Finite Group Databasebeta

← C43×#20196 #24940213

Subgroups — C43×#20196 #24940213

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3373C211yesmaximal, characteristic, complemented
2C43×#3373C211yesmaximal, characteristic, complemented
3C43×#3298C211yesmaximal, characteristic, complemented
4C43×#3276C211yesmaximal, characteristic, complemented
5C43×#1720C211yesmaximal, characteristic, complemented
6C43×#1701C211yesmaximal, characteristic, complemented
7C43×#1700C211yesmaximal, characteristic, complemented
8C43×#1690C211yesmaximal, characteristic, complemented
9C43×#1681C211yesmaximal, characteristic, complemented
10C43×#1651C211yesmaximal, characteristic, complemented
11C43×#1651C211yesmaximal, characteristic, complemented
12C43×#1640C211yesmaximal, characteristic, complemented
13C43×#1625C211yesmaximal, characteristic
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#559C2211yescharacteristic
18D4×Q8×C43C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#494C2211yescharacteristic
23C43×#489—21no—
24C43×#489—21no—
25C43×#487C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#483—21no—
30C43×#476—21no—
31C43×#476—21no—
32C43×#475C2211yescharacteristic
33C43×#475C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#470—21no—
36C43×#465—21no—
37C43×#463—21no—
38C43×#463—21no—
39C43×#462C2211yescharacteristic
40C43×#461C2211yescharacteristic
41C43×#461C2211yescharacteristic
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#451—21no—
46C43×#448—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#442—21no—
50C43×#442—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C2×#103×C43—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69C22×Q8×C43—21no—
70#137×C43—44no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43D411yescharacteristic
77C2×SD16×C43D411yescharacteristic
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87#127×C43C2311yescharacteristic
88#124×C43—21no—
89#124×C43—21no—
90#123×C43—41no—
91#123×C43—41no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—41no—
96C22⋊Q8×C43—41no—
97#121×C43—21no—
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43C2311yescharacteristic
105C4×D4×C43C2311yescharacteristic
106C2×C4⋊C4×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—41no—
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×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43D411yescharacteristic
128#103×C43D411yescharacteristic
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
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—41no—
152C2×Q8×C43—42no—
153C2×Q8×C43—42no—
154C2×Q8×C43—81no—
155C2×Q8×C43—81no—
156C2×Q8×C43C2×D411yescharacteristic
157C2×Q8×C43C2×D411yescharacteristic
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—41no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170Q16×C43—42no—
171Q16×C43—42no—
172Q16×C43—81no—
173SD16×C43—22no—
174SD16×C43—41no—
175SD16×C43—42no—
176SD16×C43—81no—
177D8×C43—42no—
178D8×C43—42no—
179M16×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
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—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43C2411yescharacteristic
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—82no—
230Q8×C43—82no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—81no—
239D4×C43—82no—
240D4×C43AGL(1,ℤ/8)12yes—
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—41no—
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—82no—
255C2×C4×C43—82no—
256C2×C4×C43—82no—
257C2×C4×C43—161no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270#20196C4311yesmaximal, characteristic, direct product factor, Sylow
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43D4211yescharacteristic
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C43#57511yescharacteristic
293C4×C43#57711yescharacteristic
294C4×C43#57711yescharacteristic
295#3373C2×C4311yescharacteristic, complemented
296#3373C2×C4311yescharacteristic, complemented
297#3298C2×C4311yescharacteristic, complemented
298#3276C2×C4311yescharacteristic, complemented
299#1720C2×C4311yescharacteristic, complemented
300#1701C2×C4311yescharacteristic, complemented
301#1700C2×C4311yescharacteristic, complemented
302#1690C2×C4311yescharacteristic, complemented
303#1681C2×C4311yescharacteristic, complemented
304#1651C2×C4311yescharacteristic, complemented
305#1651C2×C4311yescharacteristic, complemented
306#1640C2×C4311yescharacteristic, complemented
307#1625C2×C4311yescharacteristic
308#1592C2×C4311yescharacteristic, complemented
309#1582C2×C4311yescharacteristic, complemented
310C2×C43—42no—
311C2×C43—81no—
312C2×C43—161no—
313C2×C43#326511yescharacteristic
314C2×C43#327511yescharacteristic
315C2×C43#328911yescharacteristic
316C2×#137—21no—
317#559C22×C4311yescharacteristic
318D4×Q8C22×C4311yescharacteristic
319D4×Q8C22×C4311yescharacteristic
320#547C22×C4311yescharacteristic
321#498C22×C4311yescharacteristic
322#494C22×C4311yescharacteristic
323#489—21no—
324#489—21no—
