Finite Group Databasebeta

← C43×#19562 #24939579

Subgroups — C43×#19562 #24939579

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3246C211yesmaximal, characteristic
2C43×#3235C211yesmaximal, characteristic
3C43×#3231C211yesmaximal, characteristic, complemented
4C43×#2979C211yesmaximal, characteristic
5C43×#1703C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1695C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1683C211yesmaximal, characteristic, complemented
10C43×#1679C211yesmaximal, characteristic, complemented
11C43×#1675C211yesmaximal, characteristic, complemented
12C43×#1671C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic, complemented
14C43×#1554C211yesmaximal, characteristic, complemented
15C43×#1542C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C43×#501—21no—
20C43×#500C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#490—21no—
23C43×#487C2211yescharacteristic
24C43×#487C2211yescharacteristic
25C43×#485—21no—
26C43×#485—21no—
27C43×#482—21no—
28C43×#482—21no—
29C43×#479—21no—
30C43×#479—21no—
31C43×#476C2211yescharacteristic
32C43×#476C2211yescharacteristic
33C43×#476C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#475—21no—
36C43×#474C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#465—21no—
39C43×#465—21no—
40C43×#461C2211yescharacteristic
41C43×#461C2211yescharacteristic
42C43×#460—21no—
43C43×#436—21no—
44C43×#436C2211yescharacteristic
45C43×#436C2211yescharacteristic
46C8×D4×C43—21no—
47C8×D4×C43C2211yescharacteristic
48C8×D4×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C43×#408—21no—
54C43×#408—21no—
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#333C2211yescharacteristic
62C43×#333C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#41×C43—21no—
68C2×SD16×C43—21no—
69C2×SD16×C43—21no—
70C2×M16×C43—21no—
71C2×M16×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C4⋊Q8×C43D411yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#127×C43D411yescharacteristic
81#125×C43—21no—
82#125×C43—21no—
83#124×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88#121×C43—21no—
89#121×C43D411yescharacteristic
90#121×C43D411yescharacteristic
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43C2311yescharacteristic
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#106×C43—21no—
106#106×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113C4⋊C8×C43D411yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
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#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162SD16×C43—81no—
163SD16×C43—81no—
164M16×C43—81no—
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×C43—21no—
172C2×C8×C43—81no—
173C2×C8×C43—81no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
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—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43#4111yescharacteristic
205C42×C43C2411yescharacteristic
206C23×C43—21no—
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214Q8×C43—81no—
215Q8×C43—81no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—42no—
221D4×C43—81no—
222D4×C43—81no—
223D4×C43—81no—
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—41no—
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C8×C43—21no—
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—41no—
255#19562C4311yesmaximal, characteristic, direct product factor, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×#12111yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43#57711yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280#3246C2×C4311yescharacteristic
281#3235C2×C4311yescharacteristic
282#3231C2×C4311yescharacteristic, complemented
283#2979C2×C4311yescharacteristic
284#1703C2×C4311yescharacteristic, complemented
285#1699C2×C4311yescharacteristic, complemented
286#1695C2×C4311yescharacteristic, complemented
287#1691C2×C4311yescharacteristic, complemented
288#1683C2×C4311yescharacteristic, complemented
289#1679C2×C4311yescharacteristic, complemented
290#1675C2×C4311yescharacteristic, complemented
291#1671C2×C4311yescharacteristic, complemented
292#1573C2×C4311yescharacteristic, complemented
293#1554C2×C4311yescharacteristic, complemented
294#1542C2×C4311yescharacteristic, complemented
295C2×C43—41no—
296C2×C43—81no—
297C2×C43—81no—
298C2×C43#304211yescharacteristic
299C2×C43#306311yescharacteristic
300C2×C43#306711yescharacteristic
301#533C22×C4311yescharacteristic
302#533C22×C4311yescharacteristic
303#532C22×C4311yescharacteristic
304#501—21no—
305#500C22×C4311yescharacteristic
306#498C22×C4311yescharacteristic
307#490—21no—
308#487C22×C4311yescharacteristic
309#487C22×C4311yescharacteristic
310#485—21no—
311#485—21no—
312#482—21no—
313#482—21no—
314#479—21no—
315#479—21no—
316#476C22×C4311yescharacteristic
