Finite Group Databasebeta

← C43×#20215 #24940232

Subgroups — C43×#20215 #24940232

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3385C211yesmaximal, characteristic
2Q8×Q16×C43C211yesmaximal, characteristic, complemented
3C43×#3369C211yesmaximal, characteristic
4C43×#3356C211yesmaximal, characteristic
5C43×#1723C211yesmaximal, characteristic, complemented
6C43×#1704C211yesmaximal, characteristic, complemented
7C43×#1696C211yesmaximal, characteristic, complemented
8C43×#1695C211yesmaximal, characteristic
9C43×#1672C211yesmaximal, characteristic, complemented
10C43×#1645C211yesmaximal, characteristic, complemented
11C43×#1638C211yesmaximal, characteristic
12C43×#1633C211yesmaximal, characteristic, complemented
13C43×#1632C211yesmaximal, characteristic
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic
16Q82×C43C2211yescharacteristic
17Q82×C43C2211yescharacteristic
18C43×#556C2211yescharacteristic
19C43×#554C2211yescharacteristic
20C43×#501—21no—
21C43×#500—21no—
22C43×#500C2211yescharacteristic
23C43×#500C2211yescharacteristic
24C43×#498C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#489—21no—
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#483—21no—
31C43×#479—21no—
32C43×#477—21no—
33C43×#477—21no—
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#477C2211yescharacteristic
37C43×#477C2211yescharacteristic
38C43×#476C2211yescharacteristic
39C43×#476C2211yescharacteristic
40C43×#475—21no—
41C43×#475C2211yescharacteristic
42C43×#474—21no—
43C43×#470—21no—
44C43×#464—21no—
45C43×#462C2211yescharacteristic
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C43×#441—21no—
50C43×#440—21no—
51C4×Q16×C43—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×SD16×C43C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#428—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—41no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43D411yescharacteristic
71C2×M16×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—41no—
77C4⋊Q8×C43—41no—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82#126×C43—41no—
83#125×C43—21no—
84#124×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—41no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43C2311yescharacteristic
94C4×Q8×C43C2311yescharacteristic
95C4×Q8×C43C2311yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99C2×C4⋊C4×C43—21no—
100#107×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43D411yescharacteristic
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43D411yescharacteristic
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—21no—
129#103×C43—21no—
130#103×C43—41no—
131#103×C43D411yescharacteristic
132#103×C43D411yescharacteristic
133#103×C43D411yescharacteristic
134#102×C43—21no—
135#102×C43—21no—
136#102×C43D411yescharacteristic
137C22⋊C8×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—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156Q16×C43—22no—
157Q16×C43—42no—
158Q16×C43—82no—
159SD16×C43—22no—
160M16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
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—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—41no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43C2411yescharacteristic
203C23×C43—21no—
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212Q8×C43—81no—
213Q8×C43—81no—
214Q8×C43—161no—
215Q8×C43—161no—
216Q8×C43#13712yes—
217D4×C43—21no—
218D4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—161no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43#13712yes—
245#20215C4311yesmaximal, characteristic, direct product factor, Sylow
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43D4211yescharacteristic
250C4×C43—22no—
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—81no—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C2×#13711yescharacteristic
263C4×C43C2×#13711yescharacteristic
264C4×C43#57811yescharacteristic
265C4×C43#57811yescharacteristic
266#3385C2×C4311yescharacteristic
267Q8×Q16C2×C4311yescharacteristic, complemented
268#3369C2×C4311yescharacteristic
269#3356C2×C4311yescharacteristic
270#1723C2×C4311yescharacteristic, complemented
271#1704C2×C4311yescharacteristic, complemented
272#1696C2×C4311yescharacteristic, complemented
273#1695C2×C4311yescharacteristic
274#1672C2×C4311yescharacteristic, complemented
275#1645C2×C4311yescharacteristic, complemented
276#1638C2×C4311yescharacteristic
277#1633C2×C4311yescharacteristic, complemented
278#1632C2×C4311yescharacteristic
279#1593C2×C4311yescharacteristic, complemented
280#1583C2×C4311yescharacteristic
281C2×C43—81no—
282C2×C43#327011yescharacteristic
283C2×C43#327611yescharacteristic
284C2×C43#328811yescharacteristic
285Q82C22×C4311yescharacteristic
286Q82C22×C4311yescharacteristic
287#556C22×C4311yescharacteristic
288#554C22×C4311yescharacteristic
289#501—21no—
290#500—21no—
291#500C22×C4311yescharacteristic
