Finite Group Databasebeta

← C3×#14811 #10633418

Subgroups — C3×#14811 #10633418

Order 768.

3150 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#392C212yesmaximal, complemented
3C2×C3×#392C212yesmaximal, complemented
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C2×C3×#386C214yesmaximal, complemented
6C3×#1439C212yesmaximal, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1434C211yesmaximal, characteristic, complemented
9#14811C311yesmaximal, characteristic, direct product factor, Sylow
10C23×C3×D4C2211yescharacteristic
11C23×C3×D4C2214yes—
12C23×C3×D4C2211yescharacteristic
13C24×C3×C4C2212yes—
14C2×C3×C4×D4—28no—
15C2×C3×C4×D4—24no—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2214yes—
21C22×C3×C22⋊C4C2214yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C3×#392—28no—
25C3×#392—28no—
26C3×#390—24no—
27C3×#386—216no—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2214yes—
31C2×C3×#95C2212yes—
32C22×C4×D4C2×C311yescharacteristic, complemented
33C2×#392C2×C312yescomplemented
34C2×#392C2×C312yescomplemented
35C2×#390C2×C311yescharacteristic, complemented
36C2×#386C2×C314yescomplemented
37#1439C2×C312yescomplemented
38#1439C2×C312yescomplemented
39#1434C2×C311yescharacteristic, complemented
40C25×C3C2312yes—
41C25×C3C2312yes—
42C22×C3×D4—24no—
43C22×C3×D4—24no—
44C22×C3×D4—24no—
45C22×C3×D4—28no—
46C22×C3×D4—28no—
47C22×C3×D4—28no—
48C22×C3×D4—28no—
49C22×C3×D4—22no—
50C22×C3×D4—28no—
51C22×C3×D4—22no—
52C22×C3×D4—24no—
53C22×C3×D4—22no—
54C22×C3×D4—42no—
55C22×C3×D4—44no—
56C22×C3×D4—44no—
57C22×C3×D4D414yescomplemented
58C23×C3×C4—24no—
59C23×C3×C4—24no—
60C23×C3×C4—24no—
61C23×C3×C4—28no—
62C23×C3×C4—44no—
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C23×C3×C4C2314yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C3×C4×D4—232no—
70C2×C3×C4⋊C4—24no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—42no—
74C2×C3×C22⋊C4—24no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—28no—
77C2×C3×C22⋊C4—28no—
78C2×C3×C22⋊C4—28no—
79C2×C3×C22⋊C4—28no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—24no—
82C2×C3×C22⋊C4—28no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—44no—
86C2×C3×C22⋊C4—44no—
87C2×C3×C22⋊C4D418yescomplemented
88C2×C3×C42—24no—
89C2×C3×C42D414yescomplemented
90C3×#95—28no—
91C3×#95—24no—
92C3×#95—24no—
93C3×#95D418yescomplemented
94C23×D4C22×C311yescharacteristic
95C23×D4C22×C314yes—
96C23×D4C22×C311yescharacteristic
97C24×C4C22×C312yes—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C22×C4⋊C4C22×C311yescharacteristic
101C22×C4⋊C4C22×C311yescharacteristic
102C22×C22⋊C4C22×C312yes—
103C22×C22⋊C4C22×C312yes—
104C22×C22⋊C4C22×C314yes—
105C22×C22⋊C4C22×C314yes—
106C22×C22⋊C4C22×C312yes—
107C22×C42C22×C311yescharacteristic
108#392—28no—
109#392—28no—
110#390—24no—
111#386—216no—
112C2×#95C22×C312yes—
113C2×#95C22×C312yes—
114C2×#95C22×C314yes—
115C2×#95C22×C312yes—
116C24×C3—22no—
117C24×C3—22no—
118C24×C3—24no—
119C24×C3—22no—
120C24×C3—22no—
121C24×C3—24no—
