Finite Group Databasebeta

← C3×#10591380 #13158385

Subgroups — C3×#10591380 #13158385

Order 1728.

1586 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C22×C3×#624C211yesmaximal, characteristic, complemented
3C2×C3×#3722C212yesmaximal, complemented
4C2×C3×#3722C211yesmaximal, characteristic, complemented
5C32×C3⋊#95C212yesmaximal, complemented
6C3×#4665—32nomaximal
7#10591380C311yesmaximal, characteristic, direct product factor
8C23×C3×C3⋊D3C2211yescharacteristic
9C23×C3×C3⋊D3C2211yescharacteristic
10C22×C33×C4C2211yescharacteristic
11C2×C3×C4⋊(C3⋊D3)—22no—
12C2×C3×C4⋊(C3⋊D3)—22no—
13C2×C3×C4⋊(C3⋊D3)C414yescomplemented
14C22×C32×Dic3C2212yes—
15C22×C32×Dic3C2212yes—
16C2×C3×#624—22no—
17C2×C3×#624—24no—
18C3×#3722—22no—
19C3×#3722—24no—
20C22×C4⋊(C3⋊D3)C2×C311yescharacteristic
21C22×C3×D12—32no—
22C22×C3×D12—61no—
23C22×C3×C4×D3—32no—
24C22×#624C2×C311yescharacteristic, complemented
25C2×C3×(C2×D3)⋊C4—32no—
26C2×C3×(C2×D3)⋊C4—32no—
27C2×C3×(C2×D3)⋊C4—32no—
28C2×#3722C2×C312yescomplemented
29C2×#3722C2×C311yescharacteristic, complemented
30C32×#95—32no—
31C3×C3⋊#95—22no—
32C3×C3⋊#95D312yescomplemented
33C3×C3⋊#95C2×C312yescomplemented
34C23×C33C2311yescharacteristic
35C22×C3×C3⋊D3—22no—
36C22×C3×C3⋊D3—22no—
37C22×C3×C3⋊D3—21no—
38C22×C3×C3⋊D3—21no—
39C22×C3×C3⋊D3—22no—
40C22×C3×C3⋊D3—22no—
41C22×C3×C3⋊D3C2×C412yes—
42C22×C3×C3⋊D3C2×C412yescomplemented
43C22×C3×C3⋊D3D412yes—
44C22×C3×C3⋊D3D412yes—
45C2×C33×C4—21no—
46C2×C33×C4—21no—
47C2×C33×C4C2×C412yescomplemented
48C3×C4⋊(C3⋊D3)—28no—
49C2×C32×Dic3—22no—
50C2×C32×Dic3—22no—
51C2×C32×Dic3—22no—
52C2×C32×Dic3—22no—
53C2×C32×Dic3—22no—
54C2×C32×Dic3D414yescomplemented
55C3×#624—28no—
56C3×#386—91no—
57#4665—32no—
58C23×C3⋊D3C22×C311yescharacteristic
59C23×C3⋊D3C22×C311yescharacteristic
60C23×C3×D3—32no—
61C23×C3×D3—32no—
62C23×C3×D3—61no—
63C23×C3×D3—61no—
64C22×C32×C4—21no—
65C22×C32×C4—22no—
66C22×C32×C4—32no—
67C22×C32×C4—32no—
68C22×C32×C4—41no—
69C22×C32×C4C2×D312yes—
70C22×C32×C4C22×C311yescharacteristic
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)C3×C414yescomplemented
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3C2×D312yes—
77C22×C3×Dic3C2×D312yes—
78C22×C3×Dic3C22×C312yes—
79C22×C3×Dic3C22×C312yes—
80C2×C3×D12—38no—
81C2×C3×D12—64no—
82C2×C3×D12—64no—
83C2×C3×D12—64no—
84C2×C3×D12—64no—
85C2×C3×D12—64no—
86C2×C3×C4×D3—64no—
87C2×C3×C4×D3—64no—
88C2×C3×C4×D3—64no—
89C2×#624—22no—
90C2×#624—24no—
91C3×(C2×D3)⋊C4—64no—
92C3×(C2×D3)⋊C4—64no—
93C3×(C2×D3)⋊C4—64no—
94#3722—22no—
95#3722—24no—
96C22×C33C22×C411yescharacteristic
97C22×C33C2×D411yescharacteristic
98C22×C33C2×D411yescharacteristic
99C22×C33C2×D412yes—
100C22×C33#4112yes—
101C2×C3×C3⋊D3—24no—
102C2×C3×C3⋊D3—22no—
103C2×C3×C3⋊D3—24no—
104C2×C3×C3⋊D3—22no—
105C2×C3×C3⋊D3—22no—
106C2×C3×C3⋊D3—24no—
107C2×C3×C3⋊D3—41no—
108C2×C3×C3⋊D3—42no—
109C2×C3×C3⋊D3—41no—
110C2×C3×C3⋊D3C22⋊C414yescomplemented
111C33×C4—22no—
112C32×Dic3—24no—
113C32×Dic3—42no—
114C22×C3×D4—91no—
115C23×C3×C4—91no—
116C22×D12—32no—
117C22×D12—61no—
118C22×C4×D3—32no—
119C2×C3×C22⋊C4—92no—
120C2×C3×C22⋊C4—91no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—62no—
