Finite Group Databasebeta

← #13175930

Subgroups — #13175930

Order 1728.

2388 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C22×#6290C211yesmaximal, characteristic, complemented
3#11723927C211yesmaximal, characteristic, complemented
4C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#882C211yesmaximal, characteristic, complemented
6#11723630C211yesmaximal, characteristic, complemented
7#11723603C211yesmaximal, characteristic, complemented
8#11723540C212yesmaximal, complemented
9#11723523C212yesmaximal, complemented
10#11723522C212yesmaximal, complemented
11#11723520C212yesmaximal, complemented
12#10596060—31nomaximal
13#10594290—34nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C23×C32×D3C2211yescharacteristic, complemented
16C22×D3×C3⋊D3C2211yescharacteristic, complemented
17C2×#6312C2211yescharacteristic
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3C2212yescomplemented
20C2×C32×#67C2211yescharacteristic
21C2×C32×D12C2212yescomplemented
22C3⋊D3×#67—24no—
23C2×#6292C2211yescharacteristic, complemented
24C2×#6291C2212yescomplemented
25C2×#6290—24no—
26C2×#6290C2212yes—
27C2×#6290C2212yescomplemented
28C2×#6290C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C33×C22⋊C4C2211yescharacteristic, complemented
31#88859C2212yescomplemented
32C4⋊(C3⋊(C3⋊Dic3))C2212yescomplemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36#88807C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39C22×#638—31no—
40C2×D4×C3⋊D3—31no—
41C2×D3×#67—34no—
42C22×#625—34no—
43C32×#120—31no—
44#64162—31no—
45#64147—32no—
46#64146—32no—
47#64144—31no—
48#64095—31no—
49#64095—34no—
50#64095—64no—
51#64093—32no—
52#64092—32no—
53C22⋊C4×C3⋊D3D311yescharacteristic, complemented
54C3×#882D314yescomplemented
55C3×D3×C22⋊C4—34no—
56#63977—34no—
57#63962—34no—
58#63922—38no—
59#63908—38no—
60#63906—38no—
61#63891—38no—
62C23×C33C2311yescharacteristic
63C22×C3⋊(C3⋊D3)C2311yescharacteristic
64C22×C3×C3⋊D3—42no—
65C22×C3×C3⋊D3D414yescomplemented
66C22×C3×C3⋊D3C2311yescharacteristic
67C22×C3×C3⋊D3C2311yescharacteristic
68C22×C32×D3—22no—
69C22×C32×D3—42no—
70C22×C32×D3C2311yescharacteristic
71C22×C32×D3C2312yes—
72C2×D3×C3⋊D3—22no—
73C2×D3×C3⋊D3—42no—
74C2×C33×C4C2312yes—
75#6312—22no—
76C2×C3⋊(C3⋊Dic3)—22no—
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4×C3⋊D3—42no—
81C32×#67—22no—
82C2×C32×Dic3C2311yescharacteristic
83C32×D12—42no—
84#6292—22no—
85#6291—42no—
86#6290—24no—
87#6290—24no—
88#6290—22no—
89Dic3×C3⋊D3—22no—
90#5589—94no—
91#5493—91no—
92C24×C32—31no—
93C23×C3⋊D3—31no—
94C23×C3⋊D3C2×D311yescharacteristic
95C23×C3×D3—34no—
96C23×C3×D3C2×D314yescomplemented
97C22×D32—34no—
98C2×C32×D4—31no—
99C2×C32×D4—32no—
100C2×#638—31no—
101C2×#638—34no—
102C2×#638—32no—
103C2×#638—32no—
104C2×#638—31no—
105C2×#638—32no—
106C2×#638—64no—
107C2×#638—64no—
108C22×C3⋊Dic3—31no—
