Finite Group Databasebeta

← C3⋊D3×#448 #11863592

Subgroups — C3⋊D3×#448 #11863592

Order 1152.

2376 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C212yesmaximal, complemented
3C3⋊D3×#121C211yesmaximal, characteristic
4C32×#448C211yesmaximal, characteristic, complemented
5#10592926C211yesmaximal, characteristic, complemented
6#10592869C212yesmaximal, complemented
7#10592739C211yesmaximal, characteristic, complemented
8#10592505C212yesmaximal, complemented
9C3⋊D3×#103C212yesmaximal, complemented
10#10592437C211yesmaximal, characteristic, complemented
11C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
12D3×#448—34nomaximal
13C22×C32×Q8C2211yescharacteristic, complemented
14C2×Q8×C3⋊D3—28no—
15C2×Q8×C3⋊D3—21no—
16C2×Q8×C3⋊D3—21no—
17C2×Q8×C3⋊D3C2212yes—
18C2×Q8×C3⋊D3C2212yescomplemented
19C2×D4×C3⋊D3—21no—
20C2×D4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3—21no—
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×#634—21no—
24C22×#634C2211yescharacteristic, complemented
25C2×C32×SD16C2212yescomplemented
26C32×#121C2211yescharacteristic
27C2×#3755C2212yescomplemented
28#64148—21no—
29#64147C2211yescharacteristic
30C2×#3754C2212yescomplemented
31#64139C2211yescharacteristic
32SD16×C3⋊D3—28no—
33C2×#3744C2212yescomplemented
34C2×C8×C3⋊D3C2212yes—
35#64104C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64093—21no—
38C22⋊C4×C3⋊D3—21no—
39C32×#103C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63662C2212yescomplemented
42#63657C2211yescharacteristic, complemented
43#63647C2212yescomplemented
44#63643C2212yescomplemented
45#63637C2212yescomplemented
46C22×D3×Q8—34no—
47C2×D3×SD16—38no—
48D3×#121—34no—
49C3×#448D314yescomplemented
50#5227—34no—
51#5170—38no—
52#5040—34no—
53#4806—38no—
54D3×#103—38no—
55#4738—34no—
56D3×C22⋊C8—34no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3D411yescharacteristic
59C2×C32×Q8—24no—
60C2×C32×Q8—21no—
61C2×C32×Q8C2312yes—
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×#638—21no—
67C2×#638—21no—
68C2×#638—21no—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3D411yescharacteristic
71Q8×C3⋊D3—28no—
72Q8×C3⋊D3—28no—
73Q8×C3⋊D3—24no—
74Q8×C3⋊D3—24no—
75Q8×C3⋊D3—24no—
76Q8×C3⋊D3D418yescomplemented
77D4×C3⋊D3—24no—
78D4×C3⋊D3—44no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—28no—
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3D411yescharacteristic
87C2×C4×C3⋊D3D411yescharacteristic
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—28no—
91C2×#634—21no—
92C2×#634—22no—
93C2×#634—22no—
94C2×#634—24no—
95C2×#634C2312yes—
96C32×SD16—24no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3755—24no—
102#3754—24no—
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C2×C3⋊(C3⋊C8)C2312yes—
108#3744—24no—
109C8×C3⋊D3—24no—
110C2×#448—91noSylow
111C22×C3×Q8C2×D314yescomplemented
112C2×D3×Q8—38no—
113C2×D3×Q8—38no—
114C2×D3×Q8—64no—
115C2×D3×Q8—64no—
116C2×D3×Q8—632no—
117C2×D3×D4—34no—
118C2×D3×D4—64no—
119C22×C4×D3—34no—
120C22×C4×D3—64no—
121C22×Dic6—34no—
