Finite Group Databasebeta

← D43×#2643 #25263044

Subgroups — D43×#2643 #25263044

Order 11008.

2546 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140553C211yesmaximal, characteristic, complemented
2#19140552C211yesmaximal, characteristic, complemented
3#19140551C213yesmaximal, complemented
4#19140550C213yesmaximal, complemented
5#19140549C213yesmaximal, complemented
6#19140548C211yesmaximal, characteristic, complemented
7#19140547C213yesmaximal, complemented
8#401×D43C211yesmaximal, characteristic, complemented
9#400×D43C213yesmaximal, complemented
10#397×D43C213yesmaximal, complemented
11#396×D43C211yesmaximal, characteristic, complemented
12#386×D43C213yesmaximal
13#385×D43C213yesmaximal, complemented
14C2×#95×D43C211yesmaximal, characteristic, complemented
15C43×#2643C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C4×D43C2213yes—
18C2×C4⋊C4×D43C2213yes—
19C2×C4⋊C4×D43C2213yes—
20C2×C22⋊C4×D43C2213yes—
21C2×C22⋊C4×D43C2213yes—
22C2×C22⋊C4×D43C2213yes—
23C43⋊#401C2213yescomplemented
24C43⋊#401C2211yescharacteristic, complemented
25C43⋊#401C2213yescomplemented
26#14582841C2213yescomplemented
27#14582841C2213yescomplemented
28#14582840C2213yescomplemented
29#14582840C2213yescomplemented
30#14582839C2213yescomplemented
31#14582838C2213yescomplemented
32#14582837C2213yescomplemented
33#14582828C2213yescomplemented
34#14582828C2213yescomplemented
35#14582827C2213yescomplemented
36#14582827C2213yescomplemented
37#14582826C2213yescomplemented
38#14582825C2213yescomplemented
39#14582824C2213yescomplemented
40#14582823C2211yescharacteristic, complemented
41#14582822C2213yescomplemented
42#14582821C2213yescomplemented
43#14582779C2213yes—
44#14582778C2213yes—
45#14582777C2213yes—
46#14582777C2213yes—
47#14582776C2213yes—
48#14582775C2213yes—
49#14582775C2213yes—
50#14582774C2213yescomplemented
51#14582773C2213yescomplemented
52#14582773C2213yescomplemented
53#14582772C2213yescomplemented
54#14582771C2213yescomplemented
55#14582770C2213yescomplemented
56#14582770C2213yescomplemented
57C2×C43⋊#95C2213yescomplemented
58#95×D43C2211yescharacteristic
59#95×D43C2213yes—
60#95×D43C2213yes—
61#95×D43C2213yes—
62#95×D43C2213yes—
63#95×D43C2213yes—
64#95×D43C2213yescomplemented
65#95×D43C2211yescharacteristic, complemented
66C43×#401C2211yescharacteristic, complemented
67C43×#400C2213yescomplemented
68C43×#397C2213yescomplemented
69C43×#396C2211yescharacteristic, complemented
70C43×#386C2213yes—
71C43×#385C2213yescomplemented
72C2×#95×C43C2211yescharacteristic, complemented
73C24×D43C2311yescharacteristic
74C24×D43C2311yescharacteristic
75C22×D172C2311yescharacteristic
76C22×C22⋊D43C2311yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C2×D4×D43—212no—
79C23×Dic43C2313yes—
80C22×C4×D43—212no—
81C22×C4×D43—46no—
82C22×C4×D43—46no—
83C22×C4×D43C2313yes—
84C22×C4×D43C2313yes—
85C22×C4×D43C2313yes—
86C22×C4×D43C2313yes—
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2313yes—
89C22×C4×D43C2313yes—