122C24×C3—24no—
123C24×C3—24no—
124C24×C3—22no—
125C24×C3—24no—
126C24×C3—24no—
127C24×C3—22no—
128C24×C3—22no—
129C24×C3—24no—
130C24×C3—22no—
131C24×C3—22no—
132C24×C3—24no—
133C24×C3—22no—
134C24×C3C2×D414yes—
135C24×C3C2×D414yes—
136C24×C3#4114yes—
137C24×C3#4114yes—
138C24×C3C2411yescharacteristic
139C2×C3×D4—28no—
140C2×C3×D4—28no—
141C2×C3×D4—216no—
142C2×C3×D4—216no—
143C2×C3×D4—28no—
144C2×C3×D4—232no—
145C2×C3×D4—28no—
146C2×C3×D4—416no—
147C2×C3×D4—416no—
148C2×C3×D4—416no—
149C2×C3×D4—44no—
150C2×C3×D4—416no—
151C2×C3×D4—416no—
152C2×C3×D4—416no—
153C2×C3×D4—416no—
154C2×C3×D4—44no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—216no—
162C22×C3×C4—24no—
163C22×C3×C4—24no—
164C22×C3×C4—24no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—24no—
177C22×C3×C4—416no—
178C22×C3×C4—416no—
179C22×C3×C4—48no—
180C22×C3×C4—48no—
181C22×C3×C4C2×D418yes—
182C22×C3×C4C2×D414yes—
183C22×C3×C4C2×D414yes—
184C22×C3×C4C2×D412yes—
185C22×C3×C4C2×D412yes—
186C22×C3×C4C2×D412yes—
187C22×C3×C4C2×D414yes—
188C22×C3×C4C2×D412yes—
189C22×C3×C4#4112yes—
190C3×C4⋊C4—28no—
191C3×C4⋊C4—44no—
192C3×C22⋊C4—216no—
193C3×C22⋊C4—416no—
194C3×C22⋊C4—416no—
195C3×C22⋊C4—48no—
196C3×C22⋊C4—48no—
197C3×C42—28no—
198C25C23×C312yes—
199C25C23×C312yes—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—28no—
204C22×D4—28no—
205C22×D4—28no—
206C22×D4—28no—
207C22×D4—22no—
208C22×D4—28no—
209C22×D4—22no—
210C22×D4—24no—
211C22×D4—22no—
212C22×D4—42no—
213C22×D4—44no—
214C22×D4—44no—
215C22×D4C3×D414yescomplemented
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—28no—
220C23×C4—44no—
221C23×C4C23×C312yes—
222C23×C4C23×C312yes—
223C23×C4C23×C314yes—
224C23×C4C23×C311yescharacteristic
225C23×C4C23×C311yescharacteristic
226C23×C4C23×C311yescharacteristic
227C4×D4—232no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—42no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—24no—
234C2×C22⋊C4—28no—
235C2×C22⋊C4—28no—
236C2×C22⋊C4—28no—
237C2×C22⋊C4—28no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—28no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4—44no—
244C2×C22⋊C4—44no—
245C2×C22⋊C4C3×D418yescomplemented
246C2×C42—24no—
247C2×C42C3×D414yescomplemented
248#95—28no—
249#95—24no—
250#95—24no—
251#95C3×D418yescomplemented
252C23×C3—24no—
253C23×C3—24no—
254C23×C3—24no—
255C23×C3—24no—
256C23×C3—24no—
257C23×C3—24no—
258C23×C3—28no—
259C23×C3—28no—
260C23×C3—28no—
261C23×C3—28no—
262C23×C3—28no—
263C23×C3—28no—
264C23×C3—24no—
265C23×C3—28no—
266C23×C3—28no—
267C23×C3—24no—
268C23×C3—24no—
269C23×C3—42no—
270C23×C3—44no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3—44no—
275C23×C3—44no—
276C23×C3—44no—
277C23×C3—44no—
278C23×C3—44no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—44no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—44no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—44no—
289C23×C3—44no—
290C23×C3—44no—
291C23×C3—44no—
292C23×C3—44no—
293C23×C3—44no—
294C23×C3—42no—
295C23×C3—44no—
296C23×C3—42no—
