Finite Group Databasebeta

← C43×#24404 #24944421

Subgroups — C43×#24404 #24944421

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3484C211yesmaximal, characteristic, complemented
2C2×C43×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C43C211yesmaximal, characteristic, complemented
4C43×#2410C212yesmaximal, complemented
5C43×#2403C211yesmaximal, characteristic, complemented
6C43×#2044C212yesmaximal, complemented
7C43×#2021C212yesmaximal, complemented
8C43×#1898C212yesmaximal, complemented
9C43×#1889C211yesmaximal, characteristic, complemented
10C43×#1867C211yesmaximal, characteristic, complemented
11C43×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C43C2211yescharacteristic
13C23×D4×C43C2211yescharacteristic
14C23×D4×C43C2211yescharacteristic, complemented
15C43×#546—22no—
16C43×#546—22no—
17D42×C43—22no—
18D42×C43—22no—
19C43×#535—21no—
20C43×#534—21no—
21C43×#534C2212yes—
22C43×#525—21no—
23C2×#121×C43—22no—
24C2×#120×C43—21no—
25C2×#120×C43—21no—
26C2×#120×C43C2211yescharacteristic
27C2×#120×C43C2212yes—
28C2×#120×C43C2212yescomplemented
29C2×#120×C43C2211yescharacteristic, complemented
30C43×#518C2211yescharacteristic
31C22×C22⋊C4×C43C2212yescomplemented
32C43×B(4,𝔽2)—24no—
33C2×#99×C43—24no—
34C2×#99×C43C2211yescharacteristic
35C2×#99×C43C2211yescharacteristic
36C2×#99×C43C2212yescomplemented
37C2×#99×C43C2212yescomplemented
38C2×#99×C43C2212yescomplemented
39C43×#394—22no—
40C43×#392—21no—
41C43×#392—21no—
42C43×#392—22no—
43C43×#386—21no—
44C43×#386—22no—
45C43×#386C2211yescharacteristic
46C43×#386C2211yescharacteristic, complemented
47C43×#386C2212yescomplemented
48C43×#385C2212yescomplemented
49C43×#379C2212yescomplemented
50C43×#379C2211yescharacteristic, complemented
51C43×#342C2212yescomplemented
52C43×#342C2212yescomplemented
53C25×C43D411yescharacteristic, complemented
54C25×C43C2311yescharacteristic
55C25×C43C2311yescharacteristic
56H(5,𝔽2)×C43—22no—
57H(5,𝔽2)×C43—22no—
58H(5,𝔽2)×C43—42no—
59C2×#41×C43—21no—
60C2×#41×C43—22no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—22no—
70C22×D4×C43—22no—
71C22×D4×C43—21no—
72C22×D4×C43—22no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—22no—
76C22×D4×C43—44no—
77C22×D4×C43—42no—
78C22×D4×C43D411yescharacteristic, complemented
79C22×D4×C43D411yescharacteristic, complemented
80C22×D4×C43D412yescomplemented
81C22×D4×C43D412yescomplemented
82C22×D4×C43C2312yes—
83C22×D4×C43C2311yescharacteristic
84C22×D4×C43C2311yescharacteristic
85C23×C4×C43—22no—
86C23×C4×C43D411yescharacteristic, complemented
87C23×C4×C43C2311yescharacteristic
88#127×C43—22no—
89#124×C43—22no—
90#123×C43—22no—
91#123×C43—22no—
92#123×C43—22no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—48no—
104#120×C43—22no—
105#120×C43—22no—
106#120×C43—22no—
107#120×C43—22no—
108#120×C43—22no—
109#120×C43—22no—
110#120×C43—22no—
111#120×C43—22no—
112#120×C43—22no—
113#120×C43—22no—
114#120×C43—22no—
115#120×C43—24no—
116#120×C43—42no—
117#120×C43—42no—
118#120×C43—44no—
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121C4×D4×C43—22no—
122C4×D4×C43—22no—
123#117×C43—21no—
124C2×C4⋊C4×C43—22no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—24no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—42no—
