Finite Group Databasebeta

← C3×D3×#543 #11901858

Subgroups — C3×D3×#543 #11901858

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#543C211yesmaximal, characteristic, complemented
2C3×#5634C2112yesmaximal, complemented
3C3×D3×C22⋊Q8C2112yesmaximal, complemented
4C2×C3×D3×C22⋊C4C213yesmaximal
5C3×#5483C213yesmaximal, complemented
6C2×C3×#543—31nomaximal
7D3×#543C311yesmaximal, characteristic, direct product factor
8C24×C3×D3C2211yescharacteristic
9C2×C3×D3×Q8C2214yescomplemented
10C22×C3×C4×D3C2216yes—
11C32×C22⋊Q8C22112yescomplemented
12C2×C32×C22⋊C4C2213yes—
13C2×C3×#217C2213yes—
14C3×#946C22112yescomplemented
15C2×C3×(C2×D3)⋊C4C2216yes—
16C3×#924C22112yescomplemented
17C3×#897C22112yescomplemented
18C3×#896C22124yescomplemented
19C3×D3×C4⋊C4C22112yescomplemented
20C3×D3×C22⋊C4C22112yes—
21C3×D3×C22⋊C4C22112yes—
22C3×#878C22124yescomplemented
23C3×#543—21no—
24C3×#543—312no—
25C3×#543—33no—
26C3×#543D311yescharacteristic, direct product factor
27C3×#543C2×C311yescharacteristic, complemented
28C2×C3×C22⋊Q8—312no—
29C22×C3×C22⋊C4—33no—
30#5634C2×C3112yescomplemented
31D3×C22⋊Q8C2×C3112yescomplemented
32C2×D3×C22⋊C4C2×C313yes—
33#5483C2×C313yescomplemented
34C24×C32C2311yescharacteristic
35C23×C3×D3—44no—
36C23×C3×D3Q818yescomplemented
37C23×C3×D3C2313yes—
38C23×C3×D3C2313yes—
39C2×C32×Q8C2314yescomplemented
40C22×C32×C4C2316yes—
41C22×C3×Dic3C2316yes—
42C3×D3×Q8—48no—
43C2×C3×C4×D3—412no—
44C2×C3×C4×D3C23112yes—
45C2×C3×C4×D3C23112yes—
46C2×C3×Dic6C23112yescomplemented
47C32×C4⋊C4C23112yescomplemented
48C32×C22⋊C4C23112yes—
49C3×#217C23112yes—
50C3×(C2×D3)⋊C4C23124yes—
51C3×C4⋊Dic3C23112yescomplemented
52C3×Dic3⋊C4C23124yescomplemented
53C2×#543—31noSylow
54C25×C3—31no—
55C24×D3C22×C311yescharacteristic
56C22×C3×Q8—34no—
57C23×C3×C4—36no—
58C2×D3×Q8C22×C314yescomplemented
59C22×C4×D3C22×C316yes—
60C3×C22⋊Q8—212no—
61C3×C22⋊Q8—312no—
62C3×C22⋊Q8—312no—
63C3×C22⋊Q8—324no—
64C3×C22⋊Q8—312no—
65C3×C22⋊Q8—324no—
66C3×C22⋊Q8C2×D3112yescomplemented
67C3×C22⋊Q8C22×C3112yescomplemented
68C2×C3×C4⋊C4—312no—
69C2×C3×C22⋊C4—23no—
70C2×C3×C22⋊C4—33no—
71C2×C3×C22⋊C4—36no—
72C2×C3×C22⋊C4—312no—
73C2×C3×C22⋊C4—312no—
74C2×C3×C22⋊C4C2×D313yes—
75C2×C3×C22⋊C4C22×C313yes—
76C2×#217C22×C313yes—
77#946C22×C3112yescomplemented
78C2×(C2×D3)⋊C4C22×C316yes—
79#924C22×C3112yescomplemented
80#897C22×C3112yescomplemented
