Finite Group Databasebeta

← C43×#19537 #24939554

Subgroups — C43×#19537 #24939554

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3233C211yesmaximal, characteristic, complemented
2C43×#3217C211yesmaximal, characteristic
3C43×#3208C211yesmaximal, characteristic, complemented
4C43×#2993C211yesmaximal, characteristic, complemented
5C43×#1698C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1686C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1678C211yesmaximal, characteristic, complemented
10C43×#1677C211yesmaximal, characteristic, complemented
11C43×#1666C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1572C211yesmaximal, characteristic, complemented
14C43×#1559C211yesmaximal, characteristic, complemented
15C43×#1545C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C2×#127×C43C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#499—21no—
20C43×#496—21no—
21C43×#492C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#490—21no—
24C43×#488—21no—
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#485—21no—
28C43×#482—21no—
29C43×#477C2211yescharacteristic, complemented
30C43×#476C2211yescharacteristic, complemented
31C43×#475C2211yescharacteristic, complemented
32C43×#474C2211yescharacteristic, complemented
33C43×#460—21no—
34C43×#460—21no—
35C43×#460C2211yescharacteristic
36C43×#460C2211yescharacteristic
37C43×#459C2211yescharacteristic
38C43×#459C2211yescharacteristic
39C43×#450—21no—
40C43×#450—21no—
41C43×#450—21no—
42C43×#447—21no—
43C43×#446C2211yescharacteristic, complemented
44C8×Q8×C43C2211yescharacteristic, complemented
45C43×#436—21no—
46C43×#436C2211yescharacteristic, complemented
47C43×#435—21no—
48C8×D4×C43C2211yescharacteristic, complemented
49C43×#433—21no—
50C43×#432C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#431C2211yescharacteristic
53C43×#424—21no—
54C43×#423C2211yescharacteristic
55C43×#335C2211yescharacteristic, complemented
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#334C2211yescharacteristic, complemented
59C43×#333C2211yescharacteristic, complemented
60C43×#333C2211yescharacteristic, complemented
61C43×#332C2211yescharacteristic, complemented
62C43×#332C2211yescharacteristic, complemented
63C43×#331C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43—21no—
84#127×C43—21no—
85#127×C43—21no—
86#127×C43C2311yescharacteristic
87#127×C43C2311yescharacteristic
88#126×C43—21no—
89#125×C43—21no—
90#125×C43D411yescharacteristic
91#124×C43D411yescharacteristic
92#123×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43D411yescharacteristic
96#121×C43D411yescharacteristic
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#107×C43—21no—
106#107×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113C4⋊C8×C43D411yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120#103×C43—21no—
121#103×C43—21no—
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—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43D411yescharacteristic
137C22⋊C8×C43D411yescharacteristic
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43—82no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43#4111yescharacteristic
168SD16×C43—81no—
169SD16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172SD16×C43—81no—
173SD16×C43—81no—
174D8×C43—81no—
175D8×C43—81no—
176M16×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—21no—
184C2×C8×C43—81no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
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—21no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
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—21no—
206C22⋊C4×C43—41no—
207C42×C43—21no—
208C42×C43—41no—
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211C42×C43#4111yescharacteristic
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—82no—
217C23×C43—82no—
218C23×C43—82no—
219C23×C43#12111yescharacteristic