141C2×C22⋊C4×C43D412yescomplemented
142C2×C22⋊C4×C43D412yescomplemented
143C2×C22⋊C4×C43C2312yes—
144C2×C22⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43C2312yes—
147C2×C22⋊C4×C43C2312yes—
148#99×C43—22no—
149#99×C43—24no—
150#99×C43—24no—
151#99×C43—42no—
152#99×C43D414yescomplemented
153#95×C43—22no—
154#95×C43—21no—
155#95×C43—21no—
156#95×C43—22no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—22no—
160C24×C43—21no—
161C24×C43—22no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—22no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—22no—
169C24×C43—41no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43—81no—
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D412yes—
178C24×C43C2×D411yescharacteristic
179C24×C43C2×D412yes—
180C24×C43C2×D412yes—
181C24×C43C2×D411yescharacteristic
182C24×C43C2×D411yescharacteristic
183C24×C43C2411yescharacteristic
184#41×C43—44no—
185#41×C43—44no—
186#41×C43—42no—
187#41×C43—42no—
188C2×Q8×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—24no—
191C2×D4×C43—21no—
192C2×D4×C43—28no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—21no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43—22no—
209C2×D4×C43—21no—
210C2×D4×C43—22no—
211C2×D4×C43—22no—
212C2×D4×C43—22no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43—41no—
216C2×D4×C43—41no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43—42no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—42no—
228C2×D4×C43—42no—
229C2×D4×C43—44no—
230C2×D4×C43—42no—
231C2×D4×C43—42no—
232C2×D4×C43—42no—
233C2×D4×C43—44no—
234C2×D4×C43—42no—
235C2×D4×C43—44no—
236C2×D4×C43—41no—
237C2×D4×C43—42no—
238C2×D4×C43—41no—
239C2×D4×C43—42no—
240C2×D4×C43—42no—
241C2×D4×C43—82no—
242C2×D4×C43—81no—
243C2×D4×C43—81no—
244C2×D4×C43—82no—
245C2×D4×C43—82no—
246C2×D4×C43—82no—
247C2×D4×C43C2×D412yes—
248C2×D4×C43#4112yes—
249C22×C4×C43—21no—
250C22×C4×C43—22no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—22no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—22no—
258C22×C4×C43—22no—
259C22×C4×C43—22no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—41no—
263C22×C4×C43—44no—
264C22×C4×C43—44no—
265C22×C4×C43—42no—
266C22×C4×C43—82no—
267C22×C4×C43C2×D412yes—
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D412yes—
271C22×C4×C43C2×D412yes—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—22no—
275C4⋊C4×C43—22no—
276C4⋊C4×C43—44no—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—22no—
279C22⋊C4×C43—22no—
280C22⋊C4×C43—22no—
281C22⋊C4×C43—22no—
282C22⋊C4×C43—22no—
283C22⋊C4×C43—22no—
284C22⋊C4×C43—22no—
285C22⋊C4×C43—22no—
286C22⋊C4×C43—22no—
287C22⋊C4×C43—22no—
288C22⋊C4×C43—22no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—22no—
292C22⋊C4×C43—22no—
293C22⋊C4×C43—22no—
294C22⋊C4×C43—44no—
295C22⋊C4×C43—42no—
296C22⋊C4×C43—44no—
297C22⋊C4×C43—44no—
298C22⋊C4×C43—42no—
299C22⋊C4×C43—42no—
300C22⋊C4×C43—42no—
301C22⋊C4×C43—44no—
302C22⋊C4×C43—42no—
303C22⋊C4×C43—81no—
304C22⋊C4×C43—82no—
305C22⋊C4×C43C2×D414yescomplemented
306C42×C43—22no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—24no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—24no—
320C23×C43—22no—