127C3⋊#95C3×D312yescomplemented
128C23×C32—21no—
129C23×C32—22no—
130C23×C32—41no—
131C23×C32C22×D312yes—
132C23×C32C23×C311yescharacteristic
133C22×C3⋊D3—21no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3C2×C3×C412yes—
140C22×C3⋊D3C2×C3×C412yescomplemented
141C22×C3⋊D3C3×D412yes—
142C22×C3⋊D3C3×D412yes—
143C22×C3×D3—34no—
144C22×C3×D3—34no—
145C22×C3×D3—34no—
146C22×C3×D3—34no—
147C22×C3×D3—62no—
148C22×C3×D3—62no—
149C22×C3×D3—62no—
150C22×C3×D3—62no—
151C22×C3×D3—62no—
152C22×C3×D3—62no—
153C22×C3×D3—62no—
154C22×C3×D3—62no—
155C22×C3×D3—62no—
156C22×C3×D3—62no—
157C22×C3×D3—62no—
158C22×C3×D3—62no—
159C22×C3×D3—62no—
160C22×C3×D3—62no—
161C22×C3×D3—62no—
162C22×C3×D3—62no—
163C22×C3×D3—122no—
164C22×C3×D3—122no—
165C22×C3×D3—122no—
166C22×C3×D3—122no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—24no—
175C2×C32×C4—34no—
176C2×C32×C4—42no—
177C2×C32×C4—42no—
178C2×C32×C4—42no—
179C2×C32×C4—42no—
180C2×C32×C4—42no—
181C2×C32×C4—62no—
182C2×C32×C4—62no—
183C2×C32×C4—62no—
184C2×C32×C4—62no—
185C2×C32×C4—62no—
186C2×C32×C4C4×D314yescomplemented
187C2×C32×C4C2×C3×C412yescomplemented
188C4⋊(C3⋊D3)—28no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—24no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—42no—
202C2×C3×Dic3—42no—
203C2×C3×Dic3—42no—
204C2×C3×Dic3—42no—
205C2×C3×Dic3D1214yescomplemented
206C2×C3×Dic3C3×D414yescomplemented
207C3×D12—616no—
208C3×D12—616no—
209C3×C4×D3—616no—
210#624—28no—
211#386—91noSylow
212C2×C33C2×C22⋊C411yescharacteristic
213C2×C33C4×D412yes—
214C2×C33#12011yescharacteristic
215C2×C33#12112yes—
216C2×C33#12311yescharacteristic
217C3×C3⋊D3—24no—
218C3×C3⋊D3—42no—
219C24×C3—91no—
220C24×C3—91no—
221C23×D3—32no—
222C23×D3—32no—
223C23×D3—61no—
224C23×D3—61no—
225C2×C3×D4—94no—
226C2×C3×D4—182no—
227C2×C3×D4—182no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—41no—
235C22×C3×C4—62no—
236C22×C3×C4—62no—
237C22×C3×C4—184no—
238C22×C3×C4—182no—
239C22×C3×C4D3211yescharacteristic
240C22×C3×C4C2×C3×D312yes—
241C22×Dic3C2×C3×D312yes—
242C22×Dic3C2×C3×D312yes—
243C2×D12—38no—
244C2×D12—64no—
245C2×D12—64no—
246C2×D12—64no—
247C2×D12—64no—
248C2×D12—64no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C3×C22⋊C4—184no—
253C3×C22⋊C4—182no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C22×C32—22no—
258C22×C32—22no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—42no—
273C22×C32—42no—
274C22×C32C2×C4×D312yes—
275C22×C32C2×D1212yes—
276C22×C32#23512yes—
277C22×C32D3×D412yes—
278C22×C32D3×D412yes—
279C22×C32D3×D412yes—
280C22×C32#23912yes—
281C22×C32C22×C3×C411yescharacteristic
282C22×C32C2×C3×D412yes—
283C22×C32C2×C3×D411yescharacteristic
284C22×C32C2×C3×D411yescharacteristic
285C22×C32C3×#4112yes—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—24no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—24no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3C3×C22⋊C414yescomplemented
296C2×C3×D3—38no—
297C2×C3×D3—64no—
298C2×C3×D3—64no—
299C2×C3×D3—64no—
300C2×C3×D3—64no—
301C2×C3×D3—64no—
302C2×C3×D3—64no—
303C2×C3×D3—64no—
304C2×C3×D3—64no—