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236D4×C43—81no—
237D4×C43—82no—
238D4×C43—82no—
239D4×C43—82no—
240D4×C43—81no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269#19537C4311yesmaximal, characteristic, direct product factor, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43C2×#12111yescharacteristic
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#57611yescharacteristic
294C4×C43#57711yescharacteristic
295C4×C43#57711yescharacteristic
296C4×C43#57711yescharacteristic
297#3233C2×C4311yescharacteristic, complemented
298#3217C2×C4311yescharacteristic
299#3208C2×C4311yescharacteristic, complemented
300#2993C2×C4311yescharacteristic, complemented
301#1698C2×C4311yescharacteristic, complemented
302#1697C2×C4311yescharacteristic, complemented
303#1686C2×C4311yescharacteristic, complemented
304#1685C2×C4311yescharacteristic, complemented
305#1678C2×C4311yescharacteristic, complemented
306#1677C2×C4311yescharacteristic, complemented
307#1666C2×C4311yescharacteristic, complemented
308#1665C2×C4311yescharacteristic, complemented
309#1572C2×C4311yescharacteristic, complemented
310#1559C2×C4311yescharacteristic, complemented
311#1545C2×C4311yescharacteristic, complemented
312C2×C43—41no—
313C2×C43—81no—
314C2×C43—161no—
315C2×C43—161no—
316C2×C43#304511yescharacteristic
317C2×C43#305711yescharacteristic
318C2×C43#306811yescharacteristic
319#533C22×C4311yescharacteristic
320C2×#127C22×C4311yescharacteristic
321#529C22×C4311yescharacteristic
322#499—21no—
323#496—21no—
324#492C22×C4311yescharacteristic
325#492C22×C4311yescharacteristic
326#490—21no—
327#488—21no—
328#486C22×C4311yescharacteristic
329#486C22×C4311yescharacteristic
330#485—21no—
331#482—21no—
332#477C22×C4311yescharacteristic, complemented
333#476C22×C4311yescharacteristic, complemented
334#475C22×C4311yescharacteristic, complemented
335#474C22×C4311yescharacteristic, complemented
336#460—21no—
337#460—21no—
338#460C22×C4311yescharacteristic
339#460C22×C4311yescharacteristic
340#459C22×C4311yescharacteristic
341#459C22×C4311yescharacteristic
342#450—21no—
343#450—21no—
344#450—21no—
345#447—21no—
346#446C22×C4311yescharacteristic, complemented
347C8×Q8C22×C4311yescharacteristic, complemented
348#436—21no—
349#436C22×C4311yescharacteristic, complemented
350#435—21no—
351C8×D4C22×C4311yescharacteristic, complemented
352#433—21no—
353#432C22×C4311yescharacteristic
354#431C22×C4311yescharacteristic
355#431C22×C4311yescharacteristic
356#424—21no—
357#423C22×C4311yescharacteristic
358#335C22×C4311yescharacteristic, complemented
359#335C22×C4311yescharacteristic, complemented
360#334C22×C4311yescharacteristic, complemented
361#334C22×C4311yescharacteristic, complemented
362#333C22×C4311yescharacteristic, complemented
363#333C22×C4311yescharacteristic, complemented
364#332C22×C4311yescharacteristic, complemented
365#332C22×C4311yescharacteristic, complemented
366#331C22×C4311yescharacteristic
367#331C22×C4311yescharacteristic
368#331C22×C4311yescharacteristic
369#331C22×C4311yescharacteristic
370C43#1953711yescharacteristic, direct product factor, Sylow
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×M16—21no—
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8C23×C4311yescharacteristic
386C4⋊Q8C23×C4311yescharacteristic
387#127—21no—
388#127—21no—
389#127—21no—
390#127C23×C4311yescharacteristic
391#127C23×C4311yescharacteristic
392#126—21no—
393#125—21no—
394#125D4×C4311yescharacteristic
395#124D4×C4311yescharacteristic
396#123—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8D4×C4311yescharacteristic
400#121D4×C4311yescharacteristic
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8C23×C4311yescharacteristic
404C4×D4—21no—
405C4×D4C23×C4311yescharacteristic
406#117—21no—
407#117—21no—
408C2×C42C23×C4311yescharacteristic
409#107—21no—
410#107—21no—
411#106—21no—