122C22×Dic6—64no—
123C2×C3×SD16C2×D318yescomplemented
124C3×#121C2×D314yes—
125C2×#215—38no—
126#939—64no—
127#938—34no—
128C2×#214—38no—
129#930—34no—
130D3×SD16—632no—
131C2×#204—38no—
132C2×D3×C8—38no—
133#895—34no—
134D3×C4⋊C4—34no—
135#884—64no—
136D3×C22⋊C4—64no—
137C3×#103C2×D318yescomplemented
138C3×C22⋊C8C2×D314yescomplemented
139#835—38no—
140#830—34no—
141(C2×D3)⋊C8—38no—
142#816—38no—
143#810—38no—
144C23×C32—21no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3SD1614yescomplemented
153C22×C3⋊D3C2×D411yescharacteristic
154C22×C3⋊D3C2×D411yescharacteristic
155C32×Q8—24no—
156C32×Q8—22no—
157C32×Q8C2×D414yescomplemented
158C32×D4—22no—
159C32×D4—42no—
160C2×C32×C4—24no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166#638—42no—
167#638—42no—
168#638—42no—
169C2×C3⋊Dic3—24no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D411yescharacteristic
174C2×C3⋊Dic3C2×D411yescharacteristic
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—42no—
177C4×C3⋊D3—28no—
178C4×C3⋊D3—28no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3—42no—
183C4×C3⋊D3C2×D414yes—
184#634—28no—
185#634—24no—
186#634—22no—
187#634—28no—
188#634C2×D414yescomplemented
189C32×C8—22no—
190C3⋊(C3⋊C8)—22no—
191C23×Q8—91no—
192C22×SD16—92no—
193C2×#121—91no—
194#448—91no—
195#448—92no—
196#448—91no—
197#448—92no—
198#448—91no—
199#448C3⋊D311yescharacteristic, direct product factor
200C2×#103—92no—
201C2×C22⋊C8—91no—
202C23×D3—34no—
203C23×D3—64no—
204C2×C3×Q8—216no—
205C2×C3×Q8—24no—
206C2×C3×Q8C22×D318yes—
207C2×C3×D4—24no—
208C2×C3×D4C22×D314yes—
209C22×C3×C4—24no—
210C22×C3×C4C22×D314yes—
211C2×#67—64no—
212C2×#67—64no—
213C2×#67—64no—
214C22×Dic3—34no—
215C22×Dic3—64no—
216D3×Q8—332no—
217D3×Q8—616no—
218D3×Q8—616no—
219D3×Q8—632no—
220D3×Q8—632no—
221D3×Q8—616no—
222D3×D4—616no—
223D3×D4—1216no—
224C2×D12—34no—
225C2×D12—64no—
226C2×C4×D3—34no—
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—616no—
231C2×C4×D3—68no—
232C2×C4×D3—68no—
233C2×C4×D3—632no—
234C2×C4×D3—64no—
235C2×Dic6—38no—
236C2×Dic6—616no—
237C2×Dic6—68no—
238C2×Dic6—68no—
239C2×Dic6—632no—
240C2×Dic6—64no—
241C3×SD16—216no—
242C2×C3×C8C22×D318yes—
243C3×C4⋊C4C22×D314yes—
244C3×C22⋊C4—24no—
245#217—64no—
246#215—616no—
247#214—616no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250C4⋊Dic3—34no—
251Dic3⋊C4—64no—
252C2×C3⋊C8—38no—
253#204—616no—
254D3×C8—616no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—41no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32C2×SD1612yescomplemented
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—21no—
263C2×C3⋊D3—21no—
264C2×C3⋊D3—28no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—84no—
269C2×C3⋊D3#12012yes—
270C2×C3⋊D3C2×SD1612yes—
271C2×C3⋊D3C2×SD1612yescomplemented
272C2×C3⋊D3#13712yes—
273C32×C4—24no—
274C32×C4—21no—
275C32×C4—41no—
276C32×C4C22×D412yes—
277C3⋊Dic3—21no—
278C3⋊Dic3—24no—
279C3⋊Dic3—41no—
280C3⋊Dic3#12012yes—
281C22×Q8—92no—
282C22×Q8—92no—
283C22×Q8—91no—
284C22×Q8—181no—
285C22×Q8—181no—
286C22×Q8—181no—