109C22×C3⋊Dic3—34no—
110C22×C3⋊Dic3—64no—
111D4×C3⋊D3—64no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4×C3⋊D3—31no—
114C2×C4×C3⋊D3C2×D312yescomplemented
115C2×C3×#67C2×D314yes—
116C2×C3×D12C2×D318yescomplemented
117C2×C3×C4×D3—38no—
118D3×#67—616no—
119C2×#626—34no—
120C2×#626—38no—
121C2×#625—38no—
122C2×#625—38no—
123C2×#625—34no—
124C2×#625—616no—
125C2×D3×Dic3—34no—
126C32×C22⋊C4—24no—
127C32×C22⋊C4—32no—
128C32×C22⋊C4C2×D314yescomplemented
129C32×C22⋊C4C2×D311yescharacteristic, complemented
130#3757—32no—
131#3757—32no—
132#3757C2×D311yescharacteristic, complemented
133#3752—32no—
134#3752—38no—
135#3752—68no—
136#3752C2×D312yescomplemented
137C4⋊(C3⋊Dic3)—32no—
138C4⋊(C3⋊Dic3)—38no—
139C4⋊(C3⋊Dic3)—68no—
140#3750—32no—
141C3×#217—34no—
142C3×(C2×D3)⋊C4—38no—
143C3×(C2×D3)⋊C4C2×D318yescomplemented
144Dic3⋊Dic3—38no—
145(C2×D3)⋊Dic3—38no—
146(C2×D3)⋊Dic3—38no—
147C22×C33—22no—
148C22×C33C2×D412yes—
149C22×C33C2411yescharacteristic
150C2×C3⋊(C3⋊D3)—21no—
151C2×C3⋊(C3⋊D3)—22no—
152C2×C3×C3⋊D3—22no—
153C2×C3×C3⋊D3—22no—
154C2×C3×C3⋊D3—44no—
155C2×C3×C3⋊D3C2×D412yes—
156C2×C3×C3⋊D3C2×D412yes—
157C2×C32×D3—22no—
158C2×C32×D3—21no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C2×C32×D3—22no—
162C2×C32×D3—44no—
163D3×C3⋊D3—44no—
164C33×C4—22no—
165C3⋊(C3⋊Dic3)—21no—
166C3⋊(C3⋊Dic3)—22no—
167C3×C3⋊Dic3—22no—
168C32×Dic3—21no—
169C22×#67—94no—
170C22×#67—91no—
171C22×#67—91no—
172C2×D3×D4—94no—
173C3×#120—34no—
174C2×C3×C22⋊C4—91no—
175#953—94no—
176#938—98no—
177#937—98no—
178#935—94no—
179#930—92no—
180#930—92no—
181#886—91no—
182#886—94no—
183#886—91no—
184#886—92no—
185#886—184no—
186#884—98no—
187#883—98no—
188#882—91no—
189#882—92no—
190#882C3⋊D311yescharacteristic, complemented
191D3×C22⋊C4—34no—
192C23×C32—24no—
193C23×C32—31no—
194C23×C32—32no—
195C23×C32—62no—
196C23×C32—122no—
197C23×C32C22×D314yes—
198C23×C32C22×D311yescharacteristic
199C22×C3⋊D3—31no—
200C22×C3⋊D3—34no—
201C22×C3⋊D3—42no—
202C22×C3⋊D3—64no—
203C22×C3⋊D3—62no—
204C22×C3⋊D3—122no—
205C22×C3⋊D3D1214yescomplemented
206C22×C3⋊D3C22×D311yescharacteristic
207C22×C3⋊D3C22×D311yescharacteristic
208C22×C3×D3—28no—
209C22×C3×D3—34no—
210C22×C3×D3—34no—
211C22×C3×D3—316no—
212C22×C3×D3—48no—
213C22×C3×D3—128no—
214C22×C3×D3C22×D314yes—
215C22×C3×D3C22×D318yes—
216C2×D32—68no—
217C2×D32—128no—
218C32×D4—62no—
219C32×D4—122no—
220C2×C32×C4—28no—
221C2×C32×C4—31no—
222C2×C32×C4C22×D318yes—
223C2×C32×C4C22×D312yes—
224#638—62no—
225#638—62no—
226#638—64no—
227#638—64no—
228#638—68no—
229#638—128no—
230#638—122no—
231C2×C3⋊Dic3—32no—
232C2×C3⋊Dic3—31no—
233C2×C3⋊Dic3—34no—
234C2×C3⋊Dic3—38no—
235C2×C3⋊Dic3—64no—
236C2×C3⋊Dic3—68no—
237C2×C3⋊Dic3—62no—
238C2×C3⋊Dic3—68no—
239C2×C3⋊Dic3—128no—
240C2×C3⋊Dic3C22×D312yes—
241C4⋊(C3⋊D3)—62no—
242C4×C3⋊D3—42no—
243C4×C3⋊D3—62no—
244C3×#67—28no—
245C2×C3×Dic3—38no—
