Finite Group Databasebeta

← C3×#14918 #10633525

Subgroups — C3×#14918 #10633525

Order 768.

3366 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊C4C211yesmaximal, characteristic
2C2×C3×#385C211yesmaximal, characteristic, complemented
3C2×C3×#381C211yesmaximal, characteristic, complemented
4C2×C3×#381C211yesmaximal, characteristic, complemented
5C2×C3×#379C211yesmaximal, characteristic
6C2×C3×#379C211yesmaximal, characteristic
7C3×#1440C214yesmaximal, complemented
8C3×#1439C214yesmaximal, complemented
9C3×C22⋊#95C211yesmaximal, characteristic, complemented
10#14918C311yesmaximal, characteristic, direct product factor, Sylow
11C26×C3C2211yescharacteristic
12C24×C3×C4C2211yescharacteristic
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yescomplemented
15C22×C3×C22⋊C4—24no—
16C22×C3×C22⋊C4—24no—
17C22×C3×C22⋊C4—24no—
18C22×C3×C22⋊C4C2214yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2214yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C3×#385—24no—
27C3×#381—24no—
28C3×#381—24no—
29C3×#379—24no—
30C3×#379—24no—
31C2×C3×#95C2212yescomplemented
32C2×C3×#95C2214yescomplemented
33C2×C3×#95C2212yescomplemented
34C2×C3×#95C2212yescomplemented
35C2×C3×#95C2214yescomplemented
36C23×C22⋊C4C2×C311yescharacteristic
37C2×#385C2×C311yescharacteristic, complemented
38C2×#381C2×C311yescharacteristic, complemented
39C2×#381C2×C311yescharacteristic, complemented
40C2×#379C2×C311yescharacteristic
41C2×#379C2×C311yescharacteristic
42#1440C2×C314yescomplemented
43#1439C2×C314yescomplemented
44C22⋊#95C2×C311yescharacteristic, complemented
45C25×C3—22no—
46C25×C3—22no—
47C25×C3—28no—
48C25×C3—22no—
49C25×C3—22no—
50C25×C3—22no—
51C25×C3—22no—
52C25×C3—44no—
53C25×C3D414yes—
54C25×C3C2312yes—
55C25×C3C2311yescharacteristic
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—44no—
65C23×C3×C4D414yes—
66C23×C3×C4D414yes—
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2312yes—
73C23×C3×C4C2312yes—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—44no—
76C2×C3×C22⋊C4—232no—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—28no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—28no—
81C2×C3×C22⋊C4—28no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—28no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—28no—
95C2×C3×C22⋊C4—28no—
96C2×C3×C22⋊C4—44no—
97C2×C3×C22⋊C4—44no—
98C2×C3×C22⋊C4D414yes—
99C3×#95—28no—
100C3×#95—24no—
101C3×#95—24no—
102C3×#95—24no—
103C3×#95—44no—
104C26C22×C311yescharacteristic
105C24×C4C22×C311yescharacteristic
106C24×C4C22×C311yescharacteristic
107C22×C4⋊C4C22×C312yescomplemented
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4C22×C314yes—
112C22×C22⋊C4C22×C311yescharacteristic
113C22×C22⋊C4C22×C311yescharacteristic
114C22×C22⋊C4C22×C312yes—
115C22×C22⋊C4C22×C311yescharacteristic
116C22×C22⋊C4C22×C314yes—
117C22×C22⋊C4C22×C311yescharacteristic
118C22×C22⋊C4C22×C312yes—
119#385—24no—
120#381—24no—
121#381—24no—
122#379—24no—
123#379—24no—
124C2×#95C22×C312yescomplemented
