Finite Group Databasebeta

← D3×#951 #10595463

Subgroups — D3×#951 #10595463

Order 576.

546 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#41C211yesmaximal, characteristic
2C2×D3×Dic6C211yesmaximal, characteristic, complemented
3#64160C211yesmaximal, characteristic, complemented
4C3×#951C211yesmaximal, characteristic, complemented
5#63943C212yesmaximal, complemented
6D3×#216C212yesmaximal, complemented
7#63929C212yesmaximal, complemented
8D3×#214C212yesmaximal, complemented
9#63831C211yesmaximal, characteristic, complemented
10#63827C211yesmaximal, characteristic, complemented
11D3×#208C211yesmaximal, characteristic, complemented
12C2×#951—31nomaximal
13D3×#137—31nomaximal
14C32×#41C2211yescharacteristic
15C2×#634C2211yescharacteristic, complemented
16C3×#239C2211yescharacteristic
17C3×D3×Q8C2211yescharacteristic
18C3×#237—21no—
19C3×#237C2211yescharacteristic
20C3×D3×D4—21no—
21C3×D3×D4C2211yescharacteristic
22C3×#235—21no—
23C3×#235C2211yescharacteristic
24C2×C3×C4×D3—21no—
25C2×C3×C4×D3C2211yescharacteristic
26C2×C3×Dic6C2211yescharacteristic, complemented
27C2×#627—21no—
28C2×D3×Dic3—21no—
29D3×Dic6—21no—
30D3×Dic6—21no—
31D3×Dic6C2212yes—
32D3×Dic6C2212yescomplemented
33#3756C2212yescomplemented
34#3754C2212yescomplemented
35#3748C2211yescharacteristic, complemented
36C3×#216C2212yescomplemented
37C3×#214C2212yescomplemented
38C3×#208C2211yescharacteristic, complemented
39#3719C2212yescomplemented
40#3718C2212yescomplemented
41#3716C2212yescomplemented
42#3715C2212yescomplemented
43#3711C2212yescomplemented
44D3×C3⋊C8C2212yes—
45C2×C3×#41—31no—
46D3×#41D311yescharacteristic
47C2×D3×Q8—31no—
48C22×Dic6—31no—
49C3×#137—31no—
50#951—31no—
51#951—31no—
52#951—31no—
53#951—32no—
54#951—32no—
55#951—31no—
56#951—61no—
57#951D311yescharacteristic, direct product factor
58C2×#216—32no—
59#942—31no—
60C2×#214—32no—
61C2×#208—31no—
62#918—32no—
63D3×Q16—32no—
64#915—32no—
65D3×SD16—32no—
66#909—31no—
67D3×M16—31no—
68C22×C3×D3—21no—
69C22×C3×D3D411yescharacteristic
70C32×Q8C2311yescharacteristic
71C32×D4—21no—
72C32×D4C2311yescharacteristic
73C2×C32×C4—21no—
74C2×C32×C4C2311yescharacteristic
75C2×C3⋊Dic3—21no—
76#634—21no—
77#634C2312yes—
78C3×#67—21no—
79C3×#67—21no—
80C3×#67—21no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3D411yescharacteristic
84C3×D12—21no—
85C3×D12C2311yescharacteristic
86C3×C4×D3—21no—
87C3×C4×D3—21no—
88C3×C4×D3—21no—
89C3×C4×D3D411yescharacteristic
90C3×C4×D3D411yescharacteristic
91C3×C4×D3C2311yescharacteristic
92C3×C4×D3C2311yescharacteristic
93C3×Dic6—21no—
94C3×Dic6—21no—
95C3×Dic6C2312yes—
96C3×Dic6C2311yescharacteristic
97#627—22no—
98#627—22no—
99D3×Dic3—22no—
100D3×Dic3—22no—
101C3⋊(C3⋊C8)C2312yes—
102C3×C3⋊C8C2312yes—
103C2×#137—91noSylow
104C3×#41—21no—
105C3×#41—31no—
106C3×#41—31no—
107C3×#41—31no—
108C3×#41—61no—
109C3×#41—61no—
110C3×#41C2×D311yescharacteristic
111C3×#41C2×D311yescharacteristic
112C2×C3×Q8—31no—
113C2×C3×Q8—31no—
114C2×C3×D4—31no—
115C2×C3×D4—61no—
116C22×C3×C4—31no—
117C22×C3×C4—61no—
118C22×Dic3—61no—
119#239C2×D311yescharacteristic
120D3×Q8—32no—
121D3×Q8—32no—
122D3×Q8—61no—
123D3×Q8—61no—
124D3×Q8C2×D311yescharacteristic
125#237—21no—
126#237C2×D311yescharacteristic
