Finite Group Databasebeta

← D43×#1873 #25097799

Subgroups — D43×#1873 #25097799

Order 11008.

1966 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic
3C2×#103×D43C212yesmaximal, complemented
4C2×C22⋊C8×D43C211yesmaximal, characteristic
5#19134908C211yesmaximal, characteristic, complemented
6#19134907C211yesmaximal, characteristic, complemented
7#19134906C212yesmaximal, complemented
8#19134905C211yesmaximal, characteristic, complemented
9#19134904C212yesmaximal, complemented
10#340×D43C212yesmaximal, complemented
11C43×#1873C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×C8×D43C2212yes—
15C2×#13063305C2211yescharacteristic
16C2×#13063304C2211yescharacteristic
17C2×#13063303—21no—
18C2×#13063302—21no—
19C2×#13063301C2211yescharacteristic
20C22⋊Q8×D43—24no—
21C22⋊Q8×D43C418yescomplemented
22C2×#13063284C2211yescharacteristic
23C2×#13063283C2212yes—
24C2×#13063282—21no—
25C2×#13063281—21no—
26#117×D43—28no—
27C2×C4⋊C4×D43—21no—
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C4⋊C4×D43C2212yes—
30C2×C22⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32C2×C42×D43—21no—
33C2×#13063250C2212yescomplemented
34C2×#13063249C2212yescomplemented
35C2×#13063248C2212yescomplemented
36#103×D43—28no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2212yes—
39C22⋊C8×D43—24no—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C2×C22⋊Q8×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C2×#103×C43C2212yescomplemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#340C2212yescomplemented
48C24×D43D411yescharacteristic
49C22×Dic86—21no—
50C22×Dic86C2311yescharacteristic
51C2×Q8×D43—22no—
52C2×Q8×D43—24no—
53C2×Q8×D43—24no—
54C2×Q8×D43C2×C414yes—
55C23×Dic43D411yescharacteristic
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—22no—
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2×C414yes—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D414yes—
65C22×C4×D43C2311yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2312yes—
68C2×C8×D43—24no—
69C2×C8×D43—24no—
70C2×C8×D43—24no—
71#13063305—22no—
72#13063305C2×C414yescomplemented
73#13063304—22no—
74#13063304C2×C414yescomplemented
75#13063303—28no—
76#13063302—28no—
77#13063301—22no—
78#13063301C2×C414yescomplemented
79#13063284—24no—
80#13063283—24no—
81#13063283—24no—
82#13063282—28no—
83#13063281—28no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2312yes—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—21no—
91C4⋊C4×D43—28no—
92C4⋊C4×D43—24no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43C2×C414yes—
95C4⋊C4×D43D418yes—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C22⋊C4×D43—28no—
102C22⋊C4×D43—28no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—22no—
105C42×D43—28no—
106#13063250—24no—
107#13063249—24no—
108#13063248—24no—
109C22⋊(C43⋊C8)—22no—
110(C2×D43)⋊C8—24no—
111C22×Q8×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2312yes—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43C2×C414yescomplemented
116#117×C43—24no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2312yes—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123#103×C43—24no—
124C22⋊C8×C43—22no—
125C24×C43C2×D411yescharacteristic
126C23×D43—22no—
127C23×D43—22no—
128C23×D43—24no—
129C23×D43—24no—
130C23×D43C22⋊C414yes—
131C23×D43C2×D411yescharacteristic
132C23×D43C2×D411yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43C22×C412yes—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C22×C412yes—
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C22⋊C414yes—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154Q8×D43—216no—
155Q8×D43—48no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—216no—
161C2×C4×D43—216no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—22no—
165C2×C4×D43—28no—
166C2×C4×D43—22no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—44no—
170C2×C4×D43—44no—
171C2×C4×D43—44no—
172C2×C4×D43C22⋊C414yes—
173C2×C4×D43C22⋊C414yes—
174C2×C4×D43C22×C412yes—
175C2×C4×D43C22×C412yes—
176C2×C4×D43C2×D412yes—
177C2×C4×D43C2×D412yes—
178C2×C4×D43C2×D414yes—
179C2×C4×D43#4114yes—
180C2×Dic86—22no—
181C2×Dic86—22no—
182C2×Dic86—21no—
183C2×Dic86—24no—
184C2×Dic86—42no—
185C2×Dic86—42no—
186C2×Dic86C22×C412yes—
187C2×C8×C43—22no—
188C2×C8×C43—22no—
189C2×C8×C43—22no—
190C4⋊C4×C43—24no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C22×C412yes—