125C2×#95C22×C314yescomplemented
126C2×#95C22×C312yescomplemented
127C2×#95C22×C312yescomplemented
128C2×#95C22×C314yescomplemented
129C24×C3—24no—
130C24×C3—24no—
131C24×C3—216no—
132C24×C3—216no—
133C24×C3—28no—
134C24×C3—216no—
135C24×C3—22no—
136C24×C3—22no—
137C24×C3—22no—
138C24×C3—22no—
139C24×C3—24no—
140C24×C3—22no—
141C24×C3—22no—
142C24×C3—24no—
143C24×C3—24no—
144C24×C3—28no—
145C24×C3—28no—
146C24×C3—48no—
147C24×C3—416no—
148C24×C3—416no—
149C24×C3—416no—
150C24×C3—416no—
151C24×C3—48no—
152C24×C3—48no—
153C24×C3—44no—
154C24×C3—44no—
155C24×C3—44no—
156C24×C3—44no—
157C24×C3C2×D414yes—
158C24×C3C2×D412yes—
159C24×C3C2×D412yes—
160C24×C3C2×D412yes—
161C24×C3C2×D412yes—
162C24×C3#4118yes—
163C24×C3#4112yes—
164C24×C3#4112yes—
165C24×C3#4112yes—
166C24×C3C2411yescharacteristic
167C22×C3×C4—28no—
168C22×C3×C4—28no—
169C22×C3×C4—28no—
170C22×C3×C4—28no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—24no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—24no—
183C22×C3×C4—24no—
184C22×C3×C4—24no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—24no—
198C22×C3×C4—24no—
199C22×C3×C4—24no—
200C22×C3×C4—24no—
201C22×C3×C4—24no—
202C22×C3×C4—24no—
203C22×C3×C4—48no—
204C22×C3×C4—48no—
205C22×C3×C4—48no—
206C22×C3×C4—44no—
207C22×C3×C4—44no—
208C22×C3×C4—44no—
209C22×C3×C4—44no—
210C22×C3×C4C2×D414yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D414yes—
213C3×C4⋊C4—48no—
214C3×C22⋊C4—232no—
215C3×C22⋊C4—28no—
216C3×C22⋊C4—416no—
217C3×C22⋊C4—48no—
218C3×C22⋊C4—44no—
219C3×C22⋊C4—44no—
220C3×C22⋊C4—44no—
221C3×C22⋊C4—48no—
222C25—22no—
223C25—22no—
224C25—28no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—44no—
230C25C3×D414yes—
231C25C23×C312yes—
232C25C23×C311yescharacteristic
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—44no—
242C23×C4C3×D414yes—
243C23×C4C3×D414yes—
244C23×C4C23×C311yescharacteristic
245C23×C4C23×C311yescharacteristic
246C23×C4C23×C312yes—
247C23×C4C23×C312yes—
248C23×C4C23×C312yes—
249C23×C4C23×C312yes—
250C23×C4C23×C312yes—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—44no—
253C2×C22⋊C4—232no—
254C2×C22⋊C4—28no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—28no—
258C2×C22⋊C4—28no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—28no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—28no—
272C2×C22⋊C4—28no—
273C2×C22⋊C4—44no—
274C2×C22⋊C4—44no—
275C2×C22⋊C4C3×D414yes—
276#95—28no—
277#95—24no—
278#95—24no—
279#95—24no—
280#95—44no—
281C23×C3—24no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—24no—
285C23×C3—24no—
286C23×C3—24no—
287C23×C3—28no—
288C23×C3—28no—
289C23×C3—28no—
290C23×C3—28no—
291C23×C3—232no—
292C23×C3—24no—
293C23×C3—24no—
294C23×C3—24no—
295C23×C3—24no—
296C23×C3—28no—
297C23×C3—28no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—28no—
301C23×C3—28no—
302C23×C3—28no—
303C23×C3—28no—
304C23×C3—432no—
305C23×C3—432no—
306C23×C3—432no—
307C23×C3—416no—
308C23×C3—432no—
309C23×C3—432no—
310C23×C3—432no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—44no—