321C23×C43—21no—
322C23×C43—22no—
323C23×C43—21no—
324C23×C43—21no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—41no—
328C23×C43—42no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—42no—
342C23×C43—41no—
343C23×C43—42no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—42no—
347C23×C43—42no—
348C23×C43—42no—
349C23×C43—42no—
350C23×C43—42no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—42no—
355C23×C43—42no—
356C23×C43—42no—
357C23×C43—81no—
358C23×C43—81no—
359C23×C43—82no—
360C23×C43—82no—
361C23×C43—82no—
362C23×C43—82no—
363C23×C43—84no—
364C23×C43—84no—
365C23×C43—81no—
366C23×C43—81no—
367C23×C43—84no—
368C23×C43—84no—
369C23×C43#12011yescharacteristic
370C23×C43#12012yes—
371C23×C43#12011yescharacteristic
372C23×C43#12112yescomplemented
373C23×C43C22×D411yescharacteristic
374C23×C43C22×D412yes—
375C23×C43C22×D411yescharacteristic
376C23×C43C2×#4111yescharacteristic
377C23×C43H(5,𝔽2)12yes—
378Q8×C43—42no—
379D4×C43—24no—
380D4×C43—24no—
381D4×C43—44no—
382D4×C43—42no—
383D4×C43—44no—
384D4×C43—44no—
385D4×C43—48no—
386D4×C43—44no—
387D4×C43—44no—
388D4×C43—42no—
389D4×C43—42no—
390D4×C43—42no—
391D4×C43—42no—
392D4×C43—42no—
393D4×C43—42no—
394D4×C43—44no—
395D4×C43—44no—
396D4×C43—82no—
397D4×C43—82no—
398D4×C43—82no—
399D4×C43—82no—
400D4×C43—88no—
401D4×C43—84no—
402D4×C43—84no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—22no—
406C2×C4×C43—24no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—24no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—42no—
417C2×C4×C43—42no—
418C2×C4×C43—44no—
419C2×C4×C43—42no—
420C2×C4×C43—41no—
421C2×C4×C43—42no—
422C2×C4×C43—42no—
423C2×C4×C43—42no—
424C2×C4×C43—41no—
425C2×C4×C43—42no—
426C2×C4×C43—42no—
427C2×C4×C43—42no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—42no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—42no—
436C2×C4×C43—81no—
437C2×C4×C43—81no—
438C2×C4×C43—88no—
439C2×C4×C43#12112yescomplemented
440#24404C4311yesmaximal, characteristic, direct product factor, Sylow
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—22no—
444C22×C43—21no—
445C22×C43—22no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—22no—
449C22×C43—22no—
450C22×C43—21no—
451C22×C43—22no—
452C22×C43—21no—
453C22×C43—22no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—42no—
457C22×C43—44no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43—44no—
461C22×C43—42no—
462C22×C43—44no—
463C22×C43—44no—
464C22×C43—42no—
465C22×C43—42no—
466C22×C43—42no—
467C22×C43—41no—
468C22×C43—41no—
469C22×C43—41no—
470C22×C43—42no—
471C22×C43—42no—
472C22×C43—41no—
473C22×C43—42no—
474C22×C43—41no—
475C22×C43—42no—
476C22×C43—82no—
477C22×C43—81no—
478C22×C43—81no—
479C22×C43—81no—
480C22×C43—82no—
481C22×C43—84no—
482C22×C43—82no—
483C22×C43—81no—
484C22×C43—82no—
485C22×C43—82no—
486C22×C43—81no—
487C22×C43—81no—
488C22×C43—82no—
489C22×C43—84no—
490C22×C43—81no—
491C22×C43—81no—
492C22×C43—162no—
493C22×C43B(4,𝔽2)12yescomplemented
494C22×C43C2×#12011yescharacteristic
495C22×C43C2×#12111yescharacteristic
496C22×C43#53411yescharacteristic
497C22×C43D4212yes—
498C22×C43#54612yes—
499C4×C43—22no—
500C4×C43—44no—
501C4×C43—41no—
502C4×C43—42no—
503C4×C43—42no—