287C22×Q8—188no—
288C22×Q8C2×C3⋊D311yescharacteristic, complemented
289C22×D4—91no—
290C22×D4—181no—
291C23×C4—91no—
292C23×C4—181no—
293C2×SD16—92no—
294C2×SD16—92no—
295C2×SD16—92no—
296C2×SD16—188no—
297C2×SD16C2×C3⋊D312yescomplemented
298C22×C8—92no—
299#121—91no—
300#121—91no—
301#121—91no—
302#121—181no—
303#121—181no—
304#121C2×C3⋊D311yescharacteristic
305C2×C4⋊C4—91no—
306C2×C22⋊C4—181no—
307#103—92no—
308#103—92no—
309#103—92no—
310#103C2×C3⋊D312yescomplemented
311C22⋊C8—91no—
312C22⋊C8—92no—
313C22⋊C8C2×C3⋊D311yescharacteristic, complemented
314C23×C3—24no—
315C23×C3D3×D414yes—
316C22×D3—34no—
317C22×D3—316no—
318C22×D3—34no—
319C22×D3—68no—
320C22×D3—68no—
321C22×D3—64no—
322C22×D3—128no—
323C22×D3—128no—
324C22×D3—128no—
325C3×Q8—216no—
326C3×Q8—28no—
327C3×Q8D3×D4116yescomplemented
328C3×D4—28no—
329C3×D4—48no—
330C2×C3×C4—216no—
331C2×C3×C4—28no—
332C2×C3×C4—28no—
333C2×C3×C4—24no—
334C2×C3×C4D3×D414yes—
335C2×C3×C4C23×D314yes—
336#67—128no—
337#67—128no—
338#67—128no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—68no—
342C2×Dic3—616no—
343C2×Dic3—68no—
344C2×Dic3—64no—
345D12—68no—
346D12—128no—
347C4×D3—316no—
348C4×D3—68no—
349C4×D3—68no—
350C4×D3—632no—
351C4×D3—632no—
352C4×D3—68no—
353C4×D3—128no—
354Dic6—316no—
355Dic6—632no—
356Dic6—616no—
357Dic6—632no—
358Dic6—68no—
359C3×C8—28no—
360C3⋊C8—68no—
361C2×C32—22no—
362C2×C32—81no—
363C2×C32C2×#12011yescharacteristic
364C2×C32C22×SD1611yescharacteristic
365C2×C32C2×#13711yescharacteristic
366C3⋊D3—22no—
367C3⋊D3—81no—
368C3⋊D3#44814yesdirect product factor
369C24—91no—
370C24—181no—
371C2×Q8—24no—
372C2×Q8—21no—
373C2×Q8—98no—
374C2×Q8—92no—
375C2×Q8—182no—
376C2×Q8—182no—
377C2×Q8—184no—
378C2×Q8—188no—
379C2×Q8—184no—
380C2×Q8—184no—
381C2×Q8—188no—
382C2×Q8—188no—
383C2×Q8—184no—
384C2×Q8—181no—
385C2×Q8C22×C3⋊D312yes—
386C2×D4—21no—
387C2×D4—91no—
388C2×D4—181no—
389C2×D4—184no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—364no—
394C2×D4C22×C3⋊D311yescharacteristic
395C22×C4—21no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—184no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4—188no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4C22×C3⋊D311yescharacteristic
408SD16—24no—
409SD16—184no—
410SD16—184no—
411SD16—184no—
412C2×C8—92no—
413C2×C8—184no—
414C2×C8C22×C3⋊D312yes—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4C22×C3⋊D311yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22×C3—24no—
423C22×C3—24no—
424C22×C3—44no—
425C22×C3—44no—
426C22×C3—44no—
427C22×C3D3×SD1618yescomplemented
428C22×C3C2×D3×D414yes—
429C2×D3—38no—
430C2×D3—38no—
431C2×D3—38no—
432C2×D3—38no—
433C2×D3—632no—
434C2×D3—64no—
435C2×D3—64no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—124no—
439C2×D3—2416no—
440C3×C4—216no—
441C3×C4—24no—
442C3×C4—44no—
443C3×C4C2×D3×D418yes—
444Dic3—38no—
445Dic3—616no—
446Dic3—64no—
447Dic3—124no—
448C32C2×#44811yescharacteristic, complemented, Sylow
449C23—21no—
450C23—91no—
451C23—91no—
452C23—94no—
453C23—182no—
