Finite Group Databasebeta

← D43×#2071 #25125325

Subgroups — D43×#2071 #25125325

Order 11008.

1366 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C212yesmaximal
2#390×D43C211yesmaximal, characteristic
3#384×D43C211yesmaximal, characteristic, complemented
4#19136002C212yesmaximal, complemented
5#19136001C212yesmaximal, complemented
6#19136000C211yesmaximal, characteristic, complemented
7#19135999C211yesmaximal, characteristic, complemented
8#19135998C211yesmaximal, characteristic, complemented
9#340×D43C212yesmaximal, complemented
10#336×D43C211yesmaximal, characteristic, complemented
11C43×#2071C211yesmaximal, characteristic, complemented
12C22×D4×D43C2211yescharacteristic
13C22×C8×D43C2212yes—
14C2×C4⋊C4×D43—21no—
15C2×C4⋊C4×D43—21no—
16C2×C4⋊C4×D43C2211yescharacteristic
17C2×C4⋊C4×D43C2212yes—
18C2×C22⋊C4×D43—21no—
19C2×C22⋊C4×D43—21no—
20C2×C42×D43C2211yescharacteristic
21C2×#13063247C2212yes—
22C2×#13063246C2212yes—
23C2×#13063245C2212yes—
24#102×D43—28no—
25#14582802C2211yescharacteristic
26#14582801C2211yescharacteristic
27#14582800C2211yescharacteristic
28#14582799—21no—
29#14582799—21no—
30#14582769C2211yescharacteristic, complemented
31#14582768—21no—
32#14582768—21no—
33#14582768C2212yescomplemented
34#14582662C2212yescomplemented
35#14582661C2212yescomplemented
36#14582661C2212yescomplemented
37#14582654C2211yescharacteristic, complemented
38#14582653C2212yescomplemented
39C2×#102×C43C2212yes—
40C43×#390C2211yescharacteristic
41C43×#384C2211yescharacteristic, complemented
42C43×#340C2212yescomplemented
43C43×#336C2211yescharacteristic, complemented
44C24×D43—21no—
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—21no—
47C2×D4×D43—24no—
48C2×D4×D43—24no—
49C2×D4×D43—22no—
50C2×D4×D43D414yes—
51C22×C4×D43—21no—
52C22×C4×D43—22no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57C2×C8×D43—24no—
58C2×C8×D43—24no—
59C2×C8×D43—24no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2311yescharacteristic
63C2×C4⋊Dic43C2312yes—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4—22no—
68C4⋊C4×D43—24no—
69C4⋊C4×D43—24no—
70C4⋊C4×D43—24no—
71C4⋊C4×D43—44no—
72C4⋊C4×D43—44no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C22⋊C4×D43—44no—
80C22⋊C4×D43—44no—
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84C42×D43—24no—
85#13063247—24no—
86#13063246—24no—
87#13063245—24no—
88C22×D4×C43C2311yescharacteristic
89C22×C8×C43C2312yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2312yes—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C42×C43C2311yescharacteristic
97#102×C43—24no—
98C24×C43—21no—
99C23×D43—21no—
100C23×D43—24no—
101C23×D43—42no—
102C23×D43—42no—
103C23×D43—42no—
104C23×D43—42no—
105C23×D43—42no—
106C23×D43—42no—
107C23×D43C2×D411yescharacteristic
108C2×D4×C43—21no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43C2×D412yes—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C2×C22⋊D43—24no—
118C2×C22⋊D43—42no—
119C2×C22⋊D43—42no—
120C22×Dic43—21no—
121C22×Dic43—22no—
122C22×Dic43C2×D411yescharacteristic
123C22×Dic43C2×D411yescharacteristic
124C22×Dic43C2×D411yescharacteristic
125D4×D43—216no—
126D4×D43—48no—
127C2×D172—21no—
128C2×D172—22no—
129C2×D172—22no—
130C2×D172C2×D412yes—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×C4×D43—44no—
136C2×C4×D43—42no—
137C2×C4×D43—42no—
138C2×C4×D43—44no—
139C2×C4×D43—42no—
140C2×C4×D43—44no—
141C2×C4×D43D814yes—
142C2×C4×D43SD1614yes—
143C2×C4×D43C2×D412yes—
144C2×C4×D43#4112yes—
145C2×C4×D43#4114yes—
146C2×C4×D43#4114yes—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43—42no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—42no—
157C42×C43—22no—
158C22⋊Dic43—42no—
159C22⋊Dic43—42no—
160(C2×D43)⋊C4—42no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—42no—
163(C2×D43)⋊C4—42no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—42no—
168C4⋊Dic43—42no—
169Dic43⋊C4—44no—
170Dic43⋊C4—44no—
171Dic43⋊C4—42no—
172Dic43⋊C4—44no—
173C4×Dic43—22no—
174C4×Dic43—22no—
