Finite Group Databasebeta

← D3×#3699 #11722496

Subgroups — D3×#3699 #11722496

Order 864.

532 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#88742C211yesmaximal, characteristic, complemented
2D3×D4×C9C211yesmaximal, characteristic, complemented
3C3×#3699C211yesmaximal, characteristic, complemented
4D3×#611C212yesmaximal, complemented
5#88663C212yesmaximal, complemented
6#88662C212yesmaximal, complemented
7C2×D3×Dic9C212yesmaximal, complemented
8C4×D3×D9C211yesmaximal, characteristic, complemented
9#88639C211yesmaximal, characteristic, complemented
10#88638C211yesmaximal, characteristic, complemented
11D3×Dic18C211yesmaximal, characteristic, complemented
12D3×#237—31nomaximal
13C2×#3699—31nomaximal
14C22×D3×C9C2212yes—
15C2×D3×D9C2211yescharacteristic
16C3×D4×C9C2211yescharacteristic, complemented
17#6233C2212yescomplemented
18C2×C3⋊Dic9C2212yescomplemented
19C4×C3⋊D9C2211yescharacteristic, complemented
20#6226C2211yescharacteristic, complemented
21C9×#67C2212yescomplemented
22C3×#611C2212yescomplemented
23C2×C3×Dic9C2212yescomplemented
24C9×D12C2211yescharacteristic, complemented
25C4×D3×C9C2211yescharacteristic
26C3×C4×D9C2211yescharacteristic, complemented
27C3×Dic18C2211yescharacteristic, complemented
28#6195C2212yescomplemented
29#6194C2212yescomplemented
30D3×Dic9C2212yes—
31D3×Dic9C2211yescharacteristic
32D3×Dic9C2212yescomplemented
33D3×Dic9C2212yescomplemented
34(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35Dic3×D9C2211yescharacteristic, complemented
36#6189C2212yescomplemented
37#3830—31no—
38C3×#237—31no—
39C3×D3×D4D311yescharacteristic
40D3×#67—32no—
41#3805—32no—
42#3804—32no—
43C2×D3×Dic3—32no—
44C4×D32—31no—
45#3796—31no—
46#3795—31no—
47D3×Dic6—31no—
48C2×D4×C9—31no—
49C2×#611—32no—
50C22×Dic9—32no—
51#3699—31no—
52#3699—32no—
53#3699—32no—
54#3699—31no—
55#3699—31no—
56#3699—61no—
57#3699D311yescharacteristic, direct product factor
58C2×C4×D9—31no—
59C2×Dic18—31no—
60C22×C3×C9C2312yes—
61C2×C3⋊D9C2311yescharacteristic
62C2×D3×C9—24no—
63C2×D3×C9C2312yes—
64C2×D3×C9C2311yescharacteristic
65C2×C3×D9C2311yescharacteristic
66D3×D9—22no—
67C3×C4×C9C2311yescharacteristic
68C3⋊Dic9C2312yes—
69C3⋊Dic9C2311yescharacteristic
70C9×Dic3C2311yescharacteristic
71C3×Dic9C2312yes—
72C3×Dic9C2311yescharacteristic
73D3×#41—91no—
74C2×#237—91no—
75C22×C3×D3C2×D312yes—
76C2×D32—31no—
77C32×D4C2×D311yescharacteristic
78#638—32no—
79C2×C3⋊Dic3—32no—
80C4×C3⋊D3—31no—
81#634—31no—
82C3×#67—32no—
83C3×#67C2×D312yes—
84C2×C3×Dic3—32no—
85C3×D12C2×D311yescharacteristic
86C3×C4×D3—31no—
87C3×C4×D3C2×D311yescharacteristic
88C3×Dic6—31no—
89#627—32no—
90#626—32no—
91#625—32no—
92#624—31no—
93D3×Dic3—32no—
94D3×Dic3—31no—
95D3×Dic3—32no—
96D3×Dic3—32no—
97D3×Dic3—31no—
98C23×C9—32no—
99C22×D9—31no—
100D4×C9—21no—
101D4×C9—32no—
102D4×C9—31no—
103D4×C9C2×D311yescharacteristic, complemented
104C2×C4×C9—31no—
105#611—32no—
