Finite Group Databasebeta

← C3⋊D3×#929 #13177299

Subgroups — C3⋊D3×#929 #13177299

Order 1728.

2364 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic
3#11723970C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5C3⋊D3×#217C211yesmaximal, characteristic, complemented
6#11723608C211yesmaximal, characteristic, complemented
7#11723602C211yesmaximal, characteristic, complemented
8C3⋊D3×(C2×D3)⋊C4C212yesmaximal, complemented
9#11723518C212yesmaximal, complemented
10C3⋊D3×Dic3⋊C4C212yesmaximal, complemented
11#11723417C212yesmaximal, complemented
12C3⋊D3×#123—31nomaximal
13D3×#929—34nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×D3×C3⋊D3C2211yescharacteristic
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3—24no—
20C2×C3×C4×C3⋊D3C2212yes—
21C2×C3×C4×C3⋊D3C2212yescomplemented
22C2×C32×#67C2211yescharacteristic
23C3⋊D3×#67—24no—
24C2×#6292C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2212yes—
27C2×Dic3×C3⋊D3C2211yescharacteristic
28#88864C2211yescharacteristic, complemented
29#88859C2212yescomplemented
30#88857C2212yescomplemented
31C32×#217C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2212yescomplemented
33C32×Dic3⋊C4C2212yescomplemented
34#88806C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2212yescomplemented
36#88804C2212yescomplemented
37#88803C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39C2×D4×C3⋊D3—31no—
40C22×C4×C3⋊D3D311yescharacteristic, complemented
41C22×C3×C4×D3—34no—
42C2×D3×#67—34no—
43C32×#123—31no—
44#64144—31no—
45#64138—31no—
46#64138—34no—
47#64138—64no—
48#64103—32no—
49C4⋊C4×C3⋊D3—32no—
50#64095—31no—
51#64092—32no—
52C22⋊C4×C3⋊D3—32no—
53C22⋊C4×C3⋊D3—31no—
54C3×#929D314yescomplemented
55D3×#217—34no—
56#63966—34no—
57#63961—34no—
58D3×(C2×D3)⋊C4—38no—
59#63905—38no—
60D3×Dic3⋊C4—38no—
61#63850—38no—
62C23×C33C2311yescharacteristic
63C22×C3⋊(C3⋊D3)C2311yescharacteristic
64C22×C3×C3⋊D3—24no—
65C22×C3×C3⋊D3D414yes—
66C22×C3×C3⋊D3C2311yescharacteristic
67C22×C3×C3⋊D3C2311yescharacteristic
68C22×C32×D3C2311yescharacteristic
69C2×D3×C3⋊D3—22no—
70C2×D3×C3⋊D3—24no—
71C2×C33×C4—22no—
72C2×C33×C4C2312yes—
73#6312—22no—
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2312yes—
76C2×C3×C3⋊Dic3—22no—
77C2×C3×C3⋊Dic3C2312yes—
78C3×C4×C3⋊D3—24no—
79C3×C4×C3⋊D3—24no—
80C32×#67—22no—
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2311yescharacteristic
83#6292—22no—
84#6290—22no—
85Dic3×C3⋊D3—22no—
86Dic3×C3⋊D3—24no—
87C2×#929—91no—
88D3×#123—94no—
89C23×C3⋊D3—31no—
90C23×C3⋊D3C2×D311yescharacteristic
91C23×C3×D3—34no—
92C22×D32—34no—
93C2×C32×D4—31no—
94C22×C32×C4—24no—
95C22×C32×C4C2×D314yescomplemented
96C22×C32×C4C2×D311yescharacteristic, complemented
97C2×#638—31no—
98C2×#638—34no—
