Finite Group Databasebeta

← D3×#3828 #11724576

Subgroups — D3×#3828 #11724576

Order 864.

1144 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#89076C211yesmaximal, characteristic, complemented
2C3×#3828C211yesmaximal, characteristic, complemented
3C2×C32×C4×D3C211yesmaximal, characteristic, complemented
4D3×#638C212yesmaximal, complemented
5#89031C212yesmaximal, complemented
6D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
7C4×D3×C3⋊D3C212yesmaximal, complemented
8#89022C211yesmaximal, characteristic, complemented
9#89021C211yesmaximal, characteristic, complemented
10#89020C212yesmaximal, complemented
11D3×#634C211yesmaximal, characteristic, complemented
12C2×#3828—31nomaximal
13D3×#235—34nomaximal
14C22×C32×D3C2211yescharacteristic
15C2×D3×C3⋊D3C2212yes—
16C2×C33×C4C2211yescharacteristic, complemented
17#6312C2212yescomplemented
18C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
19C4×C3⋊(C3⋊D3)C2212yescomplemented
20#6308C2211yescharacteristic, complemented
21C3×#638C2212yescomplemented
22C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C3×C4×C3⋊D3C2212yescomplemented
24C3×#634C2211yescharacteristic, complemented
25C2×C32×Dic3C2211yescharacteristic, complemented
26C32×C4×D3C2211yescharacteristic
27C32×C4×D3C2211yescharacteristic
28C32×C4×D3C2211yescharacteristic, complemented
29C32×C4×D3C2211yescharacteristic, complemented
30#6293C2212yescomplemented
31#6292C2212yescomplemented
32#6291C2212yescomplemented
33#6290C2212yescomplemented
34#6289C2212yescomplemented
35Dic3×C3⋊D3C2212yescomplemented
36D3×C3⋊Dic3C2212yes—
37C22×C32×C4—31no—
38C2×#638—32no—
39#3828—31no—
40#3828—34no—
41#3828—32no—
42#3828—31no—
43#3828—32no—
44#3828—31no—
45#3828—64no—
46#3828D311yescharacteristic, direct product factor
47C2×C4⋊(C3⋊D3)—31no—
48C2×C4×C3⋊D3—32no—
49C2×#634—31no—
50C3×#235—34no—
51C2×C3×C4×D3D314yescomplemented
52D3×#67—38no—
53#3804—38no—
54D3×D12—34no—
55C4×D32—38no—
56#3799—34no—
57#3798—38no—
58#3795—34no—
59D3×Dic6—34no—
60C22×C33C2311yescharacteristic
61C2×C3⋊(C3⋊D3)C2312yes—
62C2×C3×C3⋊D3C2312yes—
63C2×C32×D3—22no—
64C2×C32×D3C2311yescharacteristic
65C2×C32×D3C2311yescharacteristic
66D3×C3⋊D3—24no—
67C33×C4C2311yescharacteristic
68C33×C4C2311yescharacteristic
69C3⋊(C3⋊Dic3)C2312yes—
70C3×C3⋊Dic3C2312yes—
71C32×Dic3C2311yescharacteristic
72C32×Dic3C2311yescharacteristic
73D3×#41—91no—
74C2×#235—94no—
75C23×C32—31no—
76C22×C3⋊D3—32no—
77C22×C3×D3C2×D314yes—
78C2×D32—38no—
79C2×C32×C4—24no—
80C2×C32×C4—31no—
81C2×C32×C4—31no—
82C2×C32×C4—31no—
83C2×C32×C4—31no—
84C2×C32×C4—31no—
85C2×C32×C4C2×D314yescomplemented
86C2×C32×C4C2×D311yescharacteristic, complemented
87#638—32no—
88#638—32no—
89#638—32no—
90#638—38no—
91#638—68no—
92#638C2×D312yescomplemented
93C2×C3⋊Dic3—32no—
94C4⋊(C3⋊D3)—32no—
95C4⋊(C3⋊D3)—31no—
96C4⋊(C3⋊D3)—34no—
97C4⋊(C3⋊D3)—64no—
98C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
99C4×C3⋊D3—32no—
100C4×C3⋊D3—32no—
101C4×C3⋊D3—32no—
102C4×C3⋊D3—38no—
103C4×C3⋊D3—68no—
104C4×C3⋊D3C2×D312yescomplemented
105#634—31no—
106#634—32no—
107#634—34no—
108#634—64no—
109#634C2×D311yescharacteristic, complemented
110C3×#67—38no—
111C2×C3×Dic3C2×D314yescomplemented
112C3×D12—34no—
113C3×C4×D3—38no—
114C3×C4×D3C2×D314yes—
115C3×C4×D3C2×D314yes—
