Finite Group Databasebeta

← C3⋊D3×#451 #11863638

Subgroups — C3⋊D3×#451 #11863638

Order 1152.

2220 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×Q16×C3⋊D3C212yesmaximal, complemented
3C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
4C32×#451C211yesmaximal, characteristic, complemented
5#10592927C211yesmaximal, characteristic, complemented
6#10592885C212yesmaximal, complemented
7#10592749C211yesmaximal, characteristic, complemented
8#10592508C212yesmaximal, complemented
9C3⋊D3×#103C212yesmaximal, complemented
10#10592438C211yesmaximal, characteristic, complemented
11C3⋊D3×C22⋊C8C211yesmaximal, characteristic
12D3×#451—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×Q8×C3⋊D3—28no—
15C2×Q8×C3⋊D3—21no—
16C2×Q8×C3⋊D3—21no—
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×Q8×C3⋊D3C2212yes—
19C2×Q8×C3⋊D3C2212yes—
20C22×C4×C3⋊D3—21no—
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634—21no—
23C22×#634C2211yescharacteristic
24C2×C32×Q16C2212yescomplemented
25C32×C22⋊Q8C2211yescharacteristic
26#64155C2211yescharacteristic
27C2×#3756C2212yescomplemented
28C2×#3756C2212yescomplemented
29#64133C2211yescharacteristic
30Q16×C3⋊D3—28no—
31C2×#3746C2212yescomplemented
32C2×C8×C3⋊D3C2212yes—
33#64106C2211yescharacteristic
34#64105—21no—
35C4⋊C4×C3⋊D3—21no—
36C4⋊C4×C3⋊D3C2211yescharacteristic
37C22⋊C4×C3⋊D3—21no—
38#64087—21no—
39C32×#103C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic
41#63662C2212yescomplemented
42#63657C2211yescharacteristic
43#63647C2212yes—
44#63643C2212yescomplemented
45#63637C2212yescomplemented
46C22×D3×Q8—34no—
47C2×D3×Q16—38no—
48D3×C22⋊Q8—34no—
49C3×#451D314yescomplemented
50#5228—34no—
51#5186—38no—
52#5050—34no—
53#4809—38no—
54D3×#103—38no—
55#4739—34no—
56D3×C22⋊C8—34no—
57C23×C3⋊D3D411yescharacteristic
58C2×C32×Q8—24no—
59C2×C32×Q8—21no—
60C2×C32×Q8C2311yescharacteristic
61C2×C32×Q8C2312yes—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C22×C3⋊Dic3D411yescharacteristic
66Q8×C3⋊D3—28no—
67Q8×C3⋊D3—28no—
68Q8×C3⋊D3—24no—
69Q8×C3⋊D3—24no—
70Q8×C3⋊D3—24no—
71Q8×C3⋊D3—24no—
72Q8×C3⋊D3D418yes—
73C2×C4×C3⋊D3—28no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×#634—28no—
84C2×#634—21no—
85C2×#634—22no—
86C2×#634—22no—
87C2×#634—24no—
88C2×#634—21no—
89C2×#634C2311yescharacteristic
90C2×#634C2312yes—
91C32×Q16—24no—
92C2×C32×C8C2312yes—
93C32×C4⋊C4—21no—
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96#3757—21no—
97#3756—24no—
98#3756—24no—
99#3752—21no—
100#3752—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
105#3750—21no—
106C2×C3⋊(C3⋊C8)C2312yes—
107#3746—24no—
108C8×C3⋊D3—24no—
109C2×#451—91noSylow
110C22×C3×Q8C2×D314yes—
111C2×D3×Q8—38no—
112C2×D3×Q8—38no—
113C2×D3×Q8—34no—
114C2×D3×Q8—64no—
115C2×D3×Q8—64no—
116C2×D3×Q8—632no—
117C22×C4×D3—34no—
118C22×C4×D3—64no—
119C22×Dic6—34no—
120C22×Dic6—64no—
121C2×C3×Q16C2×D318yescomplemented
122C3×C22⋊Q8C2×D314yes—
123#946—34no—
124C2×#216—38no—
125C2×#216—38no—
126#924—34no—
127D3×Q16—632no—
128C2×Dic12—38no—
129C2×D3×C8—38no—
130#897—34no—
131#896—64no—
132D3×C4⋊C4—34no—
133D3×C4⋊C4—64no—
134D3×C22⋊C4—64no—
135#878—64no—
136C3×#103C2×D318yescomplemented
137C3×C22⋊C8C2×D314yes—
138#835—38no—
139#830—34no—
140(C2×D3)⋊C8—38no—
141#816—38no—
142#810—38no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3Q1614yescomplemented
147C22×C3⋊D3C2×D411yescharacteristic
148C22×C3⋊D3C2×D411yescharacteristic
149C32×Q8—24no—
150C32×Q8—22no—
151C32×Q8—22no—
152C32×Q8C2×D414yes—
153C2×C32×C4—24no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4×C3⋊D3—28no—