99C2×#638—31no—
100C2×#638—64no—
101C22×C3⋊Dic3C2×D311yescharacteristic, complemented
102D4×C3⋊D3—64no—
103C2×C4⋊(C3⋊D3)—31no—
104C2×C4×C3⋊D3—24no—
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3C2×D312yes—
108C2×C4×C3⋊D3C2×D312yescomplemented
109C2×C3×#67C2×D314yes—
110C22×C3×Dic3—34no—
111C2×C3×C4×D3—38no—
112C2×C3×C4×D3—38no—
113C2×C3×C4×D3—616no—
114D3×#67—616no—
115C2×#626—34no—
116C2×#625—34no—
117C2×D3×Dic3—34no—
118C2×D3×Dic3—38no—
119C32×C4⋊C4—32no—
120C32×C22⋊C4—31no—
121C32×C22⋊C4—32no—
122#3757—31no—
123#3757—34no—
124#3757—32no—
125#3757—64no—
126#3752—32no—
127#3752—32no—
128#3752—38no—
129#3752—32no—
130#3752—68no—
131C4⋊(C3⋊Dic3)—32no—
132#3750—32no—
133#3750—38no—
134#3750—32no—
135#3750—68no—
136C3×#217C2×D314yescomplemented
137C3×(C2×D3)⋊C4C2×D318yescomplemented
138C3×Dic3⋊C4C2×D318yescomplemented
139#3724—38no—
140Dic3⋊Dic3—38no—
141#3722—38no—
142(C2×D3)⋊Dic3—38no—
143(C2×D3)⋊Dic3—38no—
144C22×C33—22no—
145C22×C33C2×D412yes—
146C22×C33C2411yescharacteristic
147C2×C3⋊(C3⋊D3)—21no—
148C2×C3⋊(C3⋊D3)—22no—
149C2×C3×C3⋊D3—22no—
150C2×C3×C3⋊D3—28no—
151C2×C3×C3⋊D3C2×D412yes—
152C2×C3×C3⋊D3C2×D412yes—
153C2×C3×C3⋊D3#4114yes—
154C2×C32×D3—21no—
155C2×C32×D3—22no—
156D3×C3⋊D3—44no—
157C33×C4—22no—
158C3⋊(C3⋊Dic3)—21no—
159C3⋊(C3⋊Dic3)—22no—
160C3×C3⋊Dic3—22no—
161C32×Dic3—21no—
162C32×Dic3—22no—
163C23×C3×C4—91no—
164C22×#67—91no—
165C2×D3×D4—94no—
166C22×C4×D3—34no—
167C3×#123—34no—
168C2×#217—91no—
169#935—94no—
170#929—94no—
171#929—91no—
172#929—91no—
173#929—91no—
174#929—92no—
175#929—92no—
176#929—184no—
177#929C3⋊D311yescharacteristic, direct product factor
178C2×(C2×D3)⋊C4—92no—
179C2×Dic3⋊C4—92no—
180#894—98no—
181D3×C4⋊C4—98no—
182#886—94no—
183#883—98no—
184D3×C22⋊C4—98no—
185D3×C22⋊C4—94no—
186C23×C32—24no—
187C23×C32—31no—
188C23×C32C22×D314yes—
189C23×C32C22×D311yescharacteristic
190C22×C3⋊D3—24no—
191C22×C3⋊D3—31no—
192C22×C3⋊D3—34no—
193C22×C3⋊D3—64no—
194C22×C3⋊D3—64no—
195C22×C3⋊D3—62no—
196C22×C3⋊D3#6714yes—
197C22×C3⋊D3C22×D311yescharacteristic
198C22×C3⋊D3C22×D311yescharacteristic
199C22×C3×D3—34no—
200C22×C3×D3—316no—
201C22×C3×D3—34no—
202C22×C3×D3—616no—
203C22×C3×D3C22×D314yes—
204C2×D32—616no—
205C2×D32—68no—
206C32×D4—62no—
207C2×C32×C4—22no—
208C2×C32×C4—28no—
209C2×C32×C4—28no—
210C2×C32×C4—31no—
211C2×C32×C4—32no—
212C2×C32×C4—48no—
213C2×C32×C4C22×D318yes—
214C2×C32×C4C22×D312yes—
215#638—62no—
216#638—62no—
217#638—68no—
218#638—128no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—31no—
221C2×C3⋊Dic3—32no—
222C2×C3⋊Dic3—38no—
223C2×C3⋊Dic3—34no—
224C2×C3⋊Dic3—64no—
225C2×C3⋊Dic3—68no—
226C2×C3⋊Dic3C22×D312yes—
227C4⋊(C3⋊D3)—62no—
228C4×C3⋊D3—24no—
229C4×C3⋊D3—24no—
230C4×C3⋊D3—64no—
