Finite Group Databasebeta

← D43×#1497 #25063218

Subgroups — D43×#1497 #25063218

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic
3#431×D43C211yesmaximal, characteristic
4#19133069C211yesmaximal, characteristic, complemented
5#19133068C211yesmaximal, characteristic, complemented
6#19133067C211yesmaximal, characteristic, complemented
7#19133066C214yesmaximal, complemented
8Q8⋊C8×D43C214yesmaximal, complemented
9C43×#1497C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic
13#14583454C411yescharacteristic
14#14583453—21no—
15#14583453C2212yes—
16#14583452—21no—
17#14583451—21no—
18#14583451C412yes—
19C4⋊Q8×D43C411yescharacteristic
20C4⋊Q8×D43C411yescharacteristic
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C412yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C2212yes—
26#117×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582955C2212yes—
30#14582954—21no—
31#14582953—21no—
32#14582952C2211yescharacteristic
33#14582951—21no—
34#14582950C2212yes—
35#14582949—21no—
36C4⋊C8×D43—21no—
37C4⋊C8×D43C2212yes—
38C22⋊C8×D43—21no—
39C22⋊C8×D43—21no—
40#97×D43—21no—
41C4×C8×D43C2212yes—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×C8×D43—22no—
55C2×C8×D43—22no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063324—21no—
59#13063324—21no—
60#13063324—21no—
61#13063324C2×C412yes—
62#13063323—21no—
63#13063323C2×C412yes—
64#13063317—21no—
65#13063316—21no—
66#13063316—21no—
67#13063315—22no—
68#13063315—22no—
69#13063305—21no—
70#13063305C2×C412yes—
71#13063304—21no—
72#13063304C2×C412yes—
73#13063303—22no—
74#13063303—22no—
75#13063302—22no—
76#13063302—22no—
77#13063301—21no—
78#13063301C2×C412yes—
79Q8×Dic43—21no—
80Q8×Dic43C2×C412yes—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86C2312yes—
85#13063290—21no—
86#13063290—22no—
87#13063290—22no—
88#13063290C2×C412yes—
89#13063284—21no—
90#13063283—21no—
91#13063283—21no—
92#13063282—22no—
93#13063281—22no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43C2×C412yes—
100C22⋊C4×D43—22no—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C42×D43—22no—
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)C2312yes—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236—21no—
122#13063235—22no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2×C412yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2312yes—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2312yes—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149Q8×D43—28no—
150Q8×D43—44no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—42no—
156C2×C4×D43C22⋊C411yescharacteristic
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86C22×C412yes—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43C22×C412yes—
180C22⋊C4×C43—22no—
181C42×C43—22no—
182C42×C43C22×C411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2411yescharacteristic
186C22⋊Dic43—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203C4×Dic43—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43C22⋊C411yescharacteristic
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22×C411yescharacteristic
213C4×Dic43C22×C411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C2×C43⋊C8—22no—
219C2×C43⋊C8—22no—
220C8×D43—44no—
221C8×D43—44no—
222C23×C43C2×C22⋊C411yescharacteristic
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43C2×C22⋊C411yescharacteristic
227C22×D43C2×C22⋊C411yescharacteristic
228Q8×C43—24no—
229Q8×C43—42no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43C2×C22⋊C411yescharacteristic
247C2×Dic43C2×C22⋊C411yescharacteristic
248C2×Dic43C2×C22⋊C411yescharacteristic
249C2×Dic43C2×C22⋊C411yescharacteristic
250C2×Dic43C2×C22⋊C411yescharacteristic
251C2×Dic43C2×C22⋊C411yescharacteristic
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—44no—
263C4×D43—44no—
264C4×D43#13114yes—
265C4×D43#13714yes—
266Dic86—24no—
267Dic86—44no—
268Dic86—42no—
269Dic86—44no—
270C8×C43—42no—
271C8×C43—42no—
272C43⋊C8—42no—
273C43⋊C8—42no—
274C2×#1497—431nomaximal, Sylow
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43C22×C22⋊C411yescharacteristic
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—44no—
283C2×D43#40812yes—
284C2×D43#41912yes—
285C2×D43#42112yes—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43C2×#13112yes—
293C4×C43C2×#13712yes—
294Dic43—21no—
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—42no—
299Dic43—42no—
300Dic43#40812yes—
301Dic43#41912yes—
302C2×#533—431no—
303C2×#432—431no—
304C2×#431—431no—
305#1497—431no—
306#1497—431no—
307#1497—434no—
308#1497—431no—
309#1497D4311yescharacteristic, direct product factor
310C2×Q8⋊C8—434no—
311C2×C43—41no—
312C2×C43C2×#40811yescharacteristic
313C2×C43C2×#41911yescharacteristic
314C2×C43C2×#42111yescharacteristic
315D43—41no—
316D43#149714yesdirect product factor
317#533—431no—
318#533—431no—
319#533—432no—
320#533—432no—