81#896C22×C3124yescomplemented
82D3×C4⋊C4C22×C3112yescomplemented
83D3×C22⋊C4C22×C3112yes—
84D3×C22⋊C4C22×C3112yes—
85#878C22×C3124yescomplemented
86C23×C32—42no—
87C23×C32C2×Q814yescomplemented
88C23×C32C2413yes—
89C22×C3×D3—212no—
90C22×C3×D3—416no—
91C22×C3×D3—46no—
92C22×C3×D3C2×Q8112yes—
93C22×C3×D3C2×Q8112yescomplemented
94C22×C3×D3C2413yes—
95C22×C3×D3C2411yescharacteristic
96C32×Q8—44no—
97C2×C32×C4—46no—
98C2×C32×C4C24112yes—
99C2×C3×Dic3—46no—
100C2×C3×Dic3C24112yes—
101C3×C4×D3—224no—
102C3×C4×D3—412no—
103C3×Dic6—412no—
104#543—312no—
105#543—33no—
106#543C3×D311yescharacteristic, direct product factor
107C2×C22⋊Q8—312no—
108C22×C22⋊C4—33no—
109C24×C3—21no—
110C24×C3—33no—
111C24×C3—38no—
112C24×C3—33no—
113C24×C3—124no—
114C24×C3C22×D311yescharacteristic
115C24×C3C23×C311yescharacteristic
116C23×D3—44no—
117C23×D3C3×Q818yescomplemented
118C23×D3C23×C313yes—
119C23×D3C23×C313yes—
120C2×C3×Q8—24no—
121C2×C3×Q8—312no—
122C2×C3×Q8—128no—
123C2×C3×Q8C22×D314yescomplemented
124C2×C3×Q8C23×C314yescomplemented
125C22×C3×C4—26no—
126C22×C3×C4—36no—
127C22×C3×C4—312no—
128C22×C3×C4—312no—
129C22×C3×C4—1212no—
130C22×C3×C4C22×D316yes—
131C22×C3×C4C23×C316yes—
132C22×Dic3C23×C316yes—
133D3×Q8—48no—
134C2×C4×D3—412no—
135C2×C4×D3C23×C3112yes—
136C2×C4×D3C23×C3112yes—
137C2×Dic6C23×C3112yescomplemented
138C3×C4⋊C4—212no—
139C3×C4⋊C4—324no—
140C3×C4⋊C4—312no—
141C3×C4⋊C4C22×D3112yescomplemented
142C3×C4⋊C4C23×C3112yescomplemented
143C3×C22⋊C4—212no—
144C3×C22⋊C4—312no—
145C3×C22⋊C4—324no—
146C3×C22⋊C4C22×D3112yes—
147C3×C22⋊C4C23×C3112yes—
148#217C23×C3112yes—
149(C2×D3)⋊C4C23×C3124yes—
150C4⋊Dic3C23×C3112yescomplemented
151Dic3⋊C4C23×C3124yescomplemented
152C22×C32—26no—
153C22×C32—44no—
154C22×C32C22×Q816yes—
155C22×C32C2511yescharacteristic
156C2×C3×D3—26no—
157C2×C3×D3—224no—
158C2×C3×D3—412no—
159C2×C3×D3C22×Q816yes—
160C2×C3×D3C22×Q812yes—
161C2×C3×D3H(5,𝔽2)14yes—
162C32×C4—212no—
163C3×Dic3—212no—
164C25—31no—
165C22×Q8—34no—
166C23×C4—36no—
167C22⋊Q8—312no—
168C22⋊Q8—312no—
169C22⋊Q8—324no—
170C22⋊Q8—312no—
171C22⋊Q8—324no—
172C22⋊Q8C2×C3×D3112yescomplemented
173C2×C4⋊C4—312no—
174C2×C22⋊C4—33no—
175C2×C22⋊C4—36no—
176C2×C22⋊C4—312no—
177C2×C22⋊C4—312no—
178C2×C22⋊C4C2×C3×D313yes—
179C23×C3—23no—
180C23×C3—24no—
181C23×C3—31no—
182C23×C3—312no—
183C23×C3—33no—
