Finite Group Databasebeta

← C43×#20237 #24940254

Subgroups — C43×#20237 #24940254

Order 11008.

550 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3374C211yesmaximal, characteristic, complemented
2C43×#3372C211yesmaximal, characteristic
3C43×#3364C211yesmaximal, characteristic
4C43×#3356C211yesmaximal, characteristic
5C43×#1718C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1699C211yesmaximal, characteristic
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1650C211yesmaximal, characteristic
11C43×#1648C211yesmaximal, characteristic, complemented
12C43×#1644C211yesmaximal, characteristic
13C43×#1636C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#556C2211yescharacteristic
19C43×#554C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#491—21no—
23C43×#491—21no—
24C43×#488—21no—
25C43×#487C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#483—21no—
31C43×#479—21no—
32C43×#479—21no—
33C43×#479—21no—
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#470—21no—
40C43×#464—21no—
41C43×#462—21no—
42C43×#462C2211yescharacteristic
43C43×#462C2211yescharacteristic
44C43×#461—21no—
45C43×#461C2211yescharacteristic
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×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43D411yescharacteristic
72C2×M16×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43C2311yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79#126×C43—41no—
80#125×C43—21no—
81#125×C43—21no—
82#125×C43—21no—
83#125×C43—41no—
84#125×C43—41no—
85#124×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—41no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43C2311yescharacteristic
95C4×Q8×C43C2311yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99#117×C43—21no—
100C2×C4⋊C4×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—21no—
104#107×C43—41no—
105#107×C43D411yescharacteristic
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—21no—
131#103×C43—41no—
132#103×C43D411yescharacteristic
133#103×C43D411yescharacteristic
134#103×C43D411yescharacteristic
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×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154Q16×C43—41no—
155Q16×C43—42no—
156Q16×C43—42no—
157SD16×C43—41no—
158SD16×C43—42no—
159M16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
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—41no—
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×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43—41no—
203C42×C43C2411yescharacteristic
204C23×C43—21no—
205Q8×C43—21no—
206Q8×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—81no—
218D4×C43—21no—
219D4×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—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—161no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246#20237C4311yesmaximal, characteristic, direct product factor, Sylow
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43D4211yescharacteristic
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43#57511yescharacteristic
264C4×C43#57511yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267#3374C2×C4311yescharacteristic, complemented
268#3372C2×C4311yescharacteristic
269#3364C2×C4311yescharacteristic
270#3356C2×C4311yescharacteristic
271#1718C2×C4311yescharacteristic, complemented
272#1700C2×C4311yescharacteristic, complemented
273#1699C2×C4311yescharacteristic
274#1692C2×C4311yescharacteristic, complemented
275#1684C2×C4311yescharacteristic, complemented
276#1650C2×C4311yescharacteristic
277#1648C2×C4311yescharacteristic, complemented
278#1644C2×C4311yescharacteristic
279#1636C2×C4311yescharacteristic, complemented
280#1592C2×C4311yescharacteristic
281#1584C2×C4311yescharacteristic, complemented
282C2×C43—81no—
283C2×C43#326911yescharacteristic
284C2×C43#327711yescharacteristic
285C2×C43#328911yescharacteristic
286#557C22×C4311yescharacteristic
287#557C22×C4311yescharacteristic
288#556C22×C4311yescharacteristic
289#554C22×C4311yescharacteristic
290#500C22×C4311yescharacteristic
291#498C22×C4311yescharacteristic
292#491—21no—
293#491—21no—
294#488—21no—
295#487C22×C4311yescharacteristic
296#487C22×C4311yescharacteristic
297#487C22×C4311yescharacteristic
298#487C22×C4311yescharacteristic
299#485—21no—
300#483—21no—
301#479—21no—
302#479—21no—
303#479—21no—
304#477C22×C4311yescharacteristic
305#477C22×C4311yescharacteristic
306#475C22×C4311yescharacteristic
