Finite Group Databasebeta

← D43×#1463 #25062435

Subgroups — D43×#1463 #25062435

Order 11008.

1718 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C211yesmaximal, characteristic
2#407×D43C212yesmaximal
3#19132925C211yesmaximal, characteristic, complemented
4#19132924C212yesmaximal, complemented
5#19132923C214yesmaximal, complemented
6#324×D43C214yesmaximal, complemented
7C43×#1463C211yesmaximal, characteristic, complemented
8C23×C4×D43C411yescharacteristic
9C23×C4×D43C411yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C2×M16×D43—22no—
12C22×C4⋊Dic43C411yescharacteristic
13C22×Dic43⋊C4C411yescharacteristic
14C22×Dic43⋊C4C2211yescharacteristic
15C2×C4⋊C4×D43—22no—
16C2×C4⋊C4×D43—22no—
17C2×C4⋊C4×D43—22no—
18C2×C4⋊C4×D43—22no—
19C2×C4⋊C4×D43C412yes—
20C2×C4⋊C4×D43C412yes—
21C2×C4⋊C4×D43C2212yes—
22C2×C4⋊C4×D43C2212yes—
23#14582863C2212yes—
24#14582862—22no—
25#14582861—22no—
26#14582861C2214yes—
27C22⋊C8×D43—22no—
28C22⋊C8×D43C2214yes—
29#14582625C2214yescomplemented
30#14582624C2218yescomplemented
31C22×C4⋊C4×C43C2211yescharacteristic
32C43×#407C2212yes—
33C43×#324C2214yescomplemented
34C24×D43C2×C411yescharacteristic
35C23×Dic43C2×C411yescharacteristic
36C23×Dic43C2×C411yescharacteristic
37C23×Dic43C2×C411yescharacteristic
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—28no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—44no—
48C22×C4×D43—44no—
49C22×C4×D43C2×C412yes—
50C22×C4×D43C2×C412yes—
51C22×C4×D43C2×C412yes—
52C22×C4×D43C2×C412yes—
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43D412yes—
56C22×C4×D43D412yes—
57C22×C4×D43D412yes—
58C22×C4×D43D412yes—
59C22×C4×D43C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621877—22no—
62C2×#10621872—24no—
63M16×D43—48no—
64C2×C8×D43—24no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43C2×C412yes—
68C2×C4⋊Dic43C2×C412yes—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4C2×C412yes—
74C2×Dic43⋊C4C2×C412yes—
75C2×Dic43⋊C4C2×C412yes—
76C2×Dic43⋊C4C2312yes—
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C4⋊C4×D43—24no—
80C4⋊C4×D43—24no—
81C4⋊C4×D43—24no—
82C4⋊C4×D43—24no—
83C4⋊C4×D43—24no—
84C4⋊C4×D43—24no—
85C22⋊(C43⋊C8)—22no—
86C22⋊(C43⋊C8)C2314yes—
87(C2×D43)⋊C8—24no—
88(C2×D43)⋊C8—24no—
89C23×C4×C43C2×C411yescharacteristic
90C23×C4×C43C2×C411yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×M16×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43C2×C412yes—
96C2×C4⋊C4×C43C2312yes—
97C22⋊C8×C43—22no—
98C22⋊C8×C43C2314yes—
99C24×C43C22×C411yescharacteristic
100C23×D43—24no—
101C23×D43—24no—
102C23×D43—24no—
103C23×D43C22⋊C411yescharacteristic
104C23×D43C22⋊C411yescharacteristic
105C23×D43C22⋊C411yescharacteristic
106C23×D43C22⋊C411yescharacteristic
107C23×D43C22×C411yescharacteristic
108C23×D43C22×C411yescharacteristic
109C22×C4×C43—24no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—42no—
115C22×C4×C43—42no—
116C22×C4×C43C22×C412yes—
117C22×C4×C43C22×C412yes—
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—24no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—42no—
128C22×Dic43—42no—
129C22×Dic43C22⋊C412yes—
130C22×Dic43C22⋊C412yes—
131C22×Dic43C22×C412yes—
132C22×Dic43C22×C412yes—
133C22×Dic43C22×C411yescharacteristic
134C22×Dic43C22×C411yescharacteristic
135C2×C4×D43—28no—
136C2×C4×D43—28no—
137C2×C4×D43—28no—
138C2×C4×D43—28no—
139C2×C4×D43—24no—
140C2×C4×D43—24no—
141C2×C4×D43—28no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—24no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—44no—
154C2×C4×D43—44no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43C22⋊C412yes—
165C2×C4×D43C22⋊C412yes—
166C2×C4×D43C22⋊C412yes—
167C2×C4×D43C22⋊C412yes—
168C2×C4×D43M1618yescomplemented
169C2×C4×D43C2×D412yes—
170C2×C4×D43C2×D412yes—
171C2×C4×D43C2×D412yes—
172C2×C4×D43C2×D412yes—
