Finite Group Databasebeta

← D3×#3830 #11724584

Subgroups — D3×#3830 #11724584

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#89078C211yesmaximal, characteristic, complemented
2C3×#3830C211yesmaximal, characteristic, complemented
3C32×D3×D4C211yesmaximal, characteristic, complemented
4D3×#638C212yesmaximal, complemented
5#89029C212yesmaximal, complemented
6#89028C212yesmaximal, complemented
7C2×D3×C3⋊Dic3C212yesmaximal, complemented
8C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
9#89015C211yesmaximal, characteristic, complemented
10#89014C211yesmaximal, characteristic, complemented
11D3×#634C211yesmaximal, characteristic, complemented
12C2×#3830—31nomaximal
13D3×#237—34nomaximal
14C22×C32×D3C2212yes—
15C2×D3×C3⋊D3C2211yescharacteristic
16C33×D4C2211yescharacteristic, complemented
17#6312C2212yescomplemented
18C2×C3⋊(C3⋊Dic3)C2212yescomplemented
19C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
20#6308C2211yescharacteristic, complemented
21C3×#638C2212yescomplemented
22C2×C3×C3⋊Dic3C2212yescomplemented
23C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C3×#634C2211yescharacteristic, complemented
25C32×#67C2212yescomplemented
26C32×D12C2211yescharacteristic, complemented
27C32×C4×D3C2211yescharacteristic
28#6293C2212yescomplemented
29#6291C2212yescomplemented
30#6290C2212yescomplemented
31#6289C2211yescharacteristic, complemented
32Dic3×C3⋊D3C2211yescharacteristic, complemented
33D3×C3⋊Dic3C2212yes—
34D3×C3⋊Dic3C2211yescharacteristic
35D3×C3⋊Dic3C2212yescomplemented
36D3×C3⋊Dic3C2212yescomplemented
37C2×C32×D4—31no—
38C2×#638—32no—
39C22×C3⋊Dic3—32no—
40#3830—31no—
41#3830—34no—
42#3830—32no—
43#3830—32no—
44#3830—31no—
45#3830—31no—
46#3830—64no—
47#3830D311yescharacteristic, direct product factor
48C2×C4×C3⋊D3—31no—
49C2×#634—31no—
50C3×#237—34no—
51C3×D3×D4D314yescomplemented
52D3×#67—38no—
53#3805—38no—
54#3804—38no—
55C2×D3×Dic3—38no—
56C4×D32—34no—
57#3796—34no—
58#3795—34no—
59D3×Dic6—34no—
60C22×C33C2312yes—
61C2×C3⋊(C3⋊D3)C2311yescharacteristic
62C2×C3×C3⋊D3C2311yescharacteristic
63C2×C32×D3—24no—
64C2×C32×D3C2312yes—
65C2×C32×D3C2311yescharacteristic
66D3×C3⋊D3—22no—
67C33×C4C2311yescharacteristic
68C3⋊(C3⋊Dic3)C2311yescharacteristic
69C3⋊(C3⋊Dic3)C2312yes—
70C3×C3⋊Dic3C2311yescharacteristic
71C3×C3⋊Dic3C2312yes—
72C32×Dic3C2311yescharacteristic
73D3×#41—91no—
74C2×#237—94no—
75C23×C32—32no—
76C22×C3⋊D3—31no—
77C22×C3×D3C2×D318yes—
78C2×D32—34no—
79C32×D4—24no—
80C32×D4—32no—
81C32×D4—31no—
82C32×D4C2×D314yescomplemented
83C32×D4C2×D311yescharacteristic, complemented
84C2×C32×C4—31no—
85#638—32no—
86#638—32no—
87#638—32no—
88#638—38no—
89#638—68no—
90#638C2×D312yescomplemented
91C2×C3⋊Dic3—32no—
92C2×C3⋊Dic3—32no—
93C2×C3⋊Dic3—31no—
94C2×C3⋊Dic3—32no—
95C2×C3⋊Dic3—32no—
96C2×C3⋊Dic3—38no—
97C2×C3⋊Dic3—68no—
98C2×C3⋊Dic3C2×D312yescomplemented
99C4×C3⋊D3—31no—
100C4×C3⋊D3—31no—
101C4×C3⋊D3—31no—
102C4×C3⋊D3—34no—
103C4×C3⋊D3—64no—
104C4×C3⋊D3C2×D311yescharacteristic, complemented
105#634—31no—
106#634—32no—
107#634—34no—
108#634—64no—
109#634C2×D311yescharacteristic, complemented
110C3×#67—38no—
111C3×#67C2×D318yescomplemented