90C2×C4⋊Dic43C2313yes—
91C2×C4⋊Dic43C2313yes—
92C2×Dic43⋊C4C2313yes—
93C2×Dic43⋊C4C2313yes—
94C2×Dic43⋊C4C2313yes—
95C2×Dic43⋊C4C2313yes—
96C4⋊C4×D43—46no—
97C4⋊C4×D43—46no—
98C2×C22⋊Dic43C2313yes—
99C2×C22⋊Dic43C2313yes—
100C2×C22⋊Dic43C2313yes—
101C2×(C2×D43)⋊C4C2313yes—
102C2×(C2×D43)⋊C4C2313yes—
103C2×(C2×D43)⋊C4C2313yes—
104C2×(C2×D43)⋊C4C2313yes—
105C2×(C2×D43)⋊C4C2313yes—
106C2×(C2×D43)⋊C4C2313yes—
107C22⋊C4×D43—212no—
108C22⋊C4×D43—46no—
109C22⋊C4×D43—46no—
110C43⋊#95C2313yes—
111C43⋊#95C2313yes—
112C43⋊#95C2313yes—
113C43⋊#95C2313yes—
114C43⋊#95C2313yes—
115C43⋊#95C2313yes—
116C43⋊#95C2313yes—
117C43⋊#95C2313yes—
118C43⋊#95C2313yes—
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2313yes—
124C43⋊#95C2313yes—
125C43⋊#95C2313yes—
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43C2313yes—
128C2×C4⋊C4×C43C2313yes—
129C2×C4⋊C4×C43C2313yes—
130C2×C22⋊C4×C43C2313yes—
131C2×C22⋊C4×C43C2313yes—
132C2×C22⋊C4×C43C2313yes—
133#95×C43C2311yescharacteristic
134#95×C43C2313yes—
135#95×C43C2313yes—
136#95×C43C2313yes—
137#95×C43C2313yes—
138#95×C43C2313yes—
139C24×C43C2411yescharacteristic
140C24×C43C2411yescharacteristic
141C23×D43—26no—
142C23×D43—22no—
143C23×D43—26no—
144C23×D43—26no—
145C23×D43—22no—
146C23×D43#41112yes—
147C23×D43C2411yescharacteristic
148C23×D43C2411yescharacteristic
149C23×D43C2411yescharacteristic
150C2×D4×C43—26no—
151C22×C4×C43—26no—
152C22×C4×C43—43no—
153C22×C4×C43—43no—
154C22×C4×C43C2411yescharacteristic
155C22×C4×C43C2413yes—
156C22×C4×C43C2413yes—
157C22×C4×C43C2413yes—
158C22×C4×C43C2413yes—
159C2×C22⋊D43—26no—
160C2×C22⋊D43—26no—
161C22×Dic43—26no—
162C22×Dic43—43no—
163C22×Dic43—43no—
164C22×Dic43C2411yescharacteristic
165C22×Dic43C2413yes—
166C22×Dic43C2413yes—
167C22×Dic43C2413yes—
168C22×Dic43C2413yes—
169D4×D43—416no—
170C2×D172—26no—
171C2×C4×D43—26no—
172C2×C4×D43—26no—
173C2×C4×D43—26no—
174C2×C4×D43—26no—
175C2×C4×D43—26no—
176C2×C4×D43—26no—
177C2×C4×D43—26no—
178C2×C4×D43—26no—
179C2×C4×D43—26no—
180C2×C4×D43—26no—
181C2×C4×D43—26no—
182C2×C4×D43—26no—
183C2×C4×D43—26no—
184C2×C4×D43—26no—
185C2×C4×D43—26no—
186C2×C4×D43—43no—
187C2×C4×D43—43no—
188C2×C4×D43—43no—
189C2×C4×D43—43no—
190C2×C4×D43—448no—
191C4⋊C4×C43—43no—
192C4⋊C4×C43—43no—
193C22⋊C4×C43—26no—
194C22⋊C4×C43—43no—
195C22⋊C4×C43—43no—
196C22⋊Dic43—26no—
197C22⋊Dic43—43no—
198C22⋊Dic43—43no—
199(C2×D43)⋊C4—26no—
200(C2×D43)⋊C4—26no—
201(C2×D43)⋊C4—43no—
202(C2×D43)⋊C4—43no—
203(C2×D43)⋊C4—43no—
204(C2×D43)⋊C4—43no—
205C4⋊Dic43—43no—
206C4⋊Dic43—43no—
207Dic43⋊C4—43no—
208Dic43⋊C4—43no—
209Dic43⋊C4—43no—
210Dic43⋊C4—43no—
211C23×C43—23no—
212C23×C43—21no—
213C23×C43—23no—
214C23×C43—23no—
215C23×C43—21no—
216C23×C43C2×#4116yes—
217C23×C43C2511yescharacteristic
218C22×D43—23no—
219C22×D43—21no—
220C22×D43—224no—
221C22×D43—224no—
222C22×D43—23no—
223C22×D43—23no—
224C22×D43—21no—
225C22×D43—44no—
226C22×D43—412no—
227C22×D43—412no—
228C22×D43#126116yes—
229C22×D43C2×#4116yes—
230C22×D43C2×#4116yes—
