Finite Group Databasebeta

← C3×#16681 #10635288

Subgroups — C3×#16681 #10635288

Order 768.

1858 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic
4C2×C3×#387C211yesmaximal, characteristic, complemented
5C3×#1446C211yesmaximal, characteristic, complemented
6C3×#1440C212yesmaximal, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1438C211yesmaximal, characteristic
11C3×#1434C211yesmaximal, characteristic, complemented
12#16681C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C2×C3×#124—24no—
16C2×C3×#124—24no—
17C2×C3×#124—24no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2211yescharacteristic
28C3×#395—24no—
29C3×#394—24no—
30C3×#387—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C22×#124C2×C311yescharacteristic
43C2×#395C2×C311yescharacteristic, complemented
44C2×#394C2×C311yescharacteristic
45C2×#387C2×C311yescharacteristic, complemented
46#1446C2×C311yescharacteristic, complemented
47#1440C2×C312yescomplemented
48#1439C2×C312yescomplemented
49#1439C2×C312yescomplemented
50#1439C2×C312yescomplemented
51#1438C2×C311yescharacteristic
52#1434C2×C311yescharacteristic, complemented
53C25×C3C2312yes—
54C22×C3×Q8—22no—
55C22×C3×Q8—22no—
56C22×C3×Q8—42no—
57C22×C3×Q8—42no—
58C22×C3×Q8D414yes—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—42no—
62C22×C3×D4—42no—
63C22×C3×D4D414yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C3×#124—232no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—42no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C42—22no—
103C2×C3×C42—22no—
104C2×C3×C42D414yes—
105C3×#95—22no—
106C3×#95—22no—
107C3×#95—22no—
108C3×#95—22no—
109C3×#95—22no—
110C3×#95—24no—
111C3×#95—22no—
112C3×#95—24no—
113C3×#95—42no—
114C3×#95—42no—
115C3×#95—42no—
116C23×Q8C22×C311yescharacteristic
117C23×D4C22×C311yescharacteristic
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—24no—
121C22×C4⋊C4C22×C311yescharacteristic
122C22×C4⋊C4C22×C311yescharacteristic
123C22×C4⋊C4C22×C312yes—
124C22×C22⋊C4C22×C312yes—
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C42C22×C311yescharacteristic
131#395—24no—
132#394—24no—
133#387—24no—
134C2×#95C22×C311yescharacteristic
135C2×#95C22×C311yescharacteristic
136C2×#95C22×C312yes—
137C2×#95C22×C312yes—
138C2×#95C22×C311yescharacteristic
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C311yescharacteristic
142C2×#95C22×C312yes—
143C2×#95C22×C312yes—
144C2×#95C22×C312yes—
145C24×C3—22no—
146C24×C3—22no—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3C2×D414yes—
160C24×C3C2411yescharacteristic
161C2×C3×Q8—28no—
162C2×C3×Q8—48no—
163C2×C3×Q8—48no—
164C2×C3×Q8—44no—
165C2×C3×Q8—44no—
166C2×C3×D4—28no—
167C2×C3×D4—48no—
168C2×C3×D4—48no—
169C2×C3×D4—44no—
170C2×C3×D4—44no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D414yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4#4114yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4112yes—
231C3×C4⋊C4—28no—
232C3×C4⋊C4—48no—
233C3×C4⋊C4—44no—
234C3×C22⋊C4—216no—
235C3×C22⋊C4—216no—
236C3×C22⋊C4—48no—
237C3×C22⋊C4—48no—
238C3×C22⋊C4—48no—
239C3×C22⋊C4—48no—
240C3×C42—28no—
241C25C23×C312yes—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8C3×D414yes—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4C3×D414yes—
252C23×C4C23×C311yescharacteristic
253C23×C4C23×C311yescharacteristic
254C23×C4C23×C312yes—
255C23×C4C23×C312yes—
256C23×C4C23×C311yescharacteristic
257C23×C4C23×C311yescharacteristic
258C23×C4C23×C311yescharacteristic
259C23×C4C23×C311yescharacteristic
260C23×C4C23×C312yes—
261C23×C4C23×C311yescharacteristic
262#124—232no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42C3×D414yes—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—24no—
299#95—22no—
300#95—24no—
301#95—42no—
302#95—42no—
303#95—42no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3C22×D411yescharacteristic
340C23×C3C22×D411yescharacteristic
341C23×C3C22×D411yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3C2×#4111yescharacteristic
344C23×C3C2×#4112yes—
345C23×C3H(5,𝔽2)12yes—
346C23×C3H(5,𝔽2)12yes—
347C23×C3H(5,𝔽2)11yescharacteristic
348C23×C32−1+412yes—
349C23×C32−1+411yescharacteristic
350C3×Q8—416no—