194C4⋊C4×C43C2×D414yes—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—24no—
197C42×C43—24no—
198C22⋊Dic43—24no—
199C22⋊Dic43—24no—
200(C2×D43)⋊C4—28no—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203C4⋊Dic43—22no—
204C4⋊Dic43—21no—
205C4⋊Dic43—24no—
206C4⋊Dic43C22×C412yes—
207C4⋊Dic43C2×D414yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—28no—
212C4×Dic43—28no—
213C4×Dic43—24no—
214C2×C43⋊C8—22no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—22no—
217C8×D43—48no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43C2×C22⋊C412yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—28no—
229C22×D43—28no—
230C22×D43—28no—
231C22×D43—48no—
232C22×D43—48no—
233C22×D43C2×C22⋊C412yes—
234C22×D43C2×C22⋊C412yes—
235C22×D43#12012yes—
236C22×D43#12312yes—
237C22×D43#13514yes—
238C22×D43#13714yes—
239Q8×C43—24no—
240Q8×C43—42no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—24no—
244C2×C4×C43—24no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D412yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4112yes—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—28no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43C2×C22⋊C412yes—
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43#12012yes—
272C2×Dic43#12312yes—
273C4×D43—28no—
274C4×D43—24no—
275C4×D43—24no—
276C4×D43—28no—
277C4×D43—48no—
278C4×D43—48no—
279C4×D43—416no—
280C4×D43C4×D418yes—
281C4×D43#12118yes—
282Dic86—24no—
283Dic86—42no—
284Dic86—48no—
285C8×C43—42no—
286C43⋊C8—42no—
287C2×#1873—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43C22×C22⋊C411yescharacteristic
294C22×C43C2×#12011yescharacteristic
295C22×C43C2×#12311yescharacteristic
296C22×C43C2×#13512yes—
297C22×C43C2×#13712yes—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—416no—
304C2×D43#38614yes—
305C2×D43#41614yes—
306C2×D43#41914yes—
307C2×D43#45218yes—
308C2×D43#48518yes—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—44no—
312C4×C43—42no—
313C4×C43C2×C4×D412yes—
314C4×C43C2×#12112yes—
315Dic43—22no—
316Dic43—42no—
317Dic43—44no—
318Dic43—42no—
319Dic43#38614yes—
320C22×C22⋊Q8—431no—
321C22×#117—431no—
322C22×#103—432no—
323C22×C22⋊C8—431no—
324#1873—432no—
325#1873—431no—
326#1873—432no—
327#1873—431no—
328#1873—431no—
329#1873D4311yescharacteristic, direct product factor
330C2×#340—432no—
331C2×C43—42no—
332C2×C43C2×#38611yescharacteristic
333C2×C43C2×#41611yescharacteristic
334C2×C43C2×#41911yescharacteristic
335C2×C43C2×#45212yes—
336C2×C43C2×#48512yes—
337D43—42no—
338D43#187318yesdirect product factor
339C23×Q8—431no—
340C24×C4—431no—
341C23×C8—432no—
342C2×C22⋊Q8—431no—
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—438no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8—861no—
347C2×C22⋊Q8—861no—
348C2×C22⋊Q8—864no—
349C2×C22⋊Q8C2×D4311yescharacteristic
350C2×#117—431no—
351C2×#117—432no—
352C2×#117—861no—
353C2×#117—861no—
354C2×#117—868no—
355C2×#117C2×D4311yescharacteristic
356C22×C4⋊C4—432no—
357C22×C4⋊C4—431no—
358C22×C4⋊C4—861no—
359C22×C22⋊C4—861no—
360C22×C22⋊C4—861no—
361C22×C42—861no—
362C2×#103—432no—
363C2×#103—432no—
364C2×#103—432no—
365C2×#103—868no—
366C2×#103C2×D4312yescomplemented
367C2×C22⋊C8—431no—
368C2×C22⋊C8—432no—
369C2×C22⋊C8—864no—
370C2×C22⋊C8C2×D4311yescharacteristic
371#340—432no—
372#340—432no—
373#340—432no—
374#340C2×D4312yescomplemented
375C43C2×#187311yescharacteristic, complemented, Sylow
376C25—431no—
377C22×Q8—434no—
378C22×Q8—431no—
379C22×Q8—861no—
380C22×Q8—862no—
381C22×Q8—864no—
382C22×Q8—864no—
383C22×Q8C22×D4311yescharacteristic
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—434no—
387C23×C4—431no—
388C23×C4—431no—
389C23×C4—434no—
390C23×C4—431no—
391C23×C4—864no—
392C23×C4—864no—
393C23×C4—861no—
394C23×C4—862no—
395C23×C4—861no—
396C23×C4C22×D4311yescharacteristic
397C22×C8—432no—
398C22×C8—864no—
399C22×C8—864no—
400C22×C8—864no—
401C22×C8C22×D4312yes—
402C22⋊Q8—22no—
403C22⋊Q8—434no—
404C22⋊Q8—434no—
405C22⋊Q8—434no—
406C22⋊Q8—868no—
407C22⋊Q8—868no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411C22⋊Q8C4×D4314yescomplemented
412#117—24no—
413#117—868no—
414#117—868no—
415#117—864no—
416#117—864no—
417#117—864no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—434no—
422C2×C4⋊C4—438no—
423C2×C4⋊C4—864no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—868no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4312yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—868no—