231C22×D43H(5,𝔽2)16yes—
232C22×D432−1+412yes—
233D4×C43—44no—
234C2×C4×C43—23no—
235C2×C4×C43—23no—
236C2×C4×C43—23no—
237C2×C4×C43—23no—
238C2×C4×C43—23no—
239C2×C4×C43—23no—
240C2×C4×C43—23no—
241C2×C4×C43—23no—
242C2×C4×C43—23no—
243C2×C4×C43—23no—
244C2×C4×C43—23no—
245C2×C4×C43—23no—
246C2×C4×C43—23no—
247C2×C4×C43—412no—
248C22⋊D43—44no—
249C22⋊D43—44no—
250C2×Dic43—23no—
251C2×Dic43—23no—
252C2×Dic43—23no—
253C2×Dic43—23no—
254C2×Dic43—23no—
255C2×Dic43—23no—
256C2×Dic43—23no—
257C2×Dic43—23no—
258C2×Dic43—23no—
259C2×Dic43—23no—
260C2×Dic43—23no—
261C2×Dic43—23no—
262C2×Dic43—23no—
263C2×Dic43—412no—
264D172—44no—
265C4×D43—412no—
266C4×D43—412no—
267C4×D43—44no—
268C4×D43—412no—
269C4×D43—412no—
270C4×D43—412no—
271C4×D43—412no—
272C2×#2643—431nomaximal, Sylow
273C22×C43—26no—
274C22×C43—26no—
275C22×C43—41no—
276C22×C43—43no—
277C22×C43—43no—
278C22×C43C2×#12614yes—
279C22×C43C22×#4113yes—
280C22×C43C2×H(5,𝔽2)13yes—
281C22×C43C2×2−1+411yescharacteristic
282C2×D43—26no—
283C2×D43—26no—
284C2×D43—232no—
285C2×D43—41no—
286C2×D43—43no—
287C2×D43—43no—
288C2×D43—88no—
289C2×D43C2×#12614yes—
290C2×D43C2×#12614yes—
291C2×D43#538112yes—
292C2×D43#539112yes—
293C4×C43—41no—
294C4×C43—43no—
295C4×C43—43no—
296C4×C43—43no—
297C4×C43—43no—
298Dic43—41no—
299Dic43—43no—
300Dic43—43no—
301Dic43—43no—
302Dic43—43no—
303#2643—431no—
304#2643—433no—
305#2643—433no—
306#2643—431no—
307#2643—433no—
308#2643—433no—
309#2643—431no—
310#2643D4311yescharacteristic, direct product factor
311C2×#401—431no—
312C2×#400—433no—
313C2×#397—433no—
314C2×#396—431no—
315C2×#386—433no—
316C2×#385—433no—
317C22×#95—431no—
318C2×C43—24no—
319C2×C43—81no—
320C2×C43C22×#12611yescharacteristic
321C2×C43C2×#53813yes—
322C2×C43C2×#53913yes—
323D43—24no—
324D43—81no—
325D43#264318yesdirect product factor
326C23×D4—431no—
327C24×C4—433no—
328C22×C4⋊C4—433no—
329C22×C4⋊C4—433no—
330C22×C22⋊C4—433no—
331C22×C22⋊C4—433no—
332C22×C22⋊C4—433no—
333#401—433no—
334#401—433no—
335#401—431no—
336#401C2×D4311yescharacteristic, complemented
337#400—433no—
338#400—433no—
339#400—433no—
340#400—433no—
341#400—433no—
342#400—433no—
343#400—433no—
344#400C2×D4313yescomplemented
345#397—433no—
346#397—433no—
347#397—433no—
348#397—433no—
349#397—433no—
350#397—433no—
351#397—433no—
352#397C2×D4313yescomplemented
353#396—433no—
354#396—433no—
355#396—431no—
356#396C2×D4311yescharacteristic, complemented
357#386—433no—
358#386—433no—
359#386—433no—
360#386—433no—
361#386—433no—
362#386—433no—
363#386—433no—
364#386C2×D4313yes—
365#385—433no—
366#385—433no—
367#385—433no—
368#385—433no—
369#385—433no—
370#385—433no—
371#385—433no—
372#385C2×D4313yescomplemented
373C2×#95—433no—
374C2×#95—433no—
375C2×#95—431no—
376C2×#95—431no—
377C2×#95—433no—
378C2×#95—433no—
379C2×#95—433no—
380C2×#95—433no—
381C2×#95—433no—
382C2×#95C2×D4311yescharacteristic, complemented
383C43C2×#264311yescharacteristic, complemented, Sylow
384C25—431no—
385C25—431no—
