Finite Group Databasebeta

← D43×#2001 #25123391

Subgroups — D43×#2001 #25123391

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D43C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D43C212yesmaximal
3C2×#103×D43C212yesmaximal, complemented
4C2×C22⋊C8×D43C211yesmaximal, characteristic
5#19135606C211yesmaximal, characteristic, complemented
6#19135605C211yesmaximal, characteristic, complemented
7#19135604C212yesmaximal, complemented
8#19135603C212yesmaximal, complemented
9#19135602C211yesmaximal, characteristic, complemented
10#340×D43C211yesmaximal, characteristic, complemented
11C43×#2001C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2212yes—
13C23×C4×D43C2211yescharacteristic
14C22×Dic172C2211yescharacteristic, complemented
15C22×#10621885C2212yescomplemented
16C2×Q16×D43—28no—
17C2×Q16×D43—24no—
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063305C2212yes—
21C2×#13063304C2212yes—
22C2×#13063303—22no—
23C2×#13063302—22no—
24C2×#13063301C2212yes—
25C22⋊Q8×D43—28no—
26C22⋊Q8×D43—28no—
27C2×C4⋊C4×D43—22no—
28C2×C4⋊C4×D43C2212yes—
29C2×C22⋊C4×D43—22no—
30C2×#13063250C2212yescomplemented
31C2×#13063249C2212yescomplemented
32C2×#13063248C2212yescomplemented
33#103×D43—28no—
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C22⋊C8×D43—24no—
38#14582662C2211yescharacteristic, complemented
39#14582661C2212yescomplemented
40C22×Q16×C43C2211yescharacteristic, complemented
41C2×C22⋊Q8×C43C2212yes—
42C2×#103×C43C2212yescomplemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#340C2211yescharacteristic, complemented
45C24×D43D411yescharacteristic
46C22×Dic86—22no—
47C22×Dic86C2312yes—
48C2×Q8×D43—24no—
49C2×Q8×D43—24no—
50C2×Q8×D43—24no—
51C2×Q8×D43—24no—
52C2×Q8×D43—24no—
53C2×Q8×D43D418yes—
54C23×Dic43D411yescharacteristic
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—24no—
59C22×C4×D43—24no—
60C22×C4×D43—22no—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×Dic172—24no—
66C2×Dic172—22no—
67C2×#10621885—24no—
68C2×#10621885—24no—
69C2×#10621885—24no—
70Q16×D43—232no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—24no—
74C2×C8×D43—22no—
75C2×C8×D43—24no—
76C2×C8×D43D414yes—
77#13063305—24no—
78#13063305—24no—
79#13063304—24no—
80#13063304—24no—
81#13063303—216no—
82#13063302—216no—
83#13063301—24no—
84#13063301—24no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43C2312yes—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C4⋊C4×D43—216no—
91C4⋊C4×D43—24no—
92C4⋊C4×D43D418yes—
93C2×C22⋊Dic43—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C22⋊C4×D43—216no—
97#13063250—24no—
98#13063249—24no—
99#13063248—24no—
100C22⋊(C43⋊C8)—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103C22×Q8×C43C2312yes—
104C23×C4×C43C2311yescharacteristic
105C2×Q16×C43—24no—
106C2×Q16×C43—22no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—24no—
110C22⋊Q8×C43—24no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43C2312yes—
113C2×C22⋊C4×C43—22no—
114#103×C43—24no—
115C22⋊C8×C43—22no—
116C24×C43C2×D411yescharacteristic
117C23×D43—24no—
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—24no—
121C23×D43Q1614yescomplemented
122C23×D43C2×D411yescharacteristic
123C23×D43C2×D411yescharacteristic