127D3×D4—21no—
128D3×D4C2×D311yescharacteristic
129#235—21no—
130#235C2×D311yescharacteristic
131C2×C4×D3—21no—
132C2×C4×D3—61no—
133C2×C4×D3C2×D311yescharacteristic
134C2×Dic6—31no—
135C2×Dic6—31no—
136C2×Dic6—32no—
137C2×Dic6—32no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—61no—
141C2×Dic6—61no—
142C2×Dic6—61no—
143C2×Dic6C2×D311yescharacteristic, complemented
144C3×Q16—32no—
145C3×SD16—32no—
146C3×M16—31no—
147#216—32no—
148#216—32no—
149#216—32no—
150#216—32no—
151#216—32no—
152#216—62no—
153#216C2×D312yescomplemented
154#215—32no—
155#214—32no—
156#214—32no—
157#214—32no—
158#214—32no—
159#214—62no—
160#214C2×D312yescomplemented
161#208—31no—
162#208—31no—
163#208—32no—
164#208—61no—
165#208C2×D311yescharacteristic, complemented
166C2×C3⋊C8—32no—
167Dic12—32no—
168#204—32no—
169ΓL(1,𝔽25)—32no—
170D3×C8—32no—
171C22×C32—21no—
172C22×C32C2×D411yescharacteristic
173C2×C3×D3—22no—
174C2×C3×D3—21no—
175C2×C3×D3—42no—
176C2×C3×D3C2×D411yescharacteristic
177C2×C3×D3C2×D411yescharacteristic
178C32×C4—21no—
179C32×C4C2×D411yescharacteristic
180C32×C4C2411yescharacteristic
181C3⋊Dic3—22no—
182C3×Dic3—22no—
183C3×Dic3—21no—
184C3×Dic3C2×D411yescharacteristic
185C3×Dic3C2×D411yescharacteristic
186C2×#41—31no—
187C22×Q8—91no—
188#137—31no—
189#137—91no—
190#137—92no—
191#137—92no—
192#137—91no—
193#137—91no—
194C2×Q16—92no—
195C2×SD16—92no—
196C2×M16—91no—
197C23×C3—31no—
198C23×C3—61no—
199C22×D3—21no—
200C22×D3#6711yescharacteristic
201C3×Q8—21no—
202C3×Q8—32no—
203C3×Q8—31no—
204C3×Q8—61no—
205C3×Q8—61no—
206C3×Q8C22×D311yescharacteristic
207C3×Q8C22×D311yescharacteristic
208C3×D4—21no—
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—31no—
212C3×D4—41no—
213C3×D4—61no—
214C3×D4—61no—
215C3×D4—61no—
216C3×D4—61no—
217C3×D4C22×D311yescharacteristic
218C3×D4C22×D311yescharacteristic
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4C22×D311yescharacteristic
234C2×C3×C4C22×D311yescharacteristic
235#67—21no—
236#67—21no—
237#67—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—121no—
245C2×Dic3#6711yescharacteristic
246D12—21no—
247D12C22×D311yescharacteristic
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—21no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3#6711yescharacteristic
254C4×D3#6711yescharacteristic
255C4×D3C22×D311yescharacteristic
256C4×D3C22×D311yescharacteristic
257Dic6—21no—
258Dic6—21no—
259Dic6—32no—
260Dic6—32no—
261Dic6—62no—
262Dic6—62no—
263Dic6—62no—
264Dic6—61no—
265Dic6—61no—
266Dic6—62no—
267Dic6—62no—
268Dic6—121no—
269Dic6C22×D311yescharacteristic
270Dic6C22×D312yes—
271C3×C8—32no—
272C3⋊C8—32no—
273C3⋊C8—32no—
274C3⋊C8—62no—
275C3⋊C8C22×D312yes—
276C2×C32—21no—
277C2×C32—41no—
278C2×C32C22×D411yescharacteristic
279C3×D3—21no—
280C3×D3—41no—
281C3×D3#13712yescomplemented
282#41—31no—
283#41—31no—
284#41—31no—
285#41—61no—
286#41—61no—
287#41D3211yescharacteristic
288C2×Q8—31no—
289C2×Q8—31no—
290C2×Q8—92no—
291C2×Q8—92no—
292C2×Q8—91no—
293C2×Q8—181no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×D4—31no—
297C2×D4—61no—
298C22×C4—31no—
299C22×C4—61no—
300C22×C4—181no—
301Q16—32no—
302Q16—92no—
303Q16—92no—
304Q16—92no—
305SD16—32no—
306SD16—92no—
