Finite Group Databasebeta

← C3⋊D3×#473 #11867952

Subgroups — C3⋊D3×#473 #11867952

Order 1152.

1344 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#137C212yesmaximal
2C2×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
3C3⋊D3×#131C211yesmaximal, characteristic
4C32×#473C211yesmaximal, characteristic, complemented
5#10592903C212yesmaximal, complemented
6#10592891C211yesmaximal, characteristic, complemented
7#10592842C211yesmaximal, characteristic, complemented
8#10592595C211yesmaximal, characteristic, complemented
9C3⋊D3×#108C211yesmaximal, characteristic, complemented
10#10592454C212yesmaximal, complemented
11C3⋊D3×#101C212yesmaximal, complemented
12D3×#473—34nomaximal
13#41×C3⋊D3C2211yescharacteristic
14C2×Q8×C3⋊D3C2212yes—
15C32×#137C2212yes—
16C2×C32×Q16C2211yescharacteristic, complemented
17C32×#131C2211yescharacteristic
18#64160C2212yes—
19#64157C2211yescharacteristic
20C2×#3756C2212yescomplemented
21#64151C2212yes—
22#64127—22no—
23Q16×C3⋊D3—22no—
24Q16×C3⋊D3—21no—
25Q16×C3⋊D3—21no—
26Q16×C3⋊D3—21no—
27Q16×C3⋊D3—21no—
28#64124—22no—
29SD16×C3⋊D3—22no—
30#64118C2212yes—
31#64116—21no—
32#64116C2211yescharacteristic
33M16×C3⋊D3—21no—
34M16×C3⋊D3C2212yes—
35M16×C3⋊D3C2211yescharacteristic
36C2×#3746C2211yescharacteristic, complemented
37#64110—21no—
38#64110C2211yescharacteristic
39C2×C8×C3⋊D3—21no—
40C2×C8×C3⋊D3C2211yescharacteristic
41C32×#108C2211yescharacteristic, complemented
42C32×#101C2212yescomplemented
43#63663C2212yescomplemented
44#63651C2212yescomplemented
45#63651C2212yescomplemented
46#63649C2212yescomplemented
47#63646C2211yescharacteristic, complemented
48D3×#137—38no—
49C2×D3×Q16—34no—
50D3×#131—34no—
51C3×#473D314yescomplemented
52#5204—38no—
53#5192—34no—
54#5143—34no—
55#4896—34no—
56D3×#108—34no—
57#4755—38no—
58D3×#101—38no—
59C32×#41C2311yescharacteristic
60C2×C32×Q8C2312yes—
61#3832D411yescharacteristic
62Q8×C3⋊D3—22no—
63Q8×C3⋊D3—22no—
64Q8×C3⋊D3—22no—
65Q8×C3⋊D3—22no—
66Q8×C3⋊D3D411yescharacteristic
67#3830—21no—
68#3830D411yescharacteristic
69D4×C3⋊D3—21no—
70D4×C3⋊D3D411yescharacteristic
71#3828—21no—
72#3828C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×#634—22no—
77C2×#634C2312yes—
78C32×Q16—22no—
79C32×Q16—21no—
80C32×Q16—21no—
81C32×SD16—22no—
82C32×M16—21no—
83C32×M16C2311yescharacteristic
84C32×M16C2312yes—
85C2×C32×C8—21no—
86C2×C32×C8C2311yescharacteristic
87#3756—22no—
88#3756—22no—
89#3756—22no—
90#3756—22no—
91#3755—22no—
92#3754—22no—
93#3748—21no—
94#3748C2311yescharacteristic
95#3748C2312yes—
96C2×C3⋊(C3⋊C8)—21no—
97C2×C3⋊(C3⋊C8)C2311yescharacteristic
98#3746—22no—
99#3746—21no—
100#3746—21no—
101#3744—22no—
102#3743—21no—
103#3743—22no—
104#3743—21no—
105#3743—21no—
106C8×C3⋊D3—21no—
107C8×C3⋊D3—22no—
