Finite Group Databasebeta

← D43×#1892 #25098256

Subgroups — D43×#1892 #25098256

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D43C211yesmaximal, characteristic
2C2×C22⋊Q8×D43C211yesmaximal, characteristic
3C2×#103×D43C212yesmaximal, complemented
4#380×D43C211yesmaximal, characteristic
5#19135019C211yesmaximal, characteristic, complemented
6#19135018C211yesmaximal, characteristic, complemented
7#19135017C212yesmaximal, complemented
8#19135016C211yesmaximal, characteristic, complemented
9#19135015C212yesmaximal, complemented
10#340×D43C212yesmaximal, complemented
11C43×#1892C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15C22×C8×D43—24no—
16C22×C8×D43—28no—
17C22×C8×D43C2212yes—
18C22×C8×D43C2212yes—
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063303—21no—
22C2×#13063302—21no—
23C2×#13063301C2211yescharacteristic
24C22⋊Q8×D43—24no—
25C22⋊Q8×D43C418yescomplemented
26C2×C4⋊C4×D43—21no—
27C2×C4⋊C4×D43C2212yes—
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30C2×C22⋊C4×D43—21no—
31C2×#13063250C2212yescomplemented
32C2×#13063249C2212yescomplemented
33C2×#13063248C2212yescomplemented
34#103×D43—28no—
35#14582759C2211yescharacteristic
36#14582758—21no—
37#14582757—21no—
38#14582756C2212yes—
39#95×D43—21no—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C23×C8×C43C2211yescharacteristic
44C2×C22⋊Q8×C43C2211yescharacteristic
45C2×#103×C43C2212yescomplemented
46C43×#380C2211yescharacteristic
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—21no—
59C22×C4×D43—21no—
60C22×C4×D43—22no—
61C22×C4×D43C2×C414yes—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D414yes—
65C22×C4×D43C2311yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8—22no—
68C22×C43⋊C8—24no—
69C22×C43⋊C8C2312yes—
70C2×C8×D43—232no—
71C2×C8×D43—24no—
72C2×C8×D43—24no—
73C2×C8×D43—24no—
74C2×C8×D43—24no—
75C2×C8×D43—24no—
76C2×C8×D43D418yes—
77#13063305—22no—
78#13063305C2×C414yescomplemented
79#13063304—22no—
80#13063304C2×C414yescomplemented
81#13063303—28no—
82#13063302—28no—
83#13063301—22no—
84#13063301C2×C414yescomplemented
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2312yes—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—22no—
92C4⋊C4×D43—28no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—24no—
95C4⋊C4×D43—24no—
96C4⋊C4×D43C2×C414yes—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—22no—
102C22⋊C4×D43—28no—
103C22⋊C4×D43—44no—
104#13063250—24no—
105#13063249—24no—
106#13063248—24no—
107C43⋊#95—21no—
108C43⋊#95—22no—
109C22×Q8×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43—22no—
112C22×C8×C43—24no—
113C22×C8×C43C2312yes—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43C2×C414yescomplemented
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2312yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#103×C43—24no—
122#95×C43—21no—
123C24×C43C2×D411yescharacteristic
124C23×D43—24no—
125C23×D43—24no—
126C23×D43C22⋊C414yes—
127C23×D43SD1614yes—
128C23×D43Q1614yes—
129C23×D43C2×D411yescharacteristic
130C23×D43C2×D411yescharacteristic
131C2×Q8×C43—21no—
132C2×Q8×C43—22no—
133C2×Q8×C43—22no—
134C2×Q8×C43C22×C412yes—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43C22⋊C414yes—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151Q8×D43—216no—
152Q8×D43—44no—
153Q8×D43—44no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—24no—
157C2×C4×D43—216no—
158C2×C4×D43—28no—
159C2×C4×D43—28no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43—44no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43C22⋊C414yes—
169C2×C4×D43C22⋊C414yes—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D414yes—
175C2×C4×D43#4114yes—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—44no—
181C2×Dic86C22×C412yes—
182C2×C8×C43—28no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C2×C8×C43C2×D414yes—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43C22×C412yes—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—42no—
193C22⋊Dic43—24no—
194C22⋊Dic43—42no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—44no—
198C4⋊Dic43—21no—
199C4⋊Dic43—24no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—24no—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—44no—
207C2×C43⋊C8—28no—
208C2×C43⋊C8—22no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8C2×D414yes—
211C8×D43—216no—
212C8×D43—216no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43C2×C22⋊C412yes—