504C4×C43—42no—
505C4×C43—42no—
506C4×C43—82no—
507C4×C43—81no—
508C4×C43—81no—
509#3484C2×C4311yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C4311yescharacteristic, complemented
511C22×#99C2×C4311yescharacteristic, complemented
512#2410C2×C4312yescomplemented
513#2403C2×C4311yescharacteristic, complemented
514#2044C2×C4312yescomplemented
515#2021C2×C4312yescomplemented
516#1898C2×C4312yescomplemented
517#1889C2×C4311yescharacteristic, complemented
518#1867C2×C4311yescharacteristic, complemented
519#1790C2×C4311yescharacteristic, complemented
520C2×C43—22no—
521C2×C43—21no—
522C2×C43—21no—
523C2×C43—22no—
524C2×C43—22no—
525C2×C43—42no—
526C2×C43—41no—
527C2×C43—42no—
528C2×C43—82no—
529C2×C43—81no—
530C2×C43—82no—
531C2×C43#241011yescharacteristic
532C2×C43C2×B(4,𝔽2)11yescharacteristic
533C2×C43#302611yescharacteristic
534C2×H(5,𝔽2)C22×C4311yescharacteristic
535C23×D4C22×C4311yescharacteristic
536C23×D4C22×C4311yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C4312yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C4311yescharacteristic
549C2×#120C22×C4312yes—
550C2×#120C22×C4312yescomplemented
551C2×#120C22×C4311yescharacteristic, complemented
552#518C22×C4311yescharacteristic
553C22×C22⋊C4C22×C4312yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C4311yescharacteristic
557C2×#99C22×C4311yescharacteristic
558C2×#99C22×C4312yescomplemented
559C2×#99C22×C4312yescomplemented
560C2×#99C22×C4312yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C4311yescharacteristic
568#386C22×C4311yescharacteristic, complemented
569#386C22×C4312yescomplemented
570#385C22×C4312yescomplemented
571#379C22×C4312yescomplemented
572#379C22×C4311yescharacteristic, complemented
573#342C22×C4312yescomplemented
574#342C22×C4312yescomplemented
575C43#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C4311yescharacteristic, complemented
577C25C23×C4311yescharacteristic
578C25C23×C4311yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C4311yescharacteristic, complemented
602C22×D4D4×C4311yescharacteristic, complemented
603C22×D4D4×C4312yescomplemented
604C22×D4D4×C4312yescomplemented
605C22×D4C23×C4312yes—
606C22×D4C23×C4311yescharacteristic
607C22×D4C23×C4311yescharacteristic
608C23×C4—22no—
609C23×C4D4×C4311yescharacteristic, complemented
610C23×C4C23×C4311yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C4312yescomplemented
665C2×C22⋊C4D4×C4312yescomplemented
666C2×C22⋊C4C23×C4312yes—
667C2×C22⋊C4C23×C4311yescharacteristic
668C2×C22⋊C4C23×C4311yescharacteristic
669C2×C22⋊C4C23×C4312yes—
670C2×C22⋊C4C23×C4312yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C4314yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—42no—
693C24—42no—
694C24—41no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C4311yescharacteristic
700C24C2×D4×C4312yes—
701C24C2×D4×C4311yescharacteristic
702C24C2×D4×C4312yes—
703C24C2×D4×C4312yes—
704C24C2×D4×C4311yescharacteristic
705C24C2×D4×C4311yescharacteristic
706C24C24×C4311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C4312yes—
771C2×D4#41×C4312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C4312yes—
791C22×C4C2×D4×C4311yescharacteristic
792C22×C4C2×D4×C4311yescharacteristic
793C22×C4C2×D4×C4312yes—