246C2×C3×Dic3C22×D314yes—
247C3×D12—48no—
248C3×C4×D3—128no—
249#626—68no—
250#626—128no—
251#625—616no—
252#625—616no—
253#625—68no—
254D3×Dic3—68no—
255#534—271noSylow
256C2×C33—22no—
257C2×C33C22×D411yescharacteristic
258C2×C33H(5,𝔽2)12yes—
259C3⋊(C3⋊D3)—41no—
260C3×C3⋊D3—22no—
261C3×C3⋊D3—22no—
262C32×D3—41no—
263C32×D3—42no—
264C24×C3—34no—
265C24×C3—91no—
266C23×D3—34no—
267C23×D3—94no—
268C23×D3—91no—
269C23×D3C2×C3⋊D311yescharacteristic, complemented
270C2×C3×D4—34no—
271C2×C3×D4—38no—
272C22×C3×C4—92no—
273C2×#67—98no—
274C2×#67—98no—
275C2×#67—98no—
276C2×#67—94no—
277C2×#67—94no—
278C2×#67—91no—
279C2×#67—92no—
280C2×#67—91no—
281C2×#67—92no—
282C2×#67—91no—
283C2×#67—184no—
284C2×#67—184no—
285C2×#67—184no—
286C2×#67—1816no—
287C2×#67C2×C3⋊D311yescharacteristic
288C22×Dic3—94no—
289C22×Dic3—91no—
290C22×Dic3—91no—
291C22×Dic3—184no—
292D3×D4—1816no—
293C2×D12—94no—
294C2×D12—92no—
295C2×D12C2×C3⋊D312yescomplemented
296C2×C4×D3—38no—
297C2×C4×D3—94no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—38no—
300C3×C22⋊C4—91no—
301C3×C22⋊C4—92no—
302C3×C22⋊C4D3214yescomplemented
303C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
304#217—34no—
305#217—98no—
306#217—98no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—92no—
309(C2×D3)⋊C4—92no—
310(C2×D3)⋊C4—98no—
311(C2×D3)⋊C4—92no—
312(C2×D3)⋊C4—188no—
313(C2×D3)⋊C4C2×C3⋊D312yescomplemented
314C4⋊Dic3—98no—
315C4⋊Dic3—92no—
316C4⋊Dic3—92no—
317C4⋊Dic3—188no—
318Dic3⋊C4—98no—
319C22×C32—22no—
320C22×C32—24no—
321C22×C32—28no—
322C22×C32—28no—
323C22×C32—48no—
324C22×C32—62no—
325C22×C32—61no—
326C22×C32—62no—
327C22×C32—62no—
328C22×C32—62no—
329C22×C32—124no—
330C22×C32C2×D1212yes—
331C22×C32D3×D418yes—
332C22×C32C23×D314yes—
333C22×C32C23×D311yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—44no—
337C2×C3⋊D3—61no—
338C2×C3⋊D3—62no—
339C2×C3⋊D3—64no—
340C2×C3⋊D3—68no—
341C2×C3⋊D3—124no—
342C2×C3⋊D3—128no—
343C2×C3⋊D3—124no—
344C2×C3⋊D3C2×D1212yes—
345C2×C3⋊D3C2×D1212yes—
346C2×C3×D3—28no—
347C2×C3×D3—24no—
348C2×C3×D3—28no—
349C2×C3×D3—28no—
350C2×C3×D3—28no—
351C2×C3×D3—38no—
352C2×C3×D3—38no—
353C2×C3×D3—416no—
354C2×C3×D3—68no—
355C2×C3×D3—68no—
356C2×C3×D3—1216no—
357D32—1216no—
358C32×C4—22no—
359C32×C4—28no—
360C32×C4—48no—
361C32×C4—61no—
362C3⋊Dic3—22no—
363C3⋊Dic3—61no—
364C3⋊Dic3—62no—
365C3⋊Dic3—64no—
366C3⋊Dic3—68no—
367C3⋊Dic3—128no—
368C3⋊Dic3—124no—
369C3×Dic3—24no—
370C3×Dic3—68no—
371C22×D4—271no—
372C22×D4—271no—
373#123—272no—
374#123—271no—
375#123—271no—
376#121—272no—
377#121—272no—
378#120—31no—
379#120—272no—
380#120—271no—
381C2×C22⋊C4—91no—
382C33#53411yescharacteristic, complemented, Sylow
383C23×C3—24no—
384C23×C3—34no—
385C23×C3—38no—
386C23×C3—68no—
387C23×C3—91no—
388C23×C3—91no—
389C23×C3—94no—
390C23×C3—128no—
391C23×C3—362no—
392C23×C3C2×D3214yes—
393C23×C3C22×C3⋊D311yescharacteristic