351C3×D4—416no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—24no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4#12014yes—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24C2×C3×D414yes—
427C24C24×C311yescharacteristic
428C2×Q8—28no—
429C2×Q8—48no—
430C2×Q8—48no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×D4—28no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—44no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4C2×C3×D412yes—
490C22×C4C2×C3×D412yes—
491C22×C4C2×C3×D414yes—
492C22×C4C2×C3×D412yes—
493C22×C4C2×C3×D412yes—
494C22×C4C2×C3×D412yes—
495C22×C4C3×#4114yes—
496C22×C4C3×#4112yes—
497C22×C4C3×#4112yes—
498C4⋊C4—28no—
499C4⋊C4—48no—
500C4⋊C4—44no—
501C22⋊C4—216no—
502C22⋊C4—216no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C42—28no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—82no—
516C22×C3—82no—
517C22×C3—82no—
518C22×C3—82no—
519C22×C3—82no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—82no—
523C22×C3C2×#12011yescharacteristic
524C22×C3#52511yescharacteristic
525C22×C3#53211yescharacteristic
526C22×C3#53412yes—
527C22×C3#53412yes—
528C22×C3#53511yescharacteristic
529C22×C3#53511yescharacteristic
530C22×C3#53611yescharacteristic
531C22×C3#53711yescharacteristic
532C22×C3#53812yes—
533C22×C3#54212yes—
534C22×C3#54212yes—
535C22×C3#54212yes—
536C22×C3#54611yescharacteristic
537C22×C3#54711yescharacteristic
538C22×C3#54712yes—
539C22×C3#54811yescharacteristic
540C22×C3#54812yes—
541C22×C3#55011yescharacteristic
542C22×C3#55112yes—
543C22×C3#55512yes—
544C22×C3#56212yes—
545C22×C3#56312yes—
546C3×C4—24no—
547C3×C4—42no—
548C3×C4—44no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—42no—
552C3×C4—44no—
553C3×C4—81no—
554C3×C4—81no—
555C3×C4—82no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23C22×C3×D411yescharacteristic
592C23C22×C3×D411yescharacteristic
593C23C22×C3×D411yescharacteristic
594C23C2×C3×#4111yescharacteristic
595C23C2×C3×#4111yescharacteristic
596C23C2×C3×#4112yes—
597C23C3×H(5,𝔽2)11yescharacteristic
598C23C3×H(5,𝔽2)12yes—
599C23C3×H(5,𝔽2)12yes—
600C23C3×2−1+412yes—
601C23C3×2−1+411yescharacteristic
602Q8—416no—
603D4—416no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4C3×#12014yes—
664C2×C3—84no—
665C2×C3#240711yescharacteristic
666C2×C3#243211yescharacteristic
667C2×C3#261011yescharacteristic
668C2×C3#261311yescharacteristic
669C2×C3#263211yescharacteristic
670C2×C3#266211yescharacteristic
671C2×C3#268612yes—
672C2×C3#271712yes—
673C2×C3#273012yes—
674C2×C3#273112yes—
675C2×C3#282011yescharacteristic
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22C2×C3×#12011yescharacteristic
692C22C3×#52511yescharacteristic
693C22C3×#53211yescharacteristic
694C22C3×#53412yes—
695C22C3×#53412yes—
696C22C3×#53511yescharacteristic
697C22C3×#53511yescharacteristic
698C22C3×#53611yescharacteristic
699C22C3×#53711yescharacteristic
700C22C3×#53812yes—
701C22C3×#54212yes—
702C22C3×#54212yes—
703C22C3×#54212yes—
704C22C3×#54611yescharacteristic
705C22C3×#54711yescharacteristic
706C22C3×#54712yes—
707C22C3×#54811yescharacteristic
708C22C3×#54812yes—
709C22C3×#55011yescharacteristic
710C22C3×#55112yes—
711C22C3×#55512yes—
712C22C3×#56212yes—
713C22C3×#56312yes—
714C4—24no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—44no—
719C4—42no—
720C4—44no—
721C4—81no—
722C4—82no—
723C4—81no—
724C3#1668111yescharacteristic, direct product factor, Sylow
725C2—84no—
726C2C3×#240711yescharacteristic
727C2C3×#243211yescharacteristic
728C2C3×#261011yescharacteristic
729C2C3×#261311yescharacteristic
730C2C3×#263211yescharacteristic
731C2C3×#266211yescharacteristic
732C2C3×#268612yes—
733C2C3×#271712yes—
734C2C3×#273012yes—
735C2C3×#273112yes—
736C2C3×#282011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#395C2semidirect
4. C2×C3×#387C2semidirect
5. C3×#1446C2semidirect
6. C3×#1440C2semidirect
7. C3×#1439C2semidirect
8. C3×#1439C2semidirect
9. C3×#1439C2semidirect
11. C3×#1434C2semidirect
12. #16681C3direct (N × H)
43. C2×#395C2×C3semidirect
45. C2×#387C2×C3semidirect
46. #1446C2×C3semidirect
47. #1440C2×C3semidirect
48. #1439C2×C3semidirect
49. #1439C2×C3semidirect
50. #1439C2×C3semidirect
52. #1434C2×C3semidirect
724. C3#16681direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C2×C3×#3952
C2×C3×#3942
C2×C3×#3872
C3×#14462
C3×#14402
C3×#14392
C3×#14382
C3×#14342
#166813