173M16×C43—44no—
174C2×C8×C43—24no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—24no—
177C4⋊Dic43—24no—
178C4⋊Dic43—24no—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183#10621877—44no—
184C2×C43⋊C8—24no—
185#10621872—48no—
186C8×D43—48no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43C2×C22⋊C411yescharacteristic
191C23×C43C2×C22⋊C411yescharacteristic
192C23×C43C23×C411yescharacteristic
193C22×D43—232no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43#9914yes—
210C22×D43#10114yes—
211C22×D43C2×C22⋊C411yescharacteristic
212C22×D43C2×C22⋊C411yescharacteristic
213C22×D43C2×C22⋊C411yescharacteristic
214C22×D43C2×C22⋊C411yescharacteristic
215C22×D43C2×M1614yes—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43C2×C22⋊C412yes—
229C2×C4×C43C2×M1614yescomplemented
230C2×C4×C43C22×D412yes—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—22no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43C2×C22⋊C412yes—
245C2×Dic43C2×M1614yescomplemented
246C4×D43—28no—
247C4×D43—28no—
248C4×D43—28no—
249C4×D43—28no—
250C4×D43—24no—
251C4×D43—24no—
252C4×D43—24no—
253C4×D43—24no—
254C4×D43—42no—
255C4×D43—42no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—44no—
259C4×D43—44no—
260C4×D43—44no—
261C4×D43—44no—
262C8×C43—44no—
263C43⋊C8—44no—
264C2×#1463—431nomaximal, Sylow
265C22×C43—28no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43C2×#9912yes—
273C22×C43C2×#10112yes—
274C22×C43C22×C22⋊C411yescharacteristic
275C22×C43C22×M1612yes—
276C2×D43—28no—
277C2×D43—28no—
278C2×D43—28no—
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—28no—
286C2×D43—28no—
287C2×D43—28no—
288C2×D43#40712yes—
289C2×D43#40712yes—
290C2×D43C2×#9912yes—
291C2×D43C2×#9912yes—
292C2×D43C2×#10112yes—
293C2×D43C2×#10112yes—
294C4×C43—24no—
295C4×C43—22no—
296C4×C43—22no—
297C4×C43—42no—
298Dic43—24no—
299Dic43—22no—
300Dic43—22no—
301Dic43—42no—
302C23×C4⋊C4—431no—
303C2×#407—432no—
304#1463—432no—
305#1463—434no—
306#1463—431no—
307#1463D4311yescharacteristic, direct product factor
308C2×#324—434no—
309C2×C43—22no—
310C2×C43—22no—
311C2×C43—22no—
312C2×C43C2×#40711yescharacteristic
313C2×C43C22×#9911yescharacteristic
314C2×C43C22×#10111yescharacteristic
315D43—22no—
316D43—22no—
317D43—22no—
318D43#146314yesdirect product factor
319C24×C4—431no—
320C24×C4—431no—
321C24×C4—431no—
322C22×M16—862no—
323C22×C4⋊C4—431no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4—431no—
326C22×C4⋊C4—432no—
327C22×C4⋊C4—432no—
328C22×C4⋊C4—432no—
329C22×C4⋊C4—432no—
330C22×C4⋊C4—862no—
331C22×C4⋊C4—862no—
332C22×C4⋊C4—862no—
333C22×C4⋊C4—862no—
334C22×C4⋊C4C2×D4311yescharacteristic
335#407—432no—
336#407—434no—
337#407—862no—
338#407—862no—
339#407C2×D4312yes—
340C2×C22⋊C8—434no—
341C2×C22⋊C8—862no—
342#324—434no—
343#324—438no—
344#324C2×D4314yescomplemented
345C43C2×#146311yescharacteristic, complemented, Sylow
346C25—431no—
347C23×C4—431no—
348C23×C4—432no—
349C23×C4—432no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—432no—
353C23×C4—432no—
354C23×C4—432no—
355C23×C4—431no—
356C23×C4—431no—
357C23×C4—431no—
358C23×C4—431no—
359C23×C4—432no—
360C23×C4—432no—
361C23×C4—432no—
362C23×C4—868no—
363C23×C4—861no—
364C23×C4—861no—
365C23×C4—861no—
366C23×C4—861no—
367C23×C4—861no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4—861no—
371C23×C4—1724no—
372C23×C4—1724no—
373C23×C4C4×D4311yescharacteristic
374C23×C4C4×D4311yescharacteristic
375C23×C4C22×D4311yescharacteristic
376C2×M16—22no—
377C2×M16—864no—
378C2×M16—862no—
379C2×M16—1728no—
380C22×C8—864no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—432no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—864no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4C4×D4312yes—
404C2×C4⋊C4C22×D4312yes—
405C22⋊C8—22no—
406C22⋊C8—434no—
407C22⋊C8—864no—
