Finite Group Databasebeta

← C43×#20261 #24940278

Subgroups — C43×#20261 #24940278

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3398C211yesmaximal, characteristic, complemented
2C43×#3386C211yesmaximal, characteristic, complemented
3C43×#3340C211yesmaximal, characteristic
4C43×#3329C211yesmaximal, characteristic
5C43×#1723C211yesmaximal, characteristic, complemented
6C43×#1704C211yesmaximal, characteristic, complemented
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1689C211yesmaximal, characteristic, complemented
9C43×#1673C211yesmaximal, characteristic, complemented
10C43×#1650C211yesmaximal, characteristic, complemented
11C43×#1649C211yesmaximal, characteristic, complemented
12C43×#1646C211yesmaximal, characteristic
13C43×#1636C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic
17C43×#556C2211yescharacteristic
18C43×#555C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#501—21no—
21C43×#500C2211yescharacteristic
22C43×#500C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#497—21no—
25C43×#494C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#485—21no—
29C43×#485—21no—
30C43×#482—21no—
31C43×#478—21no—
32C43×#477—21no—
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#475C2211yescharacteristic
36C43×#474C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#468—21no—
39C43×#465—21no—
40C43×#464—21no—
41C43×#462—21no—
42C43×#462C2211yescharacteristic
43C43×#461C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#448—21no—
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#441—21no—
49C43×#440—21no—
50C4×SD16×C43C2211yescharacteristic
51C4×SD16×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#427—21no—
55C43×#419—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C22×Q8×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43D411yescharacteristic
74C2×SD16×C43D411yescharacteristic
75C2×M16×C43—21no—
76C22×C8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
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—
87#124×C43—41no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—41no—
91#121×C43—21no—
92#121×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—41no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43D411yescharacteristic
115#106×C43D411yescharacteristic
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#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—
159Q16×C43—42no—
160Q16×C43—81no—
161Q16×C43—81no—
162SD16×C43—22no—
163SD16×C43—41no—
164SD16×C43—81no—
165SD16×C43—81no—
166M16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
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—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—41no—
206C42×C43—41no—
207C42×C43—41no—
208C42×C43C2411yescharacteristic
209C23×C43—21no—
210C23×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—81no—
222Q8×C43—82no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—161no—
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—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—82no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43#13712yes—
255#20261C4311yesmaximal, characteristic, direct product factor, Sylow
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43D4211yescharacteristic
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43C2×#13711yescharacteristic
275C4×C43#57511yescharacteristic
276C4×C43#57611yescharacteristic
277C4×C43#57811yescharacteristic
278#3398C2×C4311yescharacteristic, complemented
279#3386C2×C4311yescharacteristic, complemented
280#3340C2×C4311yescharacteristic
281#3329C2×C4311yescharacteristic
282#1723C2×C4311yescharacteristic, complemented
283#1704C2×C4311yescharacteristic, complemented
284#1692C2×C4311yescharacteristic, complemented
285#1689C2×C4311yescharacteristic, complemented
286#1673C2×C4311yescharacteristic, complemented
287#1650C2×C4311yescharacteristic, complemented
288#1649C2×C4311yescharacteristic, complemented
289#1646C2×C4311yescharacteristic
290#1636C2×C4311yescharacteristic, complemented
291#1592C2×C4311yescharacteristic, complemented
292#1582C2×C4311yescharacteristic, complemented
293C2×C43—81no—
294C2×C43—81no—
295C2×C43#326811yescharacteristic
296C2×C43#327611yescharacteristic
297C2×C43#328911yescharacteristic
298#557C22×C4311yescharacteristic
299#556C22×C4311yescharacteristic
300#555C22×C4311yescharacteristic
301D4×Q8C22×C4311yescharacteristic
302#501—21no—
303#500C22×C4311yescharacteristic
304#500C22×C4311yescharacteristic
305#498C22×C4311yescharacteristic
306#497—21no—
307#494C22×C4311yescharacteristic
308#487C22×C4311yescharacteristic
309#487C22×C4311yescharacteristic
310#485—21no—
311#485—21no—
312#482—21no—
313#478—21no—
314#477—21no—
315#477C22×C4311yescharacteristic
316#477C22×C4311yescharacteristic
317#475C22×C4311yescharacteristic
