Finite Group Databasebeta

← D43×#2210 #25250829

Subgroups — D43×#2210 #25250829

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D43C211yesmaximal, characteristic, complemented
2C2×D16×D43C211yesmaximal, characteristic
3#495×D43C211yesmaximal, characteristic, complemented
4C4×D8×D43C211yesmaximal, characteristic, complemented
5#19136653C211yesmaximal, characteristic, complemented
6#19136652C211yesmaximal, characteristic, complemented
7#19136651C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136649C211yesmaximal, characteristic, complemented
10#19136648C211yesmaximal, characteristic, complemented
11#19136647C211yesmaximal, characteristic, complemented
12C4⋊C16×D43C211yesmaximal, characteristic, complemented
13#358×D43C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2210C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17C2×SD16×D43—21no—
18C2×D8×D43C2211yescharacteristic
19C2×D8×D43C2211yescharacteristic
20#124×D43—21no—
21C4×D4×D43—21no—
22C2×#13063270C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063268C2211yescharacteristic, complemented
25SD32×D43—24no—
26C2×D688C2211yescharacteristic
27C2×#13063266C2211yescharacteristic
28C2×#13063266C2211yescharacteristic
29D16×D43—24no—
30C2×C16×D43C2211yescharacteristic
31C2×C16×D43C2211yescharacteristic
32#14583284C2211yescharacteristic, complemented
33#14583283C2211yescharacteristic, complemented
34#14583282C2211yescharacteristic, complemented
35#14583281—21no—
36#14583280—21no—
37C4×D344C2211yescharacteristic, complemented
38D8×Dic43C2211yescharacteristic, complemented
39#14582981C2211yescharacteristic, complemented
40C4×#10621882—21no—
41#14582979—21no—
42#107×D43C2211yescharacteristic
43#102×D43—21no—
44C4×C8×D43C2211yescharacteristic
45C4⋊(C43⋊C16)C2211yescharacteristic, complemented
46Dic43⋊C16C2211yescharacteristic, complemented
47Dic43⋊C16C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582703C2211yescharacteristic, complemented
50#14582702C2211yescharacteristic, complemented
51#14582701C2211yescharacteristic, complemented
52#14582700C2211yescharacteristic, complemented
53#14582699C2211yescharacteristic, complemented
54C2×SD32×C43C2211yescharacteristic, complemented
55C2×D16×C43C2211yescharacteristic
56C43×#495C2211yescharacteristic, complemented
57C4×D8×C43C2211yescharacteristic, complemented
58C43×C4⋊C16C2211yescharacteristic, complemented
59C43×#358C2211yescharacteristic, complemented
60C43×#357C2211yescharacteristic, complemented
61C2×Q8×D43—21no—
62C2×D4×D43—21no—
63C2×D4×D43—21no—
64C22×C4×D43—41no—
65C2×Dic172C2311yescharacteristic
66C2×#10621885—21no—
67Q16×D43—22no—
68Q16×D43—22no—
69C2×#10621873—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72SD16×D43—44no—
73C2×D344C2311yescharacteristic
74C2×D344C2311yescharacteristic
75C2×#10621882—21no—
76C2×#10621882—21no—
77D8×D43—22no—
78D8×D43—22no—
79D8×D43—22no—
80D8×D43D414yes—
81C2×C8×D43D411yescharacteristic
82C2×C8×D43C2311yescharacteristic
83#13063314—21no—
84#13063313—21no—
85#13063312—21no—
86#13063311—41no—
87#13063311—41no—
88C4×D172—21no—
89D4×Dic43—21no—
90#13063287—21no—
91C4×C22⋊D43—41no—
92(C22⋊D43)⋊C4—41no—
93C4⋊C4×D43—21no—
94C22⋊C4×D43—41no—
95C22⋊C4×D43—41no—
96C22⋊C4×D43—41no—
97C42×D43D411yescharacteristic
98#13063270—22no—
99#13063269—22no—
100#13063268—22no—
101D688—22no—
102#13063266—22no—
103#13063266—22no—
104C2×C43⋊C16C2311yescharacteristic
105C2×C43⋊C16C2311yescharacteristic