794C22×C4C2×D4×C4312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C4314yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C4311yescharacteristic
893C23#120×C4312yes—
894C23#120×C4311yescharacteristic
895C23#121×C4312yescomplemented
896C23C22×D4×C4311yescharacteristic
897C23C22×D4×C4312yes—
898C23C22×D4×C4311yescharacteristic
899C23C2×#41×C4311yescharacteristic
900C23H(5,𝔽2)×C4312yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C4312yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C43×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C4311yescharacteristic
1017C22C2×#121×C4311yescharacteristic
1018C22C43×#53411yescharacteristic
1019C22D42×C4312yes—
1020C22C43×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C43×#241011yescharacteristic
1043C2C2×C43×B(4,𝔽2)11yescharacteristic
1044C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3484C2semidirect
2. C2×C43×B(4,𝔽2)C2semidirect
3. C22×#99×C43C2semidirect
4. C43×#2410C2semidirect
5. C43×#2403C2semidirect
6. C43×#2044C2semidirect
7. C43×#2021C2semidirect
8. C43×#1898C2semidirect
9. C43×#1889C2semidirect
10. C43×#1867C2semidirect
11. C43×#1790C2semidirect
14. C23×D4×C43C22semidirect
28. C2×#120×C43C22semidirect
29. C2×#120×C43C22semidirect
31. C22×C22⋊C4×C43C22semidirect
36. C2×#99×C43C22semidirect
37. C2×#99×C43C22semidirect
38. C2×#99×C43C22semidirect
46. C43×#386C22semidirect
47. C43×#386C22semidirect
48. C43×#385C22semidirect
49. C43×#379C22semidirect
50. C43×#379C22semidirect
51. C43×#342C22semidirect
52. C43×#342C22semidirect
53. C25×C43D4semidirect
78. C22×D4×C43D4semidirect
79. C22×D4×C43D4semidirect
80. C22×D4×C43D4semidirect
81. C22×D4×C43D4semidirect
86. C23×C4×C43D4semidirect
141. C2×C22⋊C4×C43D4semidirect
142. C2×C22⋊C4×C43D4semidirect
152. #99×C43D4semidirect
305. C22⋊C4×C43C2×D4semidirect
372. C23×C43#121semidirect
439. C2×C4×C43#121semidirect
440. #24404C43direct (N × H)
493. C22×C43B(4,𝔽2)semidirect
509. #3484C2×C43semidirect
510. C2×B(4,𝔽2)C2×C43semidirect
511. C22×#99C2×C43semidirect
512. #2410C2×C43semidirect
513. #2403C2×C43semidirect
514. #2044C2×C43semidirect
515. #2021C2×C43semidirect
516. #1898C2×C43semidirect
517. #1889C2×C43semidirect
518. #1867C2×C43semidirect
519. #1790C2×C43semidirect
536. C23×D4C22×C43semidirect
550. C2×#120C22×C43semidirect
551. C2×#120C22×C43semidirect
553. C22×C22⋊C4C22×C43semidirect
558. C2×#99C22×C43semidirect
559. C2×#99C22×C43semidirect
560. C2×#99C22×C43semidirect
568. #386C22×C43semidirect
569. #386C22×C43semidirect
570. #385C22×C43semidirect
571. #379C22×C43semidirect
572. #379C22×C43semidirect
573. #342C22×C43semidirect
574. #342C22×C43semidirect
575. C43#24404direct (N × H)
576. C25D4×C43semidirect
601. C22×D4D4×C43semidirect
602. C22×D4D4×C43semidirect
603. C22×D4D4×C43semidirect
604. C22×D4D4×C43semidirect
609. C23×C4D4×C43semidirect
664. C2×C22⋊C4D4×C43semidirect
665. C2×C22⋊C4D4×C43semidirect
675. #99D4×C43semidirect
828. C22⋊C4C2×D4×C43semidirect
895. C23#121×C43semidirect
962. C2×C4#121×C43semidirect
1015. C22C43×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C43×#34842
C2×C43×B(4,𝔽2)2
C22×#99×C432
C43×#24102
C43×#24032
C43×#20442
C43×#20212
C43×#18982
C43×#18892
C43×#18672
C43×#17902
#2440443