Finite Group Databasebeta

← C43×#24056 #24944073

Subgroups — C43×#24056 #24944073

Order 11008.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3484C211yesmaximal, characteristic
2C43×#2849C212yesmaximal, complemented
3C2×C43×#386C211yesmaximal, characteristic, complemented
4C43×#2044C214yesmaximal, complemented
5C43×#1898C212yesmaximal, complemented
6C43×#1867C212yesmaximal, complemented
7C43×#1790C212yesmaximal, complemented
8C43×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C43C2211yescharacteristic
10C23×D4×C43C2211yescharacteristic
11C24×C4×C43C2211yescharacteristic, complemented
12C43×#546—22no—
13C43×#546—22no—
14D42×C43—22no—
15D42×C43—22no—
16C43×#535—21no—
17C43×#534—21no—
18C43×#534C2212yes—
19C43×#525—21no—
20C2×#123×C43—22no—
21C2×#120×C43—21no—
22C2×#120×C43C2212yes—
23C43×#518C2211yescharacteristic
24C22×C22⋊C4×C43—21no—
25C22×C22⋊C4×C43C2211yescharacteristic, complemented
26C2×#99×C43C2212yes—
27C2×#99×C43C2214yescomplemented
28C2×#99×C43C2212yescomplemented
29C43×#386—22no—
30C43×#386—21no—
31C43×#386—21no—
32C43×#386C2212yes—
33C43×#386C2214yescomplemented
34C43×#386C2212yescomplemented
35C43×#385—22no—
36C43×#385C2214yescomplemented
37C43×#381—22no—
38C43×#379C2212yescomplemented
39C2×#95×C43—21no—
40C43×#342C2214yescomplemented
41C25×C43D411yescharacteristic
42C25×C43C2311yescharacteristic
43H(5,𝔽2)×C43—24no—
44H(5,𝔽2)×C43—42no—
45C2×#41×C43—21no—
46C2×#41×C43—22no—
47C22×D4×C43—21no—
48C22×D4×C43—22no—
49C22×D4×C43—22no—
50C22×D4×C43—22no—
51C22×D4×C43—21no—
52C22×D4×C43—21no—
53C22×D4×C43—24no—
54C22×D4×C43—42no—
55C22×D4×C43D411yescharacteristic
56C22×D4×C43D411yescharacteristic
57C22×D4×C43D412yes—
58C22×D4×C43D412yes—
59C22×D4×C43C2312yes—
60C22×D4×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C23×C4×C43—22no—
64C23×C4×C43—21no—
65C23×C4×C43—22no—
66C23×C4×C43—21no—
67C23×C4×C43—44no—
68C23×C4×C43D411yescharacteristic
69C23×C4×C43C2312yes—
70#127×C43—22no—
71#124×C43—22no—
72#123×C43—22no—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—48no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—21no—
78#121×C43—21no—
79#121×C43—21no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—22no—
86#120×C43—22no—
87#120×C43—22no—
88#120×C43—22no—
89#120×C43—22no—
90#120×C43—22no—
91#120×C43—22no—
92#120×C43—22no—
93#120×C43—22no—
94#120×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99#117×C43—21no—
100C2×C4⋊C4×C43—24no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—24no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—42no—
111C2×C22⋊C4×C43—44no—
112C2×C22⋊C4×C43D412yes—
113C2×C22⋊C4×C43D412yes—
114C2×C22⋊C4×C43C2312yes—
115C2×C22⋊C4×C43C2314yes—
116C2×C22⋊C4×C43C2312yes—
117#99×C43—24no—
118#99×C43—42no—
119#99×C43—44no—
120#95×C43—22no—
121#95×C43—22no—
122#95×C43—24no—
123#95×C43—24no—
124C24×C43—22no—
125C24×C43—22no—
126C24×C43—21no—
127C24×C43—22no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—42no—
131C24×C43—42no—
132C24×C43—41no—
133C24×C43—42no—
134C24×C43—42no—
135C24×C43C2×D411yescharacteristic
136C24×C43C2×D412yes—
137C24×C43C2×D412yes—
138C24×C43C2×D411yescharacteristic
139C24×C43C2×D412yes—
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C24×C43C2411yescharacteristic
143#41×C43—48no—
144#41×C43—42no—
145#41×C43—42no—
146C2×Q8×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43—21no—
149C2×D4×C43—22no—
150C2×D4×C43—22no—
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—24no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—24no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43—48no—
171C2×D4×C43—48no—
172C2×D4×C43—48no—
173C2×D4×C43—42no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—42no—
177C2×D4×C43—82no—
178C2×D4×C43—82no—
179C2×D4×C43#4114yes—