175C4×Dic43—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C8×D43—48no—
180C23×C43—22no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43C22×D411yescharacteristic
188C22×D43—22no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—48no—
196C22×D43—48no—
197C22×D43—48no—
198C22×D43—84no—
199C22×D43—84no—
200C22×D43—84no—
201C22×D43—84no—
202C22×D43#12112yes—
203C22×D43#12312yes—
204C22×D43#12412yes—
205C22×D43C2×D812yes—
206C22×D43C2×SD1612yes—
207C22×D43AGL(1,ℤ/8)12yes—
208C22×D43#13712yes—
209D4×C43—24no—
210D4×C43—42no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43C2×D812yes—
222C2×C4×C43C2×SD1612yes—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4112yes—
225C2×C4×C43C2×#4112yes—
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—48no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43#12112yes—
239C2×Dic43#12312yes—
240C2×Dic43#12412yes—
241C2×Dic43C2×D812yes—
242C2×Dic43C2×SD1612yes—
243D172—24no—
244D172—42no—
245C4×D43—28no—
246C4×D43—28no—
247C4×D43—88no—
248C4×D43—84no—
249C4×D43#12318yes—
250C4×D43#12618yes—
251C8×C43—42no—
252C43⋊C8—42no—
253C2×#2071—431nomaximal, Sylow
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43C2×#12111yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C22×C43C2×#12411yescharacteristic
264C22×C43C22×D811yescharacteristic
265C22×C43C22×SD1611yescharacteristic
266C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C43C2×#13711yescharacteristic
268C2×D43—42no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—816no—
276C2×D43#39714yes—
277C2×D43#45914yes—
278C2×D43#46114yes—
279C2×D43#48014yes—
280C2×D43#48114yes—
281C2×D43#48614yes—
282C2×D43#48914yes—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—81no—
286C4×C43—82no—
287C4×C43C2×#12312yes—
288C4×C43C2×#12612yes—
289Dic43—22no—
290Dic43—22no—
291Dic43—81no—
292Dic43—82no—
293Dic43#39714yes—
294C22×#102—432no—
295C2×#390—431no—
296C2×#384—431no—
297#2071—432no—
298#2071—431no—
299#2071—431no—
300#2071—432no—
301#2071—431no—
302#2071D4311yescharacteristic, direct product factor
303C2×#340—432no—
304C2×#336—431no—
305C2×C43—82no—
306C2×C43C2×#39711yescharacteristic
307C2×C43C2×#45911yescharacteristic
308C2×C43C2×#46111yescharacteristic
309C2×C43C2×#48011yescharacteristic
310C2×C43C2×#48111yescharacteristic
311C2×C43C2×#48611yescharacteristic
312C2×C43C2×#48911yescharacteristic
313D43—82no—
314D43#207118yesdirect product factor
315C23×D4—431no—
316C23×C8—432no—
317C22×C4⋊C4—432no—
318C22×C4⋊C4—431no—
319C22×C4⋊C4—861no—
320C22×C4⋊C4—861no—
321C22×C22⋊C4—861no—
322C22×C22⋊C4—861no—
323C22×C42—431no—
324C2×#102—432no—
325C2×#102—432no—
326C2×#102—432no—
327C2×#102—868no—
328C2×#102C2×D4312yes—
329#390—431no—
330#390—431no—
331#390—431no—
332#390—861no—
333#390—861no—
334#390C2×D4311yescharacteristic
335#384—432no—
336#384—431no—
337#384—861no—
338#384—861no—
339#384C2×D4311yescharacteristic, complemented
340#340—432no—
341#340—432no—
342#340—432no—
343#340C2×D4312yescomplemented
344#336—432no—
345#336—431no—
346#336C2×D4311yescharacteristic, complemented
347C43C2×#207111yescharacteristic, complemented, Sylow
348C25—861no—
349C22×D4—434no—
350C22×D4—431no—
351C22×D4—864no—
352C22×D4—864no—
353C22×D4—862no—
354C22×D4—861no—
355C22×D4C22×D4311yescharacteristic
356C23×C4—431no—
357C23×C4—431no—
358C23×C4—431no—
359C23×C4—861no—
360C23×C4—862no—
361C22×C8—432no—
362C22×C8—864no—
363C22×C8—864no—
364C22×C8—864no—
365C22×C8C22×D4312yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—432no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—864no—
372C2×C4⋊C4—864no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—1724no—
380C2×C4⋊C4—1724no—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4312yes—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—1724no—
392C2×C22⋊C4—1724no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—864no—
397C2×C42C22×D4311yescharacteristic
398#102—24no—
399#102—864no—
400#102—864no—
401#102—864no—
402C24—21no—
