Finite Group Databasebeta

← C2×C3×#63956 #13175073

Subgroups — C2×C3×#63956 #13175073

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3757C211yesmaximal, characteristic
2C2×C32×#217C211yesmaximal, characteristic
3C2×C32×#217C211yesmaximal, characteristic
4C2×C3×#3724C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63956C218yesmaximal, direct product factor
8C2×C3×Dic32C211yesmaximal, characteristic, complemented
9C2×C3×#879—31nomaximal
10C2×C3×#879—31nomaximal
11C2×#63956C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C3×#3757C2214yes—
20C32×#217C2214yes—
21C32×#217C2214yes—
22C3×#3724C2214yescomplemented
23C3×Dic3⋊Dic3C2214yescomplemented
24C3×Dic3⋊Dic3C2214yescomplemented
25C3×Dic32C2214yescomplemented
26C2×C32×C22⋊C4—31no—
27C2×C32×C22⋊C4—31no—
28C2×#3757C2×C311yescharacteristic
29C2×C3×#217—21no—
30C2×C3×#217—21no—
31C2×C3×#217—31no—
32C2×C3×#217—31no—
33C2×C3×#217—61no—
34C2×C3×#217D311yescharacteristic
35C2×C3×#217D311yescharacteristic
36C2×C3×#217C2×C311yescharacteristic
37C2×C3×#217C2×C311yescharacteristic
38C2×C3×C4⋊Dic3—31no—
39C2×C3×C4⋊Dic3—31no—
40C2×C3×Dic3⋊C4—31no—
41C2×C3×Dic3⋊C4—31no—
42C2×C3×Dic3⋊C4—31no—
43C2×C3×Dic3⋊C4—31no—
44C2×C3×C4×Dic3—31no—
45C2×C3×C4×Dic3—31no—
46C3×#879—38no—
47C3×#879—38no—
48C2×#3724C2×C311yescharacteristic, complemented
49C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
50C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
51#63956C2×C318yesdirect product factor
52C2×Dic32C2×C311yescharacteristic, complemented
53C23×C33—22no—
54C23×C33—22no—
55C23×C33—22no—
56C23×C33C2312yes—
57C23×C33C2311yescharacteristic
58C2×C3×C3⋊Dic3—22no—
59C2×C3×C3⋊Dic3—22no—
60C2×C3×C3⋊Dic3C2312yes—
61C2×C3×C3⋊Dic3C2312yes—
62C2×C32×Dic3—22no—
63C2×C32×Dic3—22no—
64C2×C32×Dic3—22no—
65C2×C32×Dic3—22no—
66C2×C32×Dic3C2312yes—
67C2×C32×Dic3C2312yes—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C2×C3×#126—91no—
71C2×#879—31no—
72C2×#879—31no—
73C24×C32—21no—
74C24×C32—21no—
75C24×C32—21no—
76C24×C32—41no—
77C24×C32C2×D311yescharacteristic
78C24×C32C2×D311yescharacteristic
79C24×C32C22×C311yescharacteristic
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C32×C4—31no—
83C22×C32×C4—31no—
84C22×C3⋊Dic3C22×C311yescharacteristic
85C22×C3⋊Dic3C22×C311yescharacteristic
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—61no—
95C22×C3×Dic3—61no—
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C32×C22⋊C4—34no—
105C32×C22⋊C4—34no—
106#3757C22×C314yes—
107C3×#217—24no—
108C3×#217—24no—
109C3×#217—34no—
110C3×#217—34no—
111C3×#217—64no—
112C3×#217C2×D314yes—
113C3×#217C2×D314yes—
114C3×#217C22×C314yes—
115C3×#217C22×C314yes—
116C3×C4⋊Dic3—34no—
117C3×C4⋊Dic3—34no—
118C3×Dic3⋊C4—34no—
119C3×Dic3⋊C4—34no—
120C3×Dic3⋊C4—34no—
121C3×Dic3⋊C4—34no—
122C3×C4×Dic3—34no—
123C3×C4×Dic3—34no—
124#3724C22×C314yescomplemented
125Dic3⋊Dic3C22×C314yescomplemented
126Dic3⋊Dic3C22×C314yescomplemented
127Dic32C22×C314yescomplemented
128C22×C33—22no—
129C22×C33—22no—
130C22×C33—22no—
131C22×C33—44no—
132C22×C33#4112yes—
133C22×C33#4112yes—
134C22×C33#4112yes—
135C22×C33C2411yescharacteristic
136C3×C3⋊Dic3—22no—
137C3×C3⋊Dic3—22no—
138C32×Dic3—22no—
139C32×Dic3—22no—
140C32×Dic3—22no—
141C32×Dic3—22no—
142C3×#126—98no—