116C3×C4×D3C2×D314yescomplemented
117C3×C4×D3C2×D314yescomplemented
118C3×Dic6—34no—
119#627—38no—
120#626—38no—
121#626—38no—
122#625—38no—
123#624—38no—
124D3×Dic3—38no—
125D3×Dic3—38no—
126C2×C33—21no—
127C2×C33C2411yescharacteristic
128C3⋊(C3⋊D3)—22no—
129C3×C3⋊D3—22no—
130C32×D3—21no—
131C32×D3#4112yescomplemented
132C3×#41—91no—
133C22×C3×C4—34no—
134C2×#67—98no—
135#239—91no—
136D3×Q8—91no—
137#237—92no—
138#237—91no—
139D3×D4—92no—
140D3×D4—91no—
141#235—34no—
142#235—94no—
143#235—98no—
144#235—94no—
145#235—98no—
146#235—94no—
147#235—91no—
148#235—92no—
149#235—184no—
150C2×D12—94no—
151C2×C4×D3—98no—
152C2×C4×D3—92no—
153C2×C4×D3C3⋊D311yescharacteristic, complemented
154C2×Dic6—94no—
155C22×C32—24no—
156C22×C32—31no—
157C22×C32—31no—
158C22×C32—62no—
159C22×C32C22×D314yes—
160C22×C32C22×D311yescharacteristic
161C2×C3⋊D3—32no—
162C2×C3⋊D3—38no—
163C2×C3⋊D3—68no—
164C2×C3⋊D3—64no—
165C2×C3⋊D3C22×D312yes—
166C2×C3×D3—28no—
167C2×C3×D3—38no—
168C2×C3×D3C22×D314yes—
169C2×C3×D3C22×D314yes—
170D32—616no—
171C32×C4—24no—
172C32×C4—24no—
173C32×C4—31no—
174C32×C4—31no—
175C32×C4C22×D314yes—
176C32×C4C22×D314yes—
177C32×C4C22×D311yescharacteristic
178C32×C4C22×D311yescharacteristic
179C3⋊Dic3—32no—
180C3⋊Dic3—38no—
181C3⋊Dic3—68no—
182C3⋊Dic3C22×D312yes—
183C3×Dic3—38no—
184C3×Dic3C22×D314yes—
185C3×Dic3C22×D314yes—
186C2×#41—271noSylow
187C33C2×#4111yescharacteristic, complemented, Sylow
188C23×C3—34no—
189C22×D3—98no—
190C22×D3—92no—
191C22×D3C2×C3⋊D311yescharacteristic
192C3×Q8—91no—
193C3×D4—92no—
194C3×D4—91no—
195C2×C3×C4—24no—
196C2×C3×C4—34no—
197C2×C3×C4—34no—
198C2×C3×C4—34no—
199C2×C3×C4—34no—
200C2×C3×C4—34no—
201C2×C3×C4—92no—
202C2×C3×C4D3214yescomplemented
203C2×C3×C4C2×C3⋊D311yescharacteristic, complemented
204#67—38no—
205#67—98no—
206#67—98no—
207#67—98no—
208#67—92no—
209#67—92no—
210#67—92no—
211#67—188no—
212C2×Dic3—98no—
213C2×Dic3—92no—
214C2×Dic3C2×C3⋊D311yescharacteristic, complemented
215D12—34no—
216D12—98no—
217D12—92no—
218D12—94no—
219D12—91no—
220D12—184no—
221C4×D3—38no—
222C4×D3—98no—
223C4×D3—98no—
224C4×D3—92no—
225C4×D3—98no—
226C4×D3—92no—
227C4×D3—92no—
228C4×D3—188no—
229C4×D3C2×C3⋊D311yescharacteristic
230C4×D3C2×C3⋊D311yescharacteristic
231C4×D3C2×C3⋊D311yescharacteristic, complemented
232C4×D3C2×C3⋊D311yescharacteristic, complemented
233Dic6—34no—
234Dic6—98no—
235Dic6—94no—
236Dic6—91no—
237Dic6—92no—
238Dic6—184no—
239C2×C32—21no—
240C2×C32—24no—
241C2×C32—24no—
242C2×C32—32no—
243C2×C32—44no—
244C2×C32—61no—
245C2×C32C23×D314yes—
246C2×C32C23×D311yescharacteristic
247C3⋊D3—22no—
248C3⋊D3—62no—
249C3⋊D3—68no—
250C3⋊D3—128no—
251C3×D3—24no—
252C3×D3—68no—
253C3×D3#23518yescomplemented
254#41—91no—
255#41—272no—
256#41—272no—
257#41—271no—
258#41—271no—
259#41—271no—
260C2×Q8—271no—
261C2×D4—271no—
262C2×D4—272no—
263C22×C4—31no—
264C22×C4—272no—
265C22×C3—24no—
266C22×C3—34no—
267C22×C3—34no—
268C22×C3—68no—
269C22×C3—92no—
270C22×C3C2×D3214yes—
271C22×C3C22×C3⋊D311yescharacteristic
272C2×D3—22no—
273C2×D3—38no—
274C2×D3—98no—
275C2×D3—92no—
276C2×D3—188no—
277C2×D3—1816no—
278C2×D3—184no—
279C2×D3C22×C3⋊D311yescharacteristic
280C2×D3C22×C3⋊D311yescharacteristic
281C3×C4—24no—
282C3×C4—24no—
283C3×C4—34no—
284C3×C4—34no—
285C3×C4—92no—
