Finite Group Databasebeta

← C2×Dic3×#41⋊C3 #11923376

Subgroups — C2×Dic3×#41⋊C3 #11923376

Order 1152.

889 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 889 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C22×C3×#41⋊C3C211yesmaximal, characteristic
2Dic3×#41⋊C3C214yesmaximal, direct product factor
3C2×Dic3×SL(2,𝔽3)C212yesmaximal, complemented
4C2×Dic3×#41C311yesmaximal, characteristic, complemented
5C2×C4×#41⋊C3—31nomaximal
6C2×C3×#41⋊C3C414yescomplemented
7C2×C3×#41⋊C3C2212yes—
8C22×C3×SL(2,𝔽3)C2211yescharacteristic
9C2×C3×C4×Dic3—41nomaximal
10Dic3×SL(2,𝔽3)C2214yescomplemented
11C22×C3×#41C2×C311yescharacteristic
12C22×#41⋊C3—21no—
13C22×#41⋊C3D311yescharacteristic
14Dic3×#41—34no—
15Dic3×#41C2×C314yescomplemented
16C2×Q8×Dic3C2×C312yes—
17C2×D4×Dic3—32no—
18C2×#926—31no—
19C22×C4×Dic3—31no—
20C4×#41⋊C3—34no—
21C2×C4×SL(2,𝔽3)—32no—
22C22×C32×C4—41no—
23C22×C3×Dic3—42no—
24C3×#41⋊C3C2×C414yescomplemented
25C2×C3×SL(2,𝔽3)C2×C412yescomplemented
26C2×C3×SL(2,𝔽3)C2311yescharacteristic
27C3×C4×Dic3—44no—
28C2×C4×#41—31noSylow
29C2×C3×#41—34no—
30C2×C3×#41—32no—
31C2×C3×#41C3×C414yescomplemented
32C2×C3×#41C22×C312yes—
33C22×C3×Q8C22×C311yescharacteristic
34C22×C3×D4—31no—
35C23×C3×C4—31no—
36C23×Dic3—32no—
37C2×#41⋊C3—24no—
38C2×#41⋊C3—22no—
39C2×#41⋊C3Dic314yesdirect product factor
40C2×#41⋊C3C2×D312yes—
41C22×SL(2,𝔽3)—21no—
42C22×SL(2,𝔽3)C2×D311yescharacteristic
43C2×C3×C42—121no—
44C2×#217—32no—
45Q8×Dic3—34no—
46Q8×Dic3C22×C314yes—
47D4×Dic3—38no—
48D4×Dic3—38no—
49#926—34no—
50#926—34no—
51C2×C4⋊Dic3—32no—
52C2×C4×Dic3—31no—
53C2×C4×Dic3—32no—
54C2×C4×Dic3—34no—
55C2×C4×Dic3—34no—
56C2×C4×Dic3A411yescharacteristic
57C4×SL(2,𝔽3)—34no—
58C23×C32—41no—
59C2×C32×C4—44no—
60C2×C32×C4—42no—
61C2×C3×Dic3—48no—
62C2×C3×Dic3—44no—
63C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
64C22×#41C3×D311yescharacteristic
65C4×#41—34no—
66C4×#41—94no—
67C2×C4×Q8—32no—
68C2×C4×D4—92no—
69C2×#117—91no—
70C22×C42—91no—
71C24×C3—31no—
72C3×#41—38no—
73C3×#41—38no—
74C3×#41—34no—
75C3×#41C2×C3×C414yescomplemented
76C2×C3×Q8—31no—
77C2×C3×Q8—32no—
78C2×C3×Q8C2×C3×C412yes—
79C2×C3×Q8C23×C311yescharacteristic
80C2×C3×D4—32no—
81C2×C3×D4—34no—
82C2×C3×D4—32no—
83C2×C3×D4—34no—
84C22×C3×C4—31no—
85C22×C3×C4—34no—
86C22×C3×C4—34no—
87C22×C3×C4—32no—
88C22×C3×C4—32no—
89C22×C3×C4—41no—
90C22×C3×C4—81no—