436C2×C22⋊C4—868no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C42—21no—
443C2×C42—868no—
444C2×C42—862no—
445C2×C42—861no—
446#103—24no—
447#103—864no—
448#103—864no—
449#103—864no—
450C22⋊C8—22no—
451C22⋊C8—864no—
452C22⋊C8—862no—
453C24—431no—
454C24—434no—
455C24—431no—
456C24—862no—
457C24—862no—
458C24—864no—
459C24—864no—
460C24D4×D4311yescharacteristic
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—432no—
465C2×Q8—864no—
466C2×Q8—8616no—
467C2×Q8—861no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×Q8—1722no—
471C2×Q8—1722no—
472C2×Q8—1728no—
473C2×Q8C2×C4×D4312yes—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—432no—
481C22×C4—434no—
482C22×C4—432no—
483C22×C4—434no—
484C22×C4—434no—
485C22×C4—431no—
486C22×C4—434no—
487C22×C4—434no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—8616no—
493C22×C4—8616no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—868no—
497C22×C4—864no—
498C22×C4—864no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4—1724no—
509C22×C4—1724no—
510C22×C4—1724no—
511C22×C4C2×C4×D4312yes—
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4312yes—
514C22×C4C23×D4311yescharacteristic
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—862no—
519C2×C8—862no—
520C2×C8—862no—
521C2×C8—1728no—
522C4⋊C4—24no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—432no—
526C4⋊C4—434no—
527C4⋊C4—868no—
528C4⋊C4—864no—
529C4⋊C4—864no—
530C4⋊C4—864no—
531C4⋊C4—864no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4C2×C4×D4312yes—
535C4⋊C4D4×D4314yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—864no—
539C22⋊C4—864no—
540C22⋊C4—868no—
541C22⋊C4—864no—
542C22⋊C4—864no—
543C42—24no—
544C42—864no—
545C42—868no—
546C23—21no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—432no—
551C23—432no—
552C23—432no—
553C23—434no—
554C23—434no—
555C23—432no—
556C23—868no—
557C23—868no—
558C23—868no—
559C23—861no—
560C23—861no—
561C23—862no—
562C23—862no—
563C23—1728no—
564C23—1728no—
565C23C22⋊C4×D4312yes—
566C23C2×D4×D4311yescharacteristic
567Q8—24no—
568Q8—42no—
569Q8—864no—
570Q8—1728no—
571Q8—1722no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—438no—
588C2×C4—438no—
589C2×C4—432no—
590C2×C4—868no—
591C2×C4—868no—
592C2×C4—868no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—1728no—
601C2×C4—17216no—
602C2×C4—1728no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4C22⋊C4×D4312yes—
609C2×C4C22×C4×D4311yescharacteristic
610C2×C4C2×D4×D4312yes—
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4#41×D4312yes—
613C8—42no—
614C8—1722no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—42no—
619C22—42no—
620C22—438no—
621C22—438no—
622C22—434no—
623C22—434no—
624C22—434no—
625C22—862no—
626C22—862no—
627C22—862no—
628C22—17216no—
629C22—1722no—
630C22—1722no—
631C22C2×C22⋊C4×D4311yescharacteristic
632C22#120×D4311yescharacteristic
633C22#123×D4311yescharacteristic
634C22#135×D4312yes—
635C22#137×D4312yes—
636C4—22no—
637C4—44no—
638C4—42no—
639C4—42no—
640C4—434no—
641C4—862no—
642C4—1724no—
643C4—1722no—
644C4—1722no—
645C4C4×D4×D4312yes—
646C4#121×D4312yes—
647C2—42no—
648C2—438no—
649C2—1722no—
650C2#386×D4311yescharacteristic
651C2#416×D4311yescharacteristic
652C2#419×D4311yescharacteristic
653C2#452×D4312yes—
654C2#485×D4312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1873C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1873D43
hypocenterC43C2×#1873
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. C2×#103×D43C2semidirect
5. #19134908C2semidirect
6. #19134907C2semidirect
7. #19134906C2semidirect
8. #19134905C2semidirect
9. #19134904C2semidirect
10. #340×D43C2semidirect
11. C43×#1873C2semidirect
21. C22⋊Q8×D43C4semidirect
33. C2×#13063250C22semidirect
34. C2×#13063249C22semidirect
35. C2×#13063248C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#103×C43C22semidirect
47. C43×#340C22semidirect
72. #13063305C2×C4semidirect
74. #13063304C2×C4semidirect
78. #13063301C2×C4semidirect
115. C22⋊Q8×C43C2×C4semidirect
329. #1873D43direct (N × H)
338. D43#1873direct (N × H)
366. C2×#103C2×D43semidirect
374. #340C2×D43semidirect
375. C43C2×#1873semidirect
411. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#117×D432
C2×#103×D432
C2×C22⋊C8×D432
#191349082
#191349072
#191349062
#191349052
#191349042
#340×D432
C43×#18732
C2×#187343