325#487C22×C4311yescharacteristic
326#486C22×C4311yescharacteristic
327#486C22×C4311yescharacteristic
328#486C22×C4311yescharacteristic
329#483—21no—
330#476—21no—
331#476—21no—
332#475C22×C4311yescharacteristic
333#475C22×C4311yescharacteristic
334#475C22×C4311yescharacteristic
335#470—21no—
336#465—21no—
337#463—21no—
338#463—21no—
339#462C22×C4311yescharacteristic
340#461C22×C4311yescharacteristic
341#461C22×C4311yescharacteristic
342#459C22×C4311yescharacteristic
343#459C22×C4311yescharacteristic
344#452—21no—
345#451—21no—
346#448—21no—
347#446C22×C4311yescharacteristic
348#446C22×C4311yescharacteristic
349#442—21no—
350#442—21no—
351C4×SD16C22×C4311yescharacteristic
352C4×SD16C22×C4311yescharacteristic
353#436C22×C4311yescharacteristic
354C8×D4C22×C4311yescharacteristic
355C2×#103—21no—
356#335C22×C4311yescharacteristic
357#334C22×C4311yescharacteristic
358#332C22×C4311yescharacteristic
359#332C22×C4311yescharacteristic
360#332C22×C4311yescharacteristic
361#331C22×C4311yescharacteristic
362Q8⋊C8C22×C4311yescharacteristic
363Q8⋊C8C22×C4311yescharacteristic
364D4⋊C8C22×C4311yescharacteristic
365D4⋊C8C22×C4311yescharacteristic
366#322C22×C4311yescharacteristic
367C43#2019611yescharacteristic, direct product factor, Sylow
368C2×#41—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371#137—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C4311yescharacteristic
378C2×SD16D4×C4311yescharacteristic
379C2×D8—21no—
380C2×D8—21no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8C23×C4311yescharacteristic
386C4⋊Q8C23×C4311yescharacteristic
387C4⋊Q8C23×C4311yescharacteristic
388#127C23×C4311yescharacteristic
389#124—21no—
390#124—21no—
391#123—41no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398#121—21no—
399C4×Q8C23×C4311yescharacteristic
400C4×Q8C23×C4311yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C4311yescharacteristic
406C4×D4C23×C4311yescharacteristic
407C2×C4⋊C4—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—41no—
412#106D4×C4311yescharacteristic
413#106D4×C4311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8C23×C4311yescharacteristic
417C4⋊C8C23×C4311yescharacteristic
418C4⋊C8C23×C4311yescharacteristic
419C4⋊C8C23×C4311yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C4311yescharacteristic
429#103D4×C4311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—41no—
437#102D4×C4311yescharacteristic
438#102D4×C4311yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442#97—21no—
443C4×C8C23×C4311yescharacteristic
444C4×C8C23×C4311yescharacteristic
445C4×C8C23×C4311yescharacteristic
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×Q8C2×D4×C4311yescharacteristic
458C2×Q8C2×D4×C4311yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4C2×D4×C4311yescharacteristic
464C2×D4C2×D4×C4311yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472Q16—42no—
473Q16—81no—
474SD16—22no—
475SD16—41no—
476SD16—42no—
477SD16—81no—
478D8—42no—
479D8—42no—
480M16—42no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—81no—
487C2×C8C2×D4×C4311yescharacteristic
488C2×C8C2×D4×C4311yescharacteristic
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C4311yescharacteristic
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C4⋊C4C2×D4×C4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42C24×C4311yescharacteristic
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—82no—
531Q8—82no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—82no—
541D4AGL(1,ℤ/8)×C4312yes—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—161no—
559C2×C4C22×D4×C4311yescharacteristic
560C2×C4C22×D4×C4311yescharacteristic
561C2×C4H(5,𝔽2)×C4311yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
592C4C43×#57511yescharacteristic
593C4C43×#57711yescharacteristic
594C4C43×#57711yescharacteristic
595C2—42no—
596C2—81no—
597C2—161no—
598C2C43×#326511yescharacteristic
599C2C43×#327511yescharacteristic
600C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#1625C2
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×#3373C2semidirect
2. C43×#3373C2semidirect
3. C43×#3298C2semidirect
4. C43×#3276C2semidirect
5. C43×#1720C2semidirect
6. C43×#1701C2semidirect
7. C43×#1700C2semidirect
8. C43×#1690C2semidirect
9. C43×#1681C2semidirect
10. C43×#1651C2semidirect
11. C43×#1651C2semidirect
12. C43×#1640C2semidirect
14. C43×#1592C2semidirect
15. C43×#1582C2semidirect
270. #20196C43direct (N × H)
295. #3373C2×C43semidirect
296. #3373C2×C43semidirect
297. #3298C2×C43semidirect
298. #3276C2×C43semidirect
299. #1720C2×C43semidirect
300. #1701C2×C43semidirect
301. #1700C2×C43semidirect
302. #1690C2×C43semidirect
303. #1681C2×C43semidirect
304. #1651C2×C43semidirect
305. #1651C2×C43semidirect
306. #1640C2×C43semidirect
308. #1592C2×C43semidirect
309. #1582C2×C43semidirect
367. C43#20196direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33732
C43×#32982
C43×#32762
C43×#17202
C43×#17012
C43×#17002
C43×#16902
C43×#16812
C43×#16512
C43×#16402
C43×#16252
C43×#15922
C43×#15822
#2019643