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43C2×D414yes—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—24no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144Q8×D43—216no—
145Q8×D43—216no—
146Q8×D43—48no—
147Q8×D43—48no—
148C2×C4×D43—21no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—21no—
152C2×C4×D43—24no—
153C2×C4×D43—22no—
154C2×C4×D43—28no—
155C2×C4×D43—28no—
156C2×C4×D43—24no—
157C2×C4×D43—22no—
158C2×C4×D43—44no—
159C2×C4×D43—48no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43C2×D414yes—
166C2×C4×D43C2×D414yes—
167C2×C4×D43C2×D412yes—
168C2×C4×D43#4112yes—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—28no—
175C2×Dic86—44no—
176C2×Dic86—44no—
177C2×Dic86C2×D414yes—
178Q16×C43—28no—
179C2×C8×C43—22no—
180C2×C8×C43—21no—
181C2×C8×C43—22no—
182C2×C8×C43C2×D412yes—
183C4⋊C4×C43—28no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C2×D414yes—
186C22⋊C4×C43—28no—
187C22⋊Dic43—28no—
188#10621885—216no—
189(C2×D43)⋊C4—28no—
190(C2×D43)⋊C4—28no—
191C4⋊Dic43—28no—
192C4⋊Dic43—22no—
193C4⋊Dic43C2×D414yes—
194Dic43⋊C4—28no—
195Dic43⋊C4—28no—
196Dic43⋊C4—28no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8C2×D412yes—
201Dic172—28no—
202C8×D43—28no—
203C8×D43—44no—
204C23×C43—22no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—22no—
208C23×C43C2×Q1612yescomplemented
209C23×C43C22×D411yescharacteristic
210C22×D43—22no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—22no—
214C22×D43—216no—
215C22×D43—28no—
216C22×D43—44no—
217C22×D43—48no—
218C22×D43—44no—
219C22×D43#12014yes—
220C22×D43#12112yes—
221C22×D43C2×Q1612yes—
222C22×D43C2×Q1612yescomplemented
223C22×D43#13512yes—
224C22×D43#13714yes—
225Q8×C43—24no—
226Q8×C43—24no—
227Q8×C43—42no—
228Q8×C43—42no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—21no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—41no—
240C2×C4×C43C22×D412yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D412yes—
243C2×C4×C43C2×#4111yescharacteristic
244C2×Dic43—24no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—21no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—44no—
253C2×Dic43#12014yes—
254C2×Dic43#12112yes—
255C4×D43—44no—
256C4×D43—416no—
257C4×D43—416no—
258C4×D43—41no—
259C4×D43—42no—
260C4×D43—41no—
261C4×D43—44no—
262C4×D43#12014yes—
263C4×D43#12118yes—
264C4×D43#12714yes—
265Dic86—24no—
266Dic86—24no—
267Dic86—42no—
268Dic86—42no—
269Dic86—416no—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—22no—
273C43⋊C8—41no—
274C2×#2001—431nomaximal, Sylow
275C22×C43—24no—
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43C2×#12012yes—
281C22×C43C2×#12111yescharacteristic
282C22×C43C22×Q1611yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13712yes—
285C2×D43—24no—
286C2×D43—22no—
287C2×D43—41no—
288C2×D43—42no—
289C2×D43—41no—
290C2×D43—416no—
291C2×D43#39214yes—
292C2×D43#45118yes—
293C2×D43#45218yes—
294C2×D43#46714yes—
295C2×D43#47014yes—
296C4×C43—44no—
297C4×C43—41no—
298C4×C43—44no—
299C4×C43C2×#12011yescharacteristic
300C4×C43C2×#12112yes—
301C4×C43C2×#12711yescharacteristic
302Dic43—44no—
303Dic43—41no—
304Dic43—44no—
305Dic43#39214yes—
306C23×Q16—431no—
307C22×C22⋊Q8—432no—
308C22×#103—432no—
309C22×C22⋊C8—431no—
310#2001—432no—
311#2001—431no—