286C3×C4C2×D3214yes—
287C3×C4C2×D3214yes—
288C3×C4C22×C3⋊D311yescharacteristic
289C3×C4C22×C3⋊D311yescharacteristic
290Dic3—38no—
291Dic3—98no—
292Dic3—92no—
293Dic3—188no—
294Dic3C22×C3⋊D311yescharacteristic
295Dic3C22×C3⋊D311yescharacteristic
296C32—24no—
297C32C2×#23514yescomplemented
298C32D3×#4111yescharacteristic, complemented
299C23—31no—
300C23—272no—
301Q8—91no—
302Q8—272no—
303Q8—271no—
304D4—92no—
305D4—91no—
306D4—272no—
307D4—272no—
308D4—272no—
309D4—272no—
310D4—271no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—92no—
317C2×C4—272no—
318C2×C4—272no—
319C2×C4—272no—
320C2×C4—272no—
321C2×C4D3×C3⋊D311yescharacteristic, complemented
322C2×C3—24no—
323C2×C3—21no—
324C2×C3—24no—
325C2×C3—38no—
326C2×C3—44no—
327C2×C3—64no—
328C2×C3—182no—
329C2×C3C22×D3214yes—
330C2×C3C23×C3⋊D311yescharacteristic
331D3—21no—
332D3—68no—
333D3—188no—
334D3—182no—
335D3—368no—
336D3#382812yesdirect product factor
337C22—31no—
338C22—31no—
339C22—62no—
340C22—92no—
341C22—272no—
342C22—544no—
343C22C2×D3×C3⋊D311yescharacteristic
344C4—31no—
345C4—31no—
346C4—92no—
347C4—272no—
348C4C2×D3×C3⋊D311yescharacteristic
349C4C2×D3×C3⋊D311yescharacteristic
350C3—24no—
351C3D3×#23514yescomplemented
352C3C2×#382811yescharacteristic, complemented
353C2—21no—
354C2—32no—
355C2—61no—
356C2—182no—
357C2—542no—
358C2C22×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC4C2×D3×C3⋊D3
commutator, socle, cosocleC2×C33C24
FrattiniC2C22×D3×C3⋊D3
FittingC2×C33×C4C22
hypercenterC2×C4D3×C3⋊D3
hypocenterC33C2×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #89076C2semidirect
2. C3×#3828C2semidirect
3. C2×C32×C4×D3C2semidirect
4. D3×#638C2semidirect
5. #89031C2semidirect
6. D3×C4⋊(C3⋊D3)C2semidirect
7. C4×D3×C3⋊D3C2semidirect
8. #89022C2semidirect
9. #89021C2semidirect
10. #89020C2semidirect
11. D3×#634C2semidirect
16. C2×C33×C4C22semidirect
17. #6312C22semidirect
18. C4⋊(C3⋊(C3⋊D3))C22semidirect
19. C4×C3⋊(C3⋊D3)C22semidirect
20. #6308C22semidirect
21. C3×#638C22semidirect
22. C3×C4⋊(C3⋊D3)C22semidirect
23. C3×C4×C3⋊D3C22semidirect
24. C3×#634C22semidirect
25. C2×C32×Dic3C22semidirect
28. C32×C4×D3C22semidirect
29. C32×C4×D3C22semidirect
30. #6293C22semidirect
31. #6292C22semidirect
32. #6291C22semidirect
33. #6290C22semidirect
34. #6289C22semidirect
35. Dic3×C3⋊D3C22semidirect
46. #3828D3direct (N × H)
51. C2×C3×C4×D3D3semidirect
85. C2×C32×C4C2×D3semidirect
86. C2×C32×C4C2×D3semidirect
92. #638C2×D3semidirect
98. C4⋊(C3⋊D3)C2×D3semidirect
104. C4×C3⋊D3C2×D3semidirect
109. #634C2×D3semidirect
111. C2×C3×Dic3C2×D3semidirect
116. C3×C4×D3C2×D3semidirect
117. C3×C4×D3C2×D3semidirect
131. C32×D3#41semidirect
153. C2×C4×D3C3⋊D3semidirect
187. C33C2×#41semidirect
202. C2×C3×C4D32semidirect
203. C2×C3×C4C2×C3⋊D3semidirect
214. C2×Dic3C2×C3⋊D3semidirect
231. C4×D3C2×C3⋊D3semidirect
232. C4×D3C2×C3⋊D3semidirect
253. C3×D3#235semidirect
297. C32C2×#235semidirect
298. C32D3×#41semidirect
321. C2×C4D3×C3⋊D3semidirect
336. D3#3828direct (N × H)
351. C3D3×#235semidirect
352. C3C2×#3828semidirect

Maximal subgroups

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

subgroupindex
#890762
C3×#38282
C2×C32×C4×D32
D3×#6382
#890312
D3×C4⋊(C3⋊D3)2
C4×D3×C3⋊D32
#890222
#890212
#890202
D3×#6342
C2×#38283
D3×#2353