318#474C22×C4311yescharacteristic
319#474C22×C4311yescharacteristic
320#468—21no—
321#465—21no—
322#464—21no—
323#462—21no—
324#462C22×C4311yescharacteristic
325#461C22×C4311yescharacteristic
326#461C22×C4311yescharacteristic
327#448—21no—
328#446C22×C4311yescharacteristic
329#446C22×C4311yescharacteristic
330#441—21no—
331#440—21no—
332C4×SD16C22×C4311yescharacteristic
333C4×SD16C22×C4311yescharacteristic
334#436C22×C4311yescharacteristic
335C8×D4C22×C4311yescharacteristic
336#427—21no—
337#419—21no—
338#335C22×C4311yescharacteristic
339#334C22×C4311yescharacteristic
340#333C22×C4311yescharacteristic
341#332C22×C4311yescharacteristic
342#332C22×C4311yescharacteristic
343#332C22×C4311yescharacteristic
344Q8⋊C8C22×C4311yescharacteristic
345Q8⋊C8C22×C4311yescharacteristic
346D4⋊C8C22×C4311yescharacteristic
347D4⋊C8C22×C4311yescharacteristic
348#322C22×C4311yescharacteristic
349C43#2026111yescharacteristic, direct product factor, Sylow
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16D4×C4311yescharacteristic
357C2×SD16D4×C4311yescharacteristic
358C2×M16—21no—
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8C23×C4311yescharacteristic
363C4⋊Q8C23×C4311yescharacteristic
364C4⋊Q8C23×C4311yescharacteristic
365C4⋊Q8C23×C4311yescharacteristic
366#126—41no—
367#125—21no—
368#125—41no—
369#124—21no—
370#124—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374#121—21no—
375#121—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C23×C4311yescharacteristic
380C4×Q8C23×C4311yescharacteristic
381C4×D4—21no—
382C4×D4C23×C4311yescharacteristic
383C4×D4C23×C4311yescharacteristic
384#117—21no—
385#117—21no—
386#117—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107—41no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106D4×C4311yescharacteristic
398#106D4×C4311yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C4311yescharacteristic
402C4⋊C8C23×C4311yescharacteristic
403C4⋊C8C23×C4311yescharacteristic
404C4⋊C8C23×C4311yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C4311yescharacteristic
415#103D4×C4311yescharacteristic
416#102—21no—
417#102—21no—
418#102D4×C4311yescharacteristic
419#102D4×C4311yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—21no—
422#97—21no—
423#97—21no—
424C4×C8C23×C4311yescharacteristic
425C4×C8C23×C4311yescharacteristic
426C4×C8C23×C4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C4311yescharacteristic
435C2×Q8C2×D4×C4311yescharacteristic
436C2×D4—41no—
437C2×D4C2×D4×C4311yescharacteristic
438C2×D4C2×D4×C4311yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—41no—
442Q16—42no—
443Q16—81no—
444Q16—81no—
445SD16—22no—
446SD16—41no—
447SD16—81no—
448SD16—81no—
449M16—81no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—42no—
456C2×C8C2×D4×C4311yescharacteristic
457C2×C8C2×D4×C4311yescharacteristic
458C2×C8C2×D4×C4311yescharacteristic
459C2×C8C2×D4×C4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C4311yescharacteristic
476C4⋊C4C2×D4×C4311yescharacteristic
477C4⋊C4C2×D4×C4311yescharacteristic
478C4⋊C4C2×D4×C4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—41no—
490C42—41no—
491C42C24×C4311yescharacteristic
492C23—21no—
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—161no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4C22×D4×C4311yescharacteristic
527C2×C4C22×D4×C4311yescharacteristic
528C2×C4H(5,𝔽2)×C4311yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8#137×C4312yes—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22D42×C4311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#137×C4311yescharacteristic
557C4C43×#57511yescharacteristic
558C4C43×#57611yescharacteristic
559C4C43×#57811yescharacteristic
560C2—81no—
561C2—81no—
562C2C43×#326811yescharacteristic
563C2C43×#327611yescharacteristic
564C2C43×#328911yescharacteristic
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×#3398C2semidirect
2. C43×#3386C2semidirect
5. C43×#1723C2semidirect
6. C43×#1704C2semidirect
7. C43×#1692C2semidirect
8. C43×#1689C2semidirect
9. C43×#1673C2semidirect
10. C43×#1650C2semidirect
11. C43×#1649C2semidirect
13. C43×#1636C2semidirect
14. C43×#1592C2semidirect
15. C43×#1582C2semidirect
255. #20261C43direct (N × H)
278. #3398C2×C43semidirect
279. #3386C2×C43semidirect
282. #1723C2×C43semidirect
283. #1704C2×C43semidirect
284. #1692C2×C43semidirect
285. #1689C2×C43semidirect
286. #1673C2×C43semidirect
287. #1650C2×C43semidirect
288. #1649C2×C43semidirect
290. #1636C2×C43semidirect
291. #1592C2×C43semidirect
292. #1582C2×C43semidirect
349. C43#20261direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33982
C43×#33862
C43×#33402
C43×#33292
C43×#17232
C43×#17042
C43×#16922
C43×#16892
C43×#16732
C43×#16502
C43×#16492
C43×#16462
C43×#16362
C43×#15922
C43×#15822
#2026143