108C8×C3⋊D3—21no—
109C8×C3⋊D3—21no—
110C8×C3⋊D3D411yescharacteristic
111C8×C3⋊D3D411yescharacteristic
112C8×C3⋊D3D411yescharacteristic
113C8×C3⋊D3D411yescharacteristic
114C2×#473—91noSylow
115D3×#41—34no—
116C2×D3×Q8—38no—
117C3×#137C2×D318yes—
118C2×C3×Q16C2×D314yescomplemented
119C3×#131C2×D314yes—
120#951—38no—
121#948—34no—
122C2×#216—38no—
123#942—38no—
124#918—68no—
125D3×Q16—64no—
126D3×Q16—64no—
127D3×Q16—64no—
128D3×Q16—64no—
129D3×Q16—68no—
130#915—68no—
131D3×SD16—68no—
132#909—38no—
133#907—34no—
134#907—64no—
135D3×M16—38no—
136D3×M16—34no—
137D3×M16—64no—
138C2×Dic12—34no—
139#901—34no—
140#901—64no—
141C2×D3×C8—34no—
142C2×D3×C8—64no—
143C3×#108C2×D314yescomplemented
144C3×#101C2×D318yescomplemented
145#836—38no—
146#824—38no—
147#824—38no—
148#822—38no—
149#819—34no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3#4111yescharacteristic
152C32×Q8—22no—
153C32×Q8—22no—
154C32×Q8C2×D411yescharacteristic
155C32×D4—21no—
156C32×D4C2×D411yescharacteristic
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160#638—21no—
161#638—21no—
162#638—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3#4111yescharacteristic
166C4⋊(C3⋊D3)—21no—
167C4⋊(C3⋊D3)C2×D411yescharacteristic
168C4×C3⋊D3—21no—
169C4×C3⋊D3—21no—
170C4×C3⋊D3—21no—
171C4×C3⋊D3—42no—
172C4×C3⋊D3—42no—
173C4×C3⋊D3C2×D411yescharacteristic
174C4×C3⋊D3C2×D411yescharacteristic
175C4×C3⋊D3C2×D411yescharacteristic
176C4×C3⋊D3C2×D411yescharacteristic
177#634—21no—
178#634—22no—
179#634—22no—
180#634—42no—
181#634—42no—
182#634C2×D411yescharacteristic
183C32×C8—21no—
184C32×C8—22no—
185C32×C8C2×D411yescharacteristic
186C32×C8C2×D411yescharacteristic
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—22no—
189C3⋊(C3⋊C8)C2×D411yescharacteristic
190C3⋊(C3⋊C8)C2×D411yescharacteristic
191C2×#137—92no—
192C22×Q16—91no—
193C2×#131—91no—
194#473—92no—
195#473—91no—
196#473—91no—
197#473—91no—
198#473—92no—
199#473C3⋊D311yescharacteristic, direct product factor
200C2×#108—91no—
201C2×#101—92no—
202C3×#41C22×D314yes—
203C2×C3×Q8C22×D318yes—
204#239—34no—
205D3×Q8—34no—
206D3×Q8—68no—
207D3×Q8—68no—
208D3×Q8—68no—
209D3×Q8—68no—
210#237—34no—
211#237—64no—
212D3×D4—34no—
213D3×D4—64no—
214#235—34no—
215#235—64no—
216C2×C4×D3—34no—
217C2×C4×D3—64no—
218C2×C4×D3—68no—
219C2×Dic6—38no—
220C2×Dic6—68no—
221C3×Q16—28no—
222C3×Q16—24no—
223C3×Q16—24no—
224C3×SD16—28no—
225C3×M16—24no—
226C3×M16C22×D318yes—
227C3×M16C22×D314yes—
228C2×C3×C8—24no—
229C2×C3×C8C22×D314yes—
230#216—68no—
231#216—68no—
232#216—68no—
233#216—68no—
234#215—68no—
235#214—68no—
236#208—38no—
237#208—34no—
238#208—64no—
239C2×C3⋊C8—34no—
240C2×C3⋊C8—64no—
241Dic12—68no—
242Dic12—64no—
243Dic12—64no—
244#204—68no—
245ΓL(1,𝔽25)—64no—