180C22×C4×C43—21no—
181C22×C4×C43—24no—
182C22×C4×C43—22no—
183C22×C4×C43—28no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—22no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—22no—
190C22×C4×C43—24no—
191C22×C4×C43—24no—
192C22×C4×C43—22no—
193C22×C4×C43—41no—
194C22×C4×C43—42no—
195C22×C4×C43—44no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43—44no—
200C22×C4×C43—44no—
201C22×C4×C43—48no—
202C22×C4×C43—42no—
203C22×C4×C43—41no—
204C22×C4×C43—41no—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—22no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—48no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—24no—
227C22⋊C4×C43—24no—
228C22⋊C4×C43—24no—
229C22⋊C4×C43—44no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—44no—
232C22⋊C4×C43—44no—
233C22⋊C4×C43—44no—
234C22⋊C4×C43—48no—
235C42×C43—22no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—24no—
244C23×C43—24no—
245C23×C43—24no—
246C23×C43—24no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—24no—
253C23×C43—41no—
254C23×C43—42no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—42no—
258C23×C43—41no—
259C23×C43—42no—
260C23×C43—42no—
261C23×C43—48no—
262C23×C43—48no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—48no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43—81no—
274C23×C43—81no—
275C23×C43—84no—
276C23×C43—81no—
277C23×C43—81no—
278C23×C43#12012yes—
279C23×C43#12011yescharacteristic
280C23×C43#12011yescharacteristic
281C23×C43#12312yescomplemented
282C23×C43C22×D411yescharacteristic
283C23×C43C22×D412yes—
284C23×C43C2×#4112yes—
285C23×C43H(5,𝔽2)12yes—
286Q8×C43—42no—
287D4×C43—28no—
288D4×C43—44no—
289D4×C43—42no—
290D4×C43—44no—
291D4×C43—44no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—44no—
295D4×C43—44no—
296D4×C43—44no—
297D4×C43—44no—
298D4×C43—82no—
299D4×C43—82no—
300D4×C43—82no—
301D4×C43—82no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—24no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—24no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—44no—
316C2×C4×C43—42no—
317C2×C4×C43—44no—
318C2×C4×C43—44no—
319C2×C4×C43—48no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—44no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—44no—
326C2×C4×C43—42no—
327C2×C4×C43—44no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—44no—
331C2×C4×C43—81no—
332C2×C4×C43—81no—
333C2×C4×C43—84no—
334C2×C4×C43#12312yescomplemented
335#24056C4311yesmaximal, characteristic, direct product factor, Sylow
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—22no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—22no—
345C22×C43—21no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—48no—
353C22×C43—48no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—41no—
365C22×C43—42no—
366C22×C43—81no—
367C22×C43—84no—
368C22×C43—84no—
369C22×C43—84no—
370C22×C43—81no—
371C22×C43—162no—
372C22×C43B(4,𝔽2)12yes—
373C22×C43#45812yes—
374C22×C43C2×#12011yescharacteristic
375C22×C43C2×#12311yescharacteristic
376C22×C43#53411yescharacteristic
377C22×C43#54614yes—
378C4×C43—22no—
379C4×C43—41no—
380C4×C43—42no—
381C4×C43—44no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—84no—
385C4×C43—82no—
386#3484C2×C4311yescharacteristic
387#2849C2×C4312yescomplemented
388C2×#386C2×C4311yescharacteristic, complemented
389#2044C2×C4314yescomplemented
390#1898C2×C4312yescomplemented
391#1867C2×C4312yescomplemented
392#1790C2×C4312yescomplemented
393#1781C2×C4311yescharacteristic, complemented
394C2×C43—21no—
395C2×C43—24no—
396C2×C43—21no—
397C2×C43—22no—
398C2×C43—22no—
399C2×C43—42no—
400C2×C43—42no—
401C2×C43—81no—
402C2×C43—82no—
403C2×C43#240511yescharacteristic
404C2×C43C2×B(4,𝔽2)11yescharacteristic
