Finite Group Databasebeta

← D43×#1700 #25079249

Subgroups — D43×#1700 #25079249

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D43C211yesmaximal, characteristic
2#475×D43C211yesmaximal, characteristic
3#462×D43C211yesmaximal, characteristic
4#446×D43C211yesmaximal, characteristic
5#19134152C211yesmaximal, characteristic, complemented
6#19134151C211yesmaximal, characteristic, complemented
7#19134150C211yesmaximal, characteristic, complemented
8#19134149C211yesmaximal, characteristic, complemented
9#19134148C211yesmaximal, characteristic, complemented
10#19134147C211yesmaximal, characteristic, complemented
11#19134146C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic
13#332×D43C211yesmaximal, characteristic
14#332×D43C211yesmaximal, characteristic
15C43×#1700C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583248—21no—
24#14583248—21no—
25#14583185C2211yescharacteristic
26#14583184C2211yescharacteristic
27#14583183—21no—
28#14583182—21no—
29#14583181C2211yescharacteristic
30#14583110C2211yescharacteristic
31#14583109C2211yescharacteristic
32#14583108—21no—
33#14583107—21no—
34#14583106C2211yescharacteristic
35#14583030C2211yescharacteristic
36#14583029C2211yescharacteristic
37#14583028—21no—
38#14583027—21no—
39#14583026C2211yescharacteristic
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#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C43×#446C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
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#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063249—21no—
120#13063248—21no—
121#13063248—21no—
122#13063248—21no—
123#13063248—21no—
124#13063236—21no—
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148Q8×D43—22no—
149Q8×D43—22no—
150Q8×D43—42no—
151Q8×D43—42no—
152Q8×D43—42no—
153Q8×D43—42no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86C2×D411yescharacteristic
167Q16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C42×C43—21no—
180C42×C43C2411yescharacteristic
181#10621885—42no—
182#10621885—42no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—42no—
208C8×D43—22no—
209C8×D43—22no—
210C8×D43—42no—
211C8×D43—42no—
212C8×D43—42no—
213C22×D43#12111yescharacteristic
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C4×D43—22no—
235C4×D43—42no—
236C4×D43—42no—
237C4×D43—82no—
238C4×D43—82no—
239C4×D43#13512yes—
240C4×D43AGL(1,ℤ/8)12yes—
241C4×D43#13712yes—
242C4×D43#13712yes—
243Dic86—21no—
244Dic86—21no—
245Dic86—42no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251Dic86—82no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C2×#1700—431nomaximal, Sylow
263C22×C43C2×#12111yescharacteristic
264C2×D43#46412yes—
265C2×D43#46812yes—
266C2×D43#47312yes—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
274C4×C43C2×#13711yescharacteristic
275C4×C43C2×#13711yescharacteristic
276Dic43—21no—
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43#46412yes—
282Dic43#46812yes—
283C2×#487—431no—
284C2×#475—431no—
285C2×#462—431no—
286C2×#446—431no—
287#1700—431no—
288#1700—431no—
289#1700—431no—
290#1700—431no—
291#1700—431no—
292#1700—431no—
293#1700—431no—
294#1700D4311yescharacteristic, direct product factor
295C2×#335—431no—
296C2×#332—431no—
297C2×#332—431no—
298C2×C43C2×#46411yescharacteristic
299C2×C43C2×#46811yescharacteristic
300C2×C43C2×#47311yescharacteristic
301D43#170014yesdirect product factor
302C22×Q16—861no—
303C2×C4⋊Q8—431no—
304C2×C4⋊Q8—431no—
305C2×C4×Q8—431no—
306#487—431no—
307#487—431no—
308#487—431no—
309#487—861no—
310#487—861no—
311#487C2×D4311yescharacteristic
312#475—431no—
313#475—431no—
314#475—431no—
315#475—861no—
316#475—861no—
317#475C2×D4311yescharacteristic
318#462—431no—
319#462—431no—
320#462—431no—
321#462—861no—
322#462—861no—
323#462C2×D4311yescharacteristic
324#446—431no—
325#446—431no—
326#446—431no—
327#446—861no—
328#446—861no—
329#446C2×D4311yescharacteristic
330C2×#106—861no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—861no—
335C2×#103—861no—
336C2×#103—861no—
337C2×#103—861no—
338C2×#103—861no—
339C2×#97—861no—
340C2×C4×C8—431no—
341#335—431no—
342#335—431no—
343#335—431no—
344#335C2×D4311yescharacteristic
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350#332—431no—
351#332C2×D4311yescharacteristic
352#332C2×D4311yescharacteristic
353C43C2×#170011yescharacteristic, complemented, Sylow
354C22×Q8—431no—
355C22×Q8—861no—
356C22×Q8—861no—
357C2×Q16—21no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×Q16—861no—
361C2×Q16—1724no—
362C22×C8—431no—
363C22×C8—431no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8—861no—
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8—861no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8—861no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377C4×Q8—431no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×Q8C22×D4311yescharacteristic
383C2×C4⋊C4—431no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C42—431no—
390C2×C42—861no—
391#106—21no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#97—21no—
425#97—861no—
426#97—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8C22×D4311yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—1721no—
441C2×Q8—1721no—
442C2×Q8—1722no—
443C2×Q8—1722no—
444C2×Q8—1722no—
445C2×Q8—1722no—
446C2×Q8D4×D4311yescharacteristic
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1721no—
453C22×C4—1721no—
454Q16—42no—
455Q16—1722no—
456Q16—1722no—
457Q16—1722no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8—1722no—
470C2×C8—1722no—
471C2×C8D4×D4311yescharacteristic
472C2×C8D4×D4311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4D4×D4311yescharacteristic
492C42—21no—
493C42—431no—
494C42—431no—
495C42—431no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42C23×D4311yescharacteristic
500C23—431no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—861no—
508Q8—861no—
509Q8—3442no—
510Q8—3442no—
511Q8—1722no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—431no—
527C2×C4—862no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3442no—
531C2×C4—3442no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4#41×D4311yescharacteristic
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—861no—
545C8—861no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—432no—
550C22—432no—
551C22—432no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—432no—
559C4—432no—
560C4—861no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4AGL(1,ℤ/8)×D4311yescharacteristic
567C4#137×D4311yescharacteristic
568C4#137×D4311yescharacteristic
569C2—434no—
570C2#464×D4311yescharacteristic
571C2#468×D4311yescharacteristic
572C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1700C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1700D43
hypocenterC43C2×#1700
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1700

Complements

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

NH ≅ G/Ntype
5. #19134152C2semidirect
6. #19134151C2semidirect
7. #19134150C2semidirect
8. #19134149C2semidirect
9. #19134148C2semidirect
10. #19134147C2semidirect
11. #19134146C2semidirect
15. C43×#1700C2semidirect
294. #1700D43direct (N × H)
301. D43#1700direct (N × H)
353. C43C2×#1700semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#475×D432
#462×D432
#446×D432
#191341522
#191341512
#191341502
#191341492
#191341482
#191341472
#191341462
#335×D432
#332×D432
C43×#17002
C2×#170043