106#611—32no—
107#611—32no—
108#611—62no—
109#611C2×D312yescomplemented
110C2×Dic9—32no—
111C2×Dic9—32no—
112C2×Dic9—31no—
113C2×Dic9—32no—
114C2×Dic9—32no—
115C2×Dic9—62no—
116C2×Dic9C2×D312yescomplemented
117C4×D9—31no—
118C4×D9—31no—
119C4×D9—31no—
120C4×D9—61no—
121C4×D9C2×D311yescharacteristic, complemented
122Dic18—31no—
123Dic18—32no—
124Dic18—61no—
125Dic18C2×D311yescharacteristic, complemented
126C2×C3×C9—22no—
127C2×C3×C9C2411yescharacteristic
128C3⋊D9—21no—
129D3×C9—22no—
130D3×C9#4112yescomplemented
131C3×D9—21no—
132C3×#41—91no—
133C2×C3×D4—31no—
134C2×#67—92no—
135C22×Dic3—92no—
136#239—91no—
137D3×Q8—91no—
138#237—31no—
139#237—91no—
140#237—91no—
141#237—92no—
142#237—92no—
143#237—91no—
144#237—91no—
145#237—92no—
146#237—181no—
147D3×D4—92no—
148D3×D4D911yescharacteristic, complemented
149#235—92no—
150#235—91no—
151C2×C4×D3—91no—
152C2×C4×D3—92no—
153C2×C4×D3—91no—
154C2×Dic6—91no—
155C22×C32C22×D312yes—
156C2×C3⋊D3—31no—
157C2×C3×D3—24no—
158C2×C3×D3—31no—
159C2×C3×D3C22×D312yes—
160C2×C3×D3C22×D311yescharacteristic
161D32—62no—
162C32×C4C22×D311yescharacteristic
163C3⋊Dic3—31no—
164C3⋊Dic3—32no—
165C3×Dic3—31no—
166C3×Dic3—32no—
167C3×Dic3C22×D311yescharacteristic
168C22×C9—22no—
169C22×C9—31no—
170C22×C9—32no—
171C22×C9—64no—
172C22×C9C22×D312yes—
173C2×D9—31no—
174C2×D9—61no—
175C2×D9—62no—
176C2×D9C22×D311yescharacteristic
177C4×C9—21no—
178C4×C9—31no—
179C4×C9C22×D311yescharacteristic
180Dic9—32no—
181Dic9—31no—
182Dic9—62no—
183Dic9—61no—
184Dic9C22×D312yes—
185Dic9C22×D311yescharacteristic
186C2×#41—271noSylow
187C3×C9C2×#4111yescharacteristic, complemented, Sylow
188C23×C3—32no—
189C22×D3—91no—
190C22×D3—91no—
191C22×D3C2×D912yes—
192C3×Q8—91no—
193C3×D4—21no—
194C3×D4—32no—
195C3×D4—31no—
196C3×D4—92no—
197C3×D4C2×D911yescharacteristic, complemented
198C3×D4D3211yescharacteristic
199C2×C3×C4—31no—
200C2×C3×C4—92no—
201C2×C3×C4—91no—
202#67—32no—
203#67—92no—
204#67—92no—
205#67—92no—
206#67—92no—
207#67—92no—
208#67—182no—
209#67C2×D912yescomplemented
210C2×Dic3—32no—
211C2×Dic3—92no—
212C2×Dic3—91no—
213C2×Dic3—92no—
214C2×Dic3—92no—
215C2×Dic3—92no—
216C2×Dic3—92no—
217C2×Dic3—91no—
218C2×Dic3—182no—
219D12—92no—
220D12C2×D911yescharacteristic, complemented
221C4×D3—31no—
222C4×D3—91no—
223C4×D3—91no—
224C4×D3—91no—
225C4×D3—92no—
226C4×D3—92no—
227C4×D3—92no—
228C4×D3—91no—
229C4×D3—91no—
230C4×D3—91no—
231C4×D3—181no—
232C4×D3C2×D911yescharacteristic
233Dic6—31no—
234Dic6—92no—
235Dic6—91no—
236Dic6—91no—
237Dic6—92no—
238Dic6—181no—
239C2×C32—22no—
240C2×C32C23×D311yescharacteristic
241C3⋊D3—61no—
242C3×D3—22no—
243C3×D3—61no—
244C3×D3#23712yes—
245C2×C9—22no—
246C2×C9—21no—
247C2×C9—32no—
248C2×C9—42no—
249C2×C9—62no—
250C2×C9C23×D311yescharacteristic
251D9—21no—
252D9—61no—
253D9—121no—
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—22no—
266C22×C3—31no—
267C22×C3—32no—
