Finite Group Databasebeta

← C3×#14207 #10632814

Subgroups — C3×#14207 #10632814

Order 768.

2586 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#392C211yesmaximal, characteristic
2C2×C3×#390C212yesmaximal, complemented
3C2×C3×#386C212yesmaximal, complemented
4C2×C3×#386C212yesmaximal, complemented
5C2×C3×C4×C22⋊C4C212yesmaximal, complemented
6C3×#1440C211yesmaximal, characteristic, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1437C211yesmaximal, characteristic, complemented
9C3×#1436C212yesmaximal, complemented
10#14207C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2211yescharacteristic
12C23×C3×D4C2212yes—
13C24×C3×C4C2212yes—
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2212yes—
25C3×#392C418yescomplemented
26C3×#390—28no—
27C3×#386—28no—
28C3×#386—28no—
29C3×C4×C22⋊C4—28no—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×#392C2×C311yescharacteristic
38C2×#390C2×C312yescomplemented
39C2×#386C2×C312yescomplemented
40C2×#386C2×C312yescomplemented
41C2×C4×C22⋊C4C2×C312yescomplemented
42#1440C2×C311yescharacteristic, complemented
43#1439C2×C312yescomplemented
44#1437C2×C311yescharacteristic, complemented
45#1436C2×C312yescomplemented
46C25×C3C2311yescharacteristic
47C25×C3C2312yes—
48C22×C3×D4—24no—
49C22×C3×D4—24no—
50C22×C3×D4—24no—
51C22×C3×D4—24no—
52C22×C3×D4—24no—
53C22×C3×D4—24no—
54C22×C3×D4—42no—
55C22×C3×D4—42no—
56C22×C3×D4—41no—
57C22×C3×D4—41no—
58C22×C3×D4C2×C414yes—
59C22×C3×D4C2×C418yescomplemented
60C23×C3×C4—24no—
61C23×C3×C4—24no—
62C23×C3×C4—24no—
63C23×C3×C4—24no—
64C23×C3×C4—24no—
65C23×C3×C4—42no—
66C23×C3×C4—42no—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2312yes—
71C23×C3×C4C2312yes—
72C23×C3×C4C2312yes—
73C23×C3×C4C2312yes—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—24no—
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—24no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—24no—
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—41no—
91C2×C3×C22⋊C4—41no—
92C2×C3×C22⋊C4—41no—
93C2×C3×C22⋊C4—41no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4C2×C418yescomplemented
97C2×C3×C22⋊C4C2×C414yescomplemented
98C2×C3×C22⋊C4D418yescomplemented
99C2×C3×C42—24no—
100C2×C3×C42—24no—
101C2×C3×C42—24no—
102C2×C3×C42—41no—
103C2×C3×C42—42no—
104C3×#95—24no—
105C3×#95—24no—
106C3×#95—24no—
107C3×#95—24no—
108C3×#95—41no—
109C3×#95C2×C414yescomplemented
110C3×#95D418yescomplemented
111C23×D4C22×C311yescharacteristic
112C23×D4C22×C312yes—
113C24×C4C22×C312yes—
114C22×C4⋊C4C22×C312yes—
115C22×C22⋊C4C22×C312yes—
116C22×C22⋊C4C22×C312yes—
117C22×C22⋊C4C22×C312yes—
118C22×C22⋊C4C22×C311yescharacteristic
119C22×C22⋊C4C22×C311yescharacteristic
120C22×C22⋊C4C22×C312yes—
121C22×C22⋊C4C22×C312yes—
122C22×C22⋊C4C22×C311yescharacteristic
123C22×C42C22×C312yes—
124C22×C42C22×C311yescharacteristic
125#392C3×C418yescomplemented
126#390—28no—
127#386—28no—
128#386—28no—
129C4×C22⋊C4—28no—
130C2×#95C22×C312yes—
131C2×#95C22×C312yes—
132C2×#95C22×C312yes—
133C2×#95C22×C312yes—
134C2×#95C22×C311yescharacteristic
135C2×#95C22×C311yescharacteristic
136C2×#95C22×C312yes—
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×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3C22×C412yes—
158C24×C3C22×C414yes—
159C24×C3C2×D414yes—
160C24×C3#4114yes—
161C24×C3C2411yescharacteristic
162C2×C3×D4—216no—
163C2×C3×D4—216no—
164C2×C3×D4—216no—
165C2×C3×D4—44no—
166C2×C3×D4—48no—
167C2×C3×D4—48no—
168C2×C3×D4—48no—
169C2×C3×D4—48no—
170C2×C3×D4—48no—
171C2×C3×D4—44no—
172C2×C3×D4—48no—