412#106—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8D4×C4311yescharacteristic
417C4⋊C8D4×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419C4⋊C8C23×C4311yescharacteristic
420C4⋊C8C23×C4311yescharacteristic
421C4⋊C8C23×C4311yescharacteristic
422C4⋊C8C23×C4311yescharacteristic
423C4⋊C8C23×C4311yescharacteristic
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8D4×C4311yescharacteristic
441C22⋊C8D4×C4311yescharacteristic
442#97—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C4311yescharacteristic
447C4×C8C23×C4311yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C4311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—82no—
467C2×D4C2×D4×C4311yescharacteristic
468C22×C4—21no—
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4C2×D4×C4311yescharacteristic
471C22×C4#41×C4311yescharacteristic
472SD16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476SD16—81no—
477SD16—81no—
478D8—81no—
479D8—81no—
480M16—81no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C2×C8C2×D4×C4311yescharacteristic
492C2×C8C2×D4×C4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C42—21no—
512C42—41no—
513C42C2×D4×C4311yescharacteristic
514C42C2×D4×C4311yescharacteristic
515C42#41×C4311yescharacteristic
516C42C24×C4311yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23#121×C4311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4#121×C4311yescharacteristic
558C2×C4#121×C4311yescharacteristic
559C2×C4#121×C4311yescharacteristic
560C2×C4C22×D4×C4311yescharacteristic
561C2×C4C22×D4×C4311yescharacteristic
562C2×C4C2×#41×C4311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22C2×#121×C4311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C43×#57611yescharacteristic
597C4C43×#57711yescharacteristic
598C4C43×#57711yescharacteristic
599C4C43×#57711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C43×#304511yescharacteristic
605C2C43×#305711yescharacteristic
606C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3217C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3233C2semidirect
3. C43×#3208C2semidirect
4. C43×#2993C2semidirect
5. C43×#1698C2semidirect
6. C43×#1697C2semidirect
7. C43×#1686C2semidirect
8. C43×#1685C2semidirect
9. C43×#1678C2semidirect
10. C43×#1677C2semidirect
11. C43×#1666C2semidirect
12. C43×#1665C2semidirect
13. C43×#1572C2semidirect
14. C43×#1559C2semidirect
15. C43×#1545C2semidirect
29. C43×#477C22semidirect
30. C43×#476C22semidirect
31. C43×#475C22semidirect
32. C43×#474C22semidirect
43. C43×#446C22semidirect
44. C8×Q8×C43C22semidirect
46. C43×#436C22semidirect
48. C8×D4×C43C22semidirect
55. C43×#335C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#334C22semidirect
59. C43×#333C22semidirect
60. C43×#333C22semidirect
61. C43×#332C22semidirect
62. C43×#332C22semidirect
269. #19537C43direct (N × H)
297. #3233C2×C43semidirect
299. #3208C2×C43semidirect
300. #2993C2×C43semidirect
301. #1698C2×C43semidirect
302. #1697C2×C43semidirect
303. #1686C2×C43semidirect
304. #1685C2×C43semidirect
305. #1678C2×C43semidirect
306. #1677C2×C43semidirect
307. #1666C2×C43semidirect
308. #1665C2×C43semidirect
309. #1572C2×C43semidirect
310. #1559C2×C43semidirect
311. #1545C2×C43semidirect
332. #477C22×C43semidirect
333. #476C22×C43semidirect
334. #475C22×C43semidirect
335. #474C22×C43semidirect
346. #446C22×C43semidirect
347. C8×Q8C22×C43semidirect
349. #436C22×C43semidirect
351. C8×D4C22×C43semidirect
358. #335C22×C43semidirect
359. #335C22×C43semidirect
360. #334C22×C43semidirect
361. #334C22×C43semidirect
362. #333C22×C43semidirect
363. #333C22×C43semidirect
364. #332C22×C43semidirect
365. #332C22×C43semidirect
370. C43#19537direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32332
C43×#32172
C43×#32082
C43×#29932
C43×#16982
C43×#16972
C43×#16862
C43×#16852
C43×#16782
C43×#16772
C43×#16662
C43×#16652
C43×#15722
C43×#15592
C43×#15452
#1953743