321#533—431no—
322#533—861no—
323#533—861no—
324#533—861no—
325#533—861no—
326#533C2×D4311yescharacteristic
327C2×C4⋊Q8—431no—
328C2×C4⋊Q8—431no—
329C2×#125—861no—
330C2×C22⋊Q8—432no—
331C2×C22⋊Q8—861no—
332C2×C4×Q8—432no—
333C2×C4×Q8—861no—
334C2×#117—861no—
335C22×C42—431no—
336#432—431no—
337#432—432no—
338#432—861no—
339#432—861no—
340#432C2×D4311yescharacteristic
341#431—431no—
342#431—432no—
343#431—861no—
344#431—861no—
345#431C2×D4311yescharacteristic
346C2×C4⋊C8—432no—
347C2×C4⋊C8—861no—
348C2×C22⋊C8—861no—
349C2×C22⋊C8—861no—
350C2×#97—861no—
351C2×C4×C8—432no—
352Q8⋊C8—434no—
353Q8⋊C8—434no—
354Q8⋊C8—434no—
355Q8⋊C8C2×D4314yescomplemented
356C43C2×#149711yescharacteristic, complemented, Sylow
357C22×Q8—432no—
358C22×Q8—861no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—431no—
362C22×C8—862no—
363C22×C8—862no—
364C4⋊Q8—432no—
365C4⋊Q8—432no—
366C4⋊Q8—431no—
367C4⋊Q8—431no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8C4×D4311yescharacteristic
373C4⋊Q8C4×D4311yescharacteristic
374#125—21no—
375#125—862no—
376#125—862no—
377#125—861no—
378#125—861no—
379#125—861no—
380C22⋊Q8—21no—
381C22⋊Q8—432no—
382C22⋊Q8—432no—
383C22⋊Q8—432no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C22⋊Q8—861no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C22⋊Q8C4×D4312yes—
392C4×Q8—21no—
393C4×Q8—432no—
394C4×Q8—432no—
395C4×Q8—432no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—861no—
400C4×Q8—862no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8C22×D4312yes—
404#117—21no—
405#117—862no—
406#117—862no—
407#117—861no—
408#117—861no—
409#117—861no—
410C2×C4⋊C4—432no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—861no—
416C2×C22⋊C4—862no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—862no—
429C2×C42C22×D4311yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—432no—
432C4⋊C8—862no—
433C4⋊C8—862no—
434C4⋊C8—861no—
435C4⋊C8C22×D4312yes—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—862no—
439C22⋊C8—862no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442#97—21no—
443#97—862no—
444#97—861no—
445C4×C8—432no—
446C4×C8—862no—
447C4×C8C22×D4312yes—
448C24—431no—
449C2×Q8—21no—
450C2×Q8—432no—
451C2×Q8—862no—
452C2×Q8—862no—
453C2×Q8—868no—
454C2×Q8—861no—
455C2×Q8—1724no—
456C2×Q8C2×C4×D4312yes—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—1722no—
477C22×C4C2×C4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—862no—
483C2×C8—862no—
484C2×C8—1724no—
485C2×C8—1724no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—432no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—862no—
503C4⋊C4—861no—
504C4⋊C4—862no—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—22no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C42—22no—
511C42—431no—
512C42—431no—
513C42—431no—
514C42—431no—
515C42—431no—
516C42—431no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—862no—
524C42—862no—
525C42—862no—
526C42C2×C4×D4311yescharacteristic
527C42D4×D4311yescharacteristic
528C42D4×D4311yescharacteristic
529C42C23×D4311yescharacteristic
530C23—431no—
531C23—431no—
532C23—862no—
533C23—862no—
534C23—862no—
535C23C22⋊C4×D4311yescharacteristic
536Q8—24no—
537Q8—42no—
538Q8—864no—
539Q8—1722no—
540Q8—1724no—
541Q8—1724no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—431no—
548C2×C4—431no—
549C2×C4—434no—
550C2×C4—434no—
551C2×C4—431no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1724no—
570C2×C4—1724no—
571C2×C4—1721no—
572C2×C4C22⋊C4×D4311yescharacteristic
573C2×C4C22⋊C4×D4311yescharacteristic
574C2×C4C22⋊C4×D4311yescharacteristic
575C2×C4C22×C4×D4311yescharacteristic
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C8—42no—
579C8—42no—
580C8—1722no—
581C8—1722no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—432no—
586C22—432no—
587C22—432no—
588C22—861no—
589C22—861no—
590C22—861no—
591C22—1724no—
592C22C2×C22⋊C4×D4311yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—42no—
598C4—42no—
599C4—432no—
600C4—432no—
601C4—861no—
602C4—861no—
603C4—861no—
604C4—861no—
605C4—1722no—
606C4—1722no—
607C4#131×D4312yes—
608C4#137×D4312yes—
609C2—41no—
610C2—434no—
611C2—1721no—
612C2#408×D4311yescharacteristic
613C2#419×D4311yescharacteristic
614C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1497C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1497D43
hypocenterC43C2×#1497
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #19133069C2semidirect
5. #19133068C2semidirect
6. #19133067C2semidirect
7. #19133066C2semidirect
8. Q8⋊C8×D43C2semidirect
9. C43×#1497C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
309. #1497D43direct (N × H)
316. D43#1497direct (N × H)
355. Q8⋊C8C2×D43semidirect
356. C43C2×#1497semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#432×D432
#431×D432
#191330692
#191330682
#191330672
#191330662
Q8⋊C8×D432
C43×#14972
C2×#149743