173C2×C3×D4—44no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—216no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
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—48no—
211C22×C3×C4—48no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4—48no—
215C22×C3×C4—48no—
216C22×C3×C4C22×C412yes—
217C22×C3×C4C22×C412yes—
218C22×C3×C4C22×C414yes—
219C22×C3×C4C2×D414yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4C2×D414yes—
222C22×C3×C4C2×D414yes—
223C22×C3×C4C2×D414yes—
224C22×C3×C4#4114yes—
225C22×C3×C4#4114yes—
226C3×C4⋊C4—48no—
227C3×C22⋊C4—216no—
228C3×C22⋊C4—216no—
229C3×C22⋊C4—44no—
230C3×C22⋊C4—44no—
231C3×C22⋊C4—44no—
232C3×C22⋊C4—48no—
233C3×C22⋊C4—48no—
234C3×C22⋊C4—48no—
235C3×C42—44no—
236C3×C42—48no—
237C25C23×C311yescharacteristic
238C25C23×C312yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—41no—
248C22×D4—41no—
249C22×D4C2×C3×C414yes—
250C22×D4C2×C3×C418yescomplemented
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4C23×C312yes—
259C23×C4C23×C311yescharacteristic
260C23×C4C23×C311yescharacteristic
261C23×C4C23×C312yes—
262C23×C4C23×C312yes—
263C23×C4C23×C312yes—
264C23×C4C23×C312yes—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—42no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—24no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—24no—
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—41no—
282C2×C22⋊C4—41no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4C2×C3×C418yescomplemented
288C2×C22⋊C4C2×C3×C414yescomplemented
289C2×C22⋊C4C3×D418yescomplemented
290C2×C42—24no—
291C2×C42—24no—
292C2×C42—24no—
293C2×C42—41no—
294C2×C42—42no—
295#95—24no—
296#95—24no—
297#95—24no—
298#95—24no—
299#95—41no—
300#95C2×C3×C414yescomplemented
301#95C3×D418yescomplemented
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—24no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
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—41no—
348C23×C3—41no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3C4×D418yes—
358C23×C3C23×C411yescharacteristic
359C23×C3C22×D412yes—
360C23×C3C22×D412yes—
361C23×C3C2×#4112yes—
362C23×C3C2×#4112yes—
363C23×C3C2×#4112yes—
364C23×C3H(5,𝔽2)11yescharacteristic
365C23×C3H(5,𝔽2)12yes—
366C23×C3H(5,𝔽2)11yescharacteristic
367C3×D4—432no—
368C3×D4—416no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—432no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4C4×D418yes—
414C2×C3×C4#12118yes—
415C24—22no—
416C24—22no—
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—21no—
433C24—21no—
434C24—22no—
435C24C22×C3×C412yes—
436C24C22×C3×C414yes—
437C24C2×C3×D414yes—
438C24C3×#4114yes—
439C24C24×C311yescharacteristic
440C2×D4—216no—
441C2×D4—216no—
442C2×D4—216no—
443C2×D4—44no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—44no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—216no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4C22×C3×C412yes—
495C22×C4C22×C3×C412yes—
496C22×C4C22×C3×C414yes—
497C22×C4C2×C3×D414yes—
498C22×C4C2×C3×D414yes—
499C22×C4C2×C3×D414yes—
500C22×C4C2×C3×D414yes—
501C22×C4C2×C3×D414yes—
502C22×C4C3×#4114yes—
503C22×C4C3×#4114yes—
504C4⋊C4—48no—
505C22⋊C4—216no—
506C22⋊C4—216no—
507C22⋊C4—44no—
508C22⋊C4—44no—
509C22⋊C4—44no—
510C22⋊C4—48no—
511C22⋊C4—48no—
512C22⋊C4—48no—
513C42—44no—
514C42—48no—
515C22×C3—28no—
516C22×C3—28no—
517C22×C3—28no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—42no—
531C22×C3—44no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—44no—
535C22×C3—82no—
536C22×C3—82no—
537C22×C3—82no—
538C22×C3—82no—