231C4×C3⋊D3—62no—
232C3×#67—28no—
233C2×C3×Dic3—38no—
234C2×C3×Dic3—68no—
235C2×C3×Dic3C22×D318yes—
236C2×C3×Dic3C22×D314yes—
237C3×C4×D3—616no—
238C3×C4×D3—616no—
239#626—68no—
240#625—68no—
241D3×Dic3—616no—
242D3×Dic3—68no—
243C2×#123—271noSylow
244C2×C33—22no—
245C2×C33C22×D411yescharacteristic
246C2×C33C2×#4112yes—
247C3⋊(C3⋊D3)—41no—
248C3×C3⋊D3—22no—
249C3×C3⋊D3#12314yescomplemented
250C32×D3—41no—
251C24×C3—91no—
252C23×D3—34no—
253C23×D3—94no—
254C23×D3—91no—
255C2×C3×D4—34no—
256C22×C3×C4—24no—
257C22×C3×C4—91no—
258C22×C3×C4—92no—
259C22×C3×C4—92no—
260C22×C3×C4—184no—
261C22×C3×C4D3214yescomplemented
262C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
263C2×#67—94no—
264C2×#67—94no—
265C2×#67—91no—
266C2×#67—91no—
267C2×#67—91no—
268C2×#67—184no—
269C2×#67—184no—
270C2×#67C2×C3⋊D311yescharacteristic
271C22×Dic3—34no—
272C22×Dic3—91no—
273C22×Dic3—92no—
274D3×D4—1816no—
275C2×D12—94no—
276C2×C4×D3—38no—
277C2×C4×D3—38no—
278C2×C4×D3—616no—
279C2×C4×D3—98no—
280C2×C4×D3—94no—
281C3×C4⋊C4—38no—
282C3×C22⋊C4—34no—
283C3×C22⋊C4—38no—
284#217—98no—
285#217—94no—
286#217—91no—
287#217—92no—
288#217—184no—
289#217C2×C3⋊D311yescharacteristic, complemented
290(C2×D3)⋊C4—98no—
291(C2×D3)⋊C4—98no—
292(C2×D3)⋊C4—92no—
293(C2×D3)⋊C4—98no—
294(C2×D3)⋊C4—92no—
295(C2×D3)⋊C4—92no—
296(C2×D3)⋊C4—188no—
297(C2×D3)⋊C4C2×C3⋊D312yescomplemented
298C4⋊Dic3—98no—
299Dic3⋊C4—98no—
300Dic3⋊C4—98no—
301Dic3⋊C4—92no—
302Dic3⋊C4—92no—
303Dic3⋊C4—92no—
304Dic3⋊C4—188no—
305Dic3⋊C4C2×C3⋊D312yescomplemented
306C22×C32—22no—
307C22×C32—24no—
308C22×C32—28no—
309C22×C32—28no—
310C22×C32—48no—
311C22×C32—62no—
312C22×C32—61no—
313C22×C32D3×D418yes—
314C22×C32C2×#6712yes—
315C22×C32C23×D314yes—
316C22×C32C23×D311yescharacteristic
317C2×C3⋊D3—22no—
318C2×C3⋊D3—28no—
319C2×C3⋊D3—62no—
320C2×C3⋊D3—61no—
321C2×C3⋊D3—64no—
322C2×C3⋊D3—68no—
323C2×C3⋊D3—124no—
324C2×C3⋊D3—128no—
325C2×C3⋊D3—124no—
326C2×C3⋊D3#23514yes—
327C2×C3⋊D3C2×#6712yes—
328C2×C3⋊D3C2×#6712yes—
329C2×C3×D3—24no—
330C2×C3×D3—28no—
331C2×C3×D3—38no—
332C2×C3×D3—316no—
333C2×C3×D3—38no—
334C2×C3×D3—632no—
335C2×C3×D3—68no—
336D32—1216no—
337C32×C4—22no—
338C32×C4—28no—
339C32×C4—48no—
340C32×C4—62no—
341C32×C4—61no—
342C3⋊Dic3—22no—
343C3⋊Dic3—62no—
344C3⋊Dic3—61no—
345C3⋊Dic3—64no—
346C3⋊Dic3—68no—
347C3⋊Dic3—128no—
348C3⋊Dic3—124no—
349C3×Dic3—24no—
350C3×Dic3—28no—
351C3×Dic3—68no—
352C22×D4—271no—
353C23×C4—91no—
354#123—31no—
355#123—272no—
356#123—271no—
357#123—272no—
358#123—271no—
359#123—271no—
360C2×C4⋊C4—272no—
361C2×C22⋊C4—272no—
362C2×C22⋊C4—271no—
363C33C2×#12311yescharacteristic, complemented, Sylow
364C23×C3—24no—
365C23×C3—34no—
366C23×C3—91no—
367C23×C3—91no—
368C23×C3—94no—
369C23×C3—184no—