184C23×C3—312no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—612no—
188C23×C3—82no—
189C23×C3—126no—
190C23×C3—1216no—
191C23×C3D3×Q814yescomplemented
192C23×C3C2×C3×Q814yescomplemented
193C23×C3C23×D313yes—
194C23×C3C24×C313yes—
195C22×D3—212no—
196C22×D3—416no—
197C22×D3—46no—
198C22×D3C2×C3×Q8112yes—
199C22×D3C2×C3×Q8112yescomplemented
200C22×D3C24×C313yes—
201C22×D3C24×C311yescharacteristic
202C3×Q8—44no—
203C3×Q8—44no—
204C3×Q8—84no—
205C3×Q8—1212no—
206C2×C3×C4—212no—
207C2×C3×C4—312no—
208C2×C3×C4—46no—
209C2×C3×C4—46no—
210C2×C3×C4—624no—
211C2×C3×C4—86no—
212C2×C3×C4—1212no—
213C2×C3×C4—126no—
214C2×C3×C4C23×D3112yes—
215C2×C3×C4C24×C3112yes—
216C2×Dic3—46no—
217C2×Dic3C24×C3112yes—
218C4×D3—224no—
219C4×D3—412no—
220Dic6—412no—
221C2×C32—26no—
222C2×C32C23×Q811yescharacteristic
223C2×C32C2×H(5,𝔽2)12yes—
224C3×D3—26no—
225C3×D3#54314yesdirect product factor
226C24—33no—
227C24—33no—
228C24—38no—
229C24—124no—
230C24C22×C3×D311yescharacteristic
231C2×Q8—312no—
232C2×Q8—128no—
233C2×Q8C22×C3×D314yescomplemented
234C22×C4—36no—
235C22×C4—312no—
236C22×C4—312no—
237C22×C4—1212no—
238C22×C4C22×C3×D316yes—
239C4⋊C4—324no—
240C4⋊C4—312no—
241C4⋊C4C22×C3×D3112yescomplemented
242C22⋊C4—312no—
243C22⋊C4—324no—
244C22⋊C4C22×C3×D3112yes—
245C22×C3—26no—
246C22×C3—26no—
247C22×C3—26no—
248C22×C3—21no—
249C22×C3—32no—
250C22×C3—34no—
251C22×C3—36no—
252C22×C3—46no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—624no—
256C22×C3—66no—
257C22×C3—84no—
258C22×C3—1212no—
259C22×C3C2×D3×Q816yes—
260C22×C3C22×C3×Q816yes—
261C22×C3C24×D311yescharacteristic
262C22×C3C25×C311yescharacteristic
263C2×D3—26no—
264C2×D3—224no—
265C2×D3—412no—
266C2×D3C22×C3×Q816yes—
267C2×D3C22×C3×Q812yes—
268C2×D3C3×H(5,𝔽2)14yes—
269C3×C4—212no—
270C3×C4—212no—
271C3×C4—412no—
272C3×C4—612no—
273Dic3—212no—
274C32C2×#54311yescharacteristic, complemented, Sylow
275C23—31no—
276C23—312no—
277C23—33no—
278C23—312no—
279C23—42no—
280C23—612no—
281C23—126no—
282C23—1216no—
283C23C3×D3×Q814yescomplemented
284C23C23×C3×D313yes—
285Q8—44no—
286Q8—1212no—
287C2×C4—312no—
288C2×C4—46no—
289C2×C4—624no—
290C2×C4—1212no—
291C2×C4—126no—
292C2×C4C23×C3×D3112yes—
293C2×C3—26no—
294C2×C3—26no—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3—34no—
298C2×C3—46no—
299C2×C3—66no—
300C2×C3C22×D3×Q811yescharacteristic
301C2×C3D3×H(5,𝔽2)12yes—
302C2×C3C23×C3×Q811yescharacteristic