305C2×C3×D3—64no—
306C2×C3×D3—64no—
307C2×C3×D3—64no—
308C2×C3×D3—124no—
309C2×C3×D3—122no—
310C2×C3×D3—124no—
311C2×C3×D3—122no—
312C2×C3×D3—124no—
313C2×C3×D3—122no—
314C2×C3×D3—124no—
315C2×C3×D3—122no—
316C2×C3×D3—122no—
317C2×C3×D3—122no—
318C2×C3×D3—122no—
319C2×C3×D3—122no—
320C32×C4—22no—
321C32×C4—24no—
322C32×C4—24no—
323C32×C4—44no—
324C32×C4—44no—
325C32×C4—64no—
326C32×C4—122no—
327C3×Dic3—24no—
328C3×Dic3—24no—
329C3×Dic3—44no—
330C3×Dic3—44no—
331C3×Dic3—42no—
332C3×Dic3—42no—
333C22×D4—91no—
334C23×C4—91no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—91no—
337#95—32no—
338C33#38611yescharacteristic, complemented, Sylow
339C23×C3—22no—
340C23×C3—21no—
341C23×C3—41no—
342C23×C3—92no—
343C23×C3—92no—
344C23×C3—92no—
345C23×C3—92no—
346C23×C3—182no—
347C23×C3—182no—
348C23×C3—182no—
349C23×C3—182no—
350C23×C3—181no—
351C23×C3—181no—
352C23×C3C2×D3211yescharacteristic
353C23×C3C22×C3×D312yes—
354C22×D3—34no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—122no—
378C3×D4—188no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—64no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—122no—
407C2×C3×C4—122no—
408C2×C3×C4—122no—
409C2×C3×C4—122no—
410C2×C3×C4—188no—
411C2×C3×C4#62412yescomplemented
412C2×C3×C4C3×C4×D314yescomplemented
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3C3×D1214yescomplemented
419D12—616no—
420D12—616no—
421C4×D3—616no—
422C2×C32—22no—
423C2×C32—22no—
424C2×C32—22no—
425C2×C32—22no—
426C2×C32—22no—
427C2×C32—22no—
428C2×C32—22no—
429C2×C32—21no—
430C2×C32—22no—
431C2×C32—21no—
432C2×C32—21no—
433C2×C32—22no—
434C2×C32—41no—
435C2×C32—42no—
436C2×C32—41no—
437C2×C32—42no—
438C2×C32—41no—
439C2×C32C4×D1212yes—
440C2×C32D3×C22⋊C412yes—
441C2×C32#88212yes—
442C2×C32#88412yes—
443C2×C32#89312yes—
444C2×C32#89412yes—
445C2×C32#89512yes—
446C2×C32C2×C3×C22⋊C411yescharacteristic
447C2×C32C3×C4×D412yes—
448C2×C32C3×#12011yescharacteristic
449C2×C32C3×#12112yes—
450C2×C32C3×#12311yescharacteristic
451C3⋊D3—24no—
452C3⋊D3—42no—
453C3×D3—68no—
454C3×D3—124no—
455C3×D3—124no—
456C3×D3—124no—
457C24—91no—
458C24—91no—
459C2×D4—94no—
460C2×D4—182no—
461C2×D4—182no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—184no—
465C22×C4—182no—
466C22×C4C3×D3211yescharacteristic
467C22⋊C4—184no—
468C22⋊C4—182no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—21no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—94no—
487C22×C3—184no—
488C22×C3—182no—
489C22×C3—184no—
490C22×C3—182no—
491C22×C3—184no—
492C22×C3—182no—
493C22×C3—361no—
494C22×C3—362no—
495C22×C3—361no—
496C22×C3#379912yes—
497C22×C3D3×D1212yes—
498C22×C3C2×#62411yescharacteristic
499C22×C3#381111yescharacteristic
500C22×C3#381111yescharacteristic
501C22×C3C2×C3×C4×D312yes—
502C22×C3C2×C3×D1212yes—
503C22×C3C3×#23512yes—
504C22×C3C3×D3×D412yes—
505C22×C3C3×D3×D412yes—
506C22×C3C3×D3×D412yes—
507C22×C3C3×#23912yes—
508C2×D3—38no—
509C2×D3—64no—
510C2×D3—64no—
511C2×D3—64no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—64no—
520C2×D3—124no—
521C2×D3—122no—
522C2×D3—124no—
523C2×D3—122no—
524C2×D3—124no—
525C2×D3—122no—