408C22⋊C8—864no—
409C22⋊C8—862no—
410C22⋊C8C22×D4314yes—
411C24—431no—
412C24—431no—
413C24—431no—
414C24—431no—
415C24—431no—
416C24—431no—
417C24—864no—
418C24—864no—
419C24—864no—
420C24C2×C4×D4311yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—432no—
429C22×C4—432no—
430C22×C4—432no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—438no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—864no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—868no—
449C22×C4—864no—
450C22×C4—868no—
451C22×C4—868no—
452C22×C4—868no—
453C22×C4—868no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—864no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—1724no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1724no—
468C22×C4—1724no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1724no—
472C22×C4—1724no—
473C22×C4—1724no—
474C22×C4—1724no—
475C22×C4—1724no—
476C22×C4—1724no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4C2×C4×D4312yes—
480C22×C4C2×C4×D4312yes—
481C22×C4C2×C4×D4311yescharacteristic
482C22×C4D4×D4312yes—
483C22×C4D4×D4312yes—
484C22×C4C23×D4311yescharacteristic
485M16—44no—
486M16—1728no—
487M16—1724no—
488C2×C8—24no—
489C2×C8—864no—
490C2×C8—1728no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—864no—
494C4⋊C4—864no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—864no—
498C4⋊C4—864no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—431no—
503C23—431no—
504C23—431no—
505C23—431no—
506C23—434no—
507C23—434no—
508C23—434no—
509C23—862no—
510C23—862no—
511C23—862no—
512C23—862no—
513C23—862no—
514C23—862no—
515C23—862no—
516C23—862no—
517C23—862no—
518C23—862no—
519C23—862no—
520C23—862no—
521C23—8632no—
522C23—862no—
523C23—862no—
524C23—862no—
525C23C22⋊C4×D4311yescharacteristic
526C23C22⋊C4×D4311yescharacteristic
527C23C22×C4×D4311yescharacteristic
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—432no—
541C2×C4—432no—
542C2×C4—434no—
543C2×C4—864no—
544C2×C4—864no—
545C2×C4—868no—
546C2×C4—868no—
547C2×C4—864no—
548C2×C4—864no—
549C2×C4—868no—
550C2×C4—868no—
551C2×C4—864no—
552C2×C4—864no—
553C2×C4—862no—
554C2×C4—864no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1724no—
562C2×C4—1724no—
563C2×C4—1724no—
564C2×C4—1724no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4C22⋊C4×D4312yes—
572C2×C4M16×D4314yescomplemented
573C2×C4C2×D4×D4312yes—
574C8—44no—
575C8—1724no—
576C22—28no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—432no—
584C22—432no—
585C22—432no—
586C22—432no—
587C22—432no—
588C22—432no—
589C22—868no—
590C22—868no—
591C22—868no—
592C22—868no—
593C22—868no—
594C22—868no—
595C22—861no—
596C22—861no—
597C22—861no—
598C22—861no—
599C22—861no—
600C22—861no—
601C22#99×D4312yes—
602C22#101×D4312yes—
603C22C2×C22⋊C4×D4311yescharacteristic
604C22C2×M16×D4312yes—
605C4—24no—
606C4—22no—
607C4—22no—
608C4—42no—
609C4—864no—
610C4—862no—
611C4—862no—
612C4—1722no—
613C2—22no—
614C2—22no—
615C2—22no—
616C2—434no—
617C2—862no—
618C2—862no—
619C2—862no—
620C2#407×D4311yescharacteristic
621C2C2×#99×D4311yescharacteristic
622C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1463C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1463D43
hypocenterC43C2×#1463
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #19132925C2semidirect
4. #19132924C2semidirect
5. #19132923C2semidirect
6. #324×D43C2semidirect
7. C43×#1463C2semidirect
29. #14582625C22semidirect
30. #14582624C22semidirect
33. C43×#324C22semidirect
168. C2×C4×D43M16semidirect
229. C2×C4×C43C2×M16semidirect
245. C2×Dic43C2×M16semidirect
307. #1463D43direct (N × H)
318. D43#1463direct (N × H)
344. #324C2×D43semidirect
345. C43C2×#1463semidirect
572. C2×C4M16×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
#407×D432
#191329252
#191329242
#191329232
#324×D432
C43×#14632
C2×#146343