386C22×D4—431no—
387C22×D4—431no—
388C22×D4—431no—
389C22×D4—8612no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—433no—
392C23×C4—433no—
393C23×C4—433no—
394C23×C4—433no—
395C23×C4—433no—
396C23×C4—431no—
397C23×C4—433no—
398C23×C4—433no—
399C23×C4—8612no—
400C23×C4—1726no—
401C23×C4—1726no—
402C23×C4C22×D4313yes—
403C2×C4⋊C4—433no—
404C2×C4⋊C4—433no—
405C2×C4⋊C4—433no—
406C2×C4⋊C4—433no—
407C2×C4⋊C4—433no—
408C2×C4⋊C4—433no—
409C2×C4⋊C4—1726no—
410C2×C4⋊C4—1726no—
411C2×C4⋊C4C22×D4313yes—
412C2×C4⋊C4C22×D4313yes—
413C2×C22⋊C4—433no—
414C2×C22⋊C4—433no—
415C2×C22⋊C4—433no—
416C2×C22⋊C4—433no—
417C2×C22⋊C4—433no—
418C2×C22⋊C4—433no—
419C2×C22⋊C4—433no—
420C2×C22⋊C4—433no—
421C2×C22⋊C4—433no—
422C2×C22⋊C4—8612no—
423C2×C22⋊C4—1726no—
424C2×C22⋊C4—1726no—
425C2×C22⋊C4C22×D4313yes—
426C2×C22⋊C4C22×D4313yes—
427C2×C22⋊C4C22×D4313yes—
428#95—433no—
429#95—433no—
430#95—433no—
431#95—433no—
432#95—433no—
433#95—433no—
434#95—433no—
435#95—433no—
436#95—433no—
437#95—433no—
438#95—433no—
439#95—433no—
440#95—433no—
441#95—433no—
442#95—433no—
443#95—433no—
444#95C22×D4311yescharacteristic
445#95C22×D4313yes—
446#95C22×D4313yes—
447#95C22×D4313yes—
448#95C22×D4313yes—
449#95C22×D4313yes—
450C24—431no—
451C24—4312no—
452C24—431no—
453C24—431no—
454C24—866no—
455C24—862no—
456C24—866no—
457C24—866no—
458C24—862no—
459C24C23×D4311yescharacteristic
460C24C23×D4311yescharacteristic
461C2×D4—26no—
462C2×D4—866no—
463C2×D4—866no—
464C2×D4—866no—
465C2×D4—17216no—
466C22×C4—26no—
467C22×C4—43no—
468C22×C4—43no—
469C22×C4—431no—
470C22×C4—433no—
471C22×C4—433no—
472C22×C4—433no—
473C22×C4—433no—
474C22×C4—866no—
475C22×C4—866no—
476C22×C4—866no—
477C22×C4—866no—
478C22×C4—866no—
479C22×C4—866no—
480C22×C4—866no—
481C22×C4—866no—
482C22×C4—866no—
483C22×C4—866no—
484C22×C4—866no—
485C22×C4—866no—
486C22×C4—866no—
487C22×C4—866no—
488C22×C4—866no—
489C22×C4—866no—
490C22×C4—1723no—
491C22×C4—1723no—
492C22×C4—1723no—
493C22×C4—1723no—
494C22×C4—17248no—
495C22×C4—1723no—
496C22×C4—1723no—
497C22×C4C23×D4311yescharacteristic
498C22×C4C23×D4313yes—
499C22×C4C23×D4313yes—
500C22×C4C23×D4313yes—
501C22×C4C23×D4313yes—
502C4⋊C4—43no—
503C4⋊C4—43no—
504C4⋊C4—1723no—
505C4⋊C4—1723no—
506C4⋊C4—1723no—
507C4⋊C4—1723no—
508C4⋊C4—1723no—
509C4⋊C4—1723no—
510C22⋊C4—26no—
511C22⋊C4—43no—
512C22⋊C4—43no—
513C22⋊C4—866no—
514C22⋊C4—866no—
515C22⋊C4—866no—
516C22⋊C4—1723no—
517C22⋊C4—1723no—
518C22⋊C4—1723no—
519C22⋊C4—1723no—
520C22⋊C4—1723no—
521C22⋊C4—1723no—
522C23—23no—
523C23—21no—
524C23—23no—
525C23—23no—
526C23—21no—
527C23—436no—
528C23—436no—
529C23—432no—
530C23—4316no—
531C23—436no—
532C23—8624no—
533C23—8624no—
534C23—863no—
535C23—861no—
536C23—863no—
537C23—863no—
538C23—861no—
539C23—1724no—
540C23—17212no—
541C23—17212no—
542C23#41×D4316yes—
543C23C24×D4311yescharacteristic
544D4—44no—
545D4—1724no—
546D4—1724no—
547D4—1724no—
548C2×C4—23no—
549C2×C4—23no—
550C2×C4—23no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—412no—
