal
10C4×#239C2×C311yescharacteristic
11C4×#41⋊C3—31no—
12C3×C8×Q8C2×C311yescharacteristic
13Q8×C3⋊C8C2×C311yescharacteristic
14#4834—31no—
15#4833—31no—
16C8×D12—31no—
17C4×D3×C8—31no—
18C8×SL(2,𝔽3)—21no—
19C8×SL(2,𝔽3)—31no—
20C8×SL(2,𝔽3)D311yescharacteristic, complemented
21C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
22C3⋊(#41⋊C3)C812yesdirect product factor
23C2×C32×C8—41no—
24C3×C4×Dic3—41no—
25C2×C3×C3⋊C8—41no—
26C8×#41—31noSylow
27C2×#239C3×C411yescharacteristic
28C2×#41⋊C3—31no—
29C3×C4×Q8C22×C311yescharacteristic
30Q8×Dic3C3×C411yescharacteristic
31C2×D3×C8—31no—
32C2×D3×C8—31no—
33#893—31no—
34#892—31no—
35C4×D12—31no—
36C42×D3—31no—
37C4×SL(2,𝔽3)—21no—
38C4×SL(2,𝔽3)—31no—
39C4×SL(2,𝔽3)C2×D311yescharacteristic
40C3×C4⋊C8—31no—
41C3×C4×C8—31no—
42C3×C4×C8—121no—
43(C2×D3)⋊C8—32no—
44C8×Dic3—31no—
45C8×Dic3A411yescharacteristic
46C4⋊(C3⋊C8)—31no—
47C4×C3⋊C8—31no—
48C2×C32×C4—41no—
49C2×C3×Dic3—41no—
50C2×C3×Dic3—41no—
51C3×SL(2,𝔽3)C2×C811yescharacteristic, complemented
52C32×C8—42no—
53C3×C3⋊C8—42no—
54C4×#41—31no—
55C8×Q8—31no—
56C8×Q8C3×D311yescharacteristic
57C8×D4—91no—
58C8×D4—91no—
59#431—91no—
60C2×C4×C8—91no—
61C2×C3×Q8C2×C3×C411yescharacteristic
62#239—32no—
63#239C3×C812yescomplemented
64C2×D12—31no—
65C2×C4×D3—31no—
66C2×C4×D3—31no—
67C2×C4×D3—31no—
68#41⋊C3—32no—
69C2×SL(2,𝔽3)—21no—
70C2×SL(2,𝔽3)C4×D311yescharacteristic
71C2×C3×C8—31no—
72C2×C3×C8—41no—
73C2×C3×C8—81no—
74C2×C3×C8—121no—
75C2×C3×C8C2×A411yescharacteristic
76C3×C4⋊C4—31no—
77C3×C42—31no—
78C3×C42—121no—
79(C2×D3)⋊C4—32no—
80C4⋊Dic3—31no—
81C4×Dic3—31no—
82C4×Dic3—31no—
83C4×Dic3C2×A411yescharacteristic
84C2×C3⋊C8—31no—
85C2×C3⋊C8C2×A411yescharacteristic
86D3×C8—62no—
87D3×C8—62no—
88C22×C32—41no—
89C32×C4—41no—
90C32×C4—41no—
91C3×Dic3—42no—
92C3×Dic3—42no—
93C2×#41—31no—
94C22×C8—91no—
95C22×C8—91no—
96C4×Q8—31no—
97C4×Q8C2×C3×D311yescharacteristic
98C4×D4—91no—
99C4×D4—91no—
100#117—91no—
101C2×C42—91no—
102C4⋊C8—31no—
103C4⋊C8—91no—
104C22⋊C8—92no—
105C4×C8—31no—
106C4×C8—31no—
107C4×C8—91no—
108C4×C8—91no—
109C22×D3—31no—
110C3×Q8—31no—
111C3×Q8C2×C3×C811yescharacteristic
112C2×C3×C4—31no—
113C2×C3×C4—31no—
114C2×C3×C4—41no—
115C2×C3×C4—81no—
116C2×C3×C4—121no—
117C2×C3×C4—121no—
118C2×C3×C4C22×A411yescharacteristic
119C2×Dic3—31no—
120C2×Dic3C4×A411yescharacteristic
121C2×Dic3C4×A411yescharacteristic
122D12—32no—
123D12—32no—
124C4×D3—32no—
125C4×D3—32no—
126C4×D3—61no—
127C4×D3—61no—
128C4×D3—62no—
129SL(2,𝔽3)—21no—
130SL(2,𝔽3)D3×C811yescharacteristic, complemented
131C3×C8—42no—
132C3×C8—61no—
133C3×C8—82no—
