Finite Group Databasebeta

← C43×#20217 #24940234

Subgroups — C43×#20217 #24940234

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3400C211yesmaximal, characteristic
2C43×#3387C211yesmaximal, characteristic, complemented
3Q8×Q16×C43C211yesmaximal, characteristic, complemented
4C43×#3375C211yesmaximal, characteristic
5C43×#1714C211yesmaximal, characteristic
6C43×#1698C211yesmaximal, characteristic
7C43×#1696C211yesmaximal, characteristic, complemented
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1666C211yesmaximal, characteristic
10C43×#1645C211yesmaximal, characteristic, complemented
11C43×#1636C211yesmaximal, characteristic, complemented
12C43×#1630C211yesmaximal, characteristic
13C43×#1623C211yesmaximal, characteristic
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic
17Q82×C43C2211yescharacteristic
18Q82×C43C2211yescharacteristic
19C43×#557C2211yescharacteristic
20C43×#501—21no—
21C43×#500—21no—
22C43×#500C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#497—21no—
25C43×#492C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#489—21no—
28C43×#487C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#479—21no—
31C43×#477—21no—
32C43×#477—21no—
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#477C2211yescharacteristic
37C43×#475—21no—
38C43×#475C2211yescharacteristic
39C43×#474—21no—
40C43×#464—21no—
41C43×#464—21no—
42C43×#462C2211yescharacteristic
43C43×#461—21no—
44C43×#460C2211yescharacteristic
45C43×#460C2211yescharacteristic
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#441—21no—
51C43×#440—21no—
52C43×#440—21no—
53C4×Q16×C43—21no—
54C4×Q16×C43C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43D411yescharacteristic
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—41no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43—41no—
81C4⋊Q8×C43—41no—
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#125×C43—41no—
88#124×C43—21no—
89#124×C43—21no—
90#123×C43—41no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43C2311yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×Q8×C43C2311yescharacteristic
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43D411yescharacteristic
110#107×C43D411yescharacteristic
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43—21no—
117C4⋊C8×C43—21no—
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—41no—
129#103×C43D411yescharacteristic
130#103×C43D411yescharacteristic
131#103×C43D411yescharacteristic
132#103×C43D411yescharacteristic
133#102×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136#102×C43—21no—
137#97×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C22×C4×C43—41no—
157Q16×C43—22no—
158Q16×C43—22no—
159Q16×C43—81no—
160SD16×C43—42no—
161SD16×C43—42no—
162SD16×C43—81no—
163SD16×C43—81no—
164SD16×C43—82no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—41no—
203C42×C43—41no—
204C42×C43—41no—
205C42×C43C2411yescharacteristic
206C23×C43—41no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217Q8×C43—81no—
218Q8×C43—161no—
219Q8×C43—161no—
220Q8×C43#13712yes—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—161no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13712yes—
250#20217C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43D4211yescharacteristic
255C4×C43—22no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C2×#13711yescharacteristic
268C4×C43C2×#13711yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57811yescharacteristic
271#3400C2×C4311yescharacteristic
272#3387C2×C4311yescharacteristic, complemented
273Q8×Q16C2×C4311yescharacteristic, complemented
274#3375C2×C4311yescharacteristic
275#1714C2×C4311yescharacteristic
276#1698C2×C4311yescharacteristic
277#1696C2×C4311yescharacteristic, complemented
278#1692C2×C4311yescharacteristic, complemented
279#1666C2×C4311yescharacteristic
280#1645C2×C4311yescharacteristic, complemented
281#1636C2×C4311yescharacteristic, complemented
282#1630C2×C4311yescharacteristic
283#1623C2×C4311yescharacteristic
284#1593C2×C4311yescharacteristic, complemented
285#1584C2×C4311yescharacteristic, complemented
286C2×C43—161no—
287C2×C43#327011yescharacteristic
288C2×C43#327811yescharacteristic
289C2×C43#328811yescharacteristic
290#559C22×C4311yescharacteristic
291Q82C22×C4311yescharacteristic
292Q82C22×C4311yescharacteristic
293#557C22×C4311yescharacteristic
294#501—21no—
295#500—21no—
296#500C22×C4311yescharacteristic
297#498C22×C4311yescharacteristic
298#497—21no—
299#492C22×C4311yescharacteristic
300#492C22×C4311yescharacteristic
301#489—21no—
302#487C22×C4311yescharacteristic
303#486C22×C4311yescharacteristic
304#479—21no—
305#477—21no—
306#477—21no—