112C2×C3×Dic3—38no—
113C3×D12C2×D314yescomplemented
114C3×C4×D3—34no—
115C3×C4×D3C2×D314yes—
116C3×Dic6—34no—
117#627—38no—
118#626—38no—
119#625—38no—
120#624—34no—
121D3×Dic3—38no—
122D3×Dic3—34no—
123D3×Dic3—38no—
124D3×Dic3—38no—
125D3×Dic3—34no—
126C2×C33—22no—
127C2×C33C2411yescharacteristic
128C3⋊(C3⋊D3)—21no—
129C3×C3⋊D3—21no—
130C32×D3—22no—
131C32×D3#4112yescomplemented
132C3×#41—91no—
133C2×C3×D4—34no—
134C2×#67—98no—
135C22×Dic3—98no—
136#239—91no—
137D3×Q8—91no—
138#237—34no—
139#237—94no—
140#237—94no—
141#237—98no—
142#237—98no—
143#237—94no—
144#237—91no—
145#237—92no—
146#237—184no—
147D3×D4—92no—
148D3×D4C3⋊D311yescharacteristic, complemented
149#235—92no—
150#235—91no—
151C2×C4×D3—94no—
152C2×C4×D3—92no—
153C2×C4×D3—91no—
154C2×Dic6—94no—
155C22×C32—28no—
156C22×C32—31no—
157C22×C32—32no—
158C22×C32—64no—
159C22×C32C22×D318yes—
160C22×C32C22×D312yes—
161C2×C3⋊D3—31no—
162C2×C3⋊D3—34no—
163C2×C3⋊D3—64no—
164C2×C3⋊D3—62no—
165C2×C3⋊D3C22×D311yescharacteristic
166C2×C3×D3—216no—
167C2×C3×D3—34no—
168C2×C3×D3C22×D318yes—
169C2×C3×D3C22×D314yes—
170D32—68no—
171C32×C4—24no—
172C32×C4—31no—
173C32×C4C22×D314yes—
174C32×C4C22×D311yescharacteristic
175C3⋊Dic3—32no—
176C3⋊Dic3—31no—
177C3⋊Dic3—34no—
178C3⋊Dic3—38no—
179C3⋊Dic3—68no—
180C3⋊Dic3—64no—
181C3⋊Dic3C22×D312yes—
182C3⋊Dic3C22×D311yescharacteristic
183C3×Dic3—34no—
184C3×Dic3—38no—
185C3×Dic3C22×D314yes—
186C2×#41—271noSylow
187C33C2×#4111yescharacteristic, complemented, Sylow
188C23×C3—38no—
189C22×D3—94no—
190C22×D3—91no—
191C22×D3C2×C3⋊D312yes—
192C3×Q8—91no—
193C3×D4—24no—
194C3×D4—38no—
195C3×D4—34no—
196C3×D4—92no—
197C3×D4D3214yescomplemented
198C3×D4C2×C3⋊D311yescharacteristic, complemented
199C2×C3×C4—34no—
200C2×C3×C4—92no—
201C2×C3×C4—91no—
202#67—38no—
203#67—98no—
204#67—98no—
205#67—98no—
206#67—92no—
207#67—92no—
208#67—188no—
209#67C2×C3⋊D312yescomplemented
210C2×Dic3—38no—
211C2×Dic3—98no—
212C2×Dic3—94no—
213C2×Dic3—98no—
214C2×Dic3—98no—
215C2×Dic3—98no—
216C2×Dic3—92no—
217C2×Dic3—91no—
218C2×Dic3—188no—
219D12—92no—
220D12C2×C3⋊D311yescharacteristic, complemented
221C4×D3—34no—
222C4×D3—94no—
223C4×D3—94no—
224C4×D3—91no—
225C4×D3—92no—
226C4×D3—92no—
227C4×D3—92no—
228C4×D3—94no—
229C4×D3—91no—
230C4×D3—91no—
231C4×D3—184no—
232C4×D3C2×C3⋊D311yescharacteristic
233Dic6—34no—
234Dic6—98no—
235Dic6—94no—
236Dic6—91no—
237Dic6—92no—
238Dic6—184no—
239C2×C32—22no—
240C2×C32—24no—
241C2×C32—28no—
242C2×C32—32no—
243C2×C32—48no—
244C2×C32—62no—
245C2×C32C23×D314yes—
246C2×C32C23×D311yescharacteristic
247C3⋊D3—21no—
248C3⋊D3—61no—
249C3⋊D3—64no—
250C3⋊D3—124no—
251C3×D3—28no—
252C3×D3—64no—
253C3×D3#23718yescomplemented
254#41—91no—
255#41—272no—
256#41—271no—
257#41—272no—
258#41—271no—
259#41—271no—
260C2×Q8—271no—
261C2×D4—31no—
262C2×D4—272no—
263C22×C4—271no—
264C22×C4—272no—
265C22×C3—28no—
266C22×C3—34no—
267C22×C3—38no—
268C22×C3—616no—
269C22×C3—91no—
270C22×C3C2×D3218yes—
271C22×C3C22×C3⋊D312yes—
272C2×D3—24no—
273C2×D3—34no—
274C2×D3—94no—
275C2×D3—91no—
276C2×D3—184no—
277C2×D3—188no—
278C2×D3—182no—
279C2×D3C22×C3⋊D312yes—
280C2×D3C22×C3⋊D311yescharacteristic