370C23×C3C2×D3214yes—
371C23×C3C22×C3⋊D311yescharacteristic
372C22×D3—34no—
373C22×D3—34no—
374C22×D3—316no—
375C22×D3—616no—
376C22×D3—94no—
377C22×D3—91no—
378C22×D3—184no—
379C22×D3—182no—
380C22×D3—184no—
381C22×D3—188no—
382C22×D3—1816no—
383C22×D3C22×C3⋊D311yescharacteristic
384C3×D4—68no—
385C2×C3×C4—28no—
386C2×C3×C4—22no—
387C2×C3×C4—28no—
388C2×C3×C4—34no—
389C2×C3×C4—38no—
390C2×C3×C4—48no—
391C2×C3×C4—92no—
392C2×C3×C4—184no—
393C2×C3×C4—184no—
394C2×C3×C4—182no—
395C2×C3×C4C2×D3218yes—
396C2×C3×C4C22×C3⋊D312yes—
397#67—22no—
398#67—182no—
399#67—182no—
400#67—188no—
401#67—188no—
402#67—182no—
403#67—368no—
404C2×Dic3—38no—
405C2×Dic3—68no—
406C2×Dic3—94no—
407C2×Dic3—98no—
408C2×Dic3—91no—
409C2×Dic3—92no—
410C2×Dic3—184no—
411C2×Dic3—188no—
412C2×Dic3—184no—
413C2×Dic3—182no—
414C2×Dic3C22×C3⋊D311yescharacteristic
415C2×Dic3C22×C3⋊D312yes—
416D12—188no—
417C4×D3—616no—
418C4×D3—616no—
419C4×D3—1816no—
420C4×D3—188no—
421C2×C32—22no—
422C2×C32—28no—
423C2×C32—24no—
424C2×C32—28no—
425C2×C32—48no—
426C2×C32—121no—
427C2×C32C2×#23512yes—
428C2×C32C2×D3×D414yes—
429C2×C32D3×#4118yes—
430C2×C32C22×#6711yescharacteristic
431C3⋊D3—22no—
432C3⋊D3—121no—
433C3⋊D3—124no—
434C3⋊D3—244no—
435C3⋊D3#92914yesdirect product factor
436C3×D3—316no—
437C3×D3—44no—
438C3×D3—68no—
439C24—91no—
440C24—271no—
441C2×D4—31no—
442C2×D4—271no—
443C2×D4—271no—
444C2×D4—271no—
445C2×D4—544no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4—92no—
449C22×C4—184no—
450C22×C4—272no—
451C22×C4—271no—
452C22×C4D3×C3⋊D311yescharacteristic, complemented
453C4⋊C4—32no—
454C4⋊C4—272no—
455C4⋊C4—272no—
456C4⋊C4—272no—
457C22⋊C4—31no—
458C22⋊C4—32no—
459C22⋊C4—272no—
460C22⋊C4—272no—
461C22⋊C4—272no—
462C22⋊C4—271no—
463C22⋊C4—272no—
464C22×C3—28no—
465C22×C3—22no—
466C22×C3—24no—
467C22×C3—28no—
468C22×C3—48no—
469C22×C3—68no—
470C22×C3—64no—
471C22×C3—92no—
472C22×C3—94no—
473C22×C3—92no—
474C22×C3—188no—
475C22×C3—182no—
476C22×C3D3×#6718yes—
477C22×C3D4×C3⋊D312yes—
478C22×C3C22×D3214yes—
479C22×C3C23×C3⋊D311yescharacteristic
480C2×D3—21no—
481C2×D3—22no—
482C2×D3—316no—
483C2×D3—38no—
484C2×D3—38no—
485C2×D3—632no—
486C2×D3—68no—
487C2×D3—188no—
488C2×D3—184no—
489C2×D3—181no—
490C2×D3—182no—
491C2×D3—364no—
492C2×D3—368no—
493C2×D3—3616no—
494C2×D3—364no—
495C3×C4—28no—
496C3×C4—22no—
497C3×C4—48no—
498C3×C4—68no—
499C3×C4—64no—
500C3×C4—182no—
501Dic3—21no—
502Dic3—22no—
503Dic3—68no—
504Dic3—188no—
505Dic3—184no—
506Dic3—181no—
507Dic3—182no—
508Dic3—364no—
509Dic3—368no—
510C32—24no—
511C32D3×#12314yescomplemented
512C32C2×#92911yescharacteristic, complemented
513C23—31no—
514C23—91no—
515C23—91no—
516C23—94no—
517C23—184no—
518C23—271no—
519C23—542no—