292#500C22×C4311yescharacteristic
293#498C22×C4311yescharacteristic
294#494C22×C4311yescharacteristic
295#489—21no—
296#487C22×C4311yescharacteristic
297#487C22×C4311yescharacteristic
298#485—21no—
299#483—21no—
300#479—21no—
301#477—21no—
302#477—21no—
303#477C22×C4311yescharacteristic
304#477C22×C4311yescharacteristic
305#477C22×C4311yescharacteristic
306#477C22×C4311yescharacteristic
307#476C22×C4311yescharacteristic
308#476C22×C4311yescharacteristic
309#475—21no—
310#475C22×C4311yescharacteristic
311#474—21no—
312#470—21no—
313#464—21no—
314#462C22×C4311yescharacteristic
315#446C22×C4311yescharacteristic
316#446C22×C4311yescharacteristic
317C8×Q8C22×C4311yescharacteristic
318#441—21no—
319#440—21no—
320C4×Q16—21no—
321C4×Q16C22×C4311yescharacteristic
322C4×SD16C22×C4311yescharacteristic
323#436C22×C4311yescharacteristic
324#428—21no—
325#334C22×C4311yescharacteristic
326#334C22×C4311yescharacteristic
327#333C22×C4311yescharacteristic
328#333C22×C4311yescharacteristic
329#333C22×C4311yescharacteristic
330#332C22×C4311yescharacteristic
331Q8⋊C8C22×C4311yescharacteristic
332Q8⋊C8C22×C4311yescharacteristic
333Q8⋊C8C22×C4311yescharacteristic
334D4⋊C8C22×C4311yescharacteristic
335#322C22×C4311yescharacteristic
336C43#2021511yescharacteristic, direct product factor, Sylow
337C2×Q16—21no—
338C2×Q16—41no—
339C2×Q16D4×C4311yescharacteristic
340C2×SD16D4×C4311yescharacteristic
341C2×M16—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—41no—
347C4⋊Q8—41no—
348C4⋊Q8C23×C4311yescharacteristic
349C4⋊Q8C23×C4311yescharacteristic
350C4⋊Q8C23×C4311yescharacteristic
351C4⋊Q8C23×C4311yescharacteristic
352#126—41no—
353#125—21no—
354#124—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—41no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C23×C4311yescharacteristic
364C4×Q8C23×C4311yescharacteristic
365C4×Q8C23×C4311yescharacteristic
366C4×D4—21no—
367C4×D4C23×C4311yescharacteristic
368#117—21no—
369C2×C4⋊C4—21no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107D4×C4311yescharacteristic
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106D4×C4311yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8C23×C4311yescharacteristic
389C4⋊C8C23×C4311yescharacteristic
390C4⋊C8C23×C4311yescharacteristic
391C4⋊C8C23×C4311yescharacteristic
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—41no—
401#103D4×C4311yescharacteristic
402#103D4×C4311yescharacteristic
403#103D4×C4311yescharacteristic
404#102—21no—
405#102—21no—
406#102D4×C4311yescharacteristic
407C22⋊C8—21no—
408#97—21no—
409#97—21no—
410C4×C8—21no—
411C4×C8C23×C4311yescharacteristic
412C4×C8C23×C4311yescharacteristic
413C4×C8C23×C4311yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8C2×D4×C4311yescharacteristic
421C2×Q8C2×D4×C4311yescharacteristic
422C2×Q8C2×D4×C4311yescharacteristic
423C2×D4C2×D4×C4311yescharacteristic
424C22×C4—21no—
425C22×C4—41no—
426Q16—22no—
427Q16—42no—
428Q16—82no—
429SD16—22no—
430M16—42no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×D4×C4311yescharacteristic
437C2×C8C2×D4×C4311yescharacteristic
438C2×C8C2×D4×C4311yescharacteristic
439C2×C8C2×D4×C4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C4311yescharacteristic
459C4⋊C4C2×D4×C4311yescharacteristic
460C4⋊C4C2×D4×C4311yescharacteristic
461C4⋊C4C2×D4×C4311yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—41no—
471C42—41no—
472C42C24×C4311yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—81no—
483Q8—81no—
484Q8—161no—
485Q8—161no—
486Q8#137×C4312yes—
487D4—21no—
488D4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—161no—
503C2×C4C22×D4×C4311yescharacteristic
504C2×C4C22×D4×C4311yescharacteristic
505C2×C4H(5,𝔽2)×C4311yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8#137×C4312yes—
515C22—41no—
516C22—41no—
517C22—41no—
518C22D42×C4311yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4C2×#137×C4311yescharacteristic
532C4C2×#137×C4311yescharacteristic
533C4C43×#57811yescharacteristic
534C4C43×#57811yescharacteristic
535C2—81no—
536C2C43×#327011yescharacteristic
537C2C43×#327611yescharacteristic
538C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×D4×C43C2×D4
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. Q8×Q16×C43C2semidirect
5. C43×#1723C2semidirect
6. C43×#1704C2semidirect
7. C43×#1696C2semidirect
9. C43×#1672C2semidirect
10. C43×#1645C2semidirect
12. C43×#1633C2semidirect
14. C43×#1593C2semidirect
245. #20215C43direct (N × H)
267. Q8×Q16C2×C43semidirect
270. #1723C2×C43semidirect
271. #1704C2×C43semidirect
272. #1696C2×C43semidirect
274. #1672C2×C43semidirect
275. #1645C2×C43semidirect
277. #1633C2×C43semidirect
279. #1593C2×C43semidirect
336. C43#20215direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33852
Q8×Q16×C432
C43×#33692
C43×#33562
C43×#17232
C43×#17042
C43×#16962
C43×#16952
C43×#16722
C43×#16452
C43×#16382
C43×#16332
C43×#16322
C43×#15932
C43×#15832
#2021543