106C16×D43—22no—
107C16×D43—22no—
108#13063259C2311yescharacteristic
109#13063258—21no—
110#13063247—21no—
111#13063246—21no—
112#13063245—21no—
113C4×C43⋊C8D411yescharacteristic
114C8×Dic43D411yescharacteristic
115C8×Dic43C2311yescharacteristic
116C2×Q16×C43C2311yescharacteristic
117C2×SD16×C43—21no—
118C2×D8×C43C2311yescharacteristic
119C2×D8×C43C2311yescharacteristic
120#124×C43—21no—
121C4×D4×C43—21no—
122SD32×C43—22no—
123D16×C43—22no—
124C2×C16×C43C2311yescharacteristic
125C2×C16×C43C2311yescharacteristic
126#107×C43C2311yescharacteristic
127#102×C43—21no—
128C4×C8×C43C2311yescharacteristic
129C23×D43—41no—
130C23×D43—41no—
131C2×Q8×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C22×C4×C43—41no—
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C22×Dic43—41no—
138Q8×D43—42no—
139Q8×D43—42no—
140D4×D43—24no—
141D4×D43—42no—
142D4×D43—42no—
143D4×D43—42no—
144C2×D172—21no—
145C2×D172—21no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—84no—
151C2×C4×D43D811yescharacteristic
152C2×C4×D43D811yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—41no—
156Q16×C43—21no—
157Q16×C43—21no—
158SD16×C43—42no—
159D8×C43—21no—
160D8×C43—21no—
161D8×C43—21no—
162D8×C43C2×D412yes—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2411yescharacteristic
165C4⋊C4×C43—21no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C42×C43C2×D411yescharacteristic
170C22⋊Dic43—41no—
171C22⋊Dic43—41no—
172C22⋊Dic43—41no—
173#10621885—42no—
174#10621884—42no—
175#10621883—42no—
176#10621882—24no—
177#10621882—42no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185Dic43⋊C4—41no—
186C4×Dic43D811yescharacteristic
187C4×Dic43D811yescharacteristic
188C4×Dic43C2×D411yescharacteristic
189C2×C43⋊C8C2×D411yescharacteristic
190C2×C43⋊C8C2×D411yescharacteristic
191Dic172—21no—
192Dic172—21no—
193D344—21no—
194D344—21no—
195D344—21no—
196D344C2×D412yes—
197#10621873—42no—
198C8×D43—22no—
199C8×D43C2×D412yes—
200C8×D43#4112yes—
201C16×C43—21no—
202C16×C43—21no—
203C43⋊C16—21no—
204C43⋊C16—21no—
205C23×C43—41no—
206C23×C43—41no—
207C22×D43—41no—
208C22×D43—44no—
209C22×D43—41no—
210C22×D43—82no—
211C22×D43—82no—
212C22×D43—82no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43C2×D811yescharacteristic
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—22no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—82no—
225C2×C4×C43C2×D811yescharacteristic
226C2×C4×C43C2×D811yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C22⋊D43—44no—
229C22⋊D43—82no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—82no—
233C2×Dic43C2×D811yescharacteristic
234C2×Dic43C2×D811yescharacteristic
235C2×Dic43C2×D811yescharacteristic
236D172—22no—
237D172—41no—
238D172—41no—
239D172—41no—
240C4×D43—22no—
241C4×D43—22no—
242C4×D43—82no—
243C4×D43—82no—
244C4×D43—82no—
245C4×D43—82no—
246C4×D43#12112yes—
247C4×D43AGL(1,ℤ/8)12yes—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251C8×C43—21no—
252C8×C43C22×D411yescharacteristic
253C8×C43C2×#4111yescharacteristic
254C43⋊C8—21no—
255C43⋊C8#12112yes—
256C2×#2210—431nomaximal, Sylow
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C22×D811yescharacteristic
264C2×D43—42no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—88no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—164no—
272C2×D43#45912yes—
273C2×D43#50812yes—
274C2×D43#50912yes—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C2×#12111yescharacteristic
