Finite Group Databasebeta

← C3×#14181 #10632788

Subgroups — C3×#14181 #10632788

Order 768.

2062 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic
2C2×C3×#386C212yesmaximal
3C2×C3×C4×C22⋊C4C212yesmaximal, complemented
4C3×#1445C211yesmaximal, characteristic, complemented
5C3×#1440C212yesmaximal, complemented
6C3×#1437C212yesmaximal, complemented
7C3×#1436C211yesmaximal, characteristic, complemented
8C3×#1434C212yesmaximal, complemented
9C3×C22⋊#95C212yesmaximal, complemented
10#14181C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2211yescharacteristic
12C24×C3×C4C2212yes—
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C22⋊C4C2212yes—
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C42C2211yescharacteristic
20C22×C3×C42C2212yes—
21C3×#394C418yescomplemented
22C3×#386—28no—
23C3×C4×C22⋊C4—28no—
24C2×C3×#95C2212yes—
25C2×C3×#95C2212yes—
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×#394C2×C311yescharacteristic
36C2×#386C2×C312yes—
37C2×C4×C22⋊C4C2×C312yescomplemented
38#1445C2×C311yescharacteristic, complemented
39#1440C2×C312yescomplemented
40#1437C2×C312yescomplemented
41#1436C2×C311yescharacteristic, complemented
42#1434C2×C312yescomplemented
43C22⋊#95C2×C312yescomplemented
44C25×C3C2312yes—
45C22×C3×D4—24no—
46C22×C3×D4—24no—
47C22×C3×D4—41no—
48C22×C3×D4—41no—
49C22×C3×D4C2×C414yes—
50C23×C3×C4—24no—
51C23×C3×C4—24no—
52C23×C3×C4—24no—
53C23×C3×C4—24no—
54C23×C3×C4—24no—
55C23×C3×C4—42no—
56C23×C3×C4—42no—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C2×C3×C4⋊C4—41no—
66C2×C3×C4⋊C4—41no—
67C2×C3×C4⋊C4C2×C414yescomplemented
68C2×C3×C22⋊C4—24no—
69C2×C3×C22⋊C4—24no—
70C2×C3×C22⋊C4—24no—
71C2×C3×C22⋊C4—24no—
72C2×C3×C22⋊C4—24no—
73C2×C3×C22⋊C4—24no—
74C2×C3×C22⋊C4—24no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—42no—
77C2×C3×C22⋊C4—42no—
78C2×C3×C22⋊C4—42no—
79C2×C3×C22⋊C4—42no—
80C2×C3×C22⋊C4C2×C418yescomplemented
81C2×C3×C22⋊C4C2×C418yescomplemented
82C2×C3×C22⋊C4D418yes—
83C2×C3×C42—24no—
84C2×C3×C42—24no—
85C2×C3×C42—24no—
86C2×C3×C42—41no—
87C2×C3×C42—42no—
88C3×#95—24no—
89C3×#95—24no—
90C3×#95—24no—
91C3×#95—24no—
92C3×#95—24no—
93C3×#95—24no—
94C3×#95—42no—
95C3×#95—41no—
96C3×#95—41no—
97C3×#95—41no—
98C3×#95C2×C414yescomplemented
99C23×D4C22×C311yescharacteristic
100C24×C4C22×C312yes—
101C22×C4⋊C4C22×C311yescharacteristic
102C22×C22⋊C4C22×C312yes—
103C22×C22⋊C4C22×C312yes—
104C22×C22⋊C4C22×C312yes—
105C22×C22⋊C4C22×C312yes—
106C22×C22⋊C4C22×C312yes—
107C22×C42C22×C312yes—
108C22×C42C22×C311yescharacteristic
109#394C3×C418yescomplemented
110#386—28no—
111C4×C22⋊C4—28no—
112C2×#95C22×C312yes—
113C2×#95C22×C312yes—
114C2×#95C22×C312yes—
115C2×#95C22×C312yes—
116C2×#95C22×C312yes—
117C2×#95C22×C312yes—
118C2×#95C22×C311yescharacteristic
119C2×#95C22×C312yes—
120C2×#95C22×C311yescharacteristic
121C2×#95C22×C311yescharacteristic
122C2×#95C22×C311yescharacteristic
123C24×C3—22no—
124C24×C3—22no—
125C24×C3—22no—
126C24×C3—22no—
127C24×C3—22no—
128C24×C3—22no—
129C24×C3—22no—
130C24×C3—22no—
131C24×C3—22no—
132C24×C3—22no—
133C24×C3—22no—
134C24×C3—22no—
135C24×C3C22×C414yes—
136C24×C3C2×D414yes—
137C24×C3#4114yes—
138C24×C3C2411yescharacteristic
139C2×C3×D4—216no—
140C2×C3×D4—44no—
141C2×C3×D4—44no—
142C2×C3×D4—48no—
