Finite Group Databasebeta

← C3×#14842 #10633449

Subgroups — C3×#14842 #10633449

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#1445C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1440C212yesmaximal, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C212yesmaximal
10C3×#1437C212yesmaximal, complemented
11C3×#1434C212yesmaximal, complemented
12#14842C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C42C2212yes—
25C3×#397—24no—
26C3×#386—24no—
27C3×#380—24no—
28C3×C4×C22⋊C4—24no—
29C2×C3×#95C2212yes—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×#397C2×C311yescharacteristic, complemented
41C2×#386C2×C311yescharacteristic
42C2×#380C2×C311yescharacteristic, complemented
43C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
44#1445C2×C311yescharacteristic, complemented
45#1442C2×C311yescharacteristic, complemented
46#1440C2×C312yescomplemented
47#1439C2×C311yescharacteristic, complemented
48#1438C2×C312yes—
49#1437C2×C312yescomplemented
50#1434C2×C312yescomplemented
51C25×C3C2311yescharacteristic
52C25×C3C2311yescharacteristic
53C22×C3×D4—22no—
54C22×C3×D4—22no—
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—42no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—24no—
61C23×C3×C4—42no—
62C23×C3×C4D414yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—42no—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—24no—
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×C42—24no—
97C2×C3×C42—24no—
98C2×C3×C42—42no—
99C3×#95—22no—
100C3×#95—24no—
101C3×#95—22no—
102C3×#95—22no—
103C3×#95—24no—
104C3×#95—24no—
105C3×#95—24no—
106C3×#95—42no—
107C3×#95—42no—
108C3×#95—42no—
109C3×#95D414yescomplemented
110C23×D4C22×C311yescharacteristic
111C24×C4C22×C311yescharacteristic
112C22×C4⋊C4C22×C311yescharacteristic
113C22×C4⋊C4C22×C311yescharacteristic
114C22×C22⋊C4C22×C311yescharacteristic
115C22×C22⋊C4C22×C311yescharacteristic
116C22×C22⋊C4C22×C312yes—
117C22×C22⋊C4C22×C311yescharacteristic
118C22×C22⋊C4C22×C312yes—
119C22×C22⋊C4C22×C312yes—
120C22×C22⋊C4C22×C312yes—
121C22×C42C22×C312yes—
122#397—24no—
123#386—24no—
124#380—24no—
125C4×C22⋊C4—24no—
126C2×#95C22×C312yes—
127C2×#95C22×C311yescharacteristic
128C2×#95C22×C312yes—
129C2×#95C22×C312yes—
130C2×#95C22×C312yes—
131C2×#95C22×C311yescharacteristic
132C2×#95C22×C311yescharacteristic
133C2×#95C22×C312yes—
134C2×#95C22×C312yes—
135C2×#95C22×C312yes—
136C2×#95C22×C311yescharacteristic
137C24×C3—21no—
138C24×C3—22no—
139C24×C3—21no—
140C24×C3—22no—
141C24×C3—21no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—22no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—22no—
156C24×C3C2×D412yes—
157C24×C3#4112yes—
158C24×C3#4114yes—
159C24×C3C2411yescharacteristic
160C2×C3×D4—28no—
161C2×C3×D4—48no—
162C2×C3×D4—48no—
163C2×C3×D4—44no—
164C2×C3×D4—44no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
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—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—28no—
187C22×C3×C4—28no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
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—21no—
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—21no—
205C22×C3×C4—21no—
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—48no—
214C22×C3×C4—48no—
215C22×C3×C4C2×D414yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4#4112yes—
220C22×C3×C4#4114yes—
221C22×C3×C4#4112yes—
222C22×C3×C4#4114yes—
223C3×C4⋊C4—44no—
224C3×C4⋊C4—44no—
225C3×C22⋊C4—216no—
226C3×C22⋊C4—48no—
227C3×C22⋊C4—48no—
228C3×C22⋊C4—48no—
