Finite Group Databasebeta

← D43×#1672 #25078941

Subgroups — D43×#1672 #25078941

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D43C211yesmaximal, characteristic
2#477×D43C211yesmaximal, characteristic
3#462×D43C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic
5#19133980C211yesmaximal, characteristic, complemented
6#19133979C211yesmaximal, characteristic, complemented
7#19133978C211yesmaximal, characteristic, complemented
8#19133977C211yesmaximal, characteristic, complemented
9#19133976C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic
13#333×D43C211yesmaximal, characteristic
14#332×D43C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583296—21no—
22#14583296—21no—
23#14583295C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583195C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583193—21no—
28#14583192—21no—
29#14583191C2211yescharacteristic
30#14583110C2211yescharacteristic
31#14583109C2211yescharacteristic
32#14583108—21no—
33#14583107—21no—
34#14583106C2211yescharacteristic
35Q8×C43⋊C8C2211yescharacteristic
36C8×Dic86—21no—
37C8×Dic86C2211yescharacteristic
38#14583023—21no—
39#14583023C2211yescharacteristic
40#107×D43—21no—
41#106×D43—21no—
42#106×D43—21no—
43C4⋊C8×D43—21no—
44C4⋊C8×D43C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#103×D43—21no—
48#103×D43—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73Q16×D43—44no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43D411yescharacteristic
78C2×C8×D43D411yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063323—21no—
86#13063323—21no—
87Q8×Dic43D411yescharacteristic
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90#13063290—21no—
91#13063290D411yescharacteristic
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C42×D43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—21no—
104#13063257—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063250—21no—
119#13063250—21no—
120#13063249—21no—
121#13063249—21no—
122#13063248—21no—
123#13063248—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148Q8×D43—22no—
149Q8×D43—42no—
150Q8×D43—42no—
151Q8×D43—82no—
152Q8×D43SD1614yes—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—41no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—41no—
164C2×Dic86—41no—
165C2×Dic86C2×D411yescharacteristic
166Q16×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180#10621885—42no—
181#10621885—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207C8×D43—22no—
208C8×D43—42no—
209C8×D43—42no—
210C8×D43—42no—
211C8×D43Q1614yescomplemented
212C22×D43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217Q8×C43C2×SD1612yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C4×D43—24no—
233C4×D43—22no—
234C4×D43—42no—
235C4×D43—82no—
236C4×D43—82no—
237C4×D43C2×SD1612yes—
238C4×D43C2×Q1612yes—
239C4×D43#13512yes—
240C4×D43#13712yes—
241Dic86—21no—
242Dic86—24no—
243Dic86—41no—
244Dic86—41no—
245Dic86—82no—
246Dic86—82no—
247Dic86—81no—
248Dic86C2×SD1612yes—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43C2×Q1612yescomplemented
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8C2×Q1612yescomplemented
259C2×#1672—431nomaximal, Sylow
260C22×C43C2×#12111yescharacteristic
261C2×D43#46212yes—
262C2×D43#46512yes—
263C2×D43#47112yes—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43C22×SD1611yescharacteristic
270C4×C43C22×Q1611yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273Dic43—22no—
274Dic43—21no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Dic43#46212yes—
279Dic43#46512yes—
280C2×#498—431no—
281C2×#477—431no—
282C2×#462—431no—
283C2×C8×Q8—431no—
284#1672—431no—
285#1672—431no—
286#1672—431no—
287#1672—431no—
288#1672—431no—
289#1672—431no—
290#1672—431no—
291#1672D4311yescharacteristic, direct product factor
292C2×#334—431no—
293C2×#333—431no—
294C2×#332—431no—
295C2×C43C2×#46211yescharacteristic
296C2×C43C2×#46511yescharacteristic
297C2×C43C2×#47111yescharacteristic
298D43#167214yesdirect product factor
299C22×Q16—861no—
300C2×C4⋊Q8—431no—
301C2×C4⋊Q8—431no—
302C2×C4×Q8—431no—
303#498—431no—
304#498—431no—
305#498—431no—
306#498—861no—
307#498—861no—
308#498C2×D4311yescharacteristic
309#477—431no—
310#477—431no—
311#477—431no—
