Finite Group Databasebeta

← C3⋊D3×#470 #11866990

Subgroups — C3⋊D3×#470 #11866990

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic
3C3⋊D3×C22⋊Q8C212yesmaximal
4C32×#470C211yesmaximal, characteristic, complemented
5#10592888C211yesmaximal, characteristic, complemented
6#10592836C211yesmaximal, characteristic, complemented
7#10592751C212yesmaximal, complemented
8#10592566C211yesmaximal, characteristic, complemented
9C3⋊D3×#106C211yesmaximal, characteristic, complemented
10#10592515C212yesmaximal, complemented
11C3⋊D3×#103C212yesmaximal, complemented
12D3×#470—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×Q16C2211yescharacteristic, complemented
16C2×C32×M16C2211yescharacteristic
17C32×C22⋊Q8C2212yes—
18#64155C2212yes—
19C2×#3756C2212yescomplemented
20#64133C2212yes—
21C2×#3748C2211yescharacteristic
22Q16×C3⋊D3—24no—
23M16×C3⋊D3—24no—
24C2×#3746C2211yescharacteristic, complemented
25C2×#3743C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic
28C2×C8×C3⋊D3C2211yescharacteristic
29#64106C2212yes—
30#64105—22no—
31C4⋊C4×C3⋊D3—22no—
32C4⋊C4×C3⋊D3C2212yes—
33C22⋊C4×C3⋊D3—22no—
34#64087—22no—
35C32×#106C2211yescharacteristic, complemented
36C32×#103C2212yescomplemented
37#63662C2212yescomplemented
38#63644C2211yescharacteristic, complemented
39#63643C2212yescomplemented
40#63637C2212yescomplemented
41#63635C2212yescomplemented
42C2×D3×Q16—34no—
43C2×D3×M16—34no—
44D3×C22⋊Q8—38no—
45C3×#470D314yescomplemented
46#5189—34no—
47#5137—34no—
48#5052—38no—
49#4867—34no—
50D3×#106—34no—
51#4816—38no—
52D3×#103—38no—
53C23×C3⋊D3D411yescharacteristic
54C2×C32×Q8C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57Q8×C3⋊D3—24no—
58Q8×C3⋊D3—24no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×#634—22no—
68C2×#634C2312yes—
69C32×Q16—22no—
70C32×M16—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76#3757—22no—
77#3756—24no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83#3750—22no—
84#3750—22no—
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3746—22no—
89#3743—22no—
90#3743—22no—
91C8×C3⋊D3—22no—
92C8×C3⋊D3D414yes—
93C2×#470—91noSylow
94C2×D3×Q8—38no—
95C22×C4×D3—34no—
96C2×C3×Q16C2×D314yescomplemented
97C2×C3×M16C2×D314yes—
98C3×C22⋊Q8C2×D318yes—
99#946—38no—
100C2×#216—38no—
101#924—38no—
102C2×#208—34no—
103D3×Q16—616no—
104D3×M16—616no—
105C2×Dic12—34no—
106C2×ΓL(1,𝔽25)—34no—
107C2×ΓL(1,𝔽25)—34no—
108C2×D3×C8—34no—
109C2×D3×C8—34no—
110#897—38no—
111#896—68no—
112D3×C4⋊C4—38no—
113D3×C4⋊C4—68no—
114D3×C22⋊C4—68no—
115#878—68no—
116C3×#106C2×D314yescomplemented
117C3×#103C2×D318yescomplemented
118#835—38no—
119#817—34no—
120#816—38no—
121#810—38no—
122#808—38no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—24no—
126C22×C3⋊D3C2×D411yescharacteristic
127C22×C3⋊D3C2×D411yescharacteristic
128C32×Q8—22no—
129C32×Q8—22no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C4×C3⋊D3—22no—
142C4×C3⋊D3—21no—
143C4×C3⋊D3—21no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—44no—