297C23×C3#12118yes—
298C23×C3C22×D411yescharacteristic
299C23×C3C22×D412yes—
300C23×C3C22×D411yescharacteristic
301C23×C3C22×D412yes—
302C23×C3C2×#4112yes—
303C23×C3C2×#4111yescharacteristic
304C23×C3C2×#4112yes—
305C23×C3H(5,𝔽2)12yes—
306C23×C3H(5,𝔽2)12yes—
307C3×D4—232no—
308C3×D4—416no—
309C3×D4—464no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—24no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4—432no—
326C2×C3×C4—44no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—44no—
330C2×C3×C4—44no—
331C2×C3×C4—44no—
332C2×C3×C4—44no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—44no—
337C2×C3×C4—44no—
338C2×C3×C4#12014yes—
339C2×C3×C4#12114yes—
340C2×C3×C4#12714yes—
341C24—22no—
342C24—22no—
343C24—24no—
344C24—22no—
345C24—22no—
346C24—24no—
347C24—24no—
348C24—24no—
349C24—22no—
350C24—24no—
351C24—24no—
352C24—22no—
353C24—22no—
354C24—24no—
355C24—22no—
356C24—22no—
357C24—24no—
358C24—22no—
359C24C2×C3×D414yes—
360C24C2×C3×D414yes—
361C24C3×#4114yes—
362C24C3×#4114yes—
363C24C24×C311yescharacteristic
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—216no—
367C2×D4—216no—
368C2×D4—28no—
369C2×D4—232no—
370C2×D4—28no—
371C2×D4—416no—
372C2×D4—416no—
373C2×D4—416no—
374C2×D4—44no—
375C2×D4—416no—
376C2×D4—416no—
377C2×D4—416no—
378C2×D4—416no—
379C2×D4—44no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—216no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—416no—
403C22×C4—416no—
404C22×C4—48no—
405C22×C4—48no—
406C22×C4C2×C3×D418yes—
407C22×C4C2×C3×D414yes—
408C22×C4C2×C3×D414yes—
409C22×C4C2×C3×D412yes—
410C22×C4C2×C3×D412yes—
411C22×C4C2×C3×D412yes—
412C22×C4C2×C3×D414yes—
413C22×C4C2×C3×D412yes—
414C22×C4C3×#4112yes—
415C4⋊C4—28no—
416C4⋊C4—44no—
417C22⋊C4—216no—
418C22⋊C4—416no—
419C22⋊C4—416no—
420C22⋊C4—48no—
421C22⋊C4—48no—
422C42—28no—
423C22×C3—28no—
424C22×C3—216no—
425C22×C3—44no—
426C22×C3—44no—
427C22×C3—44no—
428C22×C3—48no—
429C22×C3—44no—
430C22×C3—48no—
431C22×C3—48no—
432C22×C3—44no—
433C22×C3—44no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—48no—
437C22×C3—48no—
438C22×C3—44no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—84no—
442C22×C3—82no—
443C22×C3—84no—
444C22×C3—82no—
445C22×C3C2×#12011yescharacteristic
446C22×C3C2×#12112yes—
447C22×C3C2×#12111yescharacteristic
448C22×C3#52511yescharacteristic
449C22×C3#52512yes—
450C22×C3#52511yescharacteristic
451C22×C3#52514yes—
452C22×C3C2×#12711yescharacteristic
453C22×C3#53511yescharacteristic
454C22×C3#53511yescharacteristic
455C22×C3#53814yes—
456C22×C3D4212yes—
457C22×C3D4214yes—
458C22×C3#54614yes—
459C22×C3#54612yes—
460C22×C3#55012yes—
461C22×C3#55312yes—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—48no—
466C3×C4—44no—
467C3×C4—82no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—28no—
473C23—24no—
474C23—24no—
475C23—28no—
476C23—28no—
477C23—28no—
478C23—28no—
479C23—28no—
480C23—24no—
481C23—28no—
482C23—28no—
483C23—24no—
484C23—24no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—44no—