539C22×C3C2×C4×D412yes—
540C22×C3C2×C4×D412yes—
541C22×C3C4×#4111yescharacteristic
542C22×C3#51811yescharacteristic
543C22×C3#51811yescharacteristic
544C22×C3C2×#12112yes—
545C22×C3#52512yes—
546C22×C3#52912yes—
547C22×C3#53212yes—
548C22×C3#53812yes—
549C22×C3#54012yes—
550C22×C3D4212yes—
551C22×C3D4211yescharacteristic
552C22×C3D4211yescharacteristic
553C22×C3#54612yes—
554C22×C3#54612yes—
555C22×C3#54612yes—
556C22×C3#55012yes—
557C22×C3#55111yescharacteristic
558C22×C3#55112yes—
559C22×C3#55911yescharacteristic
560C3×C4—28no—
561C3×C4—28no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—44no—
565C3×C4—44no—
566C3×C4—82no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23C3×C4×D418yes—
623C23C23×C3×C411yescharacteristic
624C23C22×C3×D412yes—
625C23C22×C3×D412yes—
626C23C2×C3×#4112yes—
627C23C2×C3×#4112yes—
628C23C2×C3×#4112yes—
629C23C3×H(5,𝔽2)11yescharacteristic
630C23C3×H(5,𝔽2)12yes—
631C23C3×H(5,𝔽2)11yescharacteristic
632D4—432no—
633D4—416no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—432no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4C3×C4×D418yes—
679C2×C4C3×#12118yes—
680C2×C3—48no—
681C2×C3—82no—
682C2×C3C4×#12112yes—
683C2×C3#233311yescharacteristic
684C2×C3#235812yes—
685C2×C3#235811yescharacteristic
686C2×C3#236611yescharacteristic
687C2×C3#242412yes—
688C2×C3#242812yes—
689C2×C3#247112yes—
690C2×C3#255712yes—
691C22—28no—
692C22—28no—
693C22—28no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—44no—
708C22—42no—
709C22—44no—
710C22—42no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22C2×C3×C4×D412yes—
716C22C2×C3×C4×D412yes—
717C22C3×C4×#4111yescharacteristic
718C22C3×#51811yescharacteristic
719C22C3×#51811yescharacteristic
720C22C2×C3×#12112yes—
721C22C3×#52512yes—
722C22C3×#52912yes—
723C22C3×#53212yes—
724C22C3×#53812yes—
725C22C3×#54012yes—
726C22C3×D4211yescharacteristic
727C22C3×D4212yes—
728C22C3×D4211yescharacteristic
729C22C3×#54612yes—
730C22C3×#54612yes—
731C22C3×#54612yes—
732C22C3×#55012yes—
733C22C3×#55111yescharacteristic
734C22C3×#55112yes—
735C22C3×#55911yescharacteristic
736C4—28no—
737C4—28no—
738C4—42no—
739C4—44no—
740C4—44no—
741C4—42no—
742C4—82no—
743C3#1420711yescharacteristic, direct product factor, Sylow
744C2—48no—
745C2—82no—
746C2C3×C4×#12112yes—
747C2C3×#233311yescharacteristic
748C2C3×#235812yes—
749C2C3×#235811yescharacteristic
750C2C3×#236611yescharacteristic
751C2C3×#242412yes—
752C2C3×#242812yes—
753C2C3×#247112yes—
754C2C3×#255712yes—
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#390C2semidirect
3. C2×C3×#386C2semidirect
4. C2×C3×#386C2semidirect
5. C2×C3×C4×C22⋊C4C2semidirect
6. C3×#1440C2semidirect
7. C3×#1439C2semidirect
8. C3×#1437C2semidirect
9. C3×#1436C2semidirect
10. #14207C3direct (N × H)
25. C3×#392C4semidirect
38. C2×#390C2×C3semidirect
39. C2×#386C2×C3semidirect
40. C2×#386C2×C3semidirect
41. C2×C4×C22⋊C4C2×C3semidirect
42. #1440C2×C3semidirect
43. #1439C2×C3semidirect
44. #1437C2×C3semidirect
45. #1436C2×C3semidirect
59. C22×C3×D4C2×C4semidirect
96. C2×C3×C22⋊C4C2×C4semidirect
97. C2×C3×C22⋊C4C2×C4semidirect
98. C2×C3×C22⋊C4D4semidirect
109. C3×#95C2×C4semidirect
110. C3×#95D4semidirect
125. #392C3×C4semidirect
250. C22×D4C2×C3×C4semidirect
287. C2×C22⋊C4C2×C3×C4semidirect
288. C2×C22⋊C4C2×C3×C4semidirect
289. C2×C22⋊C4C3×D4semidirect
300. #95C2×C3×C4semidirect
301. #95C3×D4semidirect
743. C3#14207direct (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×#3902
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14402
C3×#14392
C3×#14372
C3×#14362
#142073