Finite Group Databasebeta

← D43×#1554 #25064976

Subgroups — D43×#1554 #25064976

Order 11008.

974 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
1#533×D43C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic
3#431×D43C211yesmaximal, characteristic
4#19133306C211yesmaximal, characteristic, complemented
5#19133305C211yesmaximal, characteristic, complemented
6#19133304C212yesmaximal, complemented
7#19133303C211yesmaximal, characteristic, complemented
8#19133302C212yesmaximal, complemented
9#333×D43C212yesmaximal, complemented
10#332×D43C212yesmaximal, complemented
11C43×#1554C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583455—21no—
14#14583454C2211yescharacteristic
15#14583454C2211yescharacteristic
16#14583453—21no—
17#14583453C412yes—
18#14583452—21no—
19#14583451—21no—
20#14583451C412yes—
21C4⋊Q8×D43C2211yescharacteristic
22C4⋊Q8×D43C2211yescharacteristic
23#125×D43—21no—
24C22⋊Q8×D43—21no—
25C22⋊Q8×D43C412yes—
26C4×Q8×D43—21no—
27C4×Q8×D43C412yes—
28#117×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14582956C2211yescharacteristic
31#14582955C2212yes—
32#14582954—21no—
33#14582953—21no—
34#14582952C2211yescharacteristic
35#14582951C2212yes—
36#14582950—21no—
37#14582949—21no—
38C4⋊C8×D43C2212yes—
39C4⋊C8×D43C2212yes—
40C22⋊C8×D43—21no—
41C22⋊C8×D43—21no—
42#97×D43—21no—
43C4×C8×D43—21no—
44#14582648C2212yescomplemented
45#14582647C2212yescomplemented
46#14582647C2212yescomplemented
47#14582646C2212yescomplemented
48#14582645C2212yescomplemented
49#14582644C2212yescomplemented
50C43×#533C2211yescharacteristic
51C43×#432C2211yescharacteristic
52C43×#431C2211yescharacteristic
53C43×#333C2212yescomplemented
54C43×#332C2212yescomplemented
55C2×Q8×D43—21no—
56C2×Q8×D43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C2×C8×D43—22no—
61C2×C8×D43—22no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063324—21no—
65#13063324—21no—
66#13063324—21no—
67#13063324C2×C412yes—
68#13063323—21no—
69#13063323C2×C412yes—
70#13063317—21no—
71#13063316—21no—
72#13063316—21no—
73#13063315—22no—
74#13063315—22no—
75#13063305—21no—
76#13063305C2×C412yes—
77#13063304—21no—
78#13063304C2×C412yes—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301—21no—
84#13063301C2×C412yes—
85Q8×Dic43—21no—
86Q8×Dic43C2×C412yes—
87C4×Dic86—21no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86C2×C412yes—
91#13063290—22no—
92#13063290—22no—
93#13063290—21no—
94#13063290C2×C412yes—
95#13063284—21no—
96#13063283—21no—
97#13063283—21no—
98#13063282—22no—
99#13063281—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43C2×C412yes—
106C22⋊C4×D43—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)C2312yes—
120C4⋊(C43⋊C8)C2312yes—
121Dic43⋊C8—22no—
122Dic43⋊C8—22no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127#13063236—21no—
128#13063235—22no—
129C4×C43⋊C8—21no—
130C8×Dic43—22no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133#125×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43C2×C412yes—
136C4×Q8×C43—21no—
137C4×Q8×C43C2×C412yes—
138#117×C43—21no—
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43C2312yes—
141C4⋊C8×C43C2312yes—
142C22⋊C8×C43—21no—
143C22⋊C8×C43—21no—
144#97×C43—21no—
145C4×C8×C43—21no—
146C23×D43C22⋊C411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155Q8×D43—44no—
156Q8×D43—44no—
157C2×C4×D43—24no—
158C2×C4×D43—24no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—42no—
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×Dic86—21no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C42×C43—22no—
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2411yescharacteristic
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22×C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226C8×D43—44no—
227C8×D43—44no—
228C23×C43C2×C22⋊C411yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234Q8×C43—42no—
235Q8×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—44no—
269C4×D43—44no—
270C4×D43#13514yes—
271C4×D43#13714yes—
272Dic86—44no—
273Dic86—42no—
274Dic86—44no—
275Dic86—42no—
276C8×C43—42no—
277C8×C43—42no—
278C43⋊C8—42no—
279C43⋊C8—42no—
280C2×#1554—431nomaximal, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43C22×C22⋊C411yescharacteristic
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—44no—
289C2×D43#41312yes—
290C2×D43#41612yes—
291C2×D43#41912yes—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43C2×#13512yes—
299C4×C43C2×#13712yes—
300Dic43—21no—
301Dic43—21no—
302Dic43—21no—
303Dic43—21no—
304Dic43—42no—
305Dic43—42no—
306Dic43#41612yes—
307Dic43#41912yes—
308C2×#533—431no—
309C2×#432—431no—
310C2×#431—431no—
311#1554—431no—
312#1554—431no—
313#1554—432no—
314#1554—432no—
315#1554—431no—
316#1554D4311yescharacteristic, direct product factor
317C2×#333—432no—
318C2×#332—432no—
319C2×C43—41no—
320C2×C43C2×#41311yescharacteristic
