Finite Group Databasebeta

← C3×#10591393 #13158403

Subgroups — C3×#10591393 #13158403

Order 1728.

1738 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#626C212yesmaximal, complemented
2C22×C3×#625C211yesmaximal, characteristic, complemented
3C2×C3×#3752C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C212yesmaximal, complemented
5C3×#63579C211yesmaximal, characteristic, complemented
6C3×#4960—32nomaximal
7#10591393C311yesmaximal, characteristic, direct product factor
8C23×C3×C3⋊D3C2211yescharacteristic
9C23×C32×D3C2212yes—
10C22×C33×C4C2211yescharacteristic
11C22×C3×C3⋊Dic3C2211yescharacteristic
12C22×C32×Dic3C2212yes—
13C2×C3×#626—24no—
14C2×C3×#626—24no—
15C2×C3×#626—24no—
16C2×C3×#625—24no—
17C2×C3×#625—22no—
18C3×#3752—22no—
19C32×(C2×D3)⋊C4—24no—
20C22×C3×#67—32no—
21C22×C3×#67—32no—
22C22×C3×D12—32no—
23C22×#626C2×C312yescomplemented
24C22×#625C2×C311yescharacteristic, complemented
25C2×C32×C22⋊C4—32no—
26C2×#3752C2×C311yescharacteristic, complemented
27C2×C3×(C2×D3)⋊C4—22no—
28C2×C3×(C2×D3)⋊C4—32no—
29C2×C3×(C2×D3)⋊C4—61no—
30C2×C3×(C2×D3)⋊C4D312yescomplemented
31C2×C3×(C2×D3)⋊C4C2×C312yescomplemented
32C3×C3⋊#95—32no—
33#63579C2×C311yescharacteristic, complemented
34C23×C33C2311yescharacteristic
35C22×C3×C3⋊D3—21no—
36C22×C3×C3⋊D3—22no—
37C22×C3×C3⋊D3—22no—
38C22×C3×C3⋊D3—21no—
39C22×C3×C3⋊D3D412yescomplemented
40C22×C32×D3—22no—
41C22×C32×D3—22no—
42C22×C32×D3—22no—
43C22×C32×D3—22no—
44C22×C32×D3—22no—
45C22×C32×D3—22no—
46C22×C32×D3D414yescomplemented
47C2×C33×C4—21no—
48C2×C33×C4—22no—
49C2×C3×C3⋊Dic3—22no—
50C2×C3×C3⋊Dic3D412yescomplemented
51C2×C32×Dic3—22no—
52C2×C32×Dic3—22no—
53C2×C32×Dic3D414yescomplemented
54C3×#626—216no—
55C3×#625—28no—
56C3×#392—91no—
57#4960—32no—
58C24×C32—32no—
59C23×C3⋊D3C22×C311yescharacteristic
60C23×C3×D3—22no—
61C23×C3×D3—32no—
62C23×C3×D3—61no—
63C23×C3×D3C2×D312yes—
64C23×C3×D3C22×C312yes—
65C22×C32×C4—21no—
66C22×C32×C4—22no—
67C22×C32×C4—32no—
68C22×C32×C4—41no—
69C22×C32×C4C2×D312yes—
70C22×C32×C4C22×C311yescharacteristic
71C22×C3⋊Dic3C22×C311yescharacteristic
72C2×C3×#67—64no—
73C2×C3×#67—64no—
74C2×C3×#67—64no—
75C2×C3×#67—64no—
76C2×C3×#67—64no—
77C2×C3×#67—64no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—32no—
80C22×C3×Dic3—61no—
81C22×C3×Dic3C2×D312yes—
82C22×C3×Dic3C22×C312yes—
83C2×C3×D12—64no—
84C2×C3×D12—64no—
85C2×C3×D12—64no—
86C2×#626—24no—
87C2×#626—24no—
88C2×#626—24no—
89C2×#625—24no—
90C2×#625—22no—
91C32×C22⋊C4—64no—
92#3752—22no—
93C3×(C2×D3)⋊C4—28no—
94C3×(C2×D3)⋊C4—24no—
95C3×(C2×D3)⋊C4—24no—
96C3×(C2×D3)⋊C4—64no—
97C3×(C2×D3)⋊C4—64no—
98C22×C33C2×D412yes—
99C22×C33C2×D411yescharacteristic
100C22×C33C2×D411yescharacteristic
101C22×C33C2×D412yes—
102C22×C33#4111yescharacteristic
103C2×C3×C3⋊D3—24no—
104C2×C3×C3⋊D3—22no—
105C2×C3×C3⋊D3—41no—
106C2×C3×C3⋊D3—42no—
107C2×C3×C3⋊D3—41no—
108C2×C32×D3—24no—
109C2×C32×D3—24no—
110C2×C32×D3—24no—
111C2×C32×D3—42no—
112C2×C32×D3—42no—
113C2×C32×D3—42no—
114C2×C32×D3—42no—
115C33×C4—41no—
116C3×C3⋊Dic3—22no—
117C32×Dic3—24no—
118C22×C3×D4—92no—
119C22×C3×D4—91no—
120C22×#67—32no—
121C22×#67—32no—
122C22×D12—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—62no—
126C2×C3×C22⋊C4—91no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—61no—
129C2×(C2×D3)⋊C4C3×D312yescomplemented
130C3×#95—91no—
131C3⋊#95—32no—
132C23×C32—21no—
133C23×C32—22no—
