Finite Group Databasebeta

← C3⋊D3×#485 #11869472

Subgroups — C3⋊D3×#485 #11869472

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4#10592744C211yesmaximal, characteristic, complemented
5#10592695C211yesmaximal, characteristic, complemented
6#10592587C211yesmaximal, characteristic, complemented
7C3⋊D3×#107C211yesmaximal, characteristic, complemented
8#10592567C211yesmaximal, characteristic, complemented
9C3⋊D3×#106C211yesmaximal, characteristic, complemented
10#10592514C211yesmaximal, characteristic, complemented
11#10592513C211yesmaximal, characteristic, complemented
12C3⋊D3×#103C211yesmaximal, characteristic, complemented
13C3⋊D3×#103C211yesmaximal, characteristic, complemented
14C3⋊D3×C22⋊C8C211yesmaximal, characteristic
15#10592422C211yesmaximal, characteristic, complemented
16D3×#485—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64155C2211yescharacteristic
22#64135C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic
26#64106C2211yescharacteristic
27#64105—21no—
28#64101C2211yescharacteristic
29#64101C2211yescharacteristic
30C4⋊C4×C3⋊D3—21no—
31C4⋊C4×C3⋊D3C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34C22⋊C4×C3⋊D3—21no—
35C22⋊C4×C3⋊D3—21no—
36#64087—21no—
37#64086—21no—
38#64081—21no—
39C42×C3⋊D3—21no—
40C32×#107C2211yescharacteristic, complemented
41C32×#106C2211yescharacteristic, complemented
42C32×#103C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63657C2211yescharacteristic
48#63647C2211yescharacteristic
49#63647C2211yescharacteristic
50#63645C2211yescharacteristic, complemented
51#63644C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63635C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60D3×C22⋊Q8—34no—
61D3×#117—34no—
62C3×#485D314yescomplemented
63#5045—34no—
64#4996—34no—
65#4888—34no—
66D3×#107—34no—
67#4868—34no—
68D3×#106—34no—
69#4815—34no—
70#4814—34no—
71D3×#103—34no—
72D3×#103—34no—
73D3×C22⋊C8—34no—
74#4723—34no—
75C23×C3⋊D3D411yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3D411yescharacteristic
79Q8×C3⋊D3—22no—
80Q8×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3D411yescharacteristic
88C2×C4×C3⋊D3D411yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C2×#634C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C22⋊C4—21no—
101C32×C42—21no—
102#3757—21no—
103#3757—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—22no—
123C8×C3⋊D3—22no—
124C2×#485—91noSylow
125C2×D3×Q8—34no—
126C22×C4×D3—34no—
127C3×C22⋊Q8C2×D314yes—
128C3×#117C2×D314yes—
129#946—34no—
130#926—34no—
131#924—34no—
132C2×D3×C8—34no—
133C2×D3×C8—34no—
134#897—34no—
135#896—64no—
136#892—34no—
137#892—34no—
138D3×C4⋊C4—34no—
139D3×C4⋊C4—34no—
140D3×C4⋊C4—34no—
141D3×C4⋊C4—64no—
142D3×C22⋊C4—64no—
143D3×C22⋊C4—64no—
144#878—64no—
145#877—64no—
146#872—64no—
147C42×D3—64no—
148C3×#107C2×D314yescomplemented
149C3×#106C2×D314yescomplemented
150C3×#103C2×D314yescomplemented
151C3×#103C2×D314yescomplemented
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#830—34no—
156(C2×D3)⋊C8—34no—
157(C2×D3)⋊C8—34no—
158#818—34no—
159#817—34no—
160#816—34no—
161#816—34no—
162#810—34no—
163#810—34no—
164#808—34no—
165#808—34no—
166#807—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C4×C3⋊D3—22no—
192C4×C3⋊D3—21no—
193C4×C3⋊D3—21no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—42no—
199C4×C3⋊D3#4112yes—
200C4×C3⋊D3#4112yes—
201#634—21no—
202#634—21no—
203#634—42no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208C2×C22⋊Q8—91no—
209C2×#117—91no—
210#485—91no—
211#485—91no—
212#485—91no—
213#485—91no—
214#485—91no—
215#485—91no—
216#485—91no—
217#485C3⋊D311yescharacteristic, direct product factor
218C2×#107—91no—
219C2×#106—91no—
220C2×#103—91no—
221C2×#103—91no—
222C2×C22⋊C8—91no—
223C23×D3—34no—
224C2×C3×Q8C22×D314yes—
225C22×C3×C4C22×D314yes—
226C22×Dic3—34no—
227D3×Q8—68no—
228D3×Q8—68no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—68no—
234C2×C4×D3—68no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4C22×D314yes—
245C3×C4⋊C4C22×D314yes—
246C3×C4⋊C4C22×D314yes—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—24no—
249C3×C42—24no—
250#217—64no—
251#217—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—34no—
270D3×C8—68no—
271D3×C8—68no—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—21no—
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—44no—
280C2×C3⋊D3#12312yes—
281C2×C3⋊D3#13512yes—
282C2×C3⋊D3#13712yes—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4C2×#4111yescharacteristic
289C32×C4C2×#4111yescharacteristic
290C3⋊Dic3—21no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3#12312yes—
296C22×Q8—91no—
297C23×C4—91no—
298C22×C8—91no—
299C22×C8—91no—
300C22⋊Q8—91no—
301C22⋊Q8—91no—
302C22⋊Q8—91no—
303C22⋊Q8—181no—
304C22⋊Q8—181no—
305C22⋊Q8C2×C3⋊D311yescharacteristic
306#117—91no—
307#117—91no—