134C3×C8—122no—
135C3×C8#41⋊C312yescomplemented
136C3⋊C8—61no—
137C3⋊C8#41⋊C312yescomplemented
138C2×C32—41no—
139C2×C32—41no—
140C2×C32—41no—
141#41—32no—
142#41—92no—
143C2×Q8C3×C4×D311yescharacteristic
144C2×D4—91no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C2×C8—31no—
149C2×C8—31no—
150C2×C8—91no—
151C2×C8—182no—
152C2×C8—182no—
153C2×C8D3×A411yescharacteristic
154C4⋊C4—31no—
155C4⋊C4—91no—
156C22⋊C4—92no—
157C42—31no—
158C42—31no—
159C42—91no—
160C42—91no—
161C22×C3—41no—
162C22×C3—81no—
163C22×C3C2×C4×A411yescharacteristic
164C2×D3—32no—
165C2×D3—61no—
166C2×D3—61no—
167C3×C4—31no—
168C3×C4—31no—
169C3×C4—41no—
170C3×C4—41no—
171C3×C4—61no—
172C3×C4—81no—
173C3×C4—81no—
174C3×C4—122no—
175C3×C4—122no—
176C3×C4C2×#41⋊C311yescharacteristic
177C3×C4C2×#41⋊C311yescharacteristic
178Dic3—61no—
179Dic3C8×A412yes—
180Dic3#131⋊C312yes—
181C32—41noSylow
182C23—91no—
183Q8—31no—
184Q8C3×D3×C811yescharacteristic
185D4—92no—
186D4—92no—
187C2×C4—31no—
188C2×C4—31no—
189C2×C4—31no—
190C2×C4—31no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—182no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4C2×D3×A411yescharacteristic
198C8—32no—
199C8—61no—
200C8—181no—
201C8C3⋊(#41⋊C3)12yesdirect product factor
202C2×C3—41no—
203C2×C3—41no—
204C2×C3—41no—
205C2×C3—81no—
206C2×C3—81no—
207C2×C3—81no—
208C2×C3C4×#41⋊C311yescharacteristic
209C2×C3C2×C8×A411yescharacteristic
210C2×C3C2×#131⋊C311yescharacteristic
211D3—62no—
212C22—92no—
213C22—181no—
214C22—181no—
215C22C4×D3×A411yescharacteristic
216C4—31no—
217C4—31no—
218C4—32no—
219C4—32no—
220C4—61no—
221C4—181no—
222C4C2×C3⋊(#41⋊C3)11yescharacteristic
223C4D3×#41⋊C311yescharacteristic
224C3—41no—
225C3—81no—
226C3C8×#41⋊C311yescharacteristic, complemented
227C2—182no—
228C2C4×C3⋊(#41⋊C3)11yescharacteristic
229C2D3×C8×A411yescharacteristic
230C2D3×#131⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C8D3×A4
commutator, hypocenterC3×Q8C2×C3×C8
FrattiniC2×C4C2×D3×A4
FittingC3×C8×Q8C2×C3
socleC22×C3C2×C4×A4
prime radicalC2×C3⋊(#41⋊C3)C4
cosocleC3×C4×Q8C22×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C3×C8×SL(2,𝔽3)C2semidirect
3. C3⋊C8×SL(2,𝔽3)C2semidirect
4. C8×#239C3semidirect
20. C8×SL(2,𝔽3)D3semidirect
22. C3⋊(#41⋊C3)C8direct (N × H)
51. C3×SL(2,𝔽3)C2×C8semidirect
63. #239C3×C8semidirect
130. SL(2,𝔽3)D3×C8semidirect
135. C3×C8#41⋊C3semidirect
137. C3⋊C8#41⋊C3semidirect
201. C8C3⋊(#41⋊C3)direct (N × H)
226. C3C8×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊(#41⋊C3)2
C3×C8×SL(2,𝔽3)2
C3⋊C8×SL(2,𝔽3)2
C8×#2393
C8×#41⋊C33
C3×C8×Dic34