Finite Group Databasebeta

← C3×#16660 #10635267

Subgroups — C3×#16660 #10635267

Order 768.

2038 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#392C211yesmaximal, characteristic
2C2×C3×#386C212yesmaximal, complemented
3C2×C3×#381C211yesmaximal, characteristic, complemented
4C3×#1443C212yesmaximal, complemented
5C3×#1440C212yesmaximal, complemented
6C3×#1439C212yesmaximal, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8C3×#1438C212yesmaximal, complemented
9C3×#1438C212yesmaximal, complemented
10#16660C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2212yes—
12C23×C3×D4C2211yescharacteristic
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C3×#392—24no—
24C3×#386—28no—
25C3×#381—24no—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×#392C2×C311yescharacteristic
36C2×#386C2×C312yescomplemented
37C2×#381C2×C311yescharacteristic, complemented
38#1443C2×C312yescomplemented
39#1440C2×C312yescomplemented
40#1439C2×C312yescomplemented
41#1439C2×C311yescharacteristic, complemented
42#1438C2×C312yescomplemented
43#1438C2×C312yescomplemented
44C25×C3C2312yes—
45C25×C3C2311yescharacteristic
46C22×C3×D4—24no—
47C22×C3×D4—24no—
48C22×C3×D4—24no—
49C22×C3×D4—24no—
50C22×C3×D4—24no—
51C22×C3×D4—22no—
52C22×C3×D4—24no—
53C22×C3×D4—42no—
54C22×C3×D4—42no—
55C22×C3×D4—42no—
56C22×C3×D4—41no—
57C22×C3×D4—41no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—41no—
61C23×C3×C4—41no—
62C23×C3×C4—41no—
63C23×C3×C4—41no—
64C23×C3×C4D414yescomplemented
65C23×C3×C4C2312yes—
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C2×C3×C4⋊C4—41no—
73C2×C3×C4⋊C4—42no—
74C2×C3×C22⋊C4—22no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—41no—
82C2×C3×C22⋊C4—41no—
83C2×C3×C22⋊C4—42no—
84C2×C3×C22⋊C4—42no—
85C2×C3×C22⋊C4—42no—
86C2×C3×C22⋊C4—42no—
87C2×C3×C22⋊C4—42no—
88C2×C3×C22⋊C4—42no—
89C2×C3×C22⋊C4—41no—
90C2×C3×C22⋊C4—41no—
91C2×C3×C22⋊C4—42no—
92C2×C3×C22⋊C4—42no—
93C2×C3×C22⋊C4—42no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4D414yes—
98C3×#95—24no—
99C3×#95—24no—
100C3×#95—24no—
101C3×#95—24no—
102C3×#95—22no—
103C3×#95—24no—
104C3×#95—41no—
105C3×#95—42no—
106C3×#95—42no—
107C23×D4C22×C312yes—
108C23×D4C22×C311yescharacteristic
109C24×C4C22×C311yescharacteristic
110C22×C4⋊C4C22×C311yescharacteristic
111C22×C22⋊C4C22×C312yes—
112C22×C22⋊C4C22×C312yes—
113C22×C22⋊C4C22×C311yescharacteristic
114C22×C22⋊C4C22×C312yes—
115C22×C22⋊C4C22×C312yes—
116C22×C22⋊C4C22×C312yes—
117C22×C22⋊C4C22×C312yes—
118C22×C22⋊C4C22×C311yescharacteristic
119#392—24no—
120#386—28no—
121#381—24no—
122C2×#95C22×C311yescharacteristic
123C2×#95C22×C312yes—
124C2×#95C22×C312yes—
125C2×#95C22×C312yes—
126C2×#95C22×C312yes—
127C2×#95C22×C312yes—
128C2×#95C22×C312yes—
129C2×#95C22×C312yes—
130C2×#95C22×C311yescharacteristic
131C24×C3—22no—
132C24×C3—22no—
133C24×C3—21no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—21no—
137C24×C3—22no—
138C24×C3—22no—
139C24×C3—22no—
140C24×C3—22no—
141C24×C3—22no—
142C24×C3—22no—
143C24×C3—22no—
144C24×C3—22no—
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×C3C2×D412yes—
154C24×C3C2×D412yes—
155C24×C3#4114yes—
156C24×C3#4112yes—
157C24×C3C2411yescharacteristic
158C2×C3×D4—216no—
159C2×C3×D4—48no—
160C2×C3×D4—48no—
161C2×C3×D4—48no—
162C2×C3×D4—44no—
163C2×C3×D4—48no—
164C2×C3×D4—48no—
165C2×C3×D4—44no—