308#117—91no—
309#117—181no—
310#117—181no—
311#117C2×C3⋊D311yescharacteristic
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—181no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318C2×C42—181no—
319#107—91no—
320#107—91no—
321#107—91no—
322#107C2×C3⋊D311yescharacteristic, complemented
323#106—91no—
324#106—91no—
325#106—91no—
326#106C2×C3⋊D311yescharacteristic, complemented
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103C2×C3⋊D311yescharacteristic, complemented
334#103C2×C3⋊D311yescharacteristic, complemented
335C22⋊C8—91no—
336C22⋊C8—91no—
337C22⋊C8—91no—
338C22⋊C8C2×C3⋊D311yescharacteristic
339C23×C3D3×D414yes—
340C22×D3—34no—
341C22×D3—34no—
342C22×D3—68no—
343C22×D3—68no—
344C22×D3—68no—
345C3×Q8—24no—
346C3×Q8—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4D3×D414yes—
354C2×C3×C4C23×D314yes—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—68no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C4×D3—38no—
363C4×D3—38no—
364C4×D3—68no—
365C4×D3—68no—
366C4×D3—64no—
367C4×D3—64no—
368C4×D3—128no—
369C4×D3—128no—
370C4×D3—128no—
371C4×D3—128no—
372Dic6—64no—
373Dic6—64no—
374Dic6—128no—
375C3×C8—24no—
376C3×C8—24no—
377C3⋊C8—64no—
378C3⋊C8—64no—
379C2×C32—41no—
380C2×C32C2×#12311yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32C2×#13711yescharacteristic
383C3⋊D3—41no—
384C3⋊D3#48514yesdirect product factor
385C24—91no—
386C2×Q8—91no—
387C2×Q8—181no—
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8C22×C3⋊D311yescharacteristic
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—182no—
397C22×C4—182no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403C2×C8—91no—
404C2×C8—91no—
405C2×C8—182no—
406C2×C8—182no—
407C2×C8C22×C3⋊D311yescharacteristic
408C2×C8C22×C3⋊D311yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—91no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4C22×C3⋊D311yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C42—21no—
431C42—181no—
432C42—181no—
433C42—181no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3C2×D3×D414yes—
438C2×D3—38no—
439C2×D3—38no—
440C2×D3—38no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—1216no—
445C3×C4—24no—
446C3×C4—44no—
447C3×C4—44no—
448C3×C4—44no—
449C3×C4—44no—
450C3×C4D3×#4114yes—
451C3×C4D3×#4114yes—
452Dic3—38no—
453Dic3—64no—
454Dic3—124no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458C32C2×#48511yescharacteristic, complemented, Sylow
459C23—91no—
460C23—91no—
461C23—182no—
462C23—182no—
463C23—182no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—181no—
468Q8—181no—
469Q8—362no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—91no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—91no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4D4×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D311yescharacteristic
495C8—21no—
496C8—21no—
497C8—181no—
498C8—181no—
499C2×C3—44no—
500C2×C3D3×#12314yes—
501C2×C3D3×#13514yes—
502C2×C3D3×#13714yes—
503D3—316no—
504D3—124no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—92no—
509C22—92no—
510C22—92no—
511C22—181no—
512C22—181no—
513C22—181no—
514C22—364no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—92no—
522C4—181no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#41×C3⋊D311yescharacteristic
528C4#41×C3⋊D311yescharacteristic
529C3D3×#48514yescomplemented
530C2—41no—
531C2—94no—
532C2—361no—
533C2C3⋊D3×#12311yescharacteristic
534C2C3⋊D3×#13511yescharacteristic
535C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenter#485C3⋊D3
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C32×#485C2semidirect
4. #10592744C2semidirect
5. #10592695C2semidirect
6. #10592587C2semidirect
7. C3⋊D3×#107C2semidirect
8. #10592567C2semidirect
9. C3⋊D3×#106C2semidirect
10. #10592514C2semidirect
11. #10592513C2semidirect
12. C3⋊D3×#103C2semidirect
13. C3⋊D3×#103C2semidirect
15. #10592422C2semidirect
40. C32×#107C22semidirect
41. C32×#106C22semidirect
42. C32×#103C22semidirect
43. C32×#103C22semidirect
45. #63662C22semidirect
46. #63662C22semidirect
50. #63645C22semidirect
51. #63644C22semidirect
52. #63643C22semidirect
53. #63643C22semidirect
54. #63637C22semidirect
55. #63637C22semidirect
56. #63635C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. #63634C22semidirect
62. C3×#485D3semidirect
148. C3×#107C2×D3semidirect
149. C3×#106C2×D3semidirect
150. C3×#103C2×D3semidirect
151. C3×#103C2×D3semidirect
217. #485C3⋊D3direct (N × H)
322. #107C2×C3⋊D3semidirect
326. #106C2×C3⋊D3semidirect
333. #103C2×C3⋊D3semidirect
334. #103C2×C3⋊D3semidirect
384. C3⋊D3#485direct (N × H)
458. C32C2×#485semidirect
529. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C3⋊D3×#1172
C32×#4852
#105927442
#105926952
#105925872
C3⋊D3×#1072
#105925672
C3⋊D3×#1062
#105925142
#105925132
C3⋊D3×#1032
C3⋊D3×C22⋊C82
#105924222
D3×#4853