280C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
281Dic43—21no—
282Dic43—21no—
283Dic43—81no—
284Dic43—81no—
285Dic43#45912yes—
286C22×SD32—431no—
287C22×D16—431no—
288C2×#495—431no—
289C2×C4×D8—431no—
290#2210—431no—
291#2210—431no—
292#2210—431no—
293#2210—431no—
294#2210—431no—
295#2210—431no—
296#2210—431no—
297#2210D4311yescharacteristic, direct product factor
298C2×C4⋊C16—431no—
299C2×#358—431no—
300C2×#357—431no—
301C2×C43—82no—
302C2×C43—161no—
303C2×C43C2×#45911yescharacteristic
304C2×C43C2×#50811yescharacteristic
305C2×C43C2×#50911yescharacteristic
306D43—82no—
307D43—161no—
308D43#221014yesdirect product factor
309C22×Q16—431no—
310C22×SD16—861no—
311C22×D8—431no—
312C22×D8—431no—
313C2×#124—861no—
314C2×C4×D4—861no—
315C2×SD32—431no—
316C2×SD32—431no—
317C2×SD32—431no—
318C2×SD32—864no—
319C2×SD32C2×D4311yescharacteristic, complemented
320C2×D16—431no—
321C2×D16—431no—
322C2×D16—431no—
323C2×D16—864no—
324C2×D16C2×D4311yescharacteristic
325C22×C16—431no—
326C22×C16—431no—
327#495—431no—
328#495—431no—
329#495—431no—
330#495—861no—
331#495—861no—
332#495C2×D4311yescharacteristic, complemented
333C4×D8—431no—
334C4×D8—431no—
335C4×D8—431no—
336C4×D8—861no—
337C4×D8—861no—
338C4×D8C2×D4311yescharacteristic, complemented
339C2×#107—431no—
340C2×#102—861no—
341C2×C4×C8—431no—
342C4⋊C16—431no—
343C4⋊C16—431no—
344C4⋊C16—431no—
345C4⋊C16C2×D4311yescharacteristic, complemented
346#358—431no—
347#358—431no—
348#358—431no—
349#358C2×D4311yescharacteristic, complemented
350#357—431no—
351#357—431no—
352#357—431no—
353#357C2×D4311yescharacteristic, complemented
354C43C2×#221011yescharacteristic, complemented, Sylow
355C22×Q8—861no—
356C22×D4—861no—
357C22×D4—861no—
358C23×C4—1721no—
359C2×Q16—431no—
360C2×Q16—862no—
361C2×Q16—862no—
362C2×Q16—861no—
363C2×Q16C22×D4311yescharacteristic
364C2×SD16—21no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—1724no—
369C2×D8—434no—
370C2×D8—431no—
371C2×D8—431no—
372C2×D8—862no—
373C2×D8—862no—
374C2×D8—862no—
375C2×D8—861no—
376C2×D8—861no—
377C2×D8C22×D4311yescharacteristic
378C2×D8C22×D4311yescharacteristic
379C22×C8—431no—
380C22×C8—431no—
381#124—21no—
382#124—861no—
383#124—861no—
384#124—861no—
385#124—1721no—
386#124—1721no—
387C4×D4—21no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—1721no—
392C4×D4—1721no—
393C2×C4⋊C4—861no—
394C2×C22⋊C4—1721no—
395C2×C22⋊C4—1721no—
396C2×C22⋊C4—1721no—
397C2×C42—431no—
398SD32—22no—
399SD32—862no—
400SD32—862no—
401SD32—862no—
402D16—22no—
403D16—862no—
404D16—862no—
405D16—862no—
406C2×C16—431no—
407C2×C16—431no—
408C2×C16—862no—
409C2×C16—862no—
410C2×C16C22×D4311yescharacteristic
411C2×C16C22×D4311yescharacteristic
412#107—431no—
413#107—861no—
414#107C22×D4311yescharacteristic
415#102—21no—
416#102—861no—
417#102—861no—
418#102—861no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8C22×D4311yescharacteristic
423C24—1721no—
424C24—1721no—
425C2×Q8—21no—
426C2×Q8—861no—
427C2×Q8—1721no—
428C2×Q8—1722no—
429C2×Q8—1722no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—864no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—1722no—
436C2×D4—1722no—
437C2×D4—1722no—
438C2×D4—1721no—
439C2×D4—1721no—
440C22×C4—41no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—3444no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450Q16—21no—
451Q16—21no—
452Q16—861no—
453Q16—861no—
454Q16—1722no—