526C2×D3—124no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—22no—
535C3×C4—44no—
536C3×C4—44no—
537C3×C4—64no—
538C3×C4—64no—
539C3×C4—124no—
540C3×C4—124no—
541C3×C4—122no—
542C3×C4—122no—
543Dic3—24no—
544Dic3—42no—
545C32—22no—
546C32—21no—
547C32—41no—
548C32#466512yescomplemented
549C32C3×#38611yescharacteristic, complemented
550C23—92no—
551C23—92no—
552C23—92no—
553C23—92no—
554C23—182no—
555C23—182no—
556C23—182no—
557C23—182no—
558C23—181no—
559C23—181no—
560C23C2×C3×D3211yescharacteristic
561D4—188no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—34no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—188no—
571C2×C4C3×#62412yescomplemented
572C2×C3—21no—
573C2×C3—22no—
574C2×C3—22no—
575C2×C3—22no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—22no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—21no—
584C2×C3—41no—
585C2×C3—42no—
586C2×C3—41no—
587C2×C3—42no—
588C2×C3—41no—
589C2×C3—184no—
590C2×C3—362no—
591C2×C3#6389412yes—
592C2×C3#6389711yescharacteristic
593C2×C3#6391012yes—
594C2×C3#6392311yescharacteristic
595C2×C3#6397411yescharacteristic
596C2×C3C3×C4×D1212yes—
597C2×C3C3×D3×C22⋊C412yes—
598C2×C3C3×#88212yes—
599C2×C3C3×#88412yes—
600C2×C3C3×#89312yes—
601C2×C3C3×#89412yes—
602C2×C3C3×#89512yes—
603D3—68no—
604D3—124no—
605D3—124no—
606D3—124no—
607C22—94no—
608C22—184no—
609C22—182no—
610C22—184no—
611C22—182no—
612C22—182no—
613C22—184no—
614C22—361no—
615C22—362no—
616C22—361no—
617C22C3×#379912yes—
618C22C3×D3×D1212yes—
619C22C2×C3×#62411yescharacteristic
620C22C3×#381111yescharacteristic
621C22C3×#381111yescharacteristic
622C4—22no—
623C4—64no—
624C4—122no—
625C3—21no—
626C3—22no—
627C3—41no—
628C3#1059138011yescharacteristic, direct product factor
629C3C3×#466512yescomplemented
630C2—184no—
631C2—362no—
632C2C3×#6389412yes—
633C2C3×#6389711yescharacteristic
634C2C3×#6391012yes—
635C2C3×#6392311yescharacteristic
636C2C3×#6397411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×C4⋊(C3⋊D3)C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#386
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#624C2semidirect
3. C2×C3×#3722C2semidirect
4. C2×C3×#3722C2semidirect
5. C32×C3⋊#95C2semidirect
7. #10591380C3direct (N × H)
13. C2×C3×C4⋊(C3⋊D3)C4semidirect
24. C22×#624C2×C3semidirect
28. C2×#3722C2×C3semidirect
29. C2×#3722C2×C3semidirect
32. C3×C3⋊#95D3semidirect
33. C3×C3⋊#95C2×C3semidirect
42. C22×C3×C3⋊D3C2×C4semidirect
47. C2×C33×C4C2×C4semidirect
54. C2×C32×Dic3D4semidirect
73. C2×C4⋊(C3⋊D3)C3×C4semidirect
110. C2×C3×C3⋊D3C22⋊C4semidirect
127. C3⋊#95C3×D3semidirect
140. C22×C3⋊D3C2×C3×C4semidirect
186. C2×C32×C4C4×D3semidirect
187. C2×C32×C4C2×C3×C4semidirect
205. C2×C3×Dic3D12semidirect
206. C2×C3×Dic3C3×D4semidirect
295. C2×C3⋊D3C3×C22⋊C4semidirect
338. C33#386semidirect
411. C2×C3×C4#624semidirect
412. C2×C3×C4C3×C4×D3semidirect
418. C2×Dic3C3×D12semidirect
548. C32#4665semidirect
549. C32C3×#386semidirect
571. C2×C4C3×#624semidirect
628. C3#10591380direct (N × H)
629. C3C3×#4665semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊(C3⋊D3)2
C22×C3×#6242
C2×C3×#37222
C32×C3⋊#952
C3×#46653
#105913803