498C23—42no—
499C23—44no—
500C23—44no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—44no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—42no—
511C23—44no—
512C23—42no—
513C23C3×#12118yes—
514C23C22×C3×D411yescharacteristic
515C23C22×C3×D412yes—
516C23C22×C3×D411yescharacteristic
517C23C22×C3×D412yes—
518C23C2×C3×#4112yes—
519C23C2×C3×#4111yescharacteristic
520C23C2×C3×#4112yes—
521C23C3×H(5,𝔽2)12yes—
522C23C3×H(5,𝔽2)12yes—
523D4—232no—
524D4—416no—
525D4—464no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—28no—
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—28no—
539C2×C4—28no—
540C2×C4—28no—
541C2×C4—432no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4C3×#12014yes—
555C2×C4C3×#12114yes—
556C2×C4C3×#12714yes—
557C2×C3—48no—
558C2×C3—84no—
559C2×C3#239711yescharacteristic
560C2×C3#240411yescharacteristic
561C2×C3#242414yes—
562C2×C3#243311yescharacteristic
563C2×C3#245614yes—
564C2×C3#253511yescharacteristic
565C2×C3#254111yescharacteristic
566C2×C3#263111yescharacteristic
567C2×C3#284711yescharacteristic
568C22—216no—
569C22—28no—
570C22—44no—
571C22—44no—
572C22—44no—
573C22—48no—
574C22—44no—
575C22—48no—
576C22—48no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—48no—
582C22—48no—
583C22—44no—
584C22—82no—
585C22—84no—
586C22—82no—
587C22—84no—
588C22—82no—
589C22—82no—
590C22C2×C3×#12011yescharacteristic
591C22C2×C3×#12112yes—
592C22C2×C3×#12111yescharacteristic
593C22C3×#52511yescharacteristic
594C22C3×#52511yescharacteristic
595C22C3×#52514yes—
596C22C3×#52512yes—
597C22C2×C3×#12711yescharacteristic
598C22C3×#53511yescharacteristic
599C22C3×#53511yescharacteristic
600C22C3×#53814yes—
601C22C3×D4212yes—
602C22C3×D4214yes—
603C22C3×#54614yes—
604C22C3×#54612yes—
605C22C3×#55012yes—
606C22C3×#55312yes—
607C4—24no—
608C4—24no—
609C4—24no—
610C4—48no—
611C4—44no—
612C4—82no—
613C3#1481111yescharacteristic, direct product factor, Sylow
614C2—48no—
615C2—84no—
616C2C3×#239711yescharacteristic
617C2C3×#240411yescharacteristic
618C2C3×#242414yes—
619C2C3×#243311yescharacteristic
620C2C3×#245614yes—
621C2C3×#253511yescharacteristic
622C2C3×#254111yescharacteristic
623C2C3×#263111yescharacteristic
624C2C3×#284711yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
2. C2×C3×#392C2semidirect
3. C2×C3×#392C2semidirect
4. C2×C3×#390C2semidirect
5. C2×C3×#386C2semidirect
6. C3×#1439C2semidirect
7. C3×#1439C2semidirect
8. C3×#1434C2semidirect
9. #14811C3direct (N × H)
32. C22×C4×D4C2×C3semidirect
33. C2×#392C2×C3semidirect
34. C2×#392C2×C3semidirect
35. C2×#390C2×C3semidirect
36. C2×#386C2×C3semidirect
37. #1439C2×C3semidirect
38. #1439C2×C3semidirect
39. #1434C2×C3semidirect
57. C22×C3×D4D4semidirect
87. C2×C3×C22⋊C4D4semidirect
89. C2×C3×C42D4semidirect
93. C3×#95D4semidirect
215. C22×D4C3×D4semidirect
245. C2×C22⋊C4C3×D4semidirect
247. C2×C42C3×D4semidirect
251. #95C3×D4semidirect
613. C3#14811direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#3922
C2×C3×#3902
C2×C3×#3862
C3×#14392
C3×#14342
#148113