229C3×C22⋊C4—44no—
230C3×C22⋊C4—44no—
231C3×C22⋊C4—44no—
232C3×C42—48no—
233C25C23×C311yescharacteristic
234C25C23×C311yescharacteristic
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—42no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—42no—
244C23×C4C3×D414yes—
245C23×C4C23×C312yes—
246C23×C4C23×C312yes—
247C23×C4C23×C311yescharacteristic
248C23×C4C23×C311yescharacteristic
249C23×C4C23×C312yes—
250C23×C4C23×C312yes—
251C23×C4C23×C311yescharacteristic
252C23×C4C23×C311yescharacteristic
253C23×C4C23×C311yescharacteristic
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—42no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—24no—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C42—24no—
279C2×C42—24no—
280C2×C42—42no—
281#95—22no—
282#95—24no—
283#95—22no—
284#95—22no—
285#95—24no—
286#95—24no—
287#95—24no—
288#95—42no—
289#95—42no—
290#95—42no—
291#95C3×D414yescomplemented
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—24no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—24no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—42no—
322C23×C3—41no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—41no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—41no—
337C23×C3#12414yes—
338C23×C3C22×D411yescharacteristic
339C23×C3C22×D411yescharacteristic
340C23×C3C2×#4111yescharacteristic
341C23×C3C2×#4112yes—
342C23×C3C2×#4112yes—
343C23×C3C2×#4112yes—
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4111yescharacteristic
346C23×C3H(5,𝔽2)12yes—
347C23×C3H(5,𝔽2)11yescharacteristic
348C23×C3H(5,𝔽2)11yescharacteristic
349C3×D4—416no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—416no—
367C2×C3×C4—41no—
368C2×C3×C4—42no—
369C2×C3×C4—41no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—41no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
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#12114yes—
403C2×C3×C4#12314yes—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24C2×C3×D412yes—
424C24C3×#4112yes—
425C24C3×#4114yes—
426C24C24×C311yescharacteristic
427C2×D4—28no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—44no—
431C2×D4—44no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—44no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4C2×C3×D414yes—
483C22×C4C2×C3×D412yes—
484C22×C4C2×C3×D412yes—
485C22×C4C2×C3×D412yes—
486C22×C4C3×#4112yes—
487C22×C4C3×#4114yes—
488C22×C4C3×#4112yes—
489C22×C4C3×#4114yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C22⋊C4—216no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C22⋊C4—44no—
497C22⋊C4—44no—
498C22⋊C4—44no—
499C42—48no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—24no—
503C22×C3—44no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—44no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—44no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—81no—
519C22×C3—82no—
520C22×C3—81no—
521C22×C3—82no—
522C22×C3C2×#12111yescharacteristic
523C22×C3C2×#12311yescharacteristic
524C22×C3#52511yescharacteristic
525C22×C3#52512yes—
526C22×C3C2×#12411yescharacteristic
527C22×C3#52912yes—
528C22×C3#52912yes—
529C22×C3#52912yes—
530C22×C3#53211yescharacteristic
531C22×C3#53411yescharacteristic
532C22×C3#53511yescharacteristic
533C22×C3#53812yes—
534C22×C3#54012yes—
535C22×C3#54612yes—
536C22×C3#54611yescharacteristic
537C22×C3#55011yescharacteristic
538C22×C3#55112yes—
539C22×C3#55112yes—
540C22×C3#55112yes—
541C22×C3#55311yescharacteristic
542C22×C3#55312yes—
543C22×C3#55312yes—
544C22×C3#55511yescharacteristic
545C3×C4—24no—