166C2×C3×D4—48no—
167C2×C3×D4—48no—
168C2×C3×D4—44no—
169C2×C3×D4—48no—
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—22no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4—44no—
215C22×C3×C4—44no—
216C22×C3×C4—44no—
217C22×C3×C4—44no—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4#4114yes—
222C3×C4⋊C4—44no—
223C3×C22⋊C4—44no—
224C3×C22⋊C4—48no—
225C3×C22⋊C4—48no—
226C3×C22⋊C4—48no—
227C3×C22⋊C4—44no—
228C3×C22⋊C4—48no—
229C3×C22⋊C4—48no—
230C3×C22⋊C4—48no—
231C25C23×C312yes—
232C25C23×C311yescharacteristic
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—24no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—41no—
244C22×D4—41no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—41no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4C3×D414yescomplemented
252C23×C4C23×C312yes—
253C23×C4C23×C312yes—
254C23×C4C23×C312yes—
255C23×C4C23×C311yescharacteristic
256C23×C4C23×C312yes—
257C23×C4C23×C311yescharacteristic
258C23×C4C23×C312yes—
259C2×C4⋊C4—41no—
260C2×C4⋊C4—42no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4—41no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—41no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4C3×D414yes—
285#95—24no—
286#95—24no—
287#95—24no—
288#95—24no—
289#95—22no—
290#95—24no—
291#95—41no—
292#95—42no—
293#95—42no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—24no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—42no—
322C23×C3—41no—
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×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3#12114yes—
352C23×C3C22×D411yescharacteristic
353C23×C3C22×D411yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4112yes—
356C23×C3C2×#4112yes—
357C23×C3H(5,𝔽2)11yescharacteristic
358C23×C3H(5,𝔽2)11yescharacteristic
359C23×C3H(5,𝔽2)11yescharacteristic
360C23×C3H(5,𝔽2)11yescharacteristic
361C23×C3H(5,𝔽2)12yes—
362C23×C3H(5,𝔽2)12yes—
363C3×D4—432no—
364C3×D4—416no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—416no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
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—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24C2×C3×D412yes—
434C24C2×C3×D412yes—
435C24C3×#4114yes—
436C24C3×#4112yes—
437C24C24×C311yescharacteristic
438C2×D4—216no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—44no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—44no—
449C2×D4—48no—
450C22×C4—28no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4C2×C3×D412yes—
499C22×C4C2×C3×D412yes—
500C22×C4C2×C3×D414yes—
501C22×C4C3×#4114yes—
502C4⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4—48no—
509C22⋊C4—48no—
510C22⋊C4—48no—
511C22×C3—24no—
512C22×C3—28no—
513C22×C3—42no—
514C22×C3—44no—
515C22×C3—42no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—44no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—82no—
530C22×C3—82no—
531C22×C3—82no—
532C22×C3—82no—
533C22×C3—82no—
534C22×C3—82no—
535C22×C3—82no—
536C22×C3—82no—
537C22×C3C2×#12111yescharacteristic
538C22×C3#52512yes—
539C22×C3#53411yescharacteristic
540C22×C3#53411yescharacteristic
541C22×C3#53411yescharacteristic
542C22×C3#53511yescharacteristic
543C22×C3#53512yes—
544C22×C3#53811yescharacteristic
545C22×C3#53811yescharacteristic
546C22×C3#53812yes—
547C22×C3#53812yes—
548C22×C3#54012yes—
549C22×C3#54012yes—