143C2×C3×C4⋊C4—91no—
144C2×C3×C4⋊C4—91no—
145C2×C3×C4⋊C4—91no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—61no—
151C2×C3×C22⋊C4—61no—
152C2×C3×C22⋊C4—91no—
153C2×C3×C42—91no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—61no—
157C2×#217C3×D311yescharacteristic
158C2×#217C3×D311yescharacteristic
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167#879—38no—
168#879—38no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—24no—
173C23×C32—24no—
174C23×C32—24no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—22no—
186C23×C32—22no—
187C23×C32—41no—
188C23×C32—42no—
189C23×C32—42no—
190C23×C32—42no—
191C23×C32—42no—
192C23×C32—42no—
193C23×C32—42no—
194C23×C32—42no—
195C23×C32—44no—
196C23×C32—44no—
197C23×C32—44no—
198C23×C32C22×D312yes—
199C23×C32C22×D312yes—
200C23×C32C22×D311yescharacteristic
201C23×C32C22×D311yescharacteristic
202C23×C32C23×C312yes—
203C23×C32C23×C311yescharacteristic
204C2×C32×C4—32no—
205C2×C32×C4—32no—
206C2×C32×C4—32no—
207C2×C32×C4—32no—
208C2×C32×C4—62no—
209C2×C32×C4—62no—
210C2×C32×C4—62no—
211C2×C32×C4—62no—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3C23×C312yes—
215C2×C3⋊Dic3C23×C312yes—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—32no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—42no—
233C2×C3×Dic3—42no—
234C2×C3×Dic3—42no—
235C2×C3×Dic3—42no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—62no—
240C2×C3×Dic3—62no—
241C2×C3×Dic3—62no—
242C2×C3×Dic3—122no—
243C2×C3×Dic3—122no—
244C2×C3×Dic3C22×D312yes—
245C2×C3×Dic3C22×D312yes—
246C2×C3×Dic3C22×D312yes—
247C2×C3×Dic3C22×D312yes—
248C2×C3×Dic3C23×C312yes—
249C2×C3×Dic3C23×C312yes—
250C2×C3×Dic3C23×C312yes—
251C2×C3×Dic3C23×C312yes—
252C2×#126—91noSylow
253C2×C33—42no—
254C2×C33#12614yescomplemented
255C2×C33C2×#4111yescharacteristic
256C2×C33C2×#4111yescharacteristic
257C2×C33C2×#4111yescharacteristic
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—41no—
262C24×C3D3211yescharacteristic
263C24×C3C2×C3×D311yescharacteristic
264C24×C3C2×C3×D311yescharacteristic
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—61no—
274C22×C3×C4—61no—
275C22×C3×C4—61no—
276C22×C3×C4—61no—
277C22×C3×C4—91no—
278C22×C3×C4—91no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3C2×C3×D311yescharacteristic
286C22×Dic3C2×C3×D311yescharacteristic
287C22×Dic3C2×C3×D311yescharacteristic
288C22×Dic3C2×C3×D311yescharacteristic
289C3×C4⋊C4—94no—
290C3×C4⋊C4—94no—
291C3×C4⋊C4—94no—
292C3×C22⋊C4—34no—
293C3×C22⋊C4—34no—
294C3×C22⋊C4—34no—
295C3×C22⋊C4—34no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—94no—
299C3×C42—94no—
300#217—34no—
301#217—34no—
302#217—64no—
303#217C2×C3×D314yes—
304#217C2×C3×D314yes—
305C4⋊Dic3—34no—
306C4⋊Dic3—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—34no—
309Dic3⋊C4—34no—
310Dic3⋊C4—34no—
311C4×Dic3—34no—
312C4×Dic3—34no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—24no—
317C22×C32—24no—
318C22×C32—24no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—42no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32—41no—
341C22×C32—42no—
342C22×C32—42no—
343C22×C32—42no—
344C22×C32—42no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—44no—
348C22×C32—44no—
349C22×C32—44no—
350C22×C32—48no—