168C4×C3⋊D3—28no—
169C4×C3⋊D3—22no—
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—42no—
173C4×C3⋊D3—42no—
174C4×C3⋊D3C2×D414yes—
175#634—28no—
176#634—24no—
177#634—22no—
178#634—28no—
179#634—22no—
180#634—42no—
181#634C2×D414yes—
182C32×C8—22no—
183C3⋊(C3⋊C8)—22no—
184C23×Q8—91no—
185C22×Q16—92no—
186C2×C22⋊Q8—91no—
187#451—91no—
188#451—92no—
189#451—91no—
190#451—92no—
191#451—91no—
192#451C3⋊D311yescharacteristic, direct product factor
193C2×#103—92no—
194C2×C22⋊C8—91no—
195C23×D3—34no—
196C2×C3×Q8—216no—
197C2×C3×Q8—24no—
198C2×C3×Q8C22×D314yes—
199C2×C3×Q8C22×D318yes—
200C22×C3×C4—24no—
201C22×C3×C4C22×D314yes—
202C22×Dic3—34no—
203C22×Dic3—64no—
204D3×Q8—332no—
205D3×Q8—616no—
206D3×Q8—616no—
207D3×Q8—632no—
208D3×Q8—632no—
209D3×Q8—616no—
210D3×Q8—616no—
211C2×C4×D3—34no—
212C2×C4×D3—34no—
213C2×C4×D3—34no—
214C2×C4×D3—34no—
215C2×C4×D3—616no—
216C2×C4×D3—68no—
217C2×C4×D3—68no—
218C2×C4×D3—632no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×Dic6—38no—
222C2×Dic6—34no—
223C2×Dic6—616no—
224C2×Dic6—68no—
225C2×Dic6—68no—
226C2×Dic6—632no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C3×Q16—216no—
230C2×C3×C8C22×D318yes—
231C3×C4⋊C4—24no—
232C3×C4⋊C4C22×D314yes—
233C3×C22⋊C4—24no—
234#217—64no—
235#216—616no—
236#216—616no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—34no—
240C4⋊Dic3—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244C2×C3⋊C8—38no—
245Dic12—616no—
246D3×C8—616no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32C2×Q1612yescomplemented
250C22×C32C22×D411yescharacteristic
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3—28no—
254C2×C3⋊D3#12012yes—
255C2×C3⋊D3C2×Q1612yes—
256C2×C3⋊D3C2×Q1612yescomplemented
257C2×C3⋊D3#13712yes—
258C32×C4—24no—
259C32×C4—21no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4C22×D412yes—
263C3⋊Dic3—21no—
264C3⋊Dic3—24no—
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3#12012yes—
268C22×Q8—92no—
269C22×Q8—91no—
270C22×Q8—92no—
271C22×Q8—91no—
272C22×Q8—181no—
273C22×Q8—181no—
274C22×Q8—181no—
275C22×Q8—188no—
276C22×Q8C2×C3⋊D311yescharacteristic
277C23×C4—91no—
278C23×C4—181no—
279C2×Q16—92no—
280C2×Q16—92no—
281C2×Q16—92no—
282C2×Q16—188no—
283C2×Q16C2×C3⋊D312yescomplemented
284C22×C8—92no—
285C22⋊Q8—91no—
286C22⋊Q8—91no—
287C22⋊Q8—91no—
288C22⋊Q8—181no—
289C22⋊Q8—181no—
290C22⋊Q8C2×C3⋊D311yescharacteristic
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—181no—
294#103—92no—
295#103—92no—
296#103—92no—
297#103C2×C3⋊D312yescomplemented
298C22⋊C8—91no—
299C22⋊C8—92no—
300C22⋊C8C2×C3⋊D311yescharacteristic
301C23×C3D3×D414yes—
302C22×D3—34no—
303C22×D3—316no—
304C22×D3—34no—
305C22×D3—68no—
306C22×D3—68no—
307C3×Q8—216no—
308C3×Q8—28no—
309C3×Q8—28no—
310C3×Q8D3×D4116yes—
311C2×C3×C4—216no—
312C2×C3×C4—28no—
313C2×C3×C4—28no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4D3×D414yes—
317C2×C3×C4C23×D314yes—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—68no—
321C2×Dic3—616no—
322C2×Dic3—68no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C4×D3—316no—
326C4×D3—68no—
327C4×D3—68no—
328C4×D3—632no—
329C4×D3—632no—
330C4×D3—68no—
331C4×D3—128no—
332C4×D3—128no—
333Dic6—316no—
334Dic6—632no—
335Dic6—616no—
336Dic6—632no—
337Dic6—68no—
338Dic6—68no—
339Dic6—128no—
340C3×C8—28no—
341C3⋊C8—68no—
342C2×C32—22no—
343C2×C32C2×#12011yescharacteristic
344C2×C32C22×Q1611yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3⋊D3—22no—
347C3⋊D3#45114yesdirect product factor
348C24—91no—