312#2001—431no—
313#2001—431no—
314#2001—432no—
315#2001D4311yescharacteristic, direct product factor
316C2×#340—431no—
317C2×C43—42no—
318C2×C43C2×#39211yescharacteristic
319C2×C43C2×#45112yes—
320C2×C43C2×#45212yes—
321C2×C43C2×#46711yescharacteristic
322C2×C43C2×#47011yescharacteristic
323D43—42no—
324D43#200118yesdirect product factor
325C23×Q8—432no—
326C24×C4—431no—
327C22×Q16—432no—
328C22×Q16—431no—
329C22×Q16—864no—
330C22×Q16—868no—
331C22×Q16C2×D4311yescharacteristic, complemented
332C23×C8—431no—
333C23×C8—431no—
334C2×C22⋊Q8—432no—
335C2×C22⋊Q8—432no—
336C2×C22⋊Q8—432no—
337C2×C22⋊Q8—862no—
338C2×C22⋊Q8—862no—
339C2×C22⋊Q8—868no—
340C2×C22⋊Q8—868no—
341C2×C22⋊Q8C2×D4312yes—
342C22×C4⋊C4—432no—
343C22×C4⋊C4—862no—
344C22×C22⋊C4—862no—
345C2×#103—432no—
346C2×#103—432no—
347C2×#103—432no—
348C2×#103—868no—
349C2×#103C2×D4312yescomplemented
350C2×C22⋊C8—431no—
351C2×C22⋊C8—431no—
352C2×C22⋊C8—431no—
353C2×C22⋊C8—864no—
354C2×C22⋊C8C2×D4311yescharacteristic
355#340—431no—
356#340—432no—
357#340C2×D4311yescharacteristic, complemented
358C43C2×#200111yescharacteristic, complemented, Sylow
359C25—431no—
360C22×Q8—438no—
361C22×Q8—432no—
362C22×Q8—862no—
363C22×Q8—864no—
364C22×Q8—864no—
365C22×Q8—864no—
366C22×Q8—864no—
367C22×Q8—864no—
368C22×Q8C22×D4312yes—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—864no—
375C23×C4—864no—
376C23×C4—862no—
377C23×C4—862no—
378C23×C4—862no—
379C23×C4—862no—
380C23×C4C22×D4311yescharacteristic
381C2×Q16—24no—
382C2×Q16—22no—
383C2×Q16—864no—
384C2×Q16—864no—
385C2×Q16—8632no—
386C2×Q16—864no—
387C2×Q16—864no—
388C2×Q16—862no—
389C22×C8—431no—
390C22×C8—434no—
391C22×C8—431no—
392C22×C8—864no—
393C22×C8—862no—
394C22×C8—864no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—8616no—
400C22⋊Q8—864no—
401C22⋊Q8—8616no—
402C22⋊Q8—864no—
403C22⋊Q8—864no—
404C22⋊Q8—864no—
405C22⋊Q8—864no—
406C22⋊Q8—864no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—438no—
410C2×C4⋊C4—864no—
411C2×C4⋊C4—8616no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4C22×D4312yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—8616no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—862no—
421C2×C22⋊C4—862no—
422#103—24no—
423#103—864no—
424#103—864no—
425#103—864no—
426C22⋊C8—22no—
427C22⋊C8—862no—
428C22⋊C8—862no—
429C22⋊C8—862no—
430C24—431no—
431C24—434no—
432C24—431no—
433C24—864no—
434C24—862no—
435C24—862no—
436C24—864no—
437C24D4×D4311yescharacteristic
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—434no—
444C2×Q8—868no—
445C2×Q8—8616no—
446C2×Q8—8616no—
447C2×Q8—862no—
448C2×Q8—862no—
449C2×Q8—862no—
450C2×Q8—862no—
451C2×Q8—862no—
452C2×Q8—1724no—
453C2×Q8—1724no—
454C2×Q8—1728no—
455C2×Q8—1728no—
456C2×Q8D4×D4314yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—434no—
465C22×C4—434no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—431no—
469C22×C4—864no—
470C22×C4—862no—
471C22×C4—868no—
472C22×C4—868no—
473C22×C4—864no—
474C22×C4—862no—
475C22×C4—864no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—861no—
483C22×C4—1724no—
484C22×C4—1728no—
485C22×C4—1724no—
486C22×C4—1724no—
487C22×C4—1724no—
488C22×C4—1724no—
489C22×C4—1724no—
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—28no—