321C2×C43C2×#41611yescharacteristic
322C2×C43C2×#41911yescharacteristic
323D43—41no—
324D43#155414yesdirect product factor
325#533—431no—
326#533—431no—
327#533—432no—
328#533—432no—
329#533—431no—
330#533—861no—
331#533—861no—
332#533—861no—
333#533—861no—
334#533C2×D4311yescharacteristic
335C2×C4⋊Q8—431no—
336C2×C4⋊Q8—431no—
337C2×#125—861no—
338C2×C22⋊Q8—432no—
339C2×C22⋊Q8—861no—
340C2×C4×Q8—432no—
341C2×C4×Q8—861no—
342C2×#117—861no—
343C22×C42—431no—
344#432—431no—
345#432—432no—
346#432—861no—
347#432—861no—
348#432C2×D4311yescharacteristic
349#431—431no—
350#431—432no—
351#431—861no—
352#431—861no—
353#431C2×D4311yescharacteristic
354C2×C4⋊C8—432no—
355C2×C4⋊C8—432no—
356C2×C22⋊C8—861no—
357C2×C22⋊C8—861no—
358C2×#97—861no—
359C2×C4×C8—861no—
360#333—432no—
361#333—432no—
362#333—432no—
363#333C2×D4312yescomplemented
364#332—432no—
365#332—432no—
366#332—432no—
367#332C2×D4312yescomplemented
368C43C2×#155411yescharacteristic, complemented, Sylow
369C22×Q8—432no—
370C22×Q8—861no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C22×C8—862no—
375C22×C8—862no—
376C4⋊Q8—432no—
377C4⋊Q8—432no—
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#125—21no—
387#125—862no—
388#125—862no—
389#125—861no—
390#125—861no—
391#125—861no—
392C22⋊Q8—21no—
393C22⋊Q8—432no—
394C22⋊Q8—432no—
395C22⋊Q8—432no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8C4×D4312yes—
404C4×Q8—21no—
405C4×Q8—432no—
406C4×Q8—432no—
407C4×Q8—432no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8C4×D4312yes—
416#117—21no—
417#117—862no—
418#117—862no—
419#117—861no—
420#117—861no—
421#117—861no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—861no—
428C2×C22⋊C4—862no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—862no—
441C2×C42C22×D4311yescharacteristic
442C4⋊C8—432no—
443C4⋊C8—432no—
444C4⋊C8—862no—
445C4⋊C8—862no—
446C4⋊C8C22×D4312yes—
447C4⋊C8C22×D4312yes—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—862no—
451C22⋊C8—862no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454#97—21no—
455#97—862no—
456#97—861no—
457C4×C8—21no—
458C4×C8—862no—
459C4×C8—861no—
460C24—431no—
461C2×Q8—21no—
462C2×Q8—432no—
463C2×Q8—862no—
464C2×Q8—862no—
465C2×Q8—861no—
466C2×Q8—1724no—
467C2×Q8—1724no—
468C2×Q8C2×C4×D4312yes—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—864no—
485C22×C4—864no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—1722no—
489C22×C4C2×C4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—1724no—
497C2×C8—1724no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—432no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4C2×C4×D4312yes—
518C22⋊C4—22no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C42—22no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—862no—
536C42—862no—
537C42—862no—
538C42C2×C4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42D4×D4311yescharacteristic
541C42C23×D4311yescharacteristic
542C23—431no—
543C23—431no—
544C23—862no—
545C23—862no—
546C23—862no—
547C23C22⋊C4×D4311yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—1722no—
551Q8—1724no—
552Q8—1724no—
553Q8—1722no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—434no—
562C2×C4—434no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1724no—
582C2×C4—1724no—
583C2×C4—1721no—
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22⋊C4×D4311yescharacteristic
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C8—42no—
591C8—42no—
592C8—1722no—
593C8—1722no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—432no—
598C22—432no—
599C22—432no—
600C22—861no—
601C22—861no—
602C22—861no—
603C22—1724no—
604C22C2×C22⋊C4×D4311yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—42no—
610C4—42no—
611C4—432no—
612C4—432no—
613C4—861no—
614C4—861no—
615C4—861no—
616C4—861no—
617C4—1722no—
618C4—1722no—
619C4#135×D4312yes—
620C4#137×D4312yes—
621C2—41no—
622C2—434no—
623C2—1721no—
624C2#413×D4311yescharacteristic
625C2#416×D4311yescharacteristic
626C2#419×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1554C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1554D43
hypocenterC43C2×#1554
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
4. #19133306C2semidirect
5. #19133305C2semidirect
6. #19133304C2semidirect
7. #19133303C2semidirect
8. #19133302C2semidirect
9. #333×D43C2semidirect
10. #332×D43C2semidirect
11. C43×#1554C2semidirect
44. #14582648C22semidirect
45. #14582647C22semidirect
46. #14582647C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
53. C43×#333C22semidirect
54. C43×#332C22semidirect
316. #1554D43direct (N × H)
324. D43#1554direct (N × H)
363. #333C2×D43semidirect
367. #332C2×D43semidirect
368. C43C2×#1554semidirect

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
#191333062
#191333052
#191333042
#191333032
#191333022
#333×D432
#332×D432
C43×#15542
C2×#155443