Finite Group Databasebeta

← C43×#19775 #24939792

Subgroups — C43×#19775 #24939792

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3341C211yesmaximal, characteristic, complemented
2C43×#3325C211yesmaximal, characteristic, complemented
3C43×#3303C211yesmaximal, characteristic, complemented
4C43×#3294C211yesmaximal, characteristic, complemented
5C43×#1719C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1681C211yesmaximal, characteristic, complemented
8C43×#1677C211yesmaximal, characteristic, complemented
9C43×#1675C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic, complemented
11C43×#1635C211yesmaximal, characteristic, complemented
12C43×#1629C211yesmaximal, characteristic, complemented
13C43×#1624C211yesmaximal, characteristic, complemented
14C43×#1581C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C43×#555C2211yescharacteristic
17C43×#555C2211yescharacteristic, complemented
18C43×#547C2211yescharacteristic
19D42×C43C2211yescharacteristic
20C43×#500C2211yescharacteristic, complemented
21C43×#492C2211yescharacteristic
22C43×#487C2211yescharacteristic, complemented
23C43×#487C2211yescharacteristic, complemented
24C43×#486C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#485—21no—
27C43×#482—21no—
28C43×#482—21no—
29C43×#482—21no—
30C43×#480—21no—
31C43×#476C2211yescharacteristic
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic, complemented
35C43×#474C2211yescharacteristic
36C43×#469—21no—
37C43×#466—21no—
38C43×#466—21no—
39C43×#465—21no—
40C43×#461C2211yescharacteristic, complemented
41C43×#459C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#449—21no—
44C43×#447—21no—
45C43×#447—21no—
46C4×D8×C43C2211yescharacteristic
47C4×D8×C43C2211yescharacteristic
48C43×#436C2211yescharacteristic
49C8×D4×C43C2211yescharacteristic
50C8×D4×C43C2211yescharacteristic, complemented
51C8×D4×C43C2211yescharacteristic, complemented
52C43×#427—21no—
53C43×#418—21no—
54C43×#416—21no—
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#333C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×D4⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—41no—
72C2×D8×C43—21no—
73C2×D8×C43—21no—
74C2×D8×C43D411yescharacteristic
75C2×D8×C43D411yescharacteristic
76C2×M16×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#124×C43—41no—
85#124×C43—41no—
86#123×C43—41no—
87C22⋊Q8×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#120×C43—41no—
96C4×D4×C43C2311yescharacteristic
97C4×D4×C43C2311yescharacteristic
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104C2×C4⋊C4×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43D411yescharacteristic
109#107×C43D411yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—41no—
122#102×C43—21no—
123#102×C43—21no—
124#102×C43—21no—
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43D411yescharacteristic
134#102×C43D411yescharacteristic
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C2×D4×C43C2×D411yescharacteristic
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171SD16×C43—81no—
172SD16×C43—82no—
173D8×C43—22no—
174D8×C43—41no—
175D8×C43—81no—
176D8×C43—81no—
177M16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—42no—
184C2×C8×C43—81no—
185C2×C8×C43—81no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—41no—
212C42×C43—41no—
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—81no—
238D4×C43—82no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43—161no—
242D4×C43—161no—
243D4×C43#13512yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—82no—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272#19775C4311yesmaximal, characteristic, direct product factor, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—164no—
289C22×C43D4211yescharacteristic
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C2×#13511yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302#3341C2×C4311yescharacteristic, complemented
303#3325C2×C4311yescharacteristic, complemented
304#3303C2×C4311yescharacteristic, complemented
305#3294C2×C4311yescharacteristic, complemented
306#1719C2×C4311yescharacteristic, complemented
307#1703C2×C4311yescharacteristic, complemented
308#1681C2×C4311yescharacteristic, complemented
309#1677C2×C4311yescharacteristic, complemented
310#1675C2×C4311yescharacteristic, complemented
311#1646C2×C4311yescharacteristic, complemented
312#1635C2×C4311yescharacteristic, complemented
313#1629C2×C4311yescharacteristic, complemented
314#1624C2×C4311yescharacteristic, complemented
315#1581C2×C4311yescharacteristic, complemented
316#1580C2×C4311yescharacteristic, complemented
317C2×C43—42no—
318C2×C43—81no—
319C2×C43—81no—
320C2×C43—81no—
321C2×C43—161no—
322C2×C43#326711yescharacteristic
323C2×C43#328011yescharacteristic
324C2×C43#328811yescharacteristic
325#555C22×C4311yescharacteristic
326#555C22×C4311yescharacteristic, complemented
327#547C22×C4311yescharacteristic
328D42C22×C4311yescharacteristic
329#500C22×C4311yescharacteristic, complemented
330#492C22×C4311yescharacteristic
331#487C22×C4311yescharacteristic, complemented
332#487C22×C4311yescharacteristic, complemented
333#486C22×C4311yescharacteristic
334#486C22×C4311yescharacteristic
335#485—21no—
336#482—21no—
337#482—21no—
338#482—21no—
339#480—21no—
340#476C22×C4311yescharacteristic
341#476C22×C4311yescharacteristic
342#476C22×C4311yescharacteristic
343#476C22×C4311yescharacteristic, complemented