349C2×Q8—24no—
350C2×Q8—21no—
351C2×Q8—98no—
352C2×Q8—92no—
353C2×Q8—91no—
354C2×Q8—182no—
355C2×Q8—182no—
356C2×Q8—181no—
357C2×Q8—184no—
358C2×Q8—188no—
359C2×Q8—184no—
360C2×Q8—184no—
361C2×Q8—184no—
362C2×Q8—188no—
363C2×Q8—188no—
364C2×Q8—184no—
365C2×Q8—181no—
366C2×Q8C22×C3⋊D311yescharacteristic
367C2×Q8C22×C3⋊D312yes—
368C22×C4—21no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—184no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—188no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4C22×C3⋊D311yescharacteristic
382Q16—24no—
383Q16—184no—
384Q16—184no—
385Q16—184no—
386C2×C8—92no—
387C2×C8—184no—
388C2×C8C22×C3⋊D312yes—
389C4⋊C4—21no—
390C4⋊C4—91no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4C22×C3⋊D311yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22×C3—24no—
401C22×C3—24no—
402C22×C3D3×Q1618yescomplemented
403C22×C3C2×D3×D414yes—
404C2×D3—38no—
405C2×D3—38no—
406C2×D3—38no—
407C2×D3—38no—
408C2×D3—632no—
409C2×D3—64no—
410C2×D3—64no—
411C3×C4—216no—
412C3×C4—24no—
413C3×C4—44no—
414C3×C4—44no—
415C3×C4C2×D3×D418yes—
416Dic3—38no—
417Dic3—616no—
418Dic3—64no—
419Dic3—124no—
420Dic3—124no—
421C32C2×#45111yescharacteristic, complemented, Sylow
422C23—91no—
423C23—91no—
424C23—94no—
425C23—182no—
426C23—182no—
427C23D4×C3⋊D311yescharacteristic
428Q8—24no—
429Q8—22no—
430Q8—22no—
431Q8—94no—
432Q8—188no—
433Q8—188no—
434Q8—184no—
435Q8—182no—
436Q8—182no—
437Q8—362no—
438Q8D4×C3⋊D314yes—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—91no—
445C2×C4—94no—
446C2×C4—91no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—188no—
450C2×C4—188no—
451C2×C4—182no—
452C2×C4—184no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—362no—
458C2×C4—362no—
459C2×C4D4×C3⋊D311yescharacteristic
460C2×C4C23×C3⋊D311yescharacteristic
461C8—22no—
462C8—182no—
463C2×C3—28no—
464C2×C3D3×#12014yes—
465C2×C3C2×D3×Q1614yes—
466C2×C3D3×#13714yes—
467D3—316no—
468D3—68no—
469C22—21no—
470C22—21no—
471C22—92no—
472C22—92no—
473C22—92no—
474C22—92no—
475C22—188no—
476C22—181no—
477C22—181no—
478C22Q16×C3⋊D312yescomplemented
479C22C2×D4×C3⋊D311yescharacteristic
480C4—24no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—92no—
485C4—181no—
486C4—184no—
487C4—361no—
488C4—361no—
489C4C2×D4×C3⋊D312yes—
490C3D3×#45114yescomplemented
491C2—22no—
492C2—94no—
493C2—182no—
494C2C3⋊D3×#12011yescharacteristic
495C2C2×Q16×C3⋊D311yescharacteristic
496C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenter#451C3⋊D3
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×Q16×C3⋊D3C2semidirect
4. C32×#451C2semidirect
5. #10592927C2semidirect
6. #10592885C2semidirect
7. #10592749C2semidirect
8. #10592508C2semidirect
9. C3⋊D3×#103C2semidirect
10. #10592438C2semidirect
24. C2×C32×Q16C22semidirect
27. C2×#3756C22semidirect
28. C2×#3756C22semidirect
31. C2×#3746C22semidirect
39. C32×#103C22semidirect
41. #63662C22semidirect
44. #63643C22semidirect
45. #63637C22semidirect
49. C3×#451D3semidirect
121. C2×C3×Q16C2×D3semidirect
136. C3×#103C2×D3semidirect
146. C22×C3⋊D3Q16semidirect
192. #451C3⋊D3direct (N × H)
249. C22×C32C2×Q16semidirect
256. C2×C3⋊D3C2×Q16semidirect
283. C2×Q16C2×C3⋊D3semidirect
297. #103C2×C3⋊D3semidirect
347. C3⋊D3#451direct (N × H)
402. C22×C3D3×Q16semidirect
421. C32C2×#451semidirect
478. C22Q16×C3⋊D3semidirect
490. C3D3×#451semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×Q16×C3⋊D32
C3⋊D3×C22⋊Q82
C32×#4512
#105929272
#105928852
#105927492
#105925082
C3⋊D3×#1032
#105924382
C3⋊D3×C22⋊C82
D3×#4513