246ΓL(1,𝔽25)—64no—
247ΓL(1,𝔽25)—68no—
248ΓL(1,𝔽25)—64no—
249D3×C8—34no—
250D3×C8—34no—
251D3×C8—34no—
252D3×C8—34no—
253D3×C8—64no—
254D3×C8—64no—
255D3×C8—68no—
256D3×C8—64no—
257C22×C32—21no—
258C22×C32C2×#4111yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—21no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3#12111yescharacteristic
263C2×C3⋊D3#12111yescharacteristic
264C32×C4—21no—
265C32×C4—42no—
266C32×C4C22×D411yescharacteristic
267C32×C4C22×D411yescharacteristic
268C3⋊Dic3—21no—
269C3⋊Dic3—42no—
270C3⋊Dic3#12111yescharacteristic
271C3⋊Dic3#12111yescharacteristic
272C2×#41—91no—
273C22×Q8—92no—
274#137—92no—
275#137—92no—
276#137—92no—
277#137—182no—
278#137—182no—
279#137C2×C3⋊D312yes—
280C2×Q16—92no—
281C2×Q16—91no—
282C2×Q16—181no—
283C2×Q16—181no—
284C2×Q16—181no—
285C2×Q16—181no—
286C2×Q16—182no—
287C2×Q16C2×C3⋊D311yescharacteristic, complemented
288C2×SD16—182no—
289#131—91no—
290#131—91no—
291#131—91no—
292#131—181no—
293#131—181no—
294#131C2×C3⋊D311yescharacteristic
295C2×M16—91no—
296C2×M16—92no—
297C2×M16—181no—
298C22×C8—91no—
299C22×C8—181no—
300#108—92no—
301#108—91no—
302#108C2×C3⋊D311yescharacteristic, complemented
303#101—92no—
304#101—92no—
305#101—92no—
306#101C2×C3⋊D312yescomplemented
307C22×D3—34no—
308C22×D3—64no—
309C3×Q8—28no—
310C3×Q8—28no—
311C3×Q8D3×D414yes—
312C3×D4—24no—
313C3×D4D3×D414yes—
314C2×C3×C4—24no—
315C2×C3×C4—28no—
316C2×C3×C4C23×D314yes—
317#67—64no—
318#67—64no—
319#67—64no—
320C2×Dic3—34no—
321C2×Dic3—64no—
322C2×Dic3—68no—
323D12—34no—
324D12—64no—
325C4×D3—34no—
326C4×D3—34no—
327C4×D3—34no—
328C4×D3—34no—
329C4×D3—64no—
330C4×D3—64no—
331C4×D3—64no—
332C4×D3—128no—
333C4×D3—128no—
334Dic6—34no—
335Dic6—64no—
336Dic6—68no—
337Dic6—68no—
338Dic6—128no—
339Dic6—128no—
340C3×C8—24no—
341C3×C8—28no—
342C3×C8D3×D414yes—
343C3×C8D3×D414yes—
344C3⋊C8—34no—
345C3⋊C8—34no—
346C3⋊C8—64no—
347C3⋊C8—68no—
348C2×C32—21no—
349C2×C32—41no—
350C2×C32C2×#12111yescharacteristic
351C3⋊D3—21no—
352C3⋊D3—41no—
353C3⋊D3#47312yesdirect product factor
354#41—91no—
355#41—91no—
356#41—91no—
357#41—181no—
358#41—181no—
359#41C22×C3⋊D311yescharacteristic
360C2×Q8—91no—
361C2×Q8—92no—
362C2×Q8—182no—
363C2×Q8—182no—
364C2×Q8—182no—
365C2×Q8—182no—
366C2×Q8—182no—
367C2×Q8C22×C3⋊D312yes—
368C2×D4—91no—
369C2×D4—181no—
370C22×C4—91no—
371C22×C4—181no—
372C22×C4—182no—
373Q16—22no—
374Q16—21no—
375Q16—21no—
376Q16—182no—
377Q16—182no—
378Q16—182no—
379Q16—182no—
380Q16—182no—
381Q16—181no—
382Q16—181no—
383SD16—22no—
384SD16—182no—
385SD16—182no—
386SD16—182no—
387M16—21no—
388M16—91no—
389M16—92no—
390M16—181no—
391M16—181no—
392M16—182no—
393M16—181no—
394M16—181no—
395M16C22×C3⋊D311yescharacteristic
396M16C22×C3⋊D312yes—
