Finite Group Databasebeta

← C43×#20295 #24940312

Subgroups — C43×#20295 #24940312

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3386C211yesmaximal, characteristic, complemented
2C43×#3372C211yesmaximal, characteristic, complemented
3C43×#3357C211yesmaximal, characteristic
4C43×#3329C211yesmaximal, characteristic
5C43×#1710C211yesmaximal, characteristic, complemented
6C43×#1704C211yesmaximal, characteristic, complemented
7C43×#1703C211yesmaximal, characteristic, complemented
8C43×#1696C211yesmaximal, characteristic, complemented
9C43×#1693C211yesmaximal, characteristic, complemented
10C43×#1646C211yesmaximal, characteristic
11C43×#1643C211yesmaximal, characteristic, complemented
12C43×#1637C211yesmaximal, characteristic, complemented
13C43×#1636C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic
17C43×#555C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#501—21no—
21C43×#500C2211yescharacteristic
22C43×#500C2211yescharacteristic
23C43×#491—21no—
24C43×#487C2211yescharacteristic
25C43×#487C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#485—21no—
29C43×#485—21no—
30C43×#480—21no—
31C43×#479—21no—
32C43×#478—21no—
33C43×#477—21no—
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#477C2211yescharacteristic
37C43×#476C2211yescharacteristic
38C43×#475C2211yescharacteristic
39C43×#474C2211yescharacteristic
40C43×#468—21no—
41C43×#468—21no—
42C43×#461—21no—
43C43×#461C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#448—21no—
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#440—21no—
49C43×#440—21no—
50C4×SD16×C43C2211yescharacteristic
51C4×SD16×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#428—21no—
55C43×#419—21no—
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C22×Q8×C43—21no—
68C2×SD16×C43—21no—
69C2×SD16×C43—21no—
70C2×SD16×C43D411yescharacteristic
71C2×SD16×C43D411yescharacteristic
72C2×M16×C43—21no—
73C2×M16×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#125×C43—21no—
81#125×C43—21no—
82#125×C43—41no—
83#124×C43—41no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—41no—
87C22⋊Q8×C43—41no—
88#121×C43—21no—
89#121×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43C2311yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43C2311yescharacteristic
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43—21no—
100C2×C4⋊C4×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×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
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×C43—21no—
128#103×C43—21no—
129#103×C43—41no—
130#103×C43—41no—
131#103×C43D411yescharacteristic
132#103×C43D411yescharacteristic
133#102×C43—21no—
134#102×C43—21no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×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—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160SD16×C43—22no—
161SD16×C43—41no—
162SD16×C43—42no—
163SD16×C43—81no—
164M16×C43—42no—
165M16×C43—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
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—21no—
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—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—41no—
204C42×C43—41no—
205C42×C43C2411yescharacteristic
206C23×C43—21no—
207C23×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217Q8×C43—81no—
218Q8×C43—82no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—161no—
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—41no—
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—41no—
238C2×C4×C43—82no—
239C2×C4×C43—161no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43#13712yes—
252#20295C4311yesmaximal, characteristic, direct product factor, Sylow
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43D4211yescharacteristic
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13711yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275#3386C2×C4311yescharacteristic, complemented
276#3372C2×C4311yescharacteristic, complemented
277#3357C2×C4311yescharacteristic
278#3329C2×C4311yescharacteristic
279#1710C2×C4311yescharacteristic, complemented
280#1704C2×C4311yescharacteristic, complemented
281#1703C2×C4311yescharacteristic, complemented
282#1696C2×C4311yescharacteristic, complemented
283#1693C2×C4311yescharacteristic, complemented
284#1646C2×C4311yescharacteristic
285#1643C2×C4311yescharacteristic, complemented
286#1637C2×C4311yescharacteristic, complemented
287#1636C2×C4311yescharacteristic, complemented
288#1590C2×C4311yescharacteristic, complemented
289#1590C2×C4311yescharacteristic, complemented
290C2×C43—81no—
291C2×C43—81no—
292C2×C43#327511yescharacteristic
293C2×C43#327611yescharacteristic
294C2×C43#329011yescharacteristic
295#557C22×C4311yescharacteristic
296#555C22×C4311yescharacteristic
297#554C22×C4311yescharacteristic
298D4×Q8C22×C4311yescharacteristic
299#501—21no—
300#500C22×C4311yescharacteristic
301#500C22×C4311yescharacteristic
302#491—21no—
303#487C22×C4311yescharacteristic