134C23×C32—34no—
135C23×C32—41no—
136C23×C32—62no—
137C23×C32—62no—
138C23×C32—62no—
139C23×C32—62no—
140C23×C32—62no—
141C23×C32—62no—
142C23×C32C22×D312yes—
143C23×C32C23×C311yescharacteristic
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3C3×D412yescomplemented
149C22×C3×D3—24no—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—24no—
164C22×C3×D3—34no—
165C22×C3×D3—42no—
166C22×C3×D3—42no—
167C22×C3×D3—42no—
168C22×C3×D3—42no—
169C22×C3×D3—62no—
170C22×C3×D3—62no—
171C22×C3×D3—62no—
172C22×C3×D3—62no—
173C22×C3×D3—62no—
174C22×C3×D3—62no—
175C22×C3×D3—62no—
176C22×C3×D3—62no—
177C22×C3×D3—62no—
178C22×C3×D3—122no—
179C22×C3×D3—122no—
180C22×C3×D3D1214yescomplemented
181C22×C3×D3C3×D414yescomplemented
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—24no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—34no—
190C2×C32×C4—42no—
191C2×C32×C4—42no—
192C2×C32×C4—42no—
193C2×C32×C4—42no—
194C2×C32×C4—44no—
195C2×C32×C4—62no—
196C2×C32×C4—62no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3C3×D412yescomplemented
199C3×#67—616no—
200C3×#67—616no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—34no—
207C2×C3×Dic3—42no—
208C2×C3×Dic3—42no—
209C2×C3×Dic3—62no—
210C2×C3×Dic3—62no—
211C2×C3×Dic3—62no—
212C2×C3×Dic3—122no—
213C2×C3×Dic3#6714yescomplemented
214C2×C3×Dic3C3×D414yescomplemented
215C3×D12—616no—
216#626—216no—
217#625—28no—
218#392—91noSylow
219C2×C33#12011yescharacteristic
220C2×C33#12012yes—
221C2×C33#12111yescharacteristic
222C2×C33#12112yes—
223C2×C33#12711yescharacteristic
224C3×C3⋊D3—42no—
225C32×D3—44no—
226C24×C3—32no—
227C24×C3—32no—
228C24×C3—62no—
229C24×C3—91no—
230C23×D3—32no—
231C23×D3—61no—
232C23×D3C2×C3×D312yes—
233C2×C3×D4—184no—
234C2×C3×D4—184no—
235C2×C3×D4—184no—
236C2×C3×D4—182no—
237C2×C3×D4—184no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—41no—
243C22×C3×C4—62no—
244C22×C3×C4—91no—
245C22×C3×C4D3211yescharacteristic
246C22×C3×C4C2×C3×D312yes—
247C2×#67—64no—
248C2×#67—64no—
249C2×#67—64no—
250C2×#67—64no—
251C2×#67—64no—
252C2×#67—64no—
253C22×Dic3—32no—
254C22×Dic3—61no—
255C22×Dic3C2×C3×D312yes—
256C2×D12—64no—
257C2×D12—64no—
258C2×D12—64no—
259C3×C22⋊C4—64no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—68no—
262C3×C22⋊C4—182no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266C22×C32—21no—
267C22×C32—22no—
268C22×C32—21no—
269C22×C32—22no—
270C22×C32—21no—
271C22×C32—22no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—22no—
276C22×C32—22no—
277C22×C32—22no—
278C22×C32—42no—
279C22×C32—41no—
280C22×C32—42no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—64no—
284C22×C32—64no—
285C22×C32—64no—
286C22×C32—122no—
287C22×C32—122no—
288C22×C32—122no—
289C22×C32—122no—
290C22×C32C2×D1212yes—
291C22×C32#23512yes—
292C22×C32D3×D412yes—
293C22×C32D3×D412yes—
294C22×C32D3×D412yes—
295C22×C32D3×D412yes—
296C22×C32C2×#6712yes—
297C22×C32C2×C3×D412yes—
298C22×C32C2×C3×D411yescharacteristic
299C22×C32C2×C3×D411yescharacteristic
300C22×C32C2×C3×D412yes—
301C22×C32C3×#4111yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—24no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—41no—
307C2×C3×D3—28no—
308C2×C3×D3—24no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—24no—
312C2×C3×D3—24no—
313C2×C3×D3—24no—
314C2×C3×D3—44no—
315C2×C3×D3—44no—
316C2×C3×D3—44no—
317C2×C3×D3—44no—
318C2×C3×D3—44no—