550C22×C3#54612yes—
551C22×C3#54612yes—
552C22×C3#55111yescharacteristic
553C22×C3#55112yes—
554C22×C3#55112yes—
555C22×C3#55312yes—
556C22×C3#55911yescharacteristic
557C22×C3#56011yescharacteristic
558C22×C3#56012yes—
559C22×C3#56011yescharacteristic
560C3×C4—44no—
561C3×C4—44no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—82no—
565C3×C4—82no—
566C3×C4—82no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—24no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—41no—
587C23—41no—
588C23—42no—
589C23—41no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23C3×#12114yes—
625C23C22×C3×D411yescharacteristic
626C23C22×C3×D411yescharacteristic
627C23C2×C3×#4112yes—
628C23C2×C3×#4111yescharacteristic
629C23C2×C3×#4112yes—
630C23C3×H(5,𝔽2)11yescharacteristic
631C23C3×H(5,𝔽2)11yescharacteristic
632C23C3×H(5,𝔽2)12yes—
633C23C3×H(5,𝔽2)12yes—
634C23C3×H(5,𝔽2)11yescharacteristic
635C23C3×H(5,𝔽2)11yescharacteristic
636D4—432no—
637D4—416no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—416no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C3—44no—
685C2×C3—84no—
686C2×C3#241112yes—
687C2×C3#260011yescharacteristic
688C2×C3#261711yescharacteristic
689C2×C3#263512yes—
690C2×C3#269711yescharacteristic
691C2×C3#270312yes—
692C2×C3#270911yescharacteristic
693C2×C3#274912yes—
694C2×C3#275211yescharacteristic
695C2×C3#276011yescharacteristic
696C2×C3#281511yescharacteristic
697C22—24no—
698C22—28no—
699C22—44no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—82no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—82no—
722C22—82no—
723C22C2×C3×#12111yescharacteristic
724C22C3×#52512yes—
725C22C3×#53411yescharacteristic
726C22C3×#53411yescharacteristic
727C22C3×#53411yescharacteristic
728C22C3×#53511yescharacteristic
729C22C3×#53512yes—
730C22C3×#53811yescharacteristic
731C22C3×#53811yescharacteristic
732C22C3×#53812yes—
733C22C3×#53812yes—
734C22C3×#54012yes—
735C22C3×#54012yes—
736C22C3×#54612yes—
737C22C3×#54612yes—
738C22C3×#55112yes—
739C22C3×#55112yes—
740C22C3×#55111yescharacteristic
741C22C3×#55312yes—
742C22C3×#55911yescharacteristic
743C22C3×#56011yescharacteristic
744C22C3×#56012yes—
745C22C3×#56011yescharacteristic
746C4—44no—
747C4—44no—
748C4—42no—
749C4—42no—
750C4—82no—
751C4—82no—
752C4—82no—
753C3#1666011yescharacteristic, direct product factor, Sylow
754C2—44no—
755C2—84no—
756C2C3×#241112yes—
757C2C3×#260011yescharacteristic
758C2C3×#261711yescharacteristic
759C2C3×#263512yes—
760C2C3×#269711yescharacteristic
761C2C3×#270312yes—
762C2C3×#270911yescharacteristic
763C2C3×#274912yes—
764C2C3×#275211yescharacteristic
765C2C3×#276011yescharacteristic
766C2C3×#281511yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#386C2semidirect
3. C2×C3×#381C2semidirect
4. C3×#1443C2semidirect
5. C3×#1440C2semidirect
6. C3×#1439C2semidirect
7. C3×#1439C2semidirect
8. C3×#1438C2semidirect
9. C3×#1438C2semidirect
10. #16660C3direct (N × H)
36. C2×#386C2×C3semidirect
37. C2×#381C2×C3semidirect
38. #1443C2×C3semidirect
39. #1440C2×C3semidirect
40. #1439C2×C3semidirect
41. #1439C2×C3semidirect
42. #1438C2×C3semidirect
43. #1438C2×C3semidirect
64. C23×C3×C4D4semidirect
251. C23×C4C3×D4semidirect
753. C3#16660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3922
C2×C3×#3862
C2×C3×#3812
C3×#14432
C3×#14402
C3×#14392
C3×#14382
#166603