546C3×C4—24no—
547C3×C4—42no—
548C3×C4—44no—
549C3×C4—44no—
550C3×C4—81no—
551C3×C4—82no—
552C3×C4—82no—
553C3×C4—81no—
554C23—22no—
555C23—22no—
556C23—24no—
557C23—22no—
558C23—24no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—22no—
567C23—24no—
568C23—22no—
569C23—24no—
570C23—22no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23—42no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—41no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—41no—
599C23C3×#12414yes—
600C23C22×C3×D411yescharacteristic
601C23C22×C3×D411yescharacteristic
602C23C2×C3×#4111yescharacteristic
603C23C2×C3×#4112yes—
604C23C2×C3×#4112yes—
605C23C2×C3×#4112yes—
606C23C2×C3×#4111yescharacteristic
607C23C2×C3×#4111yescharacteristic
608C23C3×H(5,𝔽2)12yes—
609C23C3×H(5,𝔽2)11yescharacteristic
610C23C3×H(5,𝔽2)11yescharacteristic
611D4—416no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—416no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
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—42no—
663C2×C4—42no—
664C2×C4C3×#12114yes—
665C2×C4C3×#12314yes—
666C2×C3—44no—
667C2×C3—82no—
668C2×C3#239511yescharacteristic
669C2×C3#241211yescharacteristic
670C2×C3#241411yescharacteristic
671C2×C3#245712yes—
672C2×C3#246712yes—
673C2×C3#250411yescharacteristic
674C2×C3#253112yes—
675C2×C3#256111yescharacteristic
676C2×C3#257812yes—
677C2×C3#266111yescharacteristic
678C2×C3#285011yescharacteristic
679C22—24no—
680C22—24no—
681C22—24no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—42no—
694C22—44no—
695C22—81no—
696C22—81no—
697C22—82no—
698C22—81no—
699C22—82no—
700C22—81no—
701C22C2×C3×#12111yescharacteristic
702C22C2×C3×#12311yescharacteristic
703C22C3×#52511yescharacteristic
704C22C3×#52512yes—
705C22C2×C3×#12411yescharacteristic
706C22C3×#52912yes—
707C22C3×#52912yes—
708C22C3×#52912yes—
709C22C3×#53211yescharacteristic
710C22C3×#53411yescharacteristic
711C22C3×#53511yescharacteristic
712C22C3×#53812yes—
713C22C3×#54012yes—
714C22C3×#54612yes—
715C22C3×#54611yescharacteristic
716C22C3×#55011yescharacteristic
717C22C3×#55112yes—
718C22C3×#55112yes—
719C22C3×#55112yes—
720C22C3×#55311yescharacteristic
721C22C3×#55312yes—
722C22C3×#55312yes—
723C22C3×#55511yescharacteristic
724C4—24no—
725C4—24no—
726C4—44no—
727C4—44no—
728C4—42no—
729C4—82no—
730C4—82no—
731C4—81no—
732C4—81no—
733C3#1484211yescharacteristic, direct product factor, Sylow
734C2—44no—
735C2—82no—
736C2C3×#239511yescharacteristic
737C2C3×#241211yescharacteristic
738C2C3×#241411yescharacteristic
739C2C3×#245712yes—
740C2C3×#246712yes—
741C2C3×#250411yescharacteristic
742C2C3×#253112yes—
743C2C3×#256111yescharacteristic
744C2C3×#257812yes—
745C2C3×#266111yescharacteristic
746C2C3×#285011yescharacteristic
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
1. C2×C3×#397C2semidirect
3. C2×C3×#380C2semidirect
4. C2×C3×C4×C22⋊C4C2semidirect
5. C3×#1445C2semidirect
6. C3×#1442C2semidirect
7. C3×#1440C2semidirect
8. C3×#1439C2semidirect
10. C3×#1437C2semidirect
11. C3×#1434C2semidirect
12. #14842C3direct (N × H)
40. C2×#397C2×C3semidirect
42. C2×#380C2×C3semidirect
43. C2×C4×C22⋊C4C2×C3semidirect
44. #1445C2×C3semidirect
45. #1442C2×C3semidirect
46. #1440C2×C3semidirect
47. #1439C2×C3semidirect
49. #1437C2×C3semidirect
50. #1434C2×C3semidirect
109. C3×#95D4semidirect
291. #95C3×D4semidirect
733. C3#14842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3862
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14422
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14342
#148423