146C4×C3⋊D3—44no—
147C4×C3⋊D3C2×D412yes—
148C4×C3⋊D3#4112yes—
149#634—22no—
150#634—22no—
151#634—44no—
152C32×C8—21no—
153C32×C8C2×D412yes—
154C3⋊(C3⋊C8)—21no—
155C3⋊(C3⋊C8)C2×D412yes—
156C22×Q16—91no—
157C22×M16—91no—
158C2×C22⋊Q8—92no—
159#470—91no—
160#470—91no—
161#470—92no—
162#470—91no—
163#470—92no—
164#470C3⋊D311yescharacteristic, direct product factor
165C2×#106—91no—
166C2×#103—92no—
167C23×D3—34no—
168C2×C3×Q8C22×D318yes—
169C22×C3×C4C22×D314yes—
170C22×Dic3—34no—
171D3×Q8—616no—
172D3×Q8—616no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—34no—
176C2×C4×D3—34no—
177C2×C4×D3—68no—
178C2×C4×D3—68no—
179C2×C4×D3—68no—
180C2×C4×D3—68no—
181C2×Dic6—38no—
182C2×Dic6—68no—
183C3×Q16—28no—
184C3×M16—28no—
185C2×C3×C8C22×D314yes—
186C2×C3×C8C22×D314yes—
187C3×C4⋊C4—28no—
188C3×C4⋊C4C22×D318yes—
189C3×C22⋊C4—28no—
190#217—68no—
191#216—616no—
192(C2×D3)⋊C4—68no—
193(C2×D3)⋊C4—68no—
194C4⋊Dic3—38no—
195C4⋊Dic3—68no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198Dic3⋊C4—68no—
199#208—68no—
200C2×C3⋊C8—34no—
201C2×C3⋊C8—34no—
202Dic12—68no—
203ΓL(1,𝔽25)—68no—
204ΓL(1,𝔽25)—68no—
205D3×C8—316no—
206D3×C8—68no—
207C22×C32—21no—
208C22×C32—22no—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—21no—
211C2×C3⋊D3—22no—
212C2×C3⋊D3—44no—
213C2×C3⋊D3#12112yes—
214C2×C3⋊D3#13714yes—
215C32×C4—21no—
216C32×C4—42no—
217C32×C4—42no—
218C32×C4C22×D411yescharacteristic
219C32×C4C2×#4111yescharacteristic
220C3⋊Dic3—21no—
221C3⋊Dic3—42no—
222C3⋊Dic3—42no—
223C3⋊Dic3#12112yes—
224C22×Q8—92no—
225C23×C4—91no—
226C2×Q16—92no—
227C2×Q16—91no—
228C2×Q16—184no—
229C2×Q16C2×C3⋊D311yescharacteristic, complemented
230C2×M16—91no—
231C2×M16—91no—
232C2×M16—91no—
233C2×M16—184no—
234C2×M16C2×C3⋊D311yescharacteristic
235C22×C8—91no—
236C22×C8—91no—
237C22⋊Q8—92no—
238C22⋊Q8—92no—
239C22⋊Q8—92no—
240C22⋊Q8—182no—
241C22⋊Q8—182no—
242C22⋊Q8C2×C3⋊D312yes—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—182no—
245C2×C22⋊C4—182no—
246#106—91no—
247#106—92no—
248#106C2×C3⋊D311yescharacteristic, complemented
249#103—92no—
250#103—92no—
251#103—92no—
252#103C2×C3⋊D312yescomplemented
253C23×C3D3×D414yes—
254C22×D3—34no—
255C22×D3—34no—
256C22×D3—68no—
257C22×D3—616no—
258C3×Q8—28no—
259C3×Q8—28no—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—28no—
263C2×C3×C4—28no—
264C2×C3×C4D3×D414yes—
265C2×C3×C4C23×D314yes—
266C2×Dic3—34no—
267C2×Dic3—34no—
268C2×Dic3—68no—
269C2×Dic3—68no—
270C2×Dic3—68no—
271C4×D3—38no—
272C4×D3—38no—
273C4×D3—68no—
274C4×D3—68no—
275C4×D3—64no—
276C4×D3—64no—
277C4×D3—1216no—
278C4×D3—1216no—
279Dic6—68no—
280Dic6—68no—
281Dic6—1216no—
282C3×C8—24no—
283C3×C8D3×D418yes—
284C3⋊C8—38no—
285C3⋊C8—64no—
286C2×C32—41no—
287C2×C32C2×#12111yescharacteristic
288C2×C32C2×#13712yes—
289C3⋊D3—41no—
290C3⋊D3#47014yesdirect product factor
291C24—91no—
292C2×Q8—92no—
293C2×Q8—182no—
294C2×Q8—184no—
295C2×Q8—184no—
296C2×Q8C22×C3⋊D312yes—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—182no—