493Q16—868no—
494Q16—8616no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—22no—
498C2×C8—432no—
499C2×C8—868no—
500C2×C8—862no—
501C2×C8—861no—
502C2×C8—862no—
503C2×C8—1724no—
504C2×C8D4×D4312yes—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—434no—
508C4⋊C4—868no—
509C4⋊C4—868no—
510C4⋊C4—868no—
511C4⋊C4—868no—
512C4⋊C4—862no—
513C4⋊C4D4×D4314yes—
514C22⋊C4—28no—
515C22⋊C4—868no—
516C22⋊C4—868no—
517C22⋊C4—868no—
518C23—22no—
519C23—21no—
520C23—21no—
521C23—22no—
522C23—434no—
523C23—432no—
524C23—432no—
525C23—432no—
526C23—434no—
527C23—432no—
528C23—8616no—
529C23—868no—
530C23—862no—
531C23—861no—
532C23—861no—
533C23—862no—
534C23—1724no—
535C23—1724no—
536C23—1728no—
537C23Q16×D4312yescomplemented
538C23C2×D4×D4311yescharacteristic
539Q8—24no—
540Q8—24no—
541Q8—42no—
542Q8—42no—
543Q8—864no—
544Q8—864no—
545Q8—17216no—
546Q8—1722no—
547Q8—1722no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—434no—
560C2×C4—432no—
561C2×C4—434no—
562C2×C4—438no—
563C2×C4—434no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—1724no—
569C2×C4—1724no—
570C2×C4—17216no—
571C2×C4—17216no—
572C2×C4—1724no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4C2×D4×D4312yes—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4312yes—
583C2×C4#41×D4311yescharacteristic
584C8—22no—
585C8—41no—
586C8—862no—
587C8—1721no—
588C22—24no—
589C22—22no—
590C22—41no—
591C22—42no—
592C22—41no—
593C22—434no—
594C22—438no—
595C22—438no—
596C22—434no—
597C22—434no—
598C22—864no—
599C22—862no—
600C22—17216no—
601C22—1721no—
602C22—1722no—
603C22—1721no—
604C22#120×D4312yes—
605C22#121×D4311yescharacteristic
606C22C2×Q16×D4311yescharacteristic
607C22#135×D4311yescharacteristic
608C22#137×D4312yes—
609C4—44no—
610C4—41no—
611C4—44no—
612C4—434no—
613C4—1724no—
614C4—1721no—
615C4—1724no—
616C4#120×D4311yescharacteristic
617C4#121×D4312yes—
618C4#127×D4311yescharacteristic
619C2—42no—
620C2—438no—
621C2—1722no—
622C2#392×D4311yescharacteristic
623C2#451×D4312yes—
624C2#452×D4312yes—
625C2#467×D4311yescharacteristic
626C2#470×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2001C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2001D43
hypocenterC43C2×#2001
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D43C2semidirect
3. C2×#103×D43C2semidirect
5. #19135606C2semidirect
6. #19135605C2semidirect
7. #19135604C2semidirect
8. #19135603C2semidirect
9. #19135602C2semidirect
10. #340×D43C2semidirect
11. C43×#2001C2semidirect
14. C22×Dic172C22semidirect
15. C22×#10621885C22semidirect
30. C2×#13063250C22semidirect
31. C2×#13063249C22semidirect
32. C2×#13063248C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. C22×Q16×C43C22semidirect
42. C2×#103×C43C22semidirect
44. C43×#340C22semidirect
121. C23×D43Q16semidirect
208. C23×C43C2×Q16semidirect
222. C22×D43C2×Q16semidirect
315. #2001D43direct (N × H)
324. D43#2001direct (N × H)
331. C22×Q16C2×D43semidirect
349. C2×#103C2×D43semidirect
357. #340C2×D43semidirect
358. C43C2×#2001semidirect
537. C23Q16×D43semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D432
C2×C22⋊Q8×D432
C2×#103×D432
C2×C22⋊C8×D432
#191356062
#191356052
#191356042
#191356032
#191356022
#340×D432
C43×#20012
C2×#200143