319C2×C3×D3—44no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C2×C3×D3—42no—
328C2×C3×D3—64no—
329C2×C3×D3—64no—
330C2×C3×D3—64no—
331C2×C3×D3—64no—
332C2×C3×D3—124no—
333C2×C3×D3—124no—
334C2×C3×D3—122no—
335C2×C3×D3—122no—
336C2×C3×D3—122no—
337C2×C3×D3—122no—
338C2×C3×D3—122no—
339C2×C3×D3—122no—
340C32×C4—44no—
341C32×C4—42no—
342C32×C4—44no—
343C32×C4—42no—
344C32×C4—41no—
345C32×C4—64no—
346C3⋊Dic3—22no—
347C3×Dic3—24no—
348C3×Dic3—24no—
349C3×Dic3—44no—
350C3×Dic3—64no—
351C3×Dic3—122no—
352C22×D4—92no—
353C22×D4—91no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4—91no—
356#95—91no—
357C33#39211yescharacteristic, complemented, Sylow
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—34no—
361C23×C3—34no—
362C23×C3—41no—
363C23×C3—64no—
364C23×C3—64no—
365C23×C3—64no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3—92no—
379C23×C3—122no—
380C23×C3—122no—
381C23×C3—122no—
382C23×C3—122no—
383C23×C3—181no—
384C23×C3—182no—
385C23×C3—182no—
386C23×C3—181no—
387C23×C3C2×D3211yescharacteristic
388C23×C3C22×C3×D312yes—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—34no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—122no—
406C22×D3—122no—
407C22×D3C3×D1214yescomplemented
408C3×D4—1816no—
409C3×D4—188no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—34no—
418C2×C3×C4—34no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—44no—
423C2×C3×C4—42no—
424C2×C3×C4—64no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—92no—
430C2×C3×C4—122no—
431C2×C3×C4—122no—
432C2×C3×C4—182no—
433#67—616no—
434#67—616no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—34no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—122no—
442C2×Dic3C3×#6714yescomplemented
443D12—616no—
444C2×C32—22no—
445C2×C32—22no—
446C2×C32—22no—
447C2×C32—22no—
448C2×C32—22no—
449C2×C32—22no—
450C2×C32—22no—
451C2×C32—22no—
452C2×C32—21no—
453C2×C32—22no—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—42no—
457C2×C32—41no—
458C2×C32—42no—
459C2×C32—41no—
460C2×C32—41no—
461C2×C32—124no—
462C2×C32#88212yes—
463C2×C32#88212yes—
464C2×C32#88412yes—
465C2×C32#88412yes—
466C2×C32#93012yes—
467C2×C32#93712yes—
468C2×C32#94012yes—
469C2×C32C3×#12011yescharacteristic
470C2×C32C3×#12012yes—
471C2×C32C3×#12111yescharacteristic
472C2×C32C3×#12112yes—
473C2×C32C3×#12711yescharacteristic
474C3⋊D3—42no—
475C3×D3—48no—
476C3×D3—44no—
477C3×D3—44no—
478C3×D3—124no—
479C3×D3—124no—
480C24—32no—
481C24—91no—
482C2×D4—184no—
483C2×D4—184no—
484C2×D4—184no—
485C2×D4—182no—
486C2×D4—184no—
487C22×C4—32no—
488C22×C4—91no—
489C22×C4C3×D3211yescharacteristic
490C22⋊C4—64no—
491C22⋊C4—182no—
492C22×C3—21no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—41no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—68no—
510C22×C3—64no—
511C22×C3—64no—
512C22×C3—64no—
513C22×C3—64no—
514C22×C3—64no—
515C22×C3—64no—
516C22×C3—124no—
517C22×C3—124no—
518C22×C3—124no—
519C22×C3—124no—
520C22×C3—124no—
521C22×C3—124no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3—182no—
531C22×C3—184no—
532C22×C3—362no—
533C22×C3—361no—
534C22×C3—361no—
535C22×C3#379811yescharacteristic
536C22×C3D3×D1212yes—
537C22×C3#380211yescharacteristic
538C22×C3D3×#6712yes—
539C22×C3#381111yescharacteristic
540C22×C3C2×C3×D1212yes—
541C22×C3C3×#23512yes—
542C22×C3C3×D3×D412yes—
543C22×C3C3×D3×D412yes—