91C22×C3×C4—122no—
92C22×C3×C4C2×A411yescharacteristic
93C22×Dic3—32no—
94C22×Dic3—38no—
95C22×Dic3—68no—
96C22×Dic3C2×A412yes—
97#41⋊C3—24no—
98#41⋊C3C2×Dic314yesdirect product factor
99C2×SL(2,𝔽3)—22no—
100C2×SL(2,𝔽3)—21no—
101C2×SL(2,𝔽3)C2×Dic312yescomplemented
102C2×SL(2,𝔽3)C22×D311yescharacteristic
103C3×C42—124no—
104#217—38no—
105C4⋊Dic3—34no—
106C4⋊Dic3—34no—
107C4×Dic3—34no—
108C4×Dic3—34no—
109C4×Dic3—34no—
110C4×Dic3C2×A414yes—
111C22×C32—42no—
112C22×C32—44no—
113C22×C32—41no—
114C32×C4—44no—
115C3×Dic3—48no—
116C2×#41—32no—
117C2×#41—34no—
118C2×#41C3×Dic314yescomplemented
119C2×#41C2×C3×D312yes—
120C22×Q8C2×C3×D311yescharacteristic
121C22×D4—31no—
122C23×C4—31no—
123C23×C4—92no—
124C4×Q8—34no—
125C4×Q8—94no—
126C4×D4—98no—
127C4×D4—98no—
128#117—94no—
129#117—94no—
130C2×C4⋊C4—92no—
131C2×C22⋊C4—92no—
132C2×C42—31no—
133C2×C42—94no—
134C2×C42—94no—
135C2×C42—92no—
136C2×C42—91no—
137C23×C3—34no—
138C23×C3—32no—
139C23×C3—41no—
140C23×C3—64no—
141C23×C3—81no—
142C23×C3C22×A411yescharacteristic
143C3×Q8—32no—
144C3×Q8—31no—
145C3×Q8—32no—
146C3×Q8C22×C3×C411yescharacteristic
147C3×D4—34no—
148C3×D4—34no—
149C3×D4—38no—
150C2×C3×C4—32no—
151C2×C3×C4—32no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—34no—
155C2×C3×C4—38no—
156C2×C3×C4—34no—
157C2×C3×C4—42no—
158C2×C3×C4—44no—
159C2×C3×C4—82no—
160C2×C3×C4—84no—
161C2×C3×C4—124no—
162C2×C3×C4—128no—
163C2×C3×C4C4×A414yes—
164C2×C3×C4C22×A412yes—
165C2×Dic3—34no—
166C2×Dic3—64no—
167C2×Dic3—616no—
168C2×Dic3#41⋊C318yesdirect product factor
169C2×Dic3C22×A414yes—
170SL(2,𝔽3)—21no—
171SL(2,𝔽3)C22×Dic311yescharacteristic, complemented
172C2×C32—41no—
173C2×C32—42no—
174C2×C32—44no—
175C24—31no—
176#41—38no—
177#41—38no—
178#41—34no—
179#41C2×C3×Dic314yescomplemented
180C2×Q8—31no—
181C2×Q8—32no—
182C2×Q8C2×C3×Dic312yes—
183C2×Q8C22×C3×D311yescharacteristic
184C2×D4—32no—
185C2×D4—34no—
186C2×D4—32no—
187C2×D4—34no—
188C22×C4—32no—
189C22×C4—31no—
190C22×C4—32no—
191C22×C4—32no—
192C22×C4—34no—
193C22×C4—34no—
194C22×C4—98no—
195C22×C4—92no—
196C22×C4—188no—
197C22×C4D3×A411yescharacteristic
198C4⋊C4—94no—
199C4⋊C4—94no—
200C22⋊C4—98no—
201C42—34no—
202C42—94no—
203C42—94no—
204C42—94no—
205C22×C3—34no—
206C22×C3—44no—
207C22×C3—42no—
208C22×C3—41no—
209C22×C3—64no—
210C22×C3—68no—
211C22×C3—84no—
212C22×C3—82no—
213C22×C3—81no—
214C22×C3C2×C4×A412yes—