316C23×C3—44no—
317C23×C3—44no—
318C23×C3—44no—
319C23×C3—44no—
320C23×C3—44no—
321C23×C3—416no—
322C23×C3#12014yes—
323C23×C3#12114yes—
324C23×C3#12114yes—
325C23×C3#12114yes—
326C23×C3#12318yes—
327C23×C3#12314yes—
328C23×C3#12314yes—
329C23×C3#12414yes—
330C23×C3C22×D411yescharacteristic
331C23×C3C22×D411yescharacteristic
332C23×C3C22×D411yescharacteristic
333C23×C3C22×D411yescharacteristic
334C23×C3C2×#4111yescharacteristic
335C23×C3C2×#4111yescharacteristic
336C23×C3C2×#4111yescharacteristic
337C23×C3C2×#4114yes—
338C23×C3H(5,𝔽2)14yes—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—28no—
347C2×C3×C4—416no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—44no—
355C2×C3×C4—44no—
356C2×C3×C4—44no—
357C2×C3×C4—416no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—44no—
373C2×C3×C4—44no—
374C2×C3×C4—44no—
375C2×C3×C4—44no—
376C24—24no—
377C24—24no—
378C24—216no—
379C24—216no—
380C24—28no—
381C24—216no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—24no—
387C24—22no—
388C24—22no—
389C24—24no—
390C24—24no—
391C24—28no—
392C24—28no—
393C24—48no—
394C24—416no—
395C24—416no—
396C24—416no—
397C24—416no—
398C24—48no—
399C24—48no—
400C24—44no—
401C24—44no—
402C24—44no—
403C24—44no—
404C24C2×C3×D414yes—
405C24C2×C3×D412yes—
406C24C2×C3×D412yes—
407C24C2×C3×D412yes—
408C24C2×C3×D412yes—
409C24C3×#4118yes—
410C24C3×#4112yes—
411C24C3×#4112yes—
412C24C3×#4112yes—
413C24C24×C311yescharacteristic
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4C2×C3×D414yes—
458C22×C4C2×C3×D414yes—
459C22×C4C2×C3×D414yes—
460C4⋊C4—48no—
461C22⋊C4—232no—
462C22⋊C4—28no—
463C22⋊C4—416no—
464C22⋊C4—48no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—48no—
469C22×C3—28no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—28no—
473C22×C3—28no—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—28no—
477C22×C3—28no—
478C22×C3—28no—
479C22×C3—28no—
480C22×C3—464no—
481C22×C3—48no—
482C22×C3—44no—
483C22×C3—44no—
484C22×C3—48no—
485C22×C3—44no—
486C22×C3—48no—
487C22×C3—44no—
488C22×C3—48no—
489C22×C3#39418yes—
490C22×C3C2×#12011yescharacteristic
491C22×C3C2×#12111yescharacteristic
492C22×C3C2×#12111yescharacteristic
493C22×C3C2×#12111yescharacteristic
494C22×C3C2×#12312yes—
495C22×C3C2×#12311yescharacteristic
496C22×C3C2×#12311yescharacteristic
497C22×C3#52512yes—
498C22×C3#52512yes—
499C22×C3C2×#12411yescharacteristic
500C22×C3#53412yes—
501C22×C3#53412yes—
502C22×C3#53512yes—
503C22×C3#54614yes—
504C22×C3#55114yes—
505C22×C3#55114yes—
506C22×C3#55114yes—
507C3×C4—44no—
508C3×C4—44no—
509C3×C4—44no—
510C3×C4—81no—
511C3×C4—81no—
512C3×C4—82no—
513C3×C4—82no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—28no—
521C23—28no—
522C23—28no—
523C23—28no—
524C23—232no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—28no—
530C23—28no—
531C23—24no—
532C23—24no—
533C23—28no—
534C23—28no—
535C23—28no—
536C23—28no—
537C23—432no—
538C23—432no—
539C23—432no—
540C23—432no—
541C23—432no—
542C23—432no—
543C23—416no—
