Finite Group Databasebeta

← D43×#1704 #25079265

Subgroups — D43×#1704 #25079265

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D43C211yesmaximal, characteristic
2#477×D43C211yesmaximal, characteristic
3#475×D43C211yesmaximal, characteristic
4#446×D43C211yesmaximal, characteristic
5#19134180C211yesmaximal, characteristic, complemented
6#19134179C211yesmaximal, characteristic, complemented
7#19134178C211yesmaximal, characteristic, complemented
8#19134177C211yesmaximal, characteristic, complemented
9#19134176C211yesmaximal, characteristic, complemented
10#19134175C211yesmaximal, characteristic, complemented
11#19134174C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic
13#333×D43C211yesmaximal, characteristic
14#332×D43C211yesmaximal, characteristic
15C43×#1704C211yesmaximal, characteristic, complemented
16C4⋊Q8×D43C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583248—21no—
23#14583248—21no—
24#14583195C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583193—21no—
27#14583192—21no—
28#14583191C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583183—21no—
32#14583182—21no—
33#14583181C2211yescharacteristic
34#14583030C2211yescharacteristic
35#14583029C2211yescharacteristic
36#14583028—21no—
37#14583027—21no—
38#14583026C2211yescharacteristic
39#107×D43—21no—
40#106×D43—21no—
41C4⋊C8×D43—21no—
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#103×D43—21no—
46#103×D43—21no—
47#103×D43—21no—
48#103×D43—21no—
49#97×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#446C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70C2×C8×D43—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063323—21no—
82#13063323—21no—
83Q8×Dic43D411yescharacteristic
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290D411yescharacteristic
88C4⋊C4×D43—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43D411yescharacteristic
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063248—21no—
120#13063248—21no—
121#13063248—21no—
122#13063248—21no—
123#13063236—21no—
124#13063235—21no—
125#13063235—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43—22no—
149Q8×D43—42no—
150Q8×D43—42no—
151Q8×D43—82no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86—41no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C2×D411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C8×D43—22no—
203C8×D43—22no—
204C8×D43—42no—
205C8×D43—42no—
206C8×D43—42no—
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227C4×D43—22no—
228C4×D43—42no—
229C4×D43—42no—
230C4×D43—82no—
231C4×D43—82no—
232C4×D43#13512yes—
233C4×D43#13712yes—
234C4×D43#13712yes—
235C4×D43#13712yes—
236Dic86—21no—
237Dic86—21no—
238Dic86—42no—
239Dic86—41no—
240Dic86—41no—
241Dic86—82no—
242Dic86—82no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C2×#1704—431nomaximal, Sylow
255C22×C43C2×#12111yescharacteristic
256C2×D43#46412yes—
257C2×D43#47012yes—
258C2×D43#47112yes—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13711yescharacteristic
266C4×C43C2×#13711yescharacteristic
267C4×C43C2×#13711yescharacteristic
268Dic43—21no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43#46412yes—
274Dic43#47012yes—
275C2×#487—431no—
276C2×#477—431no—
277C2×#475—431no—
278C2×#446—431no—
279#1704—431no—
280#1704—431no—
281#1704—431no—
282#1704—431no—
283#1704—431no—
284#1704—431no—
285#1704—431no—
286#1704D4311yescharacteristic, direct product factor
287C2×#334—431no—
288C2×#333—431no—
289C2×#332—431no—
290C2×C43C2×#46411yescharacteristic
291C2×C43C2×#47011yescharacteristic
292C2×C43C2×#47111yescharacteristic
293D43#170414yesdirect product factor
294C2×C4⋊Q8—431no—
295C2×C4⋊Q8—431no—
296C2×C4×Q8—431no—
297#487—431no—
298#487—431no—
299#487—431no—
300#487—861no—
301#487—861no—
302#487C2×D4311yescharacteristic
303#477—431no—
304#477—431no—
305#477—431no—
306#477—861no—
307#477—861no—