351C22×C32—48no—
352C22×C32—48no—
353C22×C32—416no—
354C22×C32—44no—
355C22×C32—44no—
356C22×C32—44no—
357C22×C32#23512yes—
358C22×C32#23512yes—
359C22×C32#23712yes—
360C22×C32#23712yes—
361C22×C32#23712yes—
362C22×C32#23712yes—
363C22×C32C3×#4112yes—
364C22×C32C3×#4112yes—
365C22×C32C3×#4112yes—
366C22×C32C23×D311yescharacteristic
367C22×C32C23×D311yescharacteristic
368C22×C32C24×C311yescharacteristic
369C32×C4—62no—
370C32×C4—62no—
371C32×C4—62no—
372C32×C4—62no—
373C3⋊Dic3—22no—
374C3⋊Dic3—22no—
375C3×Dic3—22no—
376C3×Dic3—22no—
377C3×Dic3—22no—
378C3×Dic3—22no—
379C3×Dic3—22no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—42no—
384C3×Dic3—42no—
385C3×Dic3—42no—
386C3×Dic3—42no—
387C3×Dic3—62no—
388C3×Dic3—62no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—122no—
392C3×Dic3—122no—
393#126—98no—
394C2×C4⋊C4—91no—
395C2×C4⋊C4—91no—
396C2×C4⋊C4—91no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—31no—
399C2×C22⋊C4—91no—
400C2×C42—91no—
401C33C2×#12611yescharacteristic, complemented, Sylow
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—42no—
430C23×C3—41no—
431C23×C3C2×D3212yes—
432C23×C3C2×D3211yescharacteristic
433C23×C3C22×C3×D312yes—
434C23×C3C22×C3×D312yes—
435C23×C3C22×C3×D311yescharacteristic
436C23×C3C22×C3×D311yescharacteristic
437C2×C3×C4—32no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—32no—
441C2×C3×C4—32no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—92no—
458C2×C3×C4—92no—
459C2×C3×C4—122no—
460C2×C3×C4—122no—
461C2×C3×C4—122no—
462C2×C3×C4—122no—
463C2×C3×C4—182no—
464C2×C3×C4—182no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—32no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—122no—
480C2×Dic3—122no—
481C2×Dic3C22×C3×D312yes—
482C2×Dic3C22×C3×D312yes—
483C2×Dic3C22×C3×D312yes—
484C2×Dic3C22×C3×D312yes—
485C2×C32—24no—
486C2×C32—24no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—24no—
497C2×C32—44no—
498C2×C32—41no—
499C2×C32—41no—
500C2×C32—41no—
501C2×C32—44no—
502C2×C32—44no—
503C2×C32—44no—
504C2×C32—48no—
505C2×C32—42no—
506C2×C32—42no—
507C2×C32—42no—
508C2×C32#87914yescomplemented
509C2×C32#87914yescomplemented
510C2×C32C3×#12614yescomplemented
511C2×C32C2×#23511yescharacteristic
512C2×C32C2×#23511yescharacteristic
513C2×C32C2×#23711yescharacteristic
514C2×C32C2×#23711yescharacteristic
515C2×C32C2×#23711yescharacteristic
516C2×C32C2×#23711yescharacteristic
517C2×C32C2×C3×#4111yescharacteristic
518C2×C32C2×C3×#4111yescharacteristic
519C2×C32C2×C3×#4111yescharacteristic
520C24C3×D3211yescharacteristic
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—91no—
526C22×C4—91no—
527C4⋊C4—94no—
528C4⋊C4—94no—
529C4⋊C4—94no—
530C22⋊C4—34no—
531C22⋊C4—34no—
532C22⋊C4—94no—
533C42—94no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—48no—
568C22×C3—48no—
569C22×C3—48no—
570C22×C3—416no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3#380412yes—
579C22×C3#380412yes—
580C22×C3#380512yes—
581C22×C3C3×#23512yes—
582C22×C3C3×#23512yes—
583C22×C3C3×#23712yes—
584C22×C3C3×#23712yes—
585C22×C3C3×#23712yes—
586C22×C3C3×#23712yes—
587C22×C3C22×D3211yescharacteristic
588C22×C3C23×C3×D311yescharacteristic
589C22×C3C23×C3×D311yescharacteristic
590C3×C4—62no—
591C3×C4—62no—
592C3×C4—62no—