307#475C22×C4311yescharacteristic
308#474C22×C4311yescharacteristic
309#470—21no—
310#464—21no—
311#462—21no—
312#462C22×C4311yescharacteristic
313#462C22×C4311yescharacteristic
314#461—21no—
315#461C22×C4311yescharacteristic
316#446C22×C4311yescharacteristic
317#446C22×C4311yescharacteristic
318C8×Q8C22×C4311yescharacteristic
319#441—21no—
320#440—21no—
321C4×Q16—21no—
322C4×Q16C22×C4311yescharacteristic
323C4×SD16C22×C4311yescharacteristic
324#436C22×C4311yescharacteristic
325#428—21no—
326#335C22×C4311yescharacteristic
327#335C22×C4311yescharacteristic
328#333C22×C4311yescharacteristic
329#332C22×C4311yescharacteristic
330#332C22×C4311yescharacteristic
331#332C22×C4311yescharacteristic
332Q8⋊C8C22×C4311yescharacteristic
333Q8⋊C8C22×C4311yescharacteristic
334Q8⋊C8C22×C4311yescharacteristic
335D4⋊C8C22×C4311yescharacteristic
336#322C22×C4311yescharacteristic
337C43#2023711yescharacteristic, direct product factor, Sylow
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16D4×C4311yescharacteristic
341C2×SD16—21no—
342C2×SD16D4×C4311yescharacteristic
343C2×M16—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8C23×C4311yescharacteristic
347C4⋊Q8C23×C4311yescharacteristic
348C4⋊Q8C23×C4311yescharacteristic
349C4⋊Q8C23×C4311yescharacteristic
350#126—41no—
351#125—21no—
352#125—21no—
353#125—21no—
354#125—41no—
355#125—41no—
356#124—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—41no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C23×C4311yescharacteristic
366C4×Q8C23×C4311yescharacteristic
367C4×Q8C23×C4311yescharacteristic
368C4×D4—21no—
369C4×D4C23×C4311yescharacteristic
370#117—21no—
371C2×C4⋊C4—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—41no—
376#107D4×C4311yescharacteristic
377#106—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106D4×C4311yescharacteristic
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8C23×C4311yescharacteristic
386C4⋊C8C23×C4311yescharacteristic
387C4⋊C8C23×C4311yescharacteristic
388C4⋊C8C23×C4311yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
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—21no—
401#103—21no—
402#103—41no—
403#103D4×C4311yescharacteristic
404#103D4×C4311yescharacteristic
405#103D4×C4311yescharacteristic
406#102—21no—
407#102D4×C4311yescharacteristic
408C22⋊C8—21no—
409#97—21no—
410#97—21no—
411C4×C8—21no—
412C4×C8C23×C4311yescharacteristic
413C4×C8C23×C4311yescharacteristic
414C4×C8C23×C4311yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C2×D4×C4311yescharacteristic
420C2×Q8C2×D4×C4311yescharacteristic
421C2×Q8C2×D4×C4311yescharacteristic
422C2×D4C2×D4×C4311yescharacteristic
423C22×C4—21no—
424C22×C4—41no—
425Q16—41no—
426Q16—42no—
427Q16—42no—
428SD16—41no—
429SD16—42no—
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⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C4311yescharacteristic
461C4⋊C4C2×D4×C4311yescharacteristic
462C4⋊C4C2×D4×C4311yescharacteristic
463C4⋊C4C2×D4×C4311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42—41no—
474C42C24×C4311yescharacteristic
475C23—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489D4—21no—
490D4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—161no—
505C2×C4C22×D4×C4311yescharacteristic
506C2×C4C22×D4×C4311yescharacteristic
507C2×C4H(5,𝔽2)×C4311yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22D42×C4311yescharacteristic
521C4—21no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4C43×#57511yescharacteristic
534C4C43×#57511yescharacteristic
535C4C43×#57811yescharacteristic
536C4C43×#57811yescharacteristic
537C2—81no—
538C2C43×#326911yescharacteristic
539C2C43×#327711yescharacteristic
540C2C43×#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
1. C43×#3374C2semidirect
5. C43×#1718C2semidirect
6. C43×#1700C2semidirect
8. C43×#1692C2semidirect
9. C43×#1684C2semidirect
11. C43×#1648C2semidirect
13. C43×#1636C2semidirect
15. C43×#1584C2semidirect
246. #20237C43direct (N × H)
267. #3374C2×C43semidirect
271. #1718C2×C43semidirect
272. #1700C2×C43semidirect
274. #1692C2×C43semidirect
275. #1684C2×C43semidirect
277. #1648C2×C43semidirect
279. #1636C2×C43semidirect
281. #1584C2×C43semidirect
337. C43#20237direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33742
C43×#33722
C43×#33642
C43×#33562
C43×#17182
C43×#17002
C43×#16992
C43×#16922
C43×#16842
C43×#16502
C43×#16482
C43×#16442
C43×#16362
C43×#15922
C43×#15842
#2023743