143C2×C3×D4—44no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—216no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
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—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—48no—
187C22×C3×C4—48no—
188C22×C3×C4—48no—
189C22×C3×C4—48no—
190C22×C3×C4—48no—
191C22×C3×C4—48no—
192C22×C3×C4C22×C414yes—
193C22×C3×C4C22×C412yes—
194C22×C3×C4C22×C412yes—
195C22×C3×C4C22×C412yes—
196C22×C3×C4C2×D414yes—
197C22×C3×C4C2×D414yes—
198C22×C3×C4#4114yes—
199C22×C3×C4#4114yes—
200C22×C3×C4#4114yes—
201C3×C4⋊C4—44no—
202C3×C22⋊C4—216no—
203C3×C22⋊C4—216no—
204C3×C22⋊C4—48no—
205C3×C22⋊C4—48no—
206C3×C22⋊C4—48no—
207C3×C42—44no—
208C3×C42—48no—
209C25C23×C312yes—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4C2×C3×C414yes—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4C23×C312yes—
223C23×C4C23×C311yescharacteristic
224C23×C4C23×C311yescharacteristic
225C23×C4C23×C312yes—
226C23×C4C23×C311yescharacteristic
227C23×C4C23×C312yes—
228C23×C4C23×C312yes—
229C23×C4C23×C312yes—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4C2×C3×C414yescomplemented
233C2×C22⋊C4—24no—
234C2×C22⋊C4—24no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—24no—
241C2×C22⋊C4—42no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4—42no—
244C2×C22⋊C4—42no—
245C2×C22⋊C4C2×C3×C418yescomplemented
246C2×C22⋊C4C2×C3×C418yescomplemented
247C2×C22⋊C4C3×D418yes—
248C2×C42—24no—
249C2×C42—24no—
250C2×C42—24no—
251C2×C42—41no—
252C2×C42—42no—
253#95—24no—
254#95—24no—
255#95—24no—
256#95—24no—
257#95—24no—
258#95—24no—
259#95—42no—
260#95—41no—
261#95—41no—
262#95—41no—
263#95C2×C3×C414yescomplemented
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—24no—
267C23×C3—24no—
268C23×C3—24no—
269C23×C3—24no—
270C23×C3—24no—
271C23×C3—24no—
272C23×C3—24no—
273C23×C3—24no—
274C23×C3—24no—
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—24no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—24no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3C4×D418yes—
299C23×C3C23×C411yescharacteristic
300C23×C3C22×D412yes—
301C23×C3C2×#4112yes—
302C23×C3C2×#4112yes—
303C23×C3C2×#4112yes—
304C23×C3C2×#4112yes—
305C23×C3H(5,𝔽2)11yescharacteristic
306C23×C3H(5,𝔽2)12yes—
307C23×C3H(5,𝔽2)11yescharacteristic
308C3×D4—416no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—432no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
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—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4#12318yes—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24C22×C3×C414yes—
373C24C2×C3×D414yes—
374C24C3×#4114yes—
375C24C24×C311yescharacteristic
376C2×D4—216no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4—48no—
380C2×D4—44no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—216no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—48no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—48no—
427C22×C4—48no—
428C22×C4—48no—
429C22×C4C22×C3×C414yes—
430C22×C4C22×C3×C412yes—
431C22×C4C22×C3×C412yes—
432C22×C4C22×C3×C412yes—
433C22×C4C2×C3×D414yes—
434C22×C4C2×C3×D414yes—
435C22×C4C3×#4114yes—
436C22×C4C3×#4114yes—
437C22×C4C3×#4114yes—
438C4⋊C4—44no—
439C22⋊C4—216no—
440C22⋊C4—216no—
441C22⋊C4—48no—
442C22⋊C4—48no—
443C22⋊C4—48no—
444C42—44no—
445C42—48no—