454C23—182no—
455C23—181no—
456C23—362no—
457C23—362no—
458C23—362no—
459C23D4×C3⋊D311yescharacteristic
460Q8—24no—
461Q8—22no—
462Q8—94no—
463Q8—188no—
464Q8—188no—
465Q8—184no—
466Q8—182no—
467Q8D4×C3⋊D314yescomplemented
468D4—22no—
469D4—42no—
470D4—182no—
471D4—362no—
472D4—362no—
473D4—362no—
474D4—362no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—91no—
480C2×C4—94no—
481C2×C4—91no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—188no—
485C2×C4—188no—
486C2×C4—182no—
487C2×C4—184no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—181no—
491C2×C4—362no—
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4C23×C3⋊D311yescharacteristic
494C8—22no—
495C8—182no—
496C2×C3—28no—
497C2×C3—84no—
498C2×C3D3×#12014yes—
499C2×C3C2×D3×SD1614yes—
500C2×C3D3×#13714yes—
501D3—316no—
502D3—68no—
503D3—244no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—92no—
510C22—92no—
511C22—92no—
512C22—92no—
513C22—188no—
514C22—181no—
515C22—181no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—724no—
520C22SD16×C3⋊D312yescomplemented
521C22C2×D4×C3⋊D311yescharacteristic
522C4—24no—
523C4—21no—
524C4—41no—
525C4—92no—
526C4—181no—
527C4—184no—
528C4—361no—
529C4C2×D4×C3⋊D312yes—
530C3D3×#44814yescomplemented
531C2—22no—
532C2—81no—
533C2—94no—
534C2—182no—
535C2—721no—
536C2C3⋊D3×#12011yescharacteristic
537C2C2×SD16×C3⋊D311yescharacteristic
538C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#448C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#121C2
hypercenter#448C3⋊D3
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
2. C2×SD16×C3⋊D3C2semidirect
4. C32×#448C2semidirect
5. #10592926C2semidirect
6. #10592869C2semidirect
7. #10592739C2semidirect
8. #10592505C2semidirect
9. C3⋊D3×#103C2semidirect
10. #10592437C2semidirect
11. C3⋊D3×C22⋊C8C2semidirect
13. C22×C32×Q8C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
24. C22×#634C22semidirect
25. C2×C32×SD16C22semidirect
27. C2×#3755C22semidirect
30. C2×#3754C22semidirect
33. C2×#3744C22semidirect
39. C32×#103C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63662C22semidirect
42. #63657C22semidirect
43. #63647C22semidirect
44. #63643C22semidirect
45. #63637C22semidirect
49. C3×#448D3semidirect
76. Q8×C3⋊D3D4semidirect
111. C22×C3×Q8C2×D3semidirect
123. C2×C3×SD16C2×D3semidirect
137. C3×#103C2×D3semidirect
138. C3×C22⋊C8C2×D3semidirect
152. C22×C3⋊D3SD16semidirect
157. C32×Q8C2×D4semidirect
188. #634C2×D4semidirect
199. #448C3⋊D3direct (N × H)
260. C22×C32C2×SD16semidirect
271. C2×C3⋊D3C2×SD16semidirect
288. C22×Q8C2×C3⋊D3semidirect
297. C2×SD16C2×C3⋊D3semidirect
310. #103C2×C3⋊D3semidirect
313. C22⋊C8C2×C3⋊D3semidirect
327. C3×Q8D3×D4semidirect
368. C3⋊D3#448direct (N × H)
427. C22×C3D3×SD16semidirect
448. C32C2×#448semidirect
467. Q8D4×C3⋊D3semidirect
520. C22SD16×C3⋊D3semidirect
530. C3D3×#448semidirect

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×SD16×C3⋊D32
C3⋊D3×#1212
C32×#4482
#105929262
#105928692
#105927392
#105925052
C3⋊D3×#1032
#105924372
C3⋊D3×C22⋊C82
D3×#4483