268C22×C3—64no—
269C22×C3—91no—
270C22×C3C22×D912yes—
271C22×C3C2×D3212yes—
272C2×D3—24no—
273C2×D3—31no—
274C2×D3—91no—
275C2×D3—91no—
276C2×D3—181no—
277C2×D3—182no—
278C2×D3—182no—
279C2×D3C22×D912yes—
280C2×D3C22×D911yescharacteristic
281C3×C4—21no—
282C3×C4—31no—
283C3×C4—92no—
284C3×C4—91no—
285C3×C4C22×D911yescharacteristic
286C3×C4C2×D3211yescharacteristic
287Dic3—32no—
288Dic3—31no—
289Dic3—92no—
290Dic3—91no—
291Dic3—92no—
292Dic3—91no—
293Dic3—182no—
294Dic3—181no—
295Dic3C22×D911yescharacteristic
296C32C2×#23711yescharacteristic
297C9—21no—
298C9D3×#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×D911yescharacteristic, 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—22no—
323C2×C3—22no—
324C2×C3—21no—
325C2×C3—32no—
326C2×C3—42no—
327C2×C3—62no—
328C2×C3—181no—
329C2×C3C23×D911yescharacteristic
330C2×C3C22×D3211yescharacteristic
331D3—22no—
332D3—61no—
333D3—181no—
334D3—181no—
335D3—361no—
336D3#369912yesdirect product factor
337C22—31no—
338C22—32no—
339C22—64no—
340C22—91no—
341C22—271no—
342C22—542no—
343C22C2×D3×D912yes—
344C4—31no—
345C4—91no—
346C4—92no—
347C4—271no—
348C4—272no—
349C4C2×D3×D911yescharacteristic
350C3—21no—
351C3C2×#369911yescharacteristic, complemented
352C3D3×#23711yescharacteristic
353C2—22no—
354C2—32no—
355C2—62no—
356C2—181no—
357C2—541no—
358C2C22×D3×D911yescharacteristic
subgroupG/H
centerC2C22×D3×D9
commutator, cosocleC2×C3×C9C24
FrattiniC2×C3C22×D32
FittingC3×D4×C9C22
socleC2×C32C23×D3
hypercenterD4D3×D9
hypocenterC3×C9C2×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #88742C2semidirect
2. D3×D4×C9C2semidirect
3. C3×#3699C2semidirect
4. D3×#611C2semidirect
5. #88663C2semidirect
6. #88662C2semidirect
7. C2×D3×Dic9C2semidirect
8. C4×D3×D9C2semidirect
9. #88639C2semidirect
10. #88638C2semidirect
11. D3×Dic18C2semidirect
16. C3×D4×C9C22semidirect
17. #6233C22semidirect
18. C2×C3⋊Dic9C22semidirect
19. C4×C3⋊D9C22semidirect
20. #6226C22semidirect
21. C9×#67C22semidirect
22. C3×#611C22semidirect
23. C2×C3×Dic9C22semidirect
24. C9×D12C22semidirect
26. C3×C4×D9C22semidirect
27. C3×Dic18C22semidirect
28. #6195C22semidirect
29. #6194C22semidirect
32. D3×Dic9C22semidirect
33. D3×Dic9C22semidirect
34. (C3⋊D9)⋊C4C22semidirect
35. Dic3×D9C22semidirect
36. #6189C22semidirect
57. #3699D3direct (N × H)
103. D4×C9C2×D3semidirect
109. #611C2×D3semidirect
116. C2×Dic9C2×D3semidirect
121. C4×D9C2×D3semidirect
125. Dic18C2×D3semidirect
130. D3×C9#41semidirect
148. D3×D4D9semidirect
187. C3×C9C2×#41semidirect
197. C3×D4C2×D9semidirect
209. #67C2×D9semidirect
220. D12C2×D9semidirect
298. C9D3×#41semidirect
310. D4D3×D9semidirect
336. D3#3699direct (N × H)
351. C3C2×#3699semidirect

Maximal subgroups

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

subgroupindex
#887422
D3×D4×C92
C3×#36992
D3×#6112
#886632
#886622
C2×D3×Dic92
C4×D3×D92
#886392
#886382
D3×Dic182
D3×#2373
C2×#36993