446C22×C3—28no—
447C22×C3—28no—
448C22×C3—28no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3C2×C4×D412yes—
462C22×C3C4×#4111yescharacteristic
463C22×C3C4×#4112yes—
464C22×C3#51811yescharacteristic
465C22×C3#51811yescharacteristic
466C22×C3C2×#12312yes—
467C22×C3#52512yes—
468C22×C3#52912yes—
469C22×C3#52912yes—
470C22×C3#53812yes—
471C22×C3#54012yes—
472C22×C3D4211yescharacteristic
473C22×C3#54612yes—
474C22×C3#54612yes—
475C22×C3#54612yes—
476C22×C3#55111yescharacteristic
477C22×C3#55112yes—
478C22×C3#55312yes—
479C22×C3#55312yes—
480C22×C3#55511yescharacteristic
481C22×C3#55511yescharacteristic
482C3×C4—28no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—44no—
487C3×C4—44no—
488C3×C4—44no—
489C3×C4—82no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C3×C4×D418yes—
525C23C23×C3×C411yescharacteristic
526C23C22×C3×D412yes—
527C23C2×C3×#4112yes—
528C23C2×C3×#4112yes—
529C23C2×C3×#4112yes—
530C23C2×C3×#4112yes—
531C23C3×H(5,𝔽2)11yescharacteristic
532C23C3×H(5,𝔽2)12yes—
533C23C3×H(5,𝔽2)11yescharacteristic
534D4—416no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—432no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C3×#12318yes—
586C2×C3—48no—
587C2×C3C4×#12312yes—
588C2×C3#233311yescharacteristic
589C2×C3#235811yescharacteristic
590C2×C3#236412yes—
591C2×C3#237211yescharacteristic
592C2×C3#241812yes—
593C2×C3#242012yes—
594C2×C3#247612yes—
595C2×C3#257812yes—
596C22—28no—
597C22—28no—
598C22—28no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22C2×C3×C4×D412yes—
612C22C3×C4×#4112yes—
613C22C3×C4×#4111yescharacteristic
614C22C3×#51811yescharacteristic
615C22C3×#51811yescharacteristic
616C22C2×C3×#12312yes—
617C22C3×#52512yes—
618C22C3×#52912yes—
619C22C3×#52912yes—
620C22C3×#53812yes—
621C22C3×#54012yes—
622C22C3×D4211yescharacteristic
623C22C3×#54612yes—
624C22C3×#54612yes—
625C22C3×#54612yes—
626C22C3×#55112yes—
627C22C3×#55111yescharacteristic
628C22C3×#55312yes—
629C22C3×#55312yes—
630C22C3×#55511yescharacteristic
631C22C3×#55511yescharacteristic
632C4—28no—
633C4—44no—
634C4—44no—
635C4—44no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—82no—
640C3#1418111yescharacteristic, direct product factor, Sylow
641C2—48no—
642C2C3×C4×#12312yes—
643C2C3×#233311yescharacteristic
644C2C3×#235811yescharacteristic
645C2C3×#236412yes—
646C2C3×#237211yescharacteristic
647C2C3×#241812yes—
648C2C3×#242012yes—
649C2C3×#247612yes—
650C2C3×#257812yes—
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×C22⋊C4C2semidirect
4. C3×#1445C2semidirect
5. C3×#1440C2semidirect
6. C3×#1437C2semidirect
7. C3×#1436C2semidirect
8. C3×#1434C2semidirect
9. C3×C22⋊#95C2semidirect
10. #14181C3direct (N × H)
21. C3×#394C4semidirect
37. C2×C4×C22⋊C4C2×C3semidirect
38. #1445C2×C3semidirect
39. #1440C2×C3semidirect
40. #1437C2×C3semidirect
41. #1436C2×C3semidirect
42. #1434C2×C3semidirect
43. C22⋊#95C2×C3semidirect
67. C2×C3×C4⋊C4C2×C4semidirect
80. C2×C3×C22⋊C4C2×C4semidirect
81. C2×C3×C22⋊C4C2×C4semidirect
98. C3×#95C2×C4semidirect
109. #394C3×C4semidirect
232. C2×C4⋊C4C2×C3×C4semidirect
245. C2×C22⋊C4C2×C3×C4semidirect
246. C2×C22⋊C4C2×C3×C4semidirect
263. #95C2×C3×C4semidirect
640. C3#14181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14402
C3×#14372
C3×#14362
C3×#14342
C3×C22⋊#952
#141813