455SD16—42no—
456SD16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—21no—
460D8—21no—
461D8—21no—
462D8—432no—
463D8—864no—
464D8—861no—
465D8—861no—
466D8—861no—
467D8—1722no—
468D8D4×D4312yes—
469C2×C8—431no—
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—431no—
473C2×C8—862no—
474C2×C8D4×D4311yescharacteristic
475C2×C8C23×D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—431no—
492C42—431no—
493C42—431no—
494C42D4×D4311yescharacteristic
495C16—21no—
496C16—21no—
497C16—861no—
498C16—861no—
499C23—41no—
500C23—41no—
501C23—431no—
502C23—3442no—
503C23—3442no—
504C23—3442no—
505C23—3442no—
506C23—3442no—
507C23—1724no—
508C23—1721no—
509C23—1721no—
510Q8—41no—
511Q8—41no—
512Q8—3442no—
513Q8—1721no—
514Q8—1721no—
515D4—22no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—862no—
520D4—3442no—
521D4—1724no—
522D4—1721no—
523D4—1721no—
524D4—1721no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—431no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4D8×D4311yescharacteristic
543C2×C4D8×D4311yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C8—21no—
546C8—432no—
547C8—861no—
548C8C2×D4×D4311yescharacteristic
549C8#41×D4311yescharacteristic
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—432no—
557C22—432no—
558C22—432no—
559C22—3448no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—1722no—
566C22—6884no—
567C22C2×D8×D4311yescharacteristic
568C4—21no—
569C4—21no—
570C4—81no—
571C4—81no—
572C4—432no—
573C4—861no—
574C4—861no—
575C4—3441no—
576C4—3441no—
577C4#121×D4311yescharacteristic
578C4AGL(1,ℤ/8)×D4311yescharacteristic
579C2—82no—
580C2—161no—
581C2—434no—
582C2—3442no—
583C2—6881no—
584C2#459×D4311yescharacteristic
585C2#508×D4311yescharacteristic
586C2#509×D4311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2210C2
socleC22×C43C22×D8
prime radicalC2×D16×D43C2
hypercenter#2210D43
hypocenterC43C2×#2210
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D43C2semidirect
3. #495×D43C2semidirect
4. C4×D8×D43C2semidirect
5. #19136653C2semidirect
6. #19136652C2semidirect
7. #19136651C2semidirect
8. #19136650C2semidirect
9. #19136649C2semidirect
10. #19136648C2semidirect
11. #19136647C2semidirect
12. C4⋊C16×D43C2semidirect
13. #358×D43C2semidirect
14. #357×D43C2semidirect
15. C43×#2210C2semidirect
22. C2×#13063270C22semidirect
23. C2×#13063269C22semidirect
24. C2×#13063268C22semidirect
32. #14583284C22semidirect
33. #14583283C22semidirect
34. #14583282C22semidirect
37. C4×D344C22semidirect
38. D8×Dic43C22semidirect
39. #14582981C22semidirect
45. C4⋊(C43⋊C16)C22semidirect
46. Dic43⋊C16C22semidirect
47. Dic43⋊C16C22semidirect
48. #14582704C22semidirect
49. #14582703C22semidirect
50. #14582702C22semidirect
51. #14582701C22semidirect
52. #14582700C22semidirect
53. #14582699C22semidirect
54. C2×SD32×C43C22semidirect
56. C43×#495C22semidirect
57. C4×D8×C43C22semidirect
58. C43×C4⋊C16C22semidirect
59. C43×#358C22semidirect
60. C43×#357C22semidirect
297. #2210D43direct (N × H)
308. D43#2210direct (N × H)
319. C2×SD32C2×D43semidirect
332. #495C2×D43semidirect
338. C4×D8C2×D43semidirect
345. C4⋊C16C2×D43semidirect
349. #358C2×D43semidirect
353. #357C2×D43semidirect
354. C43C2×#2210semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
C2×D16×D432
#495×D432
C4×D8×D432
#191366532
#191366522
#191366512
#191366502
#191366492
#191366482
#191366472
C4⋊C16×D432
#358×D432
#357×D432
C43×#22102
C2×#221043