397C2×C8—21no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—91no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—181no—
404C2×C8—181no—
405C2×C8—182no—
406C2×C8—181no—
407C2×C8—181no—
408C2×C8C22×C3⋊D311yescharacteristic
409C22×C3—24no—
410C22×C3D3×#4114yes—
411C2×D3—34no—
412C2×D3—34no—
413C2×D3—68no—
414C2×D3—64no—
415C2×D3—128no—
416C3×C4—24no—
417C3×C4—48no—
418C3×C4C2×D3×D414yes—
419C3×C4C2×D3×D414yes—
420Dic3—34no—
421Dic3—34no—
422Dic3—64no—
423Dic3—128no—
424C32C2×#47311yescharacteristic, complemented, Sylow
425C23—91no—
426C23—181no—
427Q8—22no—
428Q8—22no—
429Q8—91no—
430Q8—181no—
431Q8—182no—
432Q8—182no—
433Q8—362no—
434Q8—362no—
435Q8D4×C3⋊D311yescharacteristic
436D4—21no—
437D4—91no—
438D4—181no—
439D4—181no—
440D4—181no—
441D4—181no—
442D4D4×C3⋊D311yescharacteristic
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—182no—
455C2×C4—362no—
456C2×C4—362no—
457C2×C4C23×C3⋊D311yescharacteristic
458C8—21no—
459C8—22no—
460C8—91no—
461C8—91no—
462C8—181no—
463C8—182no—
464C8D4×C3⋊D311yescharacteristic
465C8D4×C3⋊D311yescharacteristic
466C2×C3—24no—
467C2×C3—44no—
468C2×C3D3×#12114yes—
469D3—38no—
470D3—64no—
471D3—124no—
472C22—21no—
473C22—91no—
474C22—91no—
475C22—182no—
476C22—181no—
477C22—362no—
478C22#41×C3⋊D311yescharacteristic
479C4—21no—
480C4—42no—
481C4—91no—
482C4—91no—
483C4—181no—
484C4—362no—
485C4C2×D4×C3⋊D311yescharacteristic
486C4C2×D4×C3⋊D311yescharacteristic
487C3D3×#47314yescomplemented
488C2—21no—
489C2—41no—
490C2—92no—
491C2—181no—
492C2—361no—
493C2C3⋊D3×#12111yescharacteristic
subgroupG/H
centerC2C3⋊D3×#121
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#473C2
socleC2×C32C2×#121
prime radical#41×C3⋊D3C22
hypercenter#473C3⋊D3
hypocenterC32C2×#473
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×Q16×C3⋊D3C2semidirect
4. C32×#473C2semidirect
5. #10592903C2semidirect
6. #10592891C2semidirect
7. #10592842C2semidirect
8. #10592595C2semidirect
9. C3⋊D3×#108C2semidirect
10. #10592454C2semidirect
11. C3⋊D3×#101C2semidirect
16. C2×C32×Q16C22semidirect
20. C2×#3756C22semidirect
36. C2×#3746C22semidirect
41. C32×#108C22semidirect
42. C32×#101C22semidirect
43. #63663C22semidirect
44. #63651C22semidirect
45. #63651C22semidirect
46. #63649C22semidirect
47. #63646C22semidirect
51. C3×#473D3semidirect
118. C2×C3×Q16C2×D3semidirect
143. C3×#108C2×D3semidirect
144. C3×#101C2×D3semidirect
199. #473C3⋊D3direct (N × H)
287. C2×Q16C2×C3⋊D3semidirect
302. #108C2×C3⋊D3semidirect
306. #101C2×C3⋊D3semidirect
353. C3⋊D3#473direct (N × H)
424. C32C2×#473semidirect
487. C3D3×#473semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1372
C2×Q16×C3⋊D32
C3⋊D3×#1312
C32×#4732
#105929032
#105928912
#105928422
#105925952
C3⋊D3×#1082
#105924542
C3⋊D3×#1012
D3×#4733