317#476C22×C4311yescharacteristic
318#476C22×C4311yescharacteristic
319#476C22×C4311yescharacteristic
320#475—21no—
321#474C22×C4311yescharacteristic
322#474C22×C4311yescharacteristic
323#465—21no—
324#465—21no—
325#461C22×C4311yescharacteristic
326#461C22×C4311yescharacteristic
327#460—21no—
328#436—21no—
329#436C22×C4311yescharacteristic
330#436C22×C4311yescharacteristic
331C8×D4—21no—
332C8×D4C22×C4311yescharacteristic
333C8×D4C22×C4311yescharacteristic
334#432C22×C4311yescharacteristic
335#431C22×C4311yescharacteristic
336#431C22×C4311yescharacteristic
337C2×C4⋊C8C22×C4311yescharacteristic
338#408—21no—
339#408—21no—
340#335C22×C4311yescharacteristic
341#335C22×C4311yescharacteristic
342#334C22×C4311yescharacteristic
343#334C22×C4311yescharacteristic
344#333C22×C4311yescharacteristic
345#333C22×C4311yescharacteristic
346#333C22×C4311yescharacteristic
347#333C22×C4311yescharacteristic
348#332C22×C4311yescharacteristic
349#332C22×C4311yescharacteristic
350#332C22×C4311yescharacteristic
351#332C22×C4311yescharacteristic
352C43#1956211yescharacteristic, direct product factor, Sylow
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C4⋊Q8D4×C4311yescharacteristic
362C4⋊Q8C23×C4311yescharacteristic
363C4⋊Q8C23×C4311yescharacteristic
364C4⋊Q8C23×C4311yescharacteristic
365C4⋊Q8C23×C4311yescharacteristic
366#127D4×C4311yescharacteristic
367#125—21no—
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374#121—21no—
375#121D4×C4311yescharacteristic
376#121D4×C4311yescharacteristic
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×D4—21no—
382C4×D4C23×C4311yescharacteristic
383C4×D4C23×C4311yescharacteristic
384#117—21no—
385#117—21no—
386C2×C42C23×C4311yescharacteristic
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8D4×C4311yescharacteristic
399C4⋊C8D4×C4311yescharacteristic
400C4⋊C8C23×C4311yescharacteristic
401C4⋊C8C23×C4311yescharacteristic
402C4⋊C8C23×C4311yescharacteristic
403C4⋊C8C23×C4311yescharacteristic
404C4⋊C8C23×C4311yescharacteristic
405C4⋊C8C23×C4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8D4×C4311yescharacteristic
425C22⋊C8D4×C4311yescharacteristic
426#97—21no—
427C4×C8—21no—
428C4×C8C23×C4311yescharacteristic
429C4×C8C23×C4311yescharacteristic
430#41—81no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×D4×C4311yescharacteristic
442C2×D4C2×D4×C4311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4#41×C4311yescharacteristic
448SD16—81no—
449SD16—81no—
450M16—81no—
451M16—81no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8C2×D4×C4311yescharacteristic
462C2×C8C2×D4×C4311yescharacteristic
463C2×C8C2×D4×C4311yescharacteristic
464C2×C8C2×D4×C4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C4311yescharacteristic
479C4⋊C4C2×D4×C4311yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—41no—
487C42—41no—
488C42C2×D4×C4311yescharacteristic
489C42C2×D4×C4311yescharacteristic
490C42#41×C4311yescharacteristic
491C42C24×C4311yescharacteristic
492C23—21no—
493C23—21no—
494C23#121×C4311yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—81no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—42no—
507D4—81no—
508D4—81no—
509D4—81no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
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#121×C4311yescharacteristic
526C2×C4#121×C4311yescharacteristic
527C2×C4#121×C4311yescharacteristic
528C2×C4C22×D4×C4311yescharacteristic
529C2×C4C22×D4×C4311yescharacteristic
530C2×C4C2×#41×C4311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22C2×#121×C4311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C43×#57711yescharacteristic
562C4C43×#57711yescharacteristic
563C4C43×#57711yescharacteristic
564C4C43×#57811yescharacteristic
565C2—41no—
566C2—81no—
567C2—81no—
568C2C43×#304211yescharacteristic
569C2C43×#306311yescharacteristic
570C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C43×#3231C2semidirect
5. C43×#1703C2semidirect
6. C43×#1699C2semidirect
7. C43×#1695C2semidirect
8. C43×#1691C2semidirect
9. C43×#1683C2semidirect
10. C43×#1679C2semidirect
11. C43×#1675C2semidirect
12. C43×#1671C2semidirect
13. C43×#1573C2semidirect
14. C43×#1554C2semidirect
15. C43×#1542C2semidirect
255. #19562C43direct (N × H)
282. #3231C2×C43semidirect
284. #1703C2×C43semidirect
285. #1699C2×C43semidirect
286. #1695C2×C43semidirect
287. #1691C2×C43semidirect
288. #1683C2×C43semidirect
289. #1679C2×C43semidirect
290. #1675C2×C43semidirect
291. #1671C2×C43semidirect
292. #1573C2×C43semidirect
293. #1554C2×C43semidirect
294. #1542C2×C43semidirect
352. C43#19562direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32462
C43×#32352
C43×#32312
C43×#29792
C43×#17032
C43×#16992
C43×#16952
C43×#16912
C43×#16832
C43×#16792
C43×#16752
C43×#16712
C43×#15732
C43×#15542
C43×#15422
#1956243