544C22×C3C3×D3×D412yes—
545C22×C3C3×D3×D412yes—
546C22×C3C2×C3×#6712yes—
547C2×D3—24no—
548C2×D3—24no—
549C2×D3—24no—
550C2×D3—42no—
551C2×D3—42no—
552C2×D3—42no—
553C2×D3—42no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—64no—
557C2×D3—64no—
558C2×D3—124no—
559C2×D3—122no—
560C2×D3—124no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—122no—
566C3×C4—42no—
567C3×C4—44no—
568C3×C4—44no—
569C3×C4—42no—
570C3×C4—41no—
571C3×C4—64no—
572C3×C4—64no—
573C3×C4—124no—
574C3×C4—182no—
575Dic3—24no—
576Dic3—64no—
577Dic3—122no—
578C32—22no—
579C32—21no—
580C32—41no—
581C32#496012yescomplemented
582C32C3×#39211yescharacteristic, complemented
583C23—34no—
584C23—62no—
585C23—62no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—62no—
590C23—92no—
591C23—181no—
592C23—182no—
593C23—182no—
594C23—181no—
595C23C2×C3×D3211yescharacteristic
596D4—1816no—
597D4—188no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—34no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—92no—
604C2×C4—182no—
605C2×C3—21no—
606C2×C3—22no—
607C2×C3—22no—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—22no—
612C2×C3—22no—
613C2×C3—22no—
614C2×C3—22no—
615C2×C3—21no—
616C2×C3—22no—
617C2×C3—41no—
618C2×C3—42no—
619C2×C3—41no—
620C2×C3—42no—
621C2×C3—41no—
622C2×C3—128no—
623C2×C3—124no—
624C2×C3—124no—
625C2×C3—362no—
626C2×C3#6390612yes—
627C2×C3#6391211yescharacteristic
628C2×C3#6392212yes—
629C2×C3#6392311yescharacteristic
630C2×C3#6397911yescharacteristic
631C2×C3C3×#88212yes—
632C2×C3C3×#88212yes—
633C2×C3C3×#88412yes—
634C2×C3C3×#88412yes—
635C2×C3C3×#93012yes—
636C2×C3C3×#93712yes—
637C2×C3C3×#94012yes—
638D3—44no—
639D3—124no—
640D3—124no—
641C22—64no—
642C22—64no—
643C22—64no—
644C22—122no—
645C22—122no—
646C22—122no—
647C22—122no—
648C22—182no—
649C22—184no—
650C22—361no—
651C22—362no—
652C22—361no—
653C22C3×#379811yescharacteristic
654C22C3×D3×D1212yes—
655C22C3×#380211yescharacteristic
656C22C3×D3×#6712yes—
657C22C3×#381111yescharacteristic
658C4—41no—
659C4—64no—
660C4—182no—
661C3—21no—
662C3—22no—
663C3—41no—
664C3#1059139311yescharacteristic, direct product factor
665C3C3×#496012yescomplemented
666C2—124no—
667C2—362no—
668C2C3×#6390612yes—
669C2C3×#6391211yescharacteristic
670C2C3×#6392212yes—
671C2C3×#6392311yescharacteristic
672C2C3×#6397911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#626C2semidirect
2. C22×C3×#625C2semidirect
3. C2×C3×#3752C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. C3×#63579C2semidirect
7. #10591393C3direct (N × H)
23. C22×#626C2×C3semidirect
24. C22×#625C2×C3semidirect
26. C2×#3752C2×C3semidirect
30. C2×C3×(C2×D3)⋊C4D3semidirect
31. C2×C3×(C2×D3)⋊C4C2×C3semidirect
33. #63579C2×C3semidirect
39. C22×C3×C3⋊D3D4semidirect
46. C22×C32×D3D4semidirect
50. C2×C3×C3⋊Dic3D4semidirect
53. C2×C32×Dic3D4semidirect
129. C2×(C2×D3)⋊C4C3×D3semidirect
148. C22×C3⋊D3C3×D4semidirect
180. C22×C3×D3D12semidirect
181. C22×C3×D3C3×D4semidirect
198. C2×C3⋊Dic3C3×D4semidirect
213. C2×C3×Dic3#67semidirect
214. C2×C3×Dic3C3×D4semidirect
357. C33#392semidirect
407. C22×D3C3×D12semidirect
442. C2×Dic3C3×#67semidirect
581. C32#4960semidirect
582. C32C3×#392semidirect
664. C3#10591393direct (N × H)
665. C3C3×#4960semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6262
C22×C3×#6252
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C3×#635792
C3×#49603
#105913933