308#477C2×D4311yescharacteristic
309#475—431no—
310#475—431no—
311#475—431no—
312#475—861no—
313#475—861no—
314#475C2×D4311yescharacteristic
315#446—431no—
316#446—431no—
317#446—431no—
318#446—861no—
319#446—861no—
320#446C2×D4311yescharacteristic
321C2×#107—861no—
322C2×#106—861no—
323C2×C4⋊C8—431no—
324C2×C4⋊C8—431no—
325C2×C4⋊C8—431no—
326C2×C4⋊C8—861no—
327C2×#103—861no—
328C2×#103—861no—
329C2×#103—861no—
330C2×#103—861no—
331C2×#97—861no—
332C2×C4×C8—431no—
333#334—431no—
334#334—431no—
335#334—431no—
336#334C2×D4311yescharacteristic
337#333—431no—
338#333—431no—
339#333—431no—
340#333C2×D4311yescharacteristic
341#332—431no—
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345C43C2×#170411yescharacteristic, complemented, Sylow
346C22×Q8—431no—
347C22×Q8—861no—
348C22×Q8—861no—
349C22×C8—431no—
350C22×C8—431no—
351C22×C8—861no—
352C22×C8—861no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8C22×D4311yescharacteristic
363C4⋊Q8C22×D4311yescharacteristic
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C2×C4⋊C4—431no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42—431no—
377C2×C42—861no—
378#107—21no—
379#107—861no—
380#107—861no—
381#107—861no—
382#106—21no—
383#106—861no—
384#106—861no—
385#106—861no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#97—21no—
416#97—861no—
417#97—861no—
418#97—861no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8C22×D4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—862no—
428C2×Q8—862no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—3442no—
432C2×Q8—1721no—
433C2×Q8—1721no—
434C2×Q8—1722no—
435C2×Q8—1722no—
436C2×Q8D4×D4311yescharacteristic
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—1721no—
443C22×C4—1721no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—862no—
450C2×C8—862no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—1722no—
455C2×C8—1722no—
456C2×C8—1722no—
457C2×C8D4×D4311yescharacteristic
458C2×C8D4×D4311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4D4×D4311yescharacteristic
478C42—21no—
479C42—431no—
480C42—431no—
481C42—431no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42C23×D4311yescharacteristic
486C23—431no—
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—861no—
493Q8—861no—
494Q8—3441no—
495Q8—3442no—
496Q8—3442no—
497Q8—1722no—
498Q8—1721no—
499Q8—1721no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—432no—
509C2×C4—432no—
510C2×C4—431no—
511C2×C4—862no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—3442no—
515C2×C4—3442no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×D4×D4311yescharacteristic
522C2×C4#41×D4311yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C22—432no—
534C22—432no—
535C22—432no—
536C22#121×D4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—432no—
543C4—432no—
544C4—861no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4—1721no—
549C4#135×D4311yescharacteristic
550C4#137×D4311yescharacteristic
551C4#137×D4311yescharacteristic
552C4#137×D4311yescharacteristic
553C2—434no—
554C2#464×D4311yescharacteristic
555C2#470×D4311yescharacteristic
556C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1704C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1704D43
hypocenterC43C2×#1704
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1704

Complements

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

NH ≅ G/Ntype
5. #19134180C2semidirect
6. #19134179C2semidirect
7. #19134178C2semidirect
8. #19134177C2semidirect
9. #19134176C2semidirect
10. #19134175C2semidirect
11. #19134174C2semidirect
15. C43×#1704C2semidirect
286. #1704D43direct (N × H)
293. D43#1704direct (N × H)
345. C43C2×#1704semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#477×D432
#475×D432
#446×D432
#191341802
#191341792
#191341782
#191341772
#191341762
#191341752
#191341742
#334×D432
#333×D432
#332×D432
C43×#17042
C2×#170443