405C2×C43C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C4311yescharacteristic
407C23×D4C22×C4311yescharacteristic
408C24×C4C22×C4311yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C4312yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C4312yes—
420#518C22×C4311yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C4311yescharacteristic, complemented
423C2×#99C22×C4312yes—
424C2×#99C22×C4314yescomplemented
425C2×#99C22×C4312yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C4312yes—
430#386C22×C4314yescomplemented
431#386C22×C4312yescomplemented
432#385—22no—
433#385C22×C4314yescomplemented
434#381—22no—
435#379C22×C4312yescomplemented
436C2×#95—21no—
437#342C22×C4314yescomplemented
438C43#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C4311yescharacteristic
440C25C23×C4311yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C4311yescharacteristic
454C22×D4D4×C4311yescharacteristic
455C22×D4D4×C4312yes—
456C22×D4D4×C4312yes—
457C22×D4C23×C4312yes—
458C22×D4C23×C4311yescharacteristic
459C22×D4C23×C4311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C4311yescharacteristic
467C23×C4C23×C4312yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C4312yes—
511C2×C22⋊C4D4×C4312yes—
512C2×C22⋊C4C23×C4312yes—
513C2×C22⋊C4C23×C4314yes—
514C2×C22⋊C4C23×C4312yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C4311yescharacteristic
534C24C2×D4×C4312yes—
535C24C2×D4×C4312yes—
536C24C2×D4×C4311yescharacteristic
537C24C2×D4×C4312yes—
538C24C2×D4×C4311yescharacteristic
539C24C2×D4×C4311yescharacteristic
540C24C24×C4311yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C4314yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C4312yes—
604C22×C4C2×D4×C4311yescharacteristic
605C22×C4C2×D4×C4311yescharacteristic
606C22×C4C2×D4×C4312yes—
607C22×C4C2×D4×C4312yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C4312yes—
677C23#120×C4311yescharacteristic
678C23#120×C4311yescharacteristic
679C23#123×C4312yescomplemented
680C23C22×D4×C4311yescharacteristic
681C23C22×D4×C4312yes—
682C23C2×#41×C4312yes—
683C23H(5,𝔽2)×C4312yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C4312yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C43×B(4,𝔽2)12yes—
770C22C43×#45812yes—
771C22C2×#120×C4311yescharacteristic
772C22C2×#123×C4311yescharacteristic
773C22C43×#53411yescharacteristic
774C22C43×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C43×#240511yescharacteristic
793C2C2×C43×B(4,𝔽2)11yescharacteristic
794C2C2×C43×#45811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
prime radicalC43×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2849C2semidirect
3. C2×C43×#386C2semidirect
4. C43×#2044C2semidirect
5. C43×#1898C2semidirect
6. C43×#1867C2semidirect
7. C43×#1790C2semidirect
8. C43×#1781C2semidirect
11. C24×C4×C43C22semidirect
25. C22×C22⋊C4×C43C22semidirect
27. C2×#99×C43C22semidirect
28. C2×#99×C43C22semidirect
33. C43×#386C22semidirect
34. C43×#386C22semidirect
36. C43×#385C22semidirect
38. C43×#379C22semidirect
40. C43×#342C22semidirect
281. C23×C43#123semidirect
334. C2×C4×C43#123semidirect
335. #24056C43direct (N × H)
387. #2849C2×C43semidirect
388. C2×#386C2×C43semidirect
389. #2044C2×C43semidirect
390. #1898C2×C43semidirect
391. #1867C2×C43semidirect
392. #1790C2×C43semidirect
393. #1781C2×C43semidirect
408. C24×C4C22×C43semidirect
422. C22×C22⋊C4C22×C43semidirect
424. C2×#99C22×C43semidirect
425. C2×#99C22×C43semidirect
430. #386C22×C43semidirect
431. #386C22×C43semidirect
433. #385C22×C43semidirect
435. #379C22×C43semidirect
437. #342C22×C43semidirect
438. C43#24056direct (N × H)
679. C23#123×C43semidirect
732. C2×C4#123×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34842
C43×#28492
C2×C43×#3862
C43×#20442
C43×#18982
C43×#18672
C43×#17902
C43×#17812
#2405643