215C22×C3C2×#41⋊C314yes—
216C22×C3C23×A411yescharacteristic
217C3×C4—31no—
218C3×C4—32no—
219C3×C4—31no—
220C3×C4—44no—
221C3×C4—84no—
222C3×C4—128no—
223C3×C4C2×C4×A414yes—
224Dic3—64no—
225Dic3C2×#41⋊C318yesdirect product factor
226C32—41noSylow
227C23—34no—
228C23—32no—
229C23—64no—
230C23C2×D3×A411yescharacteristic
231Q8—32no—
232Q8—31no—
233Q8—32no—
234Q8C22×C3×Dic311yescharacteristic
235D4—34no—
236D4—34no—
237D4—38no—
238C2×C4—38no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—34no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—34no—
245C2×C4—34no—
246C2×C4—38no—
247C2×C4—94no—
248C2×C4—1816no—
249C2×C4—184no—
250C2×C4Dic3×A414yes—
251C2×C4C2×D3×A412yes—
252C2×C3—42no—
253C2×C3—41no—
254C2×C3—44no—
255C2×C3—64no—
256C2×C3—82no—
257C2×C3—81no—
258C2×C3—84no—
259C2×C3C4×#41⋊C314yescomplemented
260C2×C3C22×C4×A411yescharacteristic
261C2×C3C22×#41⋊C312yes—
262C22—34no—
263C22—64no—
264C22—68no—
265C22D3×#41⋊C314yes—
266C22C2×Dic3×A412yes—
267C22C22×D3×A411yescharacteristic
268C4—38no—
269C4—31no—
270C4—32no—
271C4—31no—
272C4—184no—
273C4C2×Dic3×A414yes—
274C3—41no—
275C3—81no—
276C3C2×C4×#41⋊C311yescharacteristic, complemented
277C2—64no—
278C2Dic3×#41⋊C314yesdirect product factor
279C2C2×D3×#41⋊C312yes—
280C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, hypercenterC22×C4D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC22C22×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C22×A4
prime radicalC22×C3×#41⋊C3C2
cosocleC2×C3×Q8C23×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. Dic3×#41⋊C3C2direct (N × H)
3. C2×Dic3×SL(2,𝔽3)C2semidirect
4. C2×Dic3×#41C3semidirect
6. C2×C3×#41⋊C3C4semidirect
10. Dic3×SL(2,𝔽3)C22semidirect
15. Dic3×#41C2×C3semidirect
24. C3×#41⋊C3C2×C4semidirect
25. C2×C3×SL(2,𝔽3)C2×C4semidirect
31. C2×C3×#41C3×C4semidirect
39. C2×#41⋊C3Dic3direct (N × H)
63. C3×SL(2,𝔽3)C22×C4semidirect
75. C3×#41C2×C3×C4semidirect
98. #41⋊C3C2×Dic3direct (N × H)
101. C2×SL(2,𝔽3)C2×Dic3semidirect
118. C2×#41C3×Dic3semidirect
168. C2×Dic3#41⋊C3direct (N × H)
171. SL(2,𝔽3)C22×Dic3semidirect
179. #41C2×C3×Dic3semidirect
225. Dic3C2×#41⋊C3direct (N × H)
259. C2×C3C4×#41⋊C3semidirect
276. C3C2×C4×#41⋊C3semidirect
278. C2Dic3×#41⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#41⋊C32
Dic3×#41⋊C32
C2×Dic3×SL(2,𝔽3)2
C2×Dic3×#413
C2×C4×#41⋊C33
C2×C3×C4×Dic34