520C23—544no—
521C23C2×D3×C3⋊D311yescharacteristic
522D4—62no—
523D4—542no—
524D4—542no—
525D4—542no—
526C2×C4—22no—
527C2×C4—32no—
528C2×C4—31no—
529C2×C4—92no—
530C2×C4—184no—
531C2×C4—184no—
532C2×C4—182no—
533C2×C4—272no—
534C2×C4—271no—
535C2×C4—542no—
536C2×C4—544no—
537C2×C4C2×D3×C3⋊D312yes—
538C2×C3—22no—
539C2×C3—28no—
540C2×C3—28no—
541C2×C3—24no—
542C2×C3—48no—
543C2×C3—94no—
544C2×C3—124no—
545C2×C3—182no—
546C2×C3D3×#23518yes—
547C2×C3C2×D3×#6714yes—
548C2×C3C2×D4×C3⋊D311yescharacteristic
549C2×C3#41×C3⋊D312yes—
550D3—316no—
551D3—41no—
552D3—68no—
553D3—361no—
554D3—364no—
555D3—724no—
556C22—22no—
557C22—62no—
558C22—61no—
559C22—94no—
560C22—92no—
561C22—92no—
562C22—188no—
563C22—182no—
564C22—542no—
565C22—541no—
566C22—1084no—
567C22C3⋊D3×#6712yes—
568C22C22×D3×C3⋊D311yescharacteristic
569C4—22no—
570C4—62no—
571C4—61no—
572C4—182no—
573C4—542no—
574C4—541no—
575C3—24no—
576C3D3×#92914yescomplemented
577C3C3⋊D3×#12311yescharacteristic, complemented
578C2—22no—
579C2—94no—
580C2—121no—
581C2—182no—
582C2—1081no—
583C2C3⋊D3×#23512yes—
584C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
prime radicalC2×C3⋊D3×#67C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×C3⋊D3C2semidirect
3. #11723970C2semidirect
4. C32×#929C2semidirect
5. C3⋊D3×#217C2semidirect
6. #11723608C2semidirect
7. #11723602C2semidirect
8. C3⋊D3×(C2×D3)⋊C4C2semidirect
9. #11723518C2semidirect
10. C3⋊D3×Dic3⋊C4C2semidirect
11. #11723417C2semidirect
16. C22×C33×C4C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
28. #88864C22semidirect
29. #88859C22semidirect
30. #88857C22semidirect
31. C32×#217C22semidirect
32. C32×(C2×D3)⋊C4C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. #88806C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
36. #88804C22semidirect
37. #88803C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
40. C22×C4×C3⋊D3D3semidirect
54. C3×#929D3semidirect
95. C22×C32×C4C2×D3semidirect
96. C22×C32×C4C2×D3semidirect
101. C22×C3⋊Dic3C2×D3semidirect
108. C2×C4×C3⋊D3C2×D3semidirect
136. C3×#217C2×D3semidirect
137. C3×(C2×D3)⋊C4C2×D3semidirect
138. C3×Dic3⋊C4C2×D3semidirect
177. #929C3⋊D3direct (N × H)
249. C3×C3⋊D3#123semidirect
261. C22×C3×C4D32semidirect
262. C22×C3×C4C2×C3⋊D3semidirect
289. #217C2×C3⋊D3semidirect
297. (C2×D3)⋊C4C2×C3⋊D3semidirect
305. Dic3⋊C4C2×C3⋊D3semidirect
363. C33C2×#123semidirect
435. C3⋊D3#929direct (N × H)
452. C22×C4D3×C3⋊D3semidirect
511. C32D3×#123semidirect
512. C32C2×#929semidirect
576. C3D3×#929semidirect
577. C3C3⋊D3×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3⋊D3×#672
#117239702
C32×#9292
C3⋊D3×#2172
#117236082
#117236022
C3⋊D3×(C2×D3)⋊C42
#117235182
C3⋊D3×Dic3⋊C42
#117234172
C3⋊D3×#1233
D3×#9293