Finite Group Databasebeta

← C43×#20193 #24940210

Subgroups — C43×#20193 #24940210

Order 11008.

672 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×#3372C211yesmaximal, characteristic, complemented
2C43×#3368C211yesmaximal, characteristic, complemented
3C43×#3295C211yesmaximal, characteristic, complemented
4C43×#3274C211yesmaximal, characteristic
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1698C211yesmaximal, characteristic, complemented
8C43×#1688C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1639C211yesmaximal, characteristic, complemented
11C43×#1631C211yesmaximal, characteristic, complemented
12C43×#1626C211yesmaximal, characteristic, complemented
13C43×#1622C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17C43×#557C2211yescharacteristic, complemented
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic, complemented
23C43×#491—21no—
24C43×#490—21no—
25C43×#487C2211yescharacteristic, complemented
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic, complemented
29C43×#481—21no—
30C43×#479—21no—
31C43×#478—21no—
32C43×#477C2211yescharacteristic, complemented
33C43×#476C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#469—21no—
36C43×#465—21no—
37C43×#461—21no—
38C43×#461C2211yescharacteristic
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#460C2211yescharacteristic, complemented
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#449—21no—
46C43×#447—21no—
47C43×#446C2211yescharacteristic, complemented
48C43×#446C2211yescharacteristic, complemented
49C43×#440—21no—
50C43×#440—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C2×#102×C43—21no—
56C43×#335C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70AGL(1,ℤ/8)×C43—44no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—41no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×M16×C43—21no—
82C22×C8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—21no—
87#127×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#125×C43—21no—
90#125×C43—21no—
91#125×C43—41no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—41no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—41no—
98#120×C43—41no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43C2311yescharacteristic
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2311yescharacteristic
107C2×C4⋊C4×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112#106×C43D411yescharacteristic
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—21no—
123#103×C43D411yescharacteristic
124#103×C43D411yescharacteristic
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×C43—21no—
134#102×C43—21no—
135#102×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172SD16×C43—22no—
173SD16×C43—41no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—42no—
177SD16×C43—81no—
178SD16×C43—82no—
179D8×C43—42no—
180D8×C43—42no—
181D8×C43—81no—
182M16×C43—42no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—81no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—161no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—81no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—81no—
243D4×C43—81no—
244D4×C43—82no—
245D4×C43—82no—
246D4×C43—82no—
247D4×C43—161no—
248D4×C43AGL(1,ℤ/8)12yes—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—82no—
262C2×C4×C43—161no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#20193C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
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—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57711yescharacteristic
302C4×C43#57711yescharacteristic
303#3372C2×C4311yescharacteristic, complemented
304#3368C2×C4311yescharacteristic, complemented
305#3295C2×C4311yescharacteristic, complemented
306#3274C2×C4311yescharacteristic
307#1717C2×C4311yescharacteristic, complemented
308#1703C2×C4311yescharacteristic, complemented
309#1698C2×C4311yescharacteristic, complemented
310#1688C2×C4311yescharacteristic, complemented
311#1681C2×C4311yescharacteristic, complemented
312#1639C2×C4311yescharacteristic, complemented
313#1631C2×C4311yescharacteristic, complemented
314#1626C2×C4311yescharacteristic, complemented
315#1622C2×C4311yescharacteristic, complemented
316#1592C2×C4311yescharacteristic, complemented
317#1582C2×C4311yescharacteristic, complemented
318C2×C43—42no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43—161no—
322C2×C43#326511yescharacteristic
323C2×C43#327511yescharacteristic
324C2×C43#328811yescharacteristic
325C2×AGL(1,ℤ/8)—21no—
326#557C22×C4311yescharacteristic, complemented
327#554C22×C4311yescharacteristic
328#550C22×C4311yescharacteristic
329D42C22×C4311yescharacteristic
330#493C22×C4311yescharacteristic
331#492C22×C4311yescharacteristic, complemented
332#491—21no—
333#490—21no—
334#487C22×C4311yescharacteristic, complemented
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#486C22×C4311yescharacteristic, complemented
338#481—21no—
339#479—21no—
340#478—21no—
341#477C22×C4311yescharacteristic, complemented
342#476C22×C4311yescharacteristic
343#474C22×C4311yescharacteristic
344#469—21no—
345#465—21no—
346#461—21no—
347#461C22×C4311yescharacteristic
348#460—21no—
349#460C22×C4311yescharacteristic
350#460C22×C4311yescharacteristic
351#460C22×C4311yescharacteristic, complemented
352#459C22×C4311yescharacteristic