394C22×D3—22no—
395C22×D3—34no—
396C22×D3—34no—
397C22×D3—316no—
398C22×D3—42no—
399C22×D3—94no—
400C22×D3—91no—
401C22×D3—128no—
402C22×D3—184no—
403C22×D3—182no—
404C22×D3—188no—
405C22×D3—362no—
406C22×D3—368no—
407C22×D3C22×C3⋊D311yescharacteristic
408C22×D3C22×C3⋊D312yes—
409C3×D4—68no—
410C3×D4—128no—
411C2×C3×C4—28no—
412C2×C3×C4—34no—
413C2×C3×C4—92no—
414C2×C3×C4—362no—
415C2×C3×C4C2×D3218yes—
416C2×C3×C4C22×C3⋊D312yes—
417#67—22no—
418#67—182no—
419#67—182no—
420#67—184no—
421#67—184no—
422#67—188no—
423#67—1816no—
424#67—1816no—
425#67—188no—
426#67—182no—
427#67—368no—
428#67—368no—
429C2×Dic3—38no—
430C2×Dic3—98no—
431C2×Dic3—94no—
432C2×Dic3—91no—
433C2×Dic3—92no—
434C2×Dic3—184no—
435C2×Dic3—188no—
436C2×Dic3—182no—
437C2×Dic3—188no—
438C2×Dic3—182no—
439C2×Dic3—368no—
440C2×Dic3C22×C3⋊D311yescharacteristic
441D12—42no—
442D12—188no—
443D12—362no—
444C4×D3—128no—
445C4×D3—188no—
446C2×C32—22no—
447C2×C32—24no—
448C2×C32—28no—
449C2×C32—28no—
450C2×C32—48no—
451C2×C32—121no—
452C2×C32—122no—
453C2×C32C22×D1211yescharacteristic
454C2×C32C2×D3×D414yes—
455C2×C32#100418yes—
456C2×C32#100412yes—
457C3⋊D3—22no—
458C3⋊D3—22no—
459C3⋊D3—121no—
460C3⋊D3—124no—
461C3⋊D3—244no—
462C3×D3—44no—
463C3×D3—48no—
464C3×D3—68no—
465C3×D3—68no—
466C24—31no—
467C24—91no—
468C24—271no—
469C2×D4—31no—
470C2×D4—32no—
471C2×D4—271no—
472C2×D4—272no—
473C2×D4—272no—
474C2×D4—272no—
475C2×D4—271no—
476C2×D4—271no—
477C2×D4—544no—
478C2×D4—544no—
479C22×C4—92no—
480C22×C4—271no—
481C22×C4—271no—
482C4⋊C4—272no—
483C4⋊C4—272no—
484C22⋊C4—32no—
485C22⋊C4—91no—
486C22⋊C4—92no—
487C22⋊C4—272no—
488C22⋊C4—272no—
489C22⋊C4—272no—
490C22⋊C4D3×C3⋊D311yescharacteristic, complemented
491C22×C3—28no—
492C22×C3—22no—
493C22×C3—24no—
494C22×C3—28no—
495C22×C3—48no—
496C22×C3—68no—
497C22×C3—64no—
498C22×C3—68no—
499C22×C3—68no—
500C22×C3—68no—
501C22×C3—92no—
502C22×C3—92no—
503C22×C3—1216no—
504C22×C3—182no—
505C22×C3—182no—
506C22×C3—364no—
507C22×C3D3×D1218yes—
508C22×C3D4×C3⋊D312yes—
509C22×C3C22×D3214yes—
510C22×C3C23×C3⋊D311yescharacteristic
511C2×D3—21no—
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—38no—
517C2×D3—38no—
518C2×D3—44no—
519C2×D3—68no—
520C2×D3—68no—
521C2×D3—1216no—
522C2×D3—184no—
523C2×D3—188no—
524C2×D3—181no—
525C2×D3—182no—
526C2×D3—364no—
527C2×D3—368no—
528C2×D3—364no—
529C2×D3—3616no—
530C3×C4—28no—
531C3×C4—22no—
532C3×C4—48no—
533C3×C4—64no—
534C3×C4—182no—
535Dic3—21no—
536Dic3—68no—
537Dic3—184no—
538Dic3—188no—
539Dic3—181no—
540Dic3—182no—
541Dic3—368no—
542Dic3—364no—
543C32—24no—
544C32#549311yescharacteristic, complemented
545C32#558914yescomplemented
546C23—32no—
547C23—31no—
548C23—62no—
549C23—91no—
550C23—91no—
551C23—94no—
552C23—122no—
553C23—271no—
554C23—362no—
555C23—542no—
556C23—1082no—
557C23C2×D3×C3⋊D311yescharacteristic
558D4—62no—
559D4—122no—
