Finite Group Databasebeta

← C43×#19830 #24939847

Subgroups — C43×#19830 #24939847

Order 11008.

572 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
1Q8×SD16×C43C211yesmaximal, characteristic
2C43×#3364C211yesmaximal, characteristic
3C43×#3363C211yesmaximal, characteristic, complemented
4C43×#3328C211yesmaximal, characteristic
5C43×#1718C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic
7C43×#1680C211yesmaximal, characteristic, complemented
8C43×#1680C211yesmaximal, characteristic, complemented
9C43×#1672C211yesmaximal, characteristic, complemented
10C43×#1649C211yesmaximal, characteristic
11C43×#1648C211yesmaximal, characteristic, complemented
12C43×#1645C211yesmaximal, characteristic, complemented
13C43×#1638C211yesmaximal, characteristic
14C43×#1583C211yesmaximal, characteristic
15C43×#1579C211yesmaximal, characteristic, complemented
16Q82×C43C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#556C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#498—21no—
22C43×#498C2211yescharacteristic
23C43×#488—21no—
24C43×#487—21no—
25C43×#487C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#479—21no—
31C43×#477—21no—
32C43×#477C2211yescharacteristic
33C43×#476—21no—
34C43×#476C2211yescharacteristic
35C43×#475—21no—
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#470—21no—
40C43×#464—21no—
41C43×#462—21no—
42C43×#462C2211yescharacteristic
43C43×#462C2211yescharacteristic
44C43×#462C2211yescharacteristic
45C43×#451—21no—
46C8×Q8×C43C2211yescharacteristic
47C8×Q8×C43C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C4×Q16×C43—21no—
50C4×Q16×C43—21no—
51C4×Q16×C43C2211yescharacteristic
52C4×SD16×C43—21no—
53C4×SD16×C43C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#419—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C22×Q8×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43D411yescharacteristic
72C2×SD16×C43D411yescharacteristic
73C2×M16×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—41no—
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#126×C43—41no—
84#125×C43—21no—
85#125×C43—41no—
86#124×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—41no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43C2311yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—41no—
104#107×C43D411yescharacteristic
105#106×C43—21no—
106#106×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43D411yescharacteristic
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
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×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—
138C4×C8×C43—21no—
139C4×C8×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×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158Q16×C43—22no—
159Q16×C43—42no—
160Q16×C43—42no—
161Q16×C43—81no—
162SD16×C43—22no—
163M16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
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—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—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—41no—
203C42×C43—41no—
204C42×C43—41no—
205C42×C43C2411yescharacteristic
206C23×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—82no—
218Q8×C43—81no—
219Q8×C43—161no—
220Q8×C43#13512yes—
221Q8×C43#13712yes—
222D4×C43—21no—
223D4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
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—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250#19830C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43D4211yescharacteristic
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C2×#13511yescharacteristic
268C4×C43C2×#13711yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57811yescharacteristic
271Q8×SD16C2×C4311yescharacteristic
272#3364C2×C4311yescharacteristic
273#3363C2×C4311yescharacteristic, complemented
274#3328C2×C4311yescharacteristic
275#1718C2×C4311yescharacteristic, complemented
276#1703C2×C4311yescharacteristic
277#1680C2×C4311yescharacteristic, complemented
278#1680C2×C4311yescharacteristic, complemented
279#1672C2×C4311yescharacteristic, complemented
280#1649C2×C4311yescharacteristic
281#1648C2×C4311yescharacteristic, complemented
282#1645C2×C4311yescharacteristic, complemented
283#1638C2×C4311yescharacteristic
284#1583C2×C4311yescharacteristic
285#1579C2×C4311yescharacteristic, complemented
286C2×C43—81no—
287C2×C43#327011yescharacteristic
288C2×C43#328211yescharacteristic
289C2×C43#328911yescharacteristic
290Q82C22×C4311yescharacteristic
291#557C22×C4311yescharacteristic
292#556C22×C4311yescharacteristic
293D4×Q8C22×C4311yescharacteristic
294#500C22×C4311yescharacteristic