281C3×C4—24no—
282C3×C4—34no—
283C3×C4—92no—
284C3×C4—91no—
285C3×C4C2×D3214yes—
286C3×C4C22×C3⋊D311yescharacteristic
287Dic3—38no—
288Dic3—34no—
289Dic3—98no—
290Dic3—94no—
291Dic3—92no—
292Dic3—91no—
293Dic3—188no—
294Dic3—184no—
295Dic3C22×C3⋊D311yescharacteristic
296C32—24no—
297C32C2×#23714yescomplemented
298C32D3×#4111yescharacteristic, complemented
299C23—32no—
300C23—271no—
301Q8—91no—
302Q8—272no—
303Q8—271no—
304D4—32no—
305D4—31no—
306D4—92no—
307D4—272no—
308D4—272no—
309D4—272no—
310D4D3×C3⋊D311yescharacteristic, complemented
311C2×C4—31no—
312C2×C4—92no—
313C2×C4—91no—
314C2×C4—271no—
315C2×C4—271no—
316C2×C4—271no—
317C2×C4—272no—
318C2×C4—272no—
319C2×C4—272no—
320C2×C4—272no—
321C2×C4—271no—
322C2×C3—28no—
323C2×C3—22no—
324C2×C3—24no—
325C2×C3—38no—
326C2×C3—48no—
327C2×C3—68no—
328C2×C3—181no—
329C2×C3C22×D3214yes—
330C2×C3C23×C3⋊D311yescharacteristic
331D3—22no—
332D3—64no—
333D3—184no—
334D3—181no—
335D3—364no—
336D3#383012yesdirect product factor
337C22—31no—
338C22—32no—
339C22—64no—
340C22—91no—
341C22—271no—
342C22—542no—
343C22C2×D3×C3⋊D312yes—
344C4—31no—
345C4—91no—
346C4—92no—
347C4—271no—
348C4—272no—
349C4C2×D3×C3⋊D311yescharacteristic
350C3—24no—
351C3D3×#23714yescomplemented
352C3C2×#383011yescharacteristic, complemented
353C2—22no—
354C2—32no—
355C2—62no—
356C2—181no—
357C2—541no—
358C2C22×D3×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×C3⋊D3
commutator, socle, cosocleC2×C33C24
FittingC33×D4C22
hypercenterD4D3×C3⋊D3
hypocenterC33C2×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #89078C2semidirect
2. C3×#3830C2semidirect
3. C32×D3×D4C2semidirect
4. D3×#638C2semidirect
5. #89029C2semidirect
6. #89028C2semidirect
7. C2×D3×C3⋊Dic3C2semidirect
8. C4×D3×C3⋊D3C2semidirect
9. #89015C2semidirect
10. #89014C2semidirect
11. D3×#634C2semidirect
16. C33×D4C22semidirect
17. #6312C22semidirect
18. C2×C3⋊(C3⋊Dic3)C22semidirect
19. C4×C3⋊(C3⋊D3)C22semidirect
20. #6308C22semidirect
21. C3×#638C22semidirect
22. C2×C3×C3⋊Dic3C22semidirect
23. C3×C4×C3⋊D3C22semidirect
24. C3×#634C22semidirect
25. C32×#67C22semidirect
26. C32×D12C22semidirect
28. #6293C22semidirect
29. #6291C22semidirect
30. #6290C22semidirect
31. #6289C22semidirect
32. Dic3×C3⋊D3C22semidirect
35. D3×C3⋊Dic3C22semidirect
36. D3×C3⋊Dic3C22semidirect
47. #3830D3direct (N × H)
51. C3×D3×D4D3semidirect
82. C32×D4C2×D3semidirect
83. C32×D4C2×D3semidirect
90. #638C2×D3semidirect
98. C2×C3⋊Dic3C2×D3semidirect
104. C4×C3⋊D3C2×D3semidirect
109. #634C2×D3semidirect
111. C3×#67C2×D3semidirect
113. C3×D12C2×D3semidirect
131. C32×D3#41semidirect
148. D3×D4C3⋊D3semidirect
187. C33C2×#41semidirect
197. C3×D4D32semidirect
198. C3×D4C2×C3⋊D3semidirect
209. #67C2×C3⋊D3semidirect
220. D12C2×C3⋊D3semidirect
253. C3×D3#237semidirect
297. C32C2×#237semidirect
298. C32D3×#41semidirect
310. D4D3×C3⋊D3semidirect
336. D3#3830direct (N × H)
351. C3D3×#237semidirect
352. C3C2×#3830semidirect

Maximal subgroups

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

subgroupindex
#890782
C3×#38302
C32×D3×D42
D3×#6382
#890292
#890282
C2×D3×C3⋊Dic32
C4×D3×C3⋊D32
#890152
#890142
D3×#6342
C2×#38303
D3×#2373