562C2×C4—863no—
563C2×C4—863no—
564C2×C4—863no—
565C2×C4—863no—
566C2×C4—863no—
567C2×C4—863no—
568C2×C4—863no—
569C2×C4—863no—
570C2×C4—863no—
571C2×C4—863no—
572C2×C4—863no—
573C2×C4—863no—
574C2×C4—863no—
575C2×C4—17212no—
576C2×C4—17212no—
577C2×C4—1724no—
578C2×C4—17212no—
579C2×C4—17212no—
580C2×C4—17212no—
581C2×C4—17212no—
582C2×C4—17212no—
583C22—26no—
584C22—26no—
585C22—41no—
586C22—43no—
587C22—43no—
588C22—434no—
589C22—4312no—
590C22—4312no—
591C22—434no—
592C22—8632no—
593C22—866no—
594C22—866no—
595C22—3448no—
596C22—1721no—
597C22—1723no—
598C22—1723no—
599C22#126×D4314yes—
600C22C2×#41×D4313yes—
601C22H(5,𝔽2)×D4313yes—
602C222−1+4×D4311yescharacteristic
603C4—41no—
604C4—43no—
605C4—43no—
606C4—43no—
607C4—43no—
608C4—1721no—
609C4—1723no—
610C4—1723no—
611C4—1723no—
612C4—1723no—
613C2—24no—
614C2—81no—
615C2—438no—
616C2—864no—
617C2—3441no—
618C2C2×#126×D4311yescharacteristic
619C2#538×D4313yes—
620C2#539×D4313yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2643C2
prime radicalC22×D4×D43C22
hypercenter#2643D43
hypocenterC43C2×#2643
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #19140553C2semidirect
2. #19140552C2semidirect
3. #19140551C2semidirect
4. #19140550C2semidirect
5. #19140549C2semidirect
6. #19140548C2semidirect
7. #19140547C2semidirect
8. #401×D43C2semidirect
9. #400×D43C2semidirect
10. #397×D43C2semidirect
11. #396×D43C2semidirect
13. #385×D43C2semidirect
14. C2×#95×D43C2semidirect
15. C43×#2643C2semidirect
23. C43⋊#401C22semidirect
24. C43⋊#401C22semidirect
25. C43⋊#401C22semidirect
26. #14582841C22semidirect
27. #14582841C22semidirect
28. #14582840C22semidirect
29. #14582840C22semidirect
30. #14582839C22semidirect
31. #14582838C22semidirect
32. #14582837C22semidirect
33. #14582828C22semidirect
34. #14582828C22semidirect
35. #14582827C22semidirect
36. #14582827C22semidirect
37. #14582826C22semidirect
38. #14582825C22semidirect
39. #14582824C22semidirect
40. #14582823C22semidirect
41. #14582822C22semidirect
42. #14582821C22semidirect
50. #14582774C22semidirect
51. #14582773C22semidirect
52. #14582773C22semidirect
53. #14582772C22semidirect
54. #14582771C22semidirect
55. #14582770C22semidirect
56. #14582770C22semidirect
57. C2×C43⋊#95C22semidirect
64. #95×D43C22semidirect
65. #95×D43C22semidirect
66. C43×#401C22semidirect
67. C43×#400C22semidirect
68. C43×#397C22semidirect
69. C43×#396C22semidirect
71. C43×#385C22semidirect
72. C2×#95×C43C22semidirect
310. #2643D43direct (N × H)
325. D43#2643direct (N × H)
336. #401C2×D43semidirect
344. #400C2×D43semidirect
352. #397C2×D43semidirect
356. #396C2×D43semidirect
372. #385C2×D43semidirect
382. C2×#95C2×D43semidirect
383. C43C2×#2643semidirect

Maximal subgroups

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

subgroupindex
#191405532
#191405522
#191405512
#191405502
#191405492
#191405482
#191405472
#401×D432
#400×D432
#397×D432
#396×D432
#386×D432
#385×D432
C2×#95×D432
C43×#26432
C2×#264343