303C2×C3C2×C3×H(5,𝔽2)12yes—
304D3—26no—
305D3C3×#54314yesdirect product factor
306C22—26no—
307C22—32no—
308C22—34no—
309C22—36no—
310C22—44no—
311C22—624no—
312C22—66no—
313C22—1212no—
314C22C2×C3×D3×Q816yes—
315C22C24×C3×D311yescharacteristic
316C4—212no—
317C4—612no—
318C3—21no—
319C3D3×#54311yescharacteristic, direct product factor
320C3C2×C3×#54311yescharacteristic, complemented
321C2—26no—
322C2—34no—
323C2—66no—
324C2C22×C3×D3×Q811yescharacteristic
325C2C3×D3×H(5,𝔽2)12yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#543C2
socleC22×C32C25
prime radicalC24×C3×D3C22
hypercenterC3×#543D3
hypocenterC3C2×C3×#543
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
1. C32×#543C2semidirect
2. C3×#5634C2semidirect
3. C3×D3×C22⋊Q8C2semidirect
5. C3×#5483C2semidirect
7. D3×#543C3direct (N × H)
9. C2×C3×D3×Q8C22semidirect
11. C32×C22⋊Q8C22semidirect
14. C3×#946C22semidirect
16. C3×#924C22semidirect
17. C3×#897C22semidirect
18. C3×#896C22semidirect
19. C3×D3×C4⋊C4C22semidirect
22. C3×#878C22semidirect
26. C3×#543D3direct (N × H)
27. C3×#543C2×C3semidirect
30. #5634C2×C3semidirect
31. D3×C22⋊Q8C2×C3semidirect
33. #5483C2×C3semidirect
36. C23×C3×D3Q8semidirect
39. C2×C32×Q8C23semidirect
46. C2×C3×Dic6C23semidirect
47. C32×C4⋊C4C23semidirect
51. C3×C4⋊Dic3C23semidirect
52. C3×Dic3⋊C4C23semidirect
58. C2×D3×Q8C22×C3semidirect
66. C3×C22⋊Q8C2×D3semidirect
67. C3×C22⋊Q8C22×C3semidirect
77. #946C22×C3semidirect
79. #924C22×C3semidirect
80. #897C22×C3semidirect
81. #896C22×C3semidirect
82. D3×C4⋊C4C22×C3semidirect
85. #878C22×C3semidirect
87. C23×C32C2×Q8semidirect
93. C22×C3×D3C2×Q8semidirect
106. #543C3×D3direct (N × H)
117. C23×D3C3×Q8semidirect
123. C2×C3×Q8C22×D3semidirect
124. C2×C3×Q8C23×C3semidirect
137. C2×Dic6C23×C3semidirect
141. C3×C4⋊C4C22×D3semidirect
142. C3×C4⋊C4C23×C3semidirect
150. C4⋊Dic3C23×C3semidirect
151. Dic3⋊C4C23×C3semidirect
172. C22⋊Q8C2×C3×D3semidirect
191. C23×C3D3×Q8semidirect
192. C23×C3C2×C3×Q8semidirect
199. C22×D3C2×C3×Q8semidirect
225. C3×D3#543direct (N × H)
233. C2×Q8C22×C3×D3semidirect
241. C4⋊C4C22×C3×D3semidirect
274. C32C2×#543semidirect
283. C23C3×D3×Q8semidirect
305. D3C3×#543direct (N × H)
319. C3D3×#543direct (N × H)
320. C3C2×C3×#543semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
C3×#56342
C3×D3×C22⋊Q82
C2×C3×D3×C22⋊C42
C3×#54832
C2×C3×#5433
D3×#5433