312#477—861no—
313#477—861no—
314#477C2×D4311yescharacteristic
315#462—431no—
316#462—431no—
317#462—431no—
318#462—861no—
319#462—861no—
320#462C2×D4311yescharacteristic
321C8×Q8—431no—
322C8×Q8—431no—
323C8×Q8—431no—
324C8×Q8—861no—
325C8×Q8—861no—
326C8×Q8C2×D4311yescharacteristic
327C2×#107—861no—
328C2×#106—861no—
329C2×#106—861no—
330C2×C4⋊C8—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—861no—
334C2×#103—861no—
335C2×#103—861no—
336C2×C4×C8—431no—
337C2×C4×C8—861no—
338#334—431no—
339#334—431no—
340#334—431no—
341#334C2×D4311yescharacteristic
342#333—431no—
343#333—431no—
344#333—431no—
345#333C2×D4311yescharacteristic
346#332—431no—
347#332—431no—
348#332—431no—
349#332C2×D4311yescharacteristic
350C43C2×#167211yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C22×Q8—861no—
353C22×Q8—861no—
354C2×Q16—21no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×Q16—861no—
358C2×Q16—1724no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8C22×D4311yescharacteristic
373C4⋊Q8C22×D4311yescharacteristic
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C2×C4⋊C4—431no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C42—431no—
387C2×C42—861no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—21no—
393#106—21no—
394#106—861no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400C4⋊C8—21no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—21no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421C4×C8—21no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—434no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—862no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—3442no—
438C2×Q8—1721no—
439C2×Q8—1721no—
440C2×Q8—1722no—
441C2×Q8—1722no—
442C2×Q8D4×D4311yescharacteristic
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449C22×C4—1721no—
450Q16—42no—
451Q16—1722no—
452Q16—1722no—
453Q16—1722no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—431no—
458C2×C8—434no—
459C2×C8—431no—
460C2×C8—862no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1722no—
465C2×C8—1722no—
466C2×C8—1722no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4D4×D4311yescharacteristic
488C42—21no—
489C42—431no—
490C42—431no—
491C42—431no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42C23×D4311yescharacteristic
496C23—431no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—432no—
502Q8—864no—
503Q8—861no—
504Q8—3441no—
505Q8—3442no—
506Q8—3442no—
507Q8—1721no—
508Q8—1721no—
509Q8SD16×D4312yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—431no—
515C2×C4—431no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—432no—
520C2×C4—431no—
521C2×C4—862no—
522C2×C4—864no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—3442no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4#41×D4311yescharacteristic
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—432no—
538C8—861no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C8Q16×D4312yescomplemented
543C22—432no—
544C22—432no—
545C22—432no—
546C22#121×D4311yescharacteristic
547C4—21no—
548C4—22no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—432no—
553C4—432no—
554C4—861no—
555C4—862no—
556C4—3441no—
557C4—3441no—
558C4—1721no—
559C4C2×SD16×D4311yescharacteristic
560C4C2×Q16×D4311yescharacteristic
561C4#135×D4311yescharacteristic
562C4#137×D4311yescharacteristic
563C2—434no—
564C2#462×D4311yescharacteristic
565C2#465×D4311yescharacteristic
566C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1672D43
hypocenterC43C2×#1672
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #19133980C2semidirect
6. #19133979C2semidirect
7. #19133978C2semidirect
8. #19133977C2semidirect
9. #19133976C2semidirect
10. #19133975C2semidirect
11. #19133974C2semidirect
15. C43×#1672C2semidirect
211. C8×D43Q16semidirect
253. C8×C43C2×Q16semidirect
258. C43⋊C8C2×Q16semidirect
291. #1672D43direct (N × H)
298. D43#1672direct (N × H)
350. C43C2×#1672semidirect
542. C8Q16×D43semidirect

Maximal subgroups

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

subgroupindex
#498×D432
#477×D432
#462×D432
C8×Q8×D432
#191339802
#191339792
#191339782
#191339772
#191339762
#191339752
#191339742
#334×D432
#333×D432
#332×D432
C43×#16722
C2×#167243