216C23×C43C2×SD1612yes—
217C23×C43C2×Q1612yes—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—28no—
222C22×D43—28no—
223C22×D43—216no—
224C22×D43—216no—
225C22×D43#103116yescomplemented
226C22×D43C2×C22⋊C412yes—
227C22×D43C2×C22⋊C412yes—
228C22×D43#12114yes—
229C22×D43C2×SD1612yes—
230C22×D43C2×SD1612yes—
231C22×D43C2×Q1612yes—
232C22×D43C2×Q1612yes—
233C22×D43#13514yes—
234Q8×C43—24no—
235Q8×C43—41no—
236Q8×C43—41no—
237C2×C4×C43—22no—
238C2×C4×C43—24no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D412yes—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4112yes—
253C2×Dic43—22no—
254C2×Dic43—28no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43C2×C22⋊C412yes—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43#12114yes—
265C4×D43—28no—
266C4×D43—24no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—28no—
270C4×D43—48no—
271C4×D43—48no—
272C4×D43—88no—
273C4×D43C4×D418yes—
274C4×D43#12014yes—
275C4×D43#12314yes—
276Dic86—24no—
277Dic86—41no—
278Dic86—41no—
279Dic86—48no—
280C8×C43—24no—
281C43⋊C8—24no—
282C2×#1892—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—22no—
287C22×C43C2×#10314yescomplemented
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43C2×#12112yes—
290C22×C43C22×SD1611yescharacteristic
291C22×C43C22×Q1611yescharacteristic
292C22×C43C2×#13512yes—
293C2×D43—22no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—22no—
297C2×D43—232no—
298C2×D43#38614yes—
299C2×D43C2×#10314yes—
300C2×D43C2×#10314yescomplemented
301C2×D43#41614yes—
302C2×D43#46518yes—
303C2×D43#46718yes—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—82no—
308C4×C43C2×C4×D412yes—
309C4×C43C2×#12011yescharacteristic
310C4×C43C2×#12311yescharacteristic
311Dic43—22no—
312Dic43—42no—
313Dic43—42no—
314Dic43—82no—
315Dic43#38614yes—
316C24×C8—431no—
317C22×C22⋊Q8—431no—
318C22×#103—432no—
319C2×#380—431no—
320#1892—432no—
321#1892—431no—
322#1892—432no—
323#1892—431no—
324#1892—431no—
325#1892D4311yescharacteristic, direct product factor
326C2×#340—432no—
327C2×C43—24no—
328C2×C43C2×#38611yescharacteristic
329C2×C43C22×#10311yescharacteristic
330C2×C43C2×#41611yescharacteristic
331C2×C43C2×#46512yes—
332C2×C43C2×#46712yes—
333D43—24no—
334D43#189218yesdirect product factor
335C23×Q8—431no—
336C24×C4—431no—
337C23×C8—432no—
338C23×C8—431no—
339C23×C8—432no—
340C23×C8—868no—
341C23×C8—864no—
342C23×C8C2×D4311yescharacteristic
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—431no—
345C2×C22⋊Q8—438no—
346C2×C22⋊Q8—431no—
347C2×C22⋊Q8—861no—
348C2×C22⋊Q8—861no—
349C2×C22⋊Q8—864no—
350C2×C22⋊Q8C2×D4311yescharacteristic
351C22×C4⋊C4—431no—
352C22×C4⋊C4—432no—
353C22×C4⋊C4—861no—
354C22×C22⋊C4—861no—
355C22×C22⋊C4—861no—
356C2×#103—432no—
357C2×#103—432no—
358C2×#103—432no—
359C2×#103—868no—
360C2×#103C2×D4312yescomplemented
361#380—431no—
362#380—432no—
363#380—861no—
364#380—861no—
365#380C2×D4311yescharacteristic
366C2×#95—861no—
367#340—432no—
368#340—432no—
369#340—432no—
370#340C2×D4312yescomplemented
371C43C2×#189211yescharacteristic, complemented, Sylow
372C25—431no—
373C22×Q8—434no—
374C22×Q8—431no—
375C22×Q8—861no—
376C22×Q8—862no—
377C22×Q8—864no—
378C22×Q8—864no—
379C22×Q8C22×D4311yescharacteristic
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—434no—
383C23×C4—431no—
384C23×C4—434no—
385C23×C4—431no—
386C23×C4—431no—
387C23×C4—864no—
388C23×C4—864no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—862no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—22no—
394C22×C8—24no—
395C22×C8—432no—
396C22×C8—438no—
397C22×C8—864no—
398C22×C8—864no—
399C22×C8—864no—
400C22×C8—864no—
401C22×C8—8632no—
402C22×C8—864no—
403C22×C8—862no—
404C22×C8—864no—
405C22×C8C22×D4312yes—
406C22⋊Q8—22no—
407C22⋊Q8—434no—
408C22⋊Q8—434no—
409C22⋊Q8—434no—
410C22⋊Q8—868no—
411C22⋊Q8—868no—
412C22⋊Q8—862no—
413C22⋊Q8—862no—
414C22⋊Q8—862no—
415C22⋊Q8C4×D4314yescomplemented
416C2×C4⋊C4—21no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—434no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—868no—
422C2×C4⋊C4—864no—
423C2×C4⋊C4—864no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4C22×D4312yes—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—868no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—1724no—
440#103—24no—
441#103—864no—
442#103—864no—
443#103—864no—
444#95—21no—
445#95—862no—
446#95—861no—
447C24—431no—
448C24—434no—
449C24—434no—
450C24—434no—
451C24—431no—
452C24—864no—