306C22×C4C22×C3⋊D311yescharacteristic
307Q16—22no—
308Q16—184no—
309Q16—182no—
310M16—22no—
311M16—182no—
312M16—182no—
313M16—182no—
314C2×C8—91no—
315C2×C8—94no—
316C2×C8—91no—
317C2×C8—182no—
318C2×C8C22×C3⋊D311yescharacteristic
319C2×C8C22×C3⋊D311yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—92no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C4⋊C4—182no—
325C4⋊C4—182no—
326C4⋊C4C22×C3⋊D312yes—
327C22⋊C4—22no—
328C22⋊C4—182no—
329C22⋊C4—182no—
330C22⋊C4—182no—
331C22×C3—28no—
332C22×C3—24no—
333C22×C3C2×D3×D414yes—
334C2×D3—316no—
335C2×D3—38no—
336C2×D3—68no—
337C2×D3—64no—
338C2×D3—1216no—
339C3×C4—24no—
340C3×C4—48no—
341C3×C4—48no—
342C3×C4C2×D3×D414yes—
343C3×C4D3×#4114yes—
344Dic3—38no—
345Dic3—64no—
346Dic3—128no—
347Dic3—128no—
348C32C2×#47011yescharacteristic, complemented, Sylow
349C23—91no—
350C23—91no—
351C23—182no—
352C23—184no—
353C23D4×C3⋊D311yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—182no—
357Q8—182no—
358Q8—364no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—91no—
364C2×C4—92no—
365C2×C4—92no—
366C2×C4—91no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—181no—
371C2×C4—181no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—364no—
375C2×C4—364no—
376C2×C4D4×C3⋊D311yescharacteristic
377C2×C4C23×C3⋊D311yescharacteristic
378C8—21no—
379C8—92no—
380C8—181no—
381C8D4×C3⋊D312yes—
382C2×C3—44no—
383C2×C3D3×#12114yes—
384C2×C3D3×#13718yes—
385D3—316no—
386D3—124no—
387C22—22no—
388C22—21no—
389C22—94no—
390C22—92no—
391C22—182no—
392C22—181no—
393C22—364no—
394C22C2×D4×C3⋊D311yescharacteristic
395C4—21no—
396C4—42no—
397C4—42no—
398C4—92no—
399C4—181no—
400C4—362no—
401C4—362no—
402C4C2×D4×C3⋊D311yescharacteristic
403C4#41×C3⋊D311yescharacteristic
404C3D3×#47014yescomplemented
405C2—41no—
406C2—94no—
407C2—361no—
408C2C3⋊D3×#12111yescharacteristic
409C2C3⋊D3×#13712yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenter#470C3⋊D3
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×Q16×C3⋊D3C2semidirect
4. C32×#470C2semidirect
5. #10592888C2semidirect
6. #10592836C2semidirect
7. #10592751C2semidirect
8. #10592566C2semidirect
9. C3⋊D3×#106C2semidirect
10. #10592515C2semidirect
11. C3⋊D3×#103C2semidirect
15. C2×C32×Q16C22semidirect
19. C2×#3756C22semidirect
24. C2×#3746C22semidirect
35. C32×#106C22semidirect
36. C32×#103C22semidirect
37. #63662C22semidirect
38. #63644C22semidirect
39. #63643C22semidirect
40. #63637C22semidirect
41. #63635C22semidirect
45. C3×#470D3semidirect
96. C2×C3×Q16C2×D3semidirect
116. C3×#106C2×D3semidirect
117. C3×#103C2×D3semidirect
164. #470C3⋊D3direct (N × H)
229. C2×Q16C2×C3⋊D3semidirect
248. #106C2×C3⋊D3semidirect
252. #103C2×C3⋊D3semidirect
290. C3⋊D3#470direct (N × H)
348. C32C2×#470semidirect
404. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
C2×M16×C3⋊D32
C3⋊D3×C22⋊Q82
C32×#4702
#105928882
#105928362
#105927512
#105925662
C3⋊D3×#1062
#105925152
C3⋊D3×#1032
D3×#4703