403C24—431no—
404C24—864no—
405C24—861no—
406C24—1722no—
407C24—1722no—
408C24—1722no—
409C24—1722no—
410C24—1722no—
411C24—1722no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—432no—
416C2×D4—8616no—
417C2×D4—864no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—861no—
421C2×D4—1728no—
422C2×D4—1722no—
423C2×D4—1722no—
424C2×D4D4×D4312yes—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—431no—
428C22×C4—432no—
429C22×C4—434no—
430C22×C4—432no—
431C22×C4—434no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—434no—
435C22×C4—434no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4—1724no—
445C22×C4—1722no—
446C22×C4—1724no—
447C22×C4—1724no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—862no—
455C2×C8—862no—
456C2×C8—862no—
457C2×C8—1728no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—1722no—
467C4⋊C4—1724no—
468C4⋊C4—1722no—
469C4⋊C4—1724no—
470C4⋊C4—1724no—
471C4⋊C4—1722no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—1722no—
475C22⋊C4—1722no—
476C22⋊C4—1722no—
477C22⋊C4—1722no—
478C22⋊C4—1722no—
479C22⋊C4—1722no—
480C42—22no—
481C42—862no—
482C42—862no—
483C42—862no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—432no—
492C23—432no—
493C23—432no—
494C23—432no—
495C23—432no—
496C23—432no—
497C23—432no—
498C23—862no—
499C23—3444no—
500C23—3444no—
501C23—3444no—
502C23—3444no—
503C23—1728no—
504C23—1728no—
505C23—1728no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23C2×D4×D4311yescharacteristic
513D4—24no—
514D4—42no—
515D4—864no—
516D4—1728no—
517D4—1722no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—438no—
532C2×C4—438no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—868no—
536C2×C4—868no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3448no—
542C2×C4—3444no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4—1722no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1722no—
549C2×C4D8×D4312yes—
550C2×C4SD16×D4312yes—
551C2×C4C2×D4×D4311yescharacteristic
552C2×C4#41×D4312yes—
553C2×C4#41×D4312yes—
554C2×C4#41×D4311yescharacteristic
555C8—42no—
556C8—1722no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—434no—
565C22—434no—
566C22—434no—
567C22—434no—
568C22—434no—
569C22—434no—
570C22—434no—
571C22—34416no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22#121×D4311yescharacteristic
580C22#123×D4311yescharacteristic
581C22#124×D4311yescharacteristic
582C22C2×D8×D4311yescharacteristic
583C22C2×SD16×D4311yescharacteristic
584C22AGL(1,ℤ/8)×D4311yescharacteristic
585C22#137×D4311yescharacteristic
586C4—22no—
587C4—22no—
588C4—82no—
589C4—81no—
590C4—434no—
591C4—862no—
592C4—862no—
593C4—3442no—
594C4—3441no—
595C4#123×D4312yes—
596C4#126×D4312yes—
597C2—82no—
598C2—438no—
599C2—3442no—
600C2#397×D4311yescharacteristic
601C2#459×D4311yescharacteristic
602C2#461×D4311yescharacteristic
603C2#480×D4311yescharacteristic
604C2#481×D4311yescharacteristic
605C2#486×D4311yescharacteristic
606C2#489×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2071C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#2071D43
hypocenterC43C2×#2071
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
3. #384×D43C2semidirect
4. #19136002C2semidirect
5. #19136001C2semidirect
6. #19136000C2semidirect
7. #19135999C2semidirect
8. #19135998C2semidirect
9. #340×D43C2semidirect
10. #336×D43C2semidirect
11. C43×#2071C2semidirect
30. #14582769C22semidirect
33. #14582768C22semidirect
34. #14582662C22semidirect
35. #14582661C22semidirect
36. #14582661C22semidirect
37. #14582654C22semidirect
38. #14582653C22semidirect
41. C43×#384C22semidirect
42. C43×#340C22semidirect
43. C43×#336C22semidirect
302. #2071D43direct (N × H)
314. D43#2071direct (N × H)
339. #384C2×D43semidirect
343. #340C2×D43semidirect
346. #336C2×D43semidirect
347. C43C2×#2071semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
#390×D432
#384×D432
#191360022
#191360012
#191360002
#191359992
#191359982
#340×D432
#336×D432
C43×#20712
C2×#207143