295#498—21no—
296#498C22×C4311yescharacteristic
297#488—21no—
298#487—21no—
299#487C22×C4311yescharacteristic
300#487C22×C4311yescharacteristic
301#487C22×C4311yescharacteristic
302#487C22×C4311yescharacteristic
303#485—21no—
304#479—21no—
305#477—21no—
306#477C22×C4311yescharacteristic
307#476—21no—
308#476C22×C4311yescharacteristic
309#475—21no—
310#475C22×C4311yescharacteristic
311#475C22×C4311yescharacteristic
312#474C22×C4311yescharacteristic
313#470—21no—
314#464—21no—
315#462—21no—
316#462C22×C4311yescharacteristic
317#462C22×C4311yescharacteristic
318#462C22×C4311yescharacteristic
319#451—21no—
320C8×Q8C22×C4311yescharacteristic
321C8×Q8C22×C4311yescharacteristic
322C8×Q8C22×C4311yescharacteristic
323C4×Q16—21no—
324C4×Q16—21no—
325C4×Q16C22×C4311yescharacteristic
326C4×SD16—21no—
327C4×SD16C22×C4311yescharacteristic
328#436C22×C4311yescharacteristic
329#419—21no—
330#334C22×C4311yescharacteristic
331#334C22×C4311yescharacteristic
332#333C22×C4311yescharacteristic
333#332C22×C4311yescharacteristic
334#332C22×C4311yescharacteristic
335#332C22×C4311yescharacteristic
336Q8⋊C8C22×C4311yescharacteristic
337Q8⋊C8C22×C4311yescharacteristic
338Q8⋊C8C22×C4311yescharacteristic
339D4⋊C8C22×C4311yescharacteristic
340#322C22×C4311yescharacteristic
341C43#1983011yescharacteristic, direct product factor, Sylow
342C22×Q8—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16D4×C4311yescharacteristic
347C2×SD16D4×C4311yescharacteristic
348C2×M16—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—41no—
354C4⋊Q8C23×C4311yescharacteristic
355C4⋊Q8C23×C4311yescharacteristic
356C4⋊Q8C23×C4311yescharacteristic
357C4⋊Q8C23×C4311yescharacteristic
358#126—41no—
359#125—21no—
360#125—41no—
361#124—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C4311yescharacteristic
371C4×Q8C23×C4311yescharacteristic
372C4×Q8C23×C4311yescharacteristic
373C4×D4—21no—
374C4×D4C23×C4311yescharacteristic
375#117—21no—
376#107—21no—
377#107—21no—
378#107—41no—
379#107D4×C4311yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106D4×C4311yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C4311yescharacteristic
390C4⋊C8C23×C4311yescharacteristic
391C4⋊C8C23×C4311yescharacteristic
392C4⋊C8C23×C4311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—41no—
406#103D4×C4311yescharacteristic
407#103D4×C4311yescharacteristic
408#103D4×C4311yescharacteristic
409#102—21no—
410#102—21no—
411#102D4×C4311yescharacteristic
412C22⋊C8—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C4311yescharacteristic
417C4×C8C23×C4311yescharacteristic
418C4×C8C23×C4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C4311yescharacteristic
428C2×Q8C2×D4×C4311yescharacteristic
429C2×Q8C2×D4×C4311yescharacteristic
430C2×D4C2×D4×C4311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437SD16—22no—
438M16—81no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C2×D4×C4311yescharacteristic
445C2×C8C2×D4×C4311yescharacteristic
446C2×C8C2×D4×C4311yescharacteristic
447C2×C8C2×D4×C4311yescharacteristic
448C4⋊C4—21no—
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—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42C24×C4311yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—82no—
493Q8—81no—
494Q8—161no—
495Q8#135×C4312yes—
496Q8#137×C4312yes—
497D4—21no—
498D4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—82no—
513C2×C4C22×D4×C4311yescharacteristic
514C2×C4C22×D4×C4311yescharacteristic
515C2×C4H(5,𝔽2)×C4311yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22D42×C4311yescharacteristic
529C4—22no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#135×C4311yescharacteristic
542C4C2×#137×C4311yescharacteristic
543C4C43×#57711yescharacteristic
544C4C43×#57811yescharacteristic
545C2—81no—
546C2C43×#327011yescharacteristic
547C2C43×#328211yescharacteristic
548C2C43×#328911yescharacteristic
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
3. C43×#3363C2semidirect
5. C43×#1718C2semidirect
7. C43×#1680C2semidirect
8. C43×#1680C2semidirect
9. C43×#1672C2semidirect
11. C43×#1648C2semidirect
12. C43×#1645C2semidirect
15. C43×#1579C2semidirect
250. #19830C43direct (N × H)
273. #3363C2×C43semidirect
275. #1718C2×C43semidirect
277. #1680C2×C43semidirect
278. #1680C2×C43semidirect
279. #1672C2×C43semidirect
281. #1648C2×C43semidirect
282. #1645C2×C43semidirect
285. #1579C2×C43semidirect
341. C43#19830direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×SD16×C432
C43×#33642
C43×#33632
C43×#33282
C43×#17182
C43×#17032
C43×#16802
C43×#16722
C43×#16492
C43×#16482
C43×#16452
C43×#16382
C43×#15832
C43×#15792
#1983043