304#487C22×C4311yescharacteristic
305#487C22×C4311yescharacteristic
306#487C22×C4311yescharacteristic
307#485—21no—
308#485—21no—
309#480—21no—
310#479—21no—
311#478—21no—
312#477—21no—
313#477C22×C4311yescharacteristic
314#477C22×C4311yescharacteristic
315#477C22×C4311yescharacteristic
316#476C22×C4311yescharacteristic
317#475C22×C4311yescharacteristic
318#474C22×C4311yescharacteristic
319#468—21no—
320#468—21no—
321#461—21no—
322#461C22×C4311yescharacteristic
323#461C22×C4311yescharacteristic
324#448—21no—
325#446C22×C4311yescharacteristic
326#446C22×C4311yescharacteristic
327#440—21no—
328#440—21no—
329C4×SD16C22×C4311yescharacteristic
330C4×SD16C22×C4311yescharacteristic
331#436C22×C4311yescharacteristic
332#436C22×C4311yescharacteristic
333#428—21no—
334#419—21no—
335#334C22×C4311yescharacteristic
336#334C22×C4311yescharacteristic
337#333C22×C4311yescharacteristic
338#333C22×C4311yescharacteristic
339#332C22×C4311yescharacteristic
340#332C22×C4311yescharacteristic
341Q8⋊C8C22×C4311yescharacteristic
342Q8⋊C8C22×C4311yescharacteristic
343D4⋊C8C22×C4311yescharacteristic
344D4⋊C8C22×C4311yescharacteristic
345C82C22×C4311yescharacteristic
346C43#2029511yescharacteristic, direct product factor, Sylow
347C22×Q8—21no—
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16D4×C4311yescharacteristic
351C2×SD16D4×C4311yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C4311yescharacteristic
357C4⋊Q8C23×C4311yescharacteristic
358C4⋊Q8C23×C4311yescharacteristic
359C4⋊Q8C23×C4311yescharacteristic
360#125—21no—
361#125—21no—
362#125—41no—
363#124—41no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—41no—
368#121—21no—
369#121—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C4311yescharacteristic
373C4×Q8C23×C4311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C23×C4311yescharacteristic
377C4×D4C23×C4311yescharacteristic
378#117—21no—
379#117—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#106—21no—
390#106—21no—
391#106D4×C4311yescharacteristic
392#106D4×C4311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C4311yescharacteristic
396C4⋊C8C23×C4311yescharacteristic
397C4⋊C8C23×C4311yescharacteristic
398C4⋊C8C23×C4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—41no—
410#103—41no—
411#103D4×C4311yescharacteristic
412#103D4×C4311yescharacteristic
413#102—21no—
414#102—21no—
415#102D4×C4311yescharacteristic
416#102D4×C4311yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—21no—
420#97—21no—
421C4×C8C23×C4311yescharacteristic
422C4×C8C23×C4311yescharacteristic
423C4×C8C23×C4311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8C2×D4×C4311yescharacteristic
432C2×Q8C2×D4×C4311yescharacteristic
433C2×D4—41no—
434C2×D4C2×D4×C4311yescharacteristic
435C2×D4C2×D4×C4311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440SD16—22no—
441SD16—41no—
442SD16—42no—
443SD16—81no—
444M16—42no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8C2×D4×C4311yescharacteristic
452C2×C8C2×D4×C4311yescharacteristic
453C2×C8C2×D4×C4311yescharacteristic
454C2×C8C2×D4×C4311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C4311yescharacteristic
472C4⋊C4C2×D4×C4311yescharacteristic
473C4⋊C4C2×D4×C4311yescharacteristic
474C4⋊C4C2×D4×C4311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42C24×C4311yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—81no—
497Q8—81no—
498Q8—82no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—161no—
520C2×C4C22×D4×C4311yescharacteristic
521C2×C4C22×D4×C4311yescharacteristic
522C2×C4H(5,𝔽2)×C4311yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8#137×C4312yes—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D42×C4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C2×#137×C4311yescharacteristic
551C4C43×#57511yescharacteristic
552C4C43×#57711yescharacteristic
553C4C43×#57811yescharacteristic
554C2—81no—
555C2—81no—
556C2C43×#327511yescharacteristic
557C2C43×#327611yescharacteristic
558C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#555C22
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×#3386C2semidirect
2. C43×#3372C2semidirect
5. C43×#1710C2semidirect
6. C43×#1704C2semidirect
7. C43×#1703C2semidirect
8. C43×#1696C2semidirect
9. C43×#1693C2semidirect
11. C43×#1643C2semidirect
12. C43×#1637C2semidirect
13. C43×#1636C2semidirect
14. C43×#1590C2semidirect
15. C43×#1590C2semidirect
252. #20295C43direct (N × H)
275. #3386C2×C43semidirect
276. #3372C2×C43semidirect
279. #1710C2×C43semidirect
280. #1704C2×C43semidirect
281. #1703C2×C43semidirect
282. #1696C2×C43semidirect
283. #1693C2×C43semidirect
285. #1643C2×C43semidirect
286. #1637C2×C43semidirect
287. #1636C2×C43semidirect
288. #1590C2×C43semidirect
289. #1590C2×C43semidirect
346. C43#20295direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33862
C43×#33722
C43×#33572
C43×#33292
C43×#17102
C43×#17042
C43×#17032
C43×#16962
C43×#16932
C43×#16462
C43×#16432
C43×#16372
C43×#16362
C43×#15902
#2029543