453C24—864no—
454C24D4×D4311yescharacteristic
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—432no—
459C2×Q8—864no—
460C2×Q8—8616no—
461C2×Q8—861no—
462C2×Q8—862no—
463C2×Q8—862no—
464C2×Q8—1724no—
465C2×Q8—1724no—
466C2×Q8—1724no—
467C2×Q8C2×C4×D4312yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—431no—
474C22×C4—432no—
475C22×C4—434no—
476C22×C4—432no—
477C22×C4—434no—
478C22×C4—434no—
479C22×C4—431no—
480C22×C4—434no—
481C22×C4—434no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—868no—
485C22×C4—864no—
486C22×C4—8616no—
487C22×C4—868no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—864no—
491C22×C4—864no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4—1724no—
500C22×C4—1724no—
501C22×C4—1724no—
502C22×C4C2×C4×D4312yes—
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4312yes—
505C22×C4C23×D4311yescharacteristic
506C2×C8—28no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—434no—
510C2×C8—8616no—
511C2×C8—8616no—
512C2×C8—868no—
513C2×C8—862no—
514C2×C8—862no—
515C2×C8D4×D4314yes—
516C4⋊C4—24no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—432no—
521C4⋊C4—864no—
522C4⋊C4—864no—
523C4⋊C4—864no—
524C4⋊C4—864no—
525C4⋊C4—861no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—1724no—
529C4⋊C4C2×C4×D4312yes—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—864no—
533C22⋊C4—864no—
534C22⋊C4—864no—
535C22⋊C4—1724no—
536C22⋊C4—1722no—
537C23—22no—
538C23—22no—
539C23—432no—
540C23—434no—
541C23—432no—
542C23—432no—
543C23—434no—
544C23—432no—
545C23—4316no—
546C23—432no—
547C23—432no—
548C23—868no—
549C23—868no—
550C23—8616no—
551C23—8616no—
552C23—862no—
553C23—862no—
554C23C22⋊C4×D4312yes—
555C23SD16×D4312yes—
556C23Q16×D4312yes—
557C23C2×D4×D4311yescharacteristic
558Q8—24no—
559Q8—41no—
560Q8—41no—
561Q8—864no—
562Q8—1728no—
563Q8—1721no—
564Q8—1721no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—432no—
577C2×C4—434no—
578C2×C4—438no—
579C2×C4—434no—
580C2×C4—434no—
581C2×C4—432no—
582C2×C4—868no—
583C2×C4—868no—
584C2×C4—868no—
585C2×C4—862no—
586C2×C4—864no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3448no—
592C2×C4—1728no—
593C2×C4—1728no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4C22⋊C4×D4312yes—
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4312yes—
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4#41×D4312yes—
604C8—24no—
605C8—864no—
606C22—22no—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—434no—
611C22—434no—
612C22—438no—
613C22—438no—
614C22—434no—
615C22—434no—
616C22—8632no—
617C22—862no—
618C22—864no—
619C22—864no—
620C22—862no—
621C22#103×D4314yescomplemented
622C22C2×C22⋊C4×D4311yescharacteristic
623C22#121×D4312yes—
624C22C2×SD16×D4311yescharacteristic
625C22C2×Q16×D4311yescharacteristic
626C22#135×D4312yes—
627C4—22no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—434no—
632C4—862no—
633C4—3442no—
634C4—1722no—
635C4—1722no—
636C4C4×D4×D4312yes—
637C4#120×D4311yescharacteristic
638C4#123×D4311yescharacteristic
639C2—24no—
640C2—438no—
641C2—864no—
642C2#386×D4311yescharacteristic
643C2C2×#103×D4311yescharacteristic
644C2#416×D4311yescharacteristic
645C2#465×D4312yes—
646C2#467×D4312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1892C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1892D43
hypocenterC43C2×#1892
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
3. C2×#103×D43C2semidirect
5. #19135019C2semidirect
6. #19135018C2semidirect
7. #19135017C2semidirect
8. #19135016C2semidirect
9. #19135015C2semidirect
10. #340×D43C2semidirect
11. C43×#1892C2semidirect
25. C22⋊Q8×D43C4semidirect
31. C2×#13063250C22semidirect
32. C2×#13063249C22semidirect
33. C2×#13063248C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#103×C43C22semidirect
47. C43×#340C22semidirect
78. #13063305C2×C4semidirect
80. #13063304C2×C4semidirect
84. #13063301C2×C4semidirect
115. C22⋊Q8×C43C2×C4semidirect
225. C22×D43#103semidirect
287. C22×C43C2×#103semidirect
300. C2×D43C2×#103semidirect
325. #1892D43direct (N × H)
334. D43#1892direct (N × H)
360. C2×#103C2×D43semidirect
370. #340C2×D43semidirect
371. C43C2×#1892semidirect
415. C22⋊Q8C4×D43semidirect
621. C22#103×D43semidirect

Maximal subgroups

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

subgroupindex
C23×C8×D432
C2×C22⋊Q8×D432
C2×#103×D432
#380×D432
#191350192
#191350182
#191350172
#191350162
#191350152
#340×D432
C43×#18922
C2×#189243