307SD16—92no—
308SD16—92no—
309M16—31no—
310M16—92no—
311M16—91no—
312C2×C8—92no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—31no—
317C22×C3—31no—
318C22×C3—41no—
319C22×C3—62no—
320C22×C3—61no—
321C22×C3—122no—
322C22×C3D3×D411yescharacteristic
323C22×C3C2×#6711yescharacteristic
324C2×D3—22no—
325C2×D3—21no—
326C2×D3—42no—
327C2×D3C2×#6711yescharacteristic
328C2×D3C2×#6711yescharacteristic
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—31no—
334C3×C4—31no—
335C3×C4—41no—
336C3×C4—61no—
337C3×C4—62no—
338C3×C4D3×D411yescharacteristic
339C3×C4C2×#6711yescharacteristic
340C3×C4C23×D311yescharacteristic
341C3×C4C23×D311yescharacteristic
342Dic3—22no—
343Dic3—21no—
344Dic3—62no—
345Dic3—62no—
346Dic3—122no—
347Dic3C2×#6711yescharacteristic
348Dic3C2×#6711yescharacteristic
349C32C2×#13711yescharacteristic, complemented, Sylow
350C23—31no—
351C23—61no—
352Q8—32no—
353Q8—31no—
354Q8—61no—
355Q8—61no—
356Q8—92no—
357Q8—182no—
358Q8—182no—
359Q8—181no—
360Q8C2×D3211yescharacteristic
361D4—21no—
362D4—31no—
363D4—61no—
364D4—61no—
365D4—61no—
366D4—61no—
367D4C2×D3211yescharacteristic
368C2×C4—21no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—31no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—181no—
382C2×C4C2×D3211yescharacteristic
383C8—32no—
384C8—92no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—32no—
389C2×C3—41no—
390C2×C3—41no—
391C2×C3—41no—
392C2×C3—61no—
393C2×C3—81no—
394C2×C3—121no—
395C2×C3C2×D3×D411yescharacteristic
396C2×C3C22×#6711yescharacteristic
397D3—21no—
398D3—41no—
399D3#95112yesdirect product factor
400C22—21no—
401C22—31no—
402C22—31no—
403C22—62no—
404C22—61no—
405C22—122no—
406C22D3×#6711yescharacteristic
407C4—21no—
408C4—31no—
409C4—31no—
410C4—61no—
411C4—62no—
412C4—182no—
413C4D3×#6711yescharacteristic
414C4C22×D3211yescharacteristic
415C3—21no—
416C3D3×#13711yescharacteristic, complemented
417C3C2×#95111yescharacteristic, complemented
418C2—21no—
419C2—32no—
420C2—41no—
421C2—61no—
422C2—121no—
423C2C2×D3×#6711yescharacteristic
subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×#41C22
socleC2×C32C22×D4
prime radicalC3×D3×#41C2
hypercenter#41D32
hypocenterC32C2×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic6C2semidirect
3. #64160C2semidirect
4. C3×#951C2semidirect
5. #63943C2semidirect
6. D3×#216C2semidirect
7. #63929C2semidirect
8. D3×#214C2semidirect
9. #63831C2semidirect
10. #63827C2semidirect
11. D3×#208C2semidirect
15. C2×#634C22semidirect
26. C2×C3×Dic6C22semidirect
32. D3×Dic6C22semidirect
33. #3756C22semidirect
34. #3754C22semidirect
35. #3748C22semidirect
36. C3×#216C22semidirect
37. C3×#214C22semidirect
38. C3×#208C22semidirect
39. #3719C22semidirect
40. #3718C22semidirect
41. #3716C22semidirect
42. #3715C22semidirect
43. #3711C22semidirect
57. #951D3direct (N × H)
143. C2×Dic6C2×D3semidirect
153. #216C2×D3semidirect
160. #214C2×D3semidirect
165. #208C2×D3semidirect
281. C3×D3#137semidirect
349. C32C2×#137semidirect
399. D3#951direct (N × H)
416. C3D3×#137semidirect
417. C3C2×#951semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#412
C2×D3×Dic62
#641602
C3×#9512
#639432
D3×#2162
#639292
D3×#2142
#638312
#638272
D3×#2082
C2×#9513
D3×#1373