344#474C22×C4311yescharacteristic
345#469—21no—
346#466—21no—
347#466—21no—
348#465—21no—
349#461C22×C4311yescharacteristic, complemented
350#459C22×C4311yescharacteristic
351#459C22×C4311yescharacteristic
352#449—21no—
353#447—21no—
354#447—21no—
355C4×D8C22×C4311yescharacteristic
356C4×D8C22×C4311yescharacteristic
357#436C22×C4311yescharacteristic
358C8×D4C22×C4311yescharacteristic
359C8×D4C22×C4311yescharacteristic, complemented
360C8×D4C22×C4311yescharacteristic, complemented
361#427—21no—
362#418—21no—
363#416—21no—
364C2×#102—21no—
365#335C22×C4311yescharacteristic, complemented
366#334C22×C4311yescharacteristic, complemented
367#333C22×C4311yescharacteristic, complemented
368#333C22×C4311yescharacteristic, complemented
369#332C22×C4311yescharacteristic, complemented
370#331C22×C4311yescharacteristic
371D4⋊C8C22×C4311yescharacteristic
372D4⋊C8C22×C4311yescharacteristic
373D4⋊C8C22×C4311yescharacteristic, complemented
374D4⋊C8C22×C4311yescharacteristic, complemented
375#322C22×C4311yescharacteristic, complemented
376C43#1977511yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C4311yescharacteristic
385C2×D8D4×C4311yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C4⋊Q8C23×C4311yescharacteristic
391C4⋊Q8C23×C4311yescharacteristic
392C4⋊Q8C23×C4311yescharacteristic
393#127C23×C4311yescharacteristic
394#124—41no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#120—41no—
406C4×D4C23×C4311yescharacteristic
407C4×D4C23×C4311yescharacteristic
408C4×D4C23×C4311yescharacteristic
409C4×D4C23×C4311yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#107—21no—
417#107—21no—
418#107D4×C4311yescharacteristic
419#107D4×C4311yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8C23×C4311yescharacteristic
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—41no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102D4×C4311yescharacteristic
444#102D4×C4311yescharacteristic
445#102D4×C4311yescharacteristic
446#102D4×C4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C4311yescharacteristic
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454C24—41no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C4311yescharacteristic
473C2×D4C2×D4×C4311yescharacteristic
474C2×D4C2×D4×C4311yescharacteristic
475C2×D4C2×D4×C4311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481SD16—81no—
482SD16—82no—
483D8—22no—
484D8—41no—
485D8—81no—
486D8—81no—
487M16—81no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C4311yescharacteristic
497C2×C8C2×D4×C4311yescharacteristic
498C2×C8C2×D4×C4311yescharacteristic
499C2×C8C2×D4×C4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C4311yescharacteristic
508C4⋊C4C2×D4×C4311yescharacteristic
509C4⋊C4C2×D4×C4311yescharacteristic
510C4⋊C4C2×D4×C4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42—41no—
523C42C24×C4311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—82no—
530C23—82no—
531C23—161no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—161no—
553D4#135×C4312yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4C22×D4×C4311yescharacteristic
571C2×C4C22×D4×C4311yescharacteristic
572C2×C4H(5,𝔽2)×C4311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C2×#135×C4311yescharacteristic
608C4C43×#57511yescharacteristic
609C4C43×#57611yescharacteristic
610C4C43×#57711yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C43×#326711yescharacteristic
617C2C43×#328011yescharacteristic
618C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3341C2semidirect
2. C43×#3325C2semidirect
3. C43×#3303C2semidirect
4. C43×#3294C2semidirect
5. C43×#1719C2semidirect
6. C43×#1703C2semidirect
7. C43×#1681C2semidirect
8. C43×#1677C2semidirect
9. C43×#1675C2semidirect
10. C43×#1646C2semidirect
11. C43×#1635C2semidirect
12. C43×#1629C2semidirect
13. C43×#1624C2semidirect
14. C43×#1581C2semidirect
15. C43×#1580C2semidirect
17. C43×#555C22semidirect
20. C43×#500C22semidirect
22. C43×#487C22semidirect
23. C43×#487C22semidirect
34. C43×#476C22semidirect
40. C43×#461C22semidirect
50. C8×D4×C43C22semidirect
51. C8×D4×C43C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#333C22semidirect
60. C43×#332C22semidirect
64. C43×D4⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
272. #19775C43direct (N × H)
302. #3341C2×C43semidirect
303. #3325C2×C43semidirect
304. #3303C2×C43semidirect
305. #3294C2×C43semidirect
306. #1719C2×C43semidirect
307. #1703C2×C43semidirect
308. #1681C2×C43semidirect
309. #1677C2×C43semidirect
310. #1675C2×C43semidirect
311. #1646C2×C43semidirect
312. #1635C2×C43semidirect
313. #1629C2×C43semidirect
314. #1624C2×C43semidirect
315. #1581C2×C43semidirect
316. #1580C2×C43semidirect
326. #555C22×C43semidirect
329. #500C22×C43semidirect
331. #487C22×C43semidirect
332. #487C22×C43semidirect
343. #476C22×C43semidirect
349. #461C22×C43semidirect
359. C8×D4C22×C43semidirect
360. C8×D4C22×C43semidirect
365. #335C22×C43semidirect
366. #334C22×C43semidirect
367. #333C22×C43semidirect
368. #333C22×C43semidirect
369. #332C22×C43semidirect
373. D4⋊C8C22×C43semidirect
374. D4⋊C8C22×C43semidirect
375. #322C22×C43semidirect
376. C43#19775direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33412
C43×#33252
C43×#33032
C43×#32942
C43×#17192
C43×#17032
C43×#16812
C43×#16772
C43×#16752
C43×#16462
C43×#16352
C43×#16292
C43×#16242
C43×#15812
C43×#15802
#1977543