593C3×C4—62no—
594C3×C4—62no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—62no—
598C3×C4—122no—
599C3×C4—122no—
600C3×C4—122no—
601C3×C4—122no—
602C3×C4—182no—
603C3×C4—182no—
604Dic3—22no—
605Dic3—22no—
606Dic3—22no—
607Dic3—22no—
608Dic3—62no—
609Dic3—62no—
610Dic3—62no—
611Dic3—62no—
612Dic3—122no—
613Dic3—122no—
614C32—21no—
615C32—21no—
616C32—21no—
617C32—41no—
618C32C2×#87911yescharacteristic, complemented
619C32C2×#87911yescharacteristic, complemented
620C32C2×C3×#12611yescharacteristic, complemented
621C23—22no—
622C23—22no—
623C23—22no—
624C23C2×C3×D3212yes—
625C23C2×C3×D3211yescharacteristic
626C2×C4—32no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—92no—
635C2×C4—92no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—24no—
648C2×C3—24no—
649C2×C3—24no—
650C2×C3—44no—
651C2×C3—44no—
652C2×C3—44no—
653C2×C3—48no—
654C2×C3—42no—
655C2×C3—42no—
656C2×C3—42no—
657C2×C3—41no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—44no—
661C2×C3#6395614yesdirect product factor
662C2×C3C3×#87914yescomplemented
663C2×C3C3×#87914yescomplemented
664C2×C3C2×#380411yescharacteristic
665C2×C3C2×#380411yescharacteristic
666C2×C3C2×#380511yescharacteristic
667C2×C3C2×C3×#23511yescharacteristic
668C2×C3C2×C3×#23511yescharacteristic
669C2×C3C2×C3×#23711yescharacteristic
670C2×C3C2×C3×#23711yescharacteristic
671C2×C3C2×C3×#23711yescharacteristic
672C2×C3C2×C3×#23711yescharacteristic
673C22—22no—
674C22—22no—
675C22—22no—
676C22—44no—
677C22C3×#380412yes—
678C22C3×#380412yes—
679C22C3×#380512yes—
680C22C22×C3×D3211yescharacteristic
681C4—62no—
682C4—62no—
683C4—62no—
684C4—62no—
685C4—182no—
686C4—182no—
687C3—21no—
688C3—21no—
689C3—21no—
690C3—41no—
691C3C2×#6395611yescharacteristic, direct product factor
692C3C2×C3×#87911yescharacteristic, complemented
693C3C2×C3×#87911yescharacteristic, complemented
694C2—42no—
695C2C3×#6395614yesdirect product factor
696C2C2×C3×#380411yescharacteristic
697C2C2×C3×#380411yescharacteristic
698C2C2×C3×#380511yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
Fitting, prime radicalC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3724C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C3×#63956C2direct (N × H)
8. C2×C3×Dic32C2semidirect
11. C2×#63956C3direct (N × H)
22. C3×#3724C22semidirect
23. C3×Dic3⋊Dic3C22semidirect
24. C3×Dic3⋊Dic3C22semidirect
25. C3×Dic32C22semidirect
48. C2×#3724C2×C3semidirect
49. C2×Dic3⋊Dic3C2×C3semidirect
50. C2×Dic3⋊Dic3C2×C3semidirect
51. #63956C2×C3direct (N × H)
52. C2×Dic32C2×C3semidirect
124. #3724C22×C3semidirect
125. Dic3⋊Dic3C22×C3semidirect
126. Dic3⋊Dic3C22×C3semidirect
127. Dic32C22×C3semidirect
254. C2×C33#126semidirect
401. C33C2×#126semidirect
508. C2×C32#879semidirect
509. C2×C32#879semidirect
510. C2×C32C3×#126semidirect
618. C32C2×#879semidirect
619. C32C2×#879semidirect
620. C32C2×C3×#126semidirect
661. C2×C3#63956direct (N × H)
662. C2×C3C3×#879semidirect
663. C2×C3C3×#879semidirect
691. C3C2×#63956direct (N × H)
692. C3C2×C3×#879semidirect
693. C3C2×C3×#879semidirect
695. C2C3×#63956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37572
C2×C32×#2172
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C3×#639562
C2×C3×Dic322
C2×C3×#8793
C2×#639563