353#450—21no—
354#449—21no—
355#447—21no—
356#446C22×C4311yescharacteristic, complemented
357#446C22×C4311yescharacteristic, complemented
358#440—21no—
359#440—21no—
360C4×SD16C22×C4311yescharacteristic
361C4×SD16C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic
363C8×D4C22×C4311yescharacteristic
364C2×#102—21no—
365#335C22×C4311yescharacteristic, complemented
366#334C22×C4311yescharacteristic, complemented
367#333C22×C4311yescharacteristic, complemented
368#332C22×C4311yescharacteristic, complemented
369#331C22×C4311yescharacteristic
370#331C22×C4311yescharacteristic, complemented
371Q8⋊C8C22×C4311yescharacteristic, complemented
372Q8⋊C8C22×C4311yescharacteristic, complemented
373D4⋊C8C22×C4311yescharacteristic
374D4⋊C8C22×C4311yescharacteristic
375#322C22×C4311yescharacteristic, complemented
376C43#2019311yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—44no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—41no—
386C2×SD16D4×C4311yescharacteristic
387C2×SD16D4×C4311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×M16—21no—
392C22×C8—21no—
393C4⋊Q8—21no—
394C4⋊Q8C23×C4311yescharacteristic
395C4⋊Q8C23×C4311yescharacteristic
396#127—21no—
397#127C23×C4311yescharacteristic
398#127C23×C4311yescharacteristic
399#125—21no—
400#125—21no—
401#125—41no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—41no—
408#120—41no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C23×C4311yescharacteristic
412C4×Q8C23×C4311yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C23×C4311yescharacteristic
416C4×D4C23×C4311yescharacteristic
417C2×C4⋊C4—21no—
418#107—21no—
419#107—21no—
420#106—21no—
421#106D4×C4311yescharacteristic
422#106D4×C4311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C4311yescharacteristic
434#103D4×C4311yescharacteristic
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#102—21no—
444#102—21no—
445#102—41no—
446#102D4×C4311yescharacteristic
447#102D4×C4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450#97—21no—
451#97—21no—
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454C4×C8C23×C4311yescharacteristic
455C24—41no—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C4311yescharacteristic
461C2×Q8C2×D4×C4311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4C2×D4×C4311yescharacteristic
477C2×D4C2×D4×C4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482SD16—22no—
483SD16—41no—
484SD16—42no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—82no—
489D8—42no—
490D8—42no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—81no—
499C2×C8C2×D4×C4311yescharacteristic
500C2×C8C2×D4×C4311yescharacteristic
501C2×C8C2×D4×C4311yescharacteristic
502C2×C8C2×D4×C4311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C42—21no—
524C42—21no—
525C42—41no—
526C42C24×C4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—41no—
531C23—82no—
532C23—82no—
533C23—161no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—82no—
557D4—161no—
558D4AGL(1,ℤ/8)×C4312yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—161no—
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4C22×D4×C4311yescharacteristic
575C2×C4H(5,𝔽2)×C4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—41no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
609C4C43×#57511yescharacteristic
610C4C43×#57711yescharacteristic
611C4C43×#57711yescharacteristic
612C2—42no—
613C2—81no—
614C2—161no—
615C2—161no—
616C2C43×#326511yescharacteristic
617C2C43×#327511yescharacteristic
618C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3274C2
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×#3372C2semidirect
2. C43×#3368C2semidirect
3. C43×#3295C2semidirect
5. C43×#1717C2semidirect
6. C43×#1703C2semidirect
7. C43×#1698C2semidirect
8. C43×#1688C2semidirect
9. C43×#1681C2semidirect
10. C43×#1639C2semidirect
11. C43×#1631C2semidirect
12. C43×#1626C2semidirect
13. C43×#1622C2semidirect
14. C43×#1592C2semidirect
15. C43×#1582C2semidirect
17. C43×#557C22semidirect
22. C43×#492C22semidirect
25. C43×#487C22semidirect
28. C43×#486C22semidirect
32. C43×#477C22semidirect
42. C43×#460C22semidirect
47. C43×#446C22semidirect
48. C43×#446C22semidirect
56. C43×#335C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
275. #20193C43direct (N × H)
303. #3372C2×C43semidirect
304. #3368C2×C43semidirect
305. #3295C2×C43semidirect
307. #1717C2×C43semidirect
308. #1703C2×C43semidirect
309. #1698C2×C43semidirect
310. #1688C2×C43semidirect
311. #1681C2×C43semidirect
312. #1639C2×C43semidirect
313. #1631C2×C43semidirect
314. #1626C2×C43semidirect
315. #1622C2×C43semidirect
316. #1592C2×C43semidirect
317. #1582C2×C43semidirect
326. #557C22×C43semidirect
331. #492C22×C43semidirect
334. #487C22×C43semidirect
337. #486C22×C43semidirect
341. #477C22×C43semidirect
351. #460C22×C43semidirect
356. #446C22×C43semidirect
357. #446C22×C43semidirect
365. #335C22×C43semidirect
366. #334C22×C43semidirect
367. #333C22×C43semidirect
368. #332C22×C43semidirect
370. #331C22×C43semidirect
371. Q8⋊C8C22×C43semidirect
372. Q8⋊C8C22×C43semidirect
375. #322C22×C43semidirect
376. C43#20193direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33722
C43×#33682
C43×#32952
C43×#32742
C43×#17172
C43×#17032
C43×#16982
C43×#16882
C43×#16812
C43×#16392
C43×#16312
C43×#16262
C43×#16222
C43×#15922
C43×#15822
#2019343