307#477C22×C4311yescharacteristic
308#477C22×C4311yescharacteristic
309#477C22×C4311yescharacteristic
310#477C22×C4311yescharacteristic
311#475—21no—
312#475C22×C4311yescharacteristic
313#474—21no—
314#464—21no—
315#464—21no—
316#462C22×C4311yescharacteristic
317#461—21no—
318#460C22×C4311yescharacteristic
319#460C22×C4311yescharacteristic
320#446C22×C4311yescharacteristic
321#446C22×C4311yescharacteristic
322#446C22×C4311yescharacteristic
323C8×Q8C22×C4311yescharacteristic
324#441—21no—
325#440—21no—
326#440—21no—
327C4×Q16—21no—
328C4×Q16C22×C4311yescharacteristic
329C4×Q16C22×C4311yescharacteristic
330#335C22×C4311yescharacteristic
331#334C22×C4311yescharacteristic
332#333C22×C4311yescharacteristic
333#333C22×C4311yescharacteristic
334#332C22×C4311yescharacteristic
335#331C22×C4311yescharacteristic
336Q8⋊C8C22×C4311yescharacteristic
337Q8⋊C8C22×C4311yescharacteristic
338Q8⋊C8C22×C4311yescharacteristic
339Q8⋊C8C22×C4311yescharacteristic
340#322C22×C4311yescharacteristic
341C43#2021711yescharacteristic, direct product factor, Sylow
342C2×Q16—21no—
343C2×Q16D4×C4311yescharacteristic
344C2×Q16D4×C4311yescharacteristic
345C2×SD16—21no—
346C2×SD16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—41no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—41no—
356C4⋊Q8—41no—
357C4⋊Q8C23×C4311yescharacteristic
358C4⋊Q8C23×C4311yescharacteristic
359C4⋊Q8C23×C4311yescharacteristic
360#127C23×C4311yescharacteristic
361#125—21no—
362#125—41no—
363#124—21no—
364#124—21no—
365#123—41no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C4311yescharacteristic
373C4×Q8C23×C4311yescharacteristic
374C4×Q8C23×C4311yescharacteristic
375C4×Q8C23×C4311yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107D4×C4311yescharacteristic
385#107D4×C4311yescharacteristic
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C23×C4311yescharacteristic
394C4⋊C8C23×C4311yescharacteristic
395C4⋊C8C23×C4311yescharacteristic
396C4⋊C8C23×C4311yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—41no—
404#103D4×C4311yescharacteristic
405#103D4×C4311yescharacteristic
406#103D4×C4311yescharacteristic
407#103D4×C4311yescharacteristic
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#97—21no—
413#97—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8C23×C4311yescharacteristic
417C4×C8C23×C4311yescharacteristic
418C4×C8C23×C4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8C2×D4×C4311yescharacteristic
425C2×Q8C2×D4×C4311yescharacteristic
426C2×Q8C2×D4×C4311yescharacteristic
427C2×Q8C2×D4×C4311yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C22×C4—41no—
432Q16—22no—
433Q16—22no—
434Q16—81no—
435SD16—42no—
436SD16—42no—
437SD16—81no—
438SD16—81no—
439SD16—82no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×D4×C4311yescharacteristic
446C2×C8C2×D4×C4311yescharacteristic
447C2×C8C2×D4×C4311yescharacteristic
448C2×C8C2×D4×C4311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C4311yescharacteristic
467C4⋊C4C2×D4×C4311yescharacteristic
468C4⋊C4C2×D4×C4311yescharacteristic
469C4⋊C4C2×D4×C4311yescharacteristic
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42C24×C4311yescharacteristic
481C23—41no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—81no—
493Q8—161no—
494Q8—161no—
495Q8#137×C4312yes—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—161no—
513C2×C4C22×D4×C4311yescharacteristic
514C2×C4C22×D4×C4311yescharacteristic
515C2×C4H(5,𝔽2)×C4311yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8#137×C4312yes—
525C22—81no—
526C22—81no—
527C22—81no—
528C22D42×C4311yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#137×C4311yescharacteristic
542C4C2×#137×C4311yescharacteristic
543C4C43×#57711yescharacteristic
544C4C43×#57811yescharacteristic
545C2—161no—
546C2C43×#327011yescharacteristic
547C2C43×#327811yescharacteristic
548C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radical#127×C43C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3387C2semidirect
3. Q8×Q16×C43C2semidirect
7. C43×#1696C2semidirect
8. C43×#1692C2semidirect
10. C43×#1645C2semidirect
11. C43×#1636C2semidirect
14. C43×#1593C2semidirect
15. C43×#1584C2semidirect
250. #20217C43direct (N × H)
272. #3387C2×C43semidirect
273. Q8×Q16C2×C43semidirect
277. #1696C2×C43semidirect
278. #1692C2×C43semidirect
280. #1645C2×C43semidirect
281. #1636C2×C43semidirect
284. #1593C2×C43semidirect
285. #1584C2×C43semidirect
341. C43#20217direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34002
C43×#33872
Q8×Q16×C432
C43×#33752
C43×#17142
C43×#16982
C43×#16962
C43×#16922
C43×#16662
C43×#16452
C43×#16362
C43×#16302
C43×#16232
C43×#15932
C43×#15842
#2021743