544C23—416no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—44no—
550C23—44no—
551C23—44no—
552C23—44no—
553C23—44no—
554C23—44no—
555C23C3×#12014yes—
556C23C3×#12114yes—
557C23C3×#12114yes—
558C23C3×#12114yes—
559C23C3×#12318yes—
560C23C3×#12314yes—
561C23C3×#12314yes—
562C23C3×#12414yes—
563C23C22×C3×D411yescharacteristic
564C23C22×C3×D411yescharacteristic
565C23C22×C3×D411yescharacteristic
566C23C22×C3×D411yescharacteristic
567C23C2×C3×#4111yescharacteristic
568C23C2×C3×#4111yescharacteristic
569C23C2×C3×#4111yescharacteristic
570C23C2×C3×#4114yes—
571C23C3×H(5,𝔽2)14yes—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—28no—
580C2×C4—416no—
581C2×C4—416no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C3—28no—
610C2×C3—48no—
611C2×C3C2×#39411yescharacteristic
612C2×C3#241112yes—
613C2×C3#241212yes—
614C2×C3#248212yes—
615C2×C3#248312yes—
616C2×C3#253412yes—
617C2×C3#256112yes—
618C2×C3#261311yescharacteristic
619C2×C3#284911yescharacteristic
620C22—28no—
621C22—28no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—28no—
626C22—24no—
627C22—24no—
628C22—28no—
629C22—28no—
630C22—28no—
631C22—464no—
632C22—44no—
633C22—48no—
634C22—44no—
635C22—48no—
636C22—44no—
637C22—48no—
638C22—48no—
639C22—44no—
640C22C3×#39418yes—
641C22C2×C3×#12011yescharacteristic
642C22C2×C3×#12111yescharacteristic
643C22C2×C3×#12111yescharacteristic
644C22C2×C3×#12111yescharacteristic
645C22C2×C3×#12311yescharacteristic
646C22C2×C3×#12311yescharacteristic
647C22C2×C3×#12312yes—
648C22C3×#52512yes—
649C22C3×#52512yes—
650C22C2×C3×#12411yescharacteristic
651C22C3×#53412yes—
652C22C3×#53412yes—
653C22C3×#53512yes—
654C22C3×#54614yes—
655C22C3×#55114yes—
656C22C3×#55114yes—
657C22C3×#55114yes—
658C4—44no—
659C4—44no—
660C4—44no—
661C4—82no—
662C4—82no—
663C4—81no—
664C4—81no—
665C3#1491811yescharacteristic, direct product factor, Sylow
666C2—28no—
667C2—48no—
668C2C2×C3×#39411yescharacteristic
669C2C3×#241112yes—
670C2C3×#241212yes—
671C2C3×#248212yes—
672C2C3×#248312yes—
673C2C3×#253412yes—
674C2C3×#256112yes—
675C2C3×#261311yescharacteristic
676C2C3×#284911yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC26×C3C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#385C2semidirect
3. C2×C3×#381C2semidirect
4. C2×C3×#381C2semidirect
7. C3×#1440C2semidirect
8. C3×#1439C2semidirect
9. C3×C22⋊#95C2semidirect
10. #14918C3direct (N × H)
14. C22×C3×C4⋊C4C22semidirect
31. C2×C3×#95C22semidirect
32. C2×C3×#95C22semidirect
33. C2×C3×#95C22semidirect
34. C2×C3×#95C22semidirect
35. C2×C3×#95C22semidirect
37. C2×#385C2×C3semidirect
38. C2×#381C2×C3semidirect
39. C2×#381C2×C3semidirect
42. #1440C2×C3semidirect
43. #1439C2×C3semidirect
44. C22⋊#95C2×C3semidirect
107. C22×C4⋊C4C22×C3semidirect
124. C2×#95C22×C3semidirect
125. C2×#95C22×C3semidirect
126. C2×#95C22×C3semidirect
127. C2×#95C22×C3semidirect
128. C2×#95C22×C3semidirect
665. C3#14918direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊C42
C2×C3×#3852
C2×C3×#3812
C2×C3×#3792
C3×#14402
C3×#14392
C3×C22⋊#952
#149183