560D4—542no—
561D4—542no—
562D4—544no—
563D4—544no—
564D4—542no—
565D4—1082no—
566C2×C4—31no—
567C2×C4—92no—
568C2×C4—271no—
569C2×C4—272no—
570C2×C4—362no—
571C2×C4—542no—
572C2×C4—542no—
573C2×C4C2×D3×C3⋊D312yes—
574C2×C3—22no—
575C2×C3—28no—
576C2×C3—24no—
577C2×C3—28no—
578C2×C3—48no—
579C2×C3—124no—
580C2×C3—128no—
581C2×C3—182no—
582C2×C3—182no—
583C2×C3C2×D3×D1214yes—
584C2×C3#6431318yes—
585C2×C3C2×D4×C3⋊D311yescharacteristic
586C2×C3#6436112yes—
587D3—42no—
588D3—41no—
589D3—68no—
590D3—68no—
591D3—361no—
592D3—364no—
593D3—724no—
594C22—22no—
595C22—61no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—62no—
600C22—92no—
601C22—92no—
602C22—124no—
603C22—182no—
604C22—182no—
605C22—364no—
606C22—541no—
607C22—542no—
608C22—1084no—
609C22C3⋊D3×D1212yes—
610C22C22×D3×C3⋊D311yescharacteristic
611C4—22no—
612C4—61no—
613C4—182no—
614C4—541no—
615C4—542no—
616C3—24no—
617C3#1059429014yescomplemented
618C3#1059606011yescharacteristic, complemented
619C2—22no—
620C2—122no—
621C2—121no—
622C2—182no—
623C2—182no—
624C2—1081no—
625C2C2×C3⋊D3×D1211yescharacteristic
626C2#1172458712yes—
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C22×#6290C2semidirect
3. #11723927C2semidirect
4. C3×C22⋊C4×C3⋊D3C2semidirect
5. C32×#882C2semidirect
6. #11723630C2semidirect
7. #11723603C2semidirect
8. #11723540C2semidirect
9. #11723523C2semidirect
10. #11723522C2semidirect
11. #11723520C2semidirect
15. C23×C32×D3C22semidirect
16. C22×D3×C3⋊D3C22semidirect
18. C22×C3⋊(C3⋊Dic3)C22semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
21. C2×C32×D12C22semidirect
23. C2×#6292C22semidirect
24. C2×#6291C22semidirect
27. C2×#6290C22semidirect
28. C2×#6290C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C33×C22⋊C4C22semidirect
31. #88859C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
33. C3×#3757C22semidirect
34. C3×#3752C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. #88807C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. C22⋊C4×C3⋊D3D3semidirect
54. C3×#882D3semidirect
65. C22×C3×C3⋊D3D4semidirect
96. C23×C3×D3C2×D3semidirect
114. C2×C4×C3⋊D3C2×D3semidirect
116. C2×C3×D12C2×D3semidirect
128. C32×C22⋊C4C2×D3semidirect
129. C32×C22⋊C4C2×D3semidirect
132. #3757C2×D3semidirect
136. #3752C2×D3semidirect
143. C3×(C2×D3)⋊C4C2×D3semidirect
190. #882C3⋊D3semidirect
205. C22×C3⋊D3D12semidirect
269. C23×D3C2×C3⋊D3semidirect
295. C2×D12C2×C3⋊D3semidirect
302. C3×C22⋊C4D32semidirect
303. C3×C22⋊C4C2×C3⋊D3semidirect
313. (C2×D3)⋊C4C2×C3⋊D3semidirect
382. C33#534semidirect
490. C22⋊C4D3×C3⋊D3semidirect
544. C32#5493semidirect
545. C32#5589semidirect
617. C3#10594290semidirect
618. C3#10596060semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C22×#62902
#117239272
C3×C22⋊C4×C3⋊D32
C32×#8822
#117236302
#117236032
#117235402
#117235232
#117235222
#117235202
#105960603
#105942903