Finite Group Databasebeta

← C43×#19278 #24939295

Subgroups — C43×#19278 #24939295

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3131C211yesmaximal, characteristic, complemented
2C43×#3116C211yesmaximal, characteristic, complemented
3C43×#3115C211yesmaximal, characteristic
4C8×#41×C43C211yesmaximal, characteristic, complemented
5C43×#1684C211yesmaximal, characteristic, complemented
6C43×#1683C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1681C211yesmaximal, characteristic, complemented
9C43×#1680C211yesmaximal, characteristic, complemented
10C43×#1679C211yesmaximal, characteristic, complemented
11C43×#1678C211yesmaximal, characteristic, complemented
12C43×#1677C211yesmaximal, characteristic, complemented
13C43×#1568C211yesmaximal, characteristic, complemented
14C43×#1554C211yesmaximal, characteristic, complemented
15C43×#1553C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C4×#41×C43C2211yescharacteristic
19C43×#488—21no—
20C43×#488—21no—
21C43×#487C2211yescharacteristic
22C43×#487C2211yescharacteristic
23C43×#486C2211yescharacteristic
24C43×#486C2211yescharacteristic
25C43×#485—21no—
26C43×#482—21no—
27C43×#477C2211yescharacteristic
28C43×#476C2211yescharacteristic
29C43×#475C2211yescharacteristic
30C43×#474C2211yescharacteristic
31C43×#462C2211yescharacteristic
32C43×#461C2211yescharacteristic
33C43×#460C2211yescharacteristic
34C43×#459C2211yescharacteristic
35C43×#452—21no—
36C43×#449—21no—
37C8×Q8×C43C2211yescharacteristic
38C8×Q8×C43C2211yescharacteristic
39C43×#442—21no—
40C43×#441—21no—
41C43×#440—21no—
42C43×#440—21no—
43C8×D4×C43—21no—
44C8×D4×C43—21no—
45C8×D4×C43C2211yescharacteristic
46C8×D4×C43C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#432C2211yescharacteristic
49C43×#431—21no—
50C43×#431C2211yescharacteristic
51C43×#416—21no—
52C43×#416—21no—
53C2×C4×C8×C43—21no—
54C2×C4×C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43D411yescharacteristic
69C2×Q16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×D8×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43D411yescharacteristic
76C22×C8×C43D411yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#127×C43C2311yescharacteristic
81#125×C43—21no—
82#124×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—21no—
85#121×C43—21no—
86#121×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43D411yescharacteristic
90C4×Q8×C43C2311yescharacteristic
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D411yescharacteristic
96C4×D4×C43C2311yescharacteristic
97#117×C43—21no—
98#117×C43—21no—
99#117×C43D411yescharacteristic
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#107×C43—21no—
103#107×C43—21no—
104#106×C43—21no—
105#106×C43—21no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2311yescharacteristic
109C4⋊C8×C43C2311yescharacteristic
110C4⋊C8×C43C2311yescharacteristic
111C4⋊C8×C43C2311yescharacteristic
112C4⋊C8×C43C2311yescharacteristic
113C4⋊C8×C43C2311yescharacteristic
114#103×C43—21no—
115#103×C43—21no—
116#103×C43—21no—
117#103×C43—21no—
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#102×C43—21no—
123#102×C43—21no—
124#102×C43—21no—
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130C22⋊C8×C43—21no—
131C22⋊C8×C43—21no—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135#97×C43—21no—
136#97×C43—21no—
137C4×C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—42no—
147#41×C43—42no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165Q16×C43—42no—
166SD16×C43—42no—
167SD16×C43—42no—
168D8×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C2×C8×C43—42no—
178C2×C8×C43—42no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—41no—
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C42×C43#4111yescharacteristic
208C42×C43C2411yescharacteristic
209C23×C43—21no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218Q8×C43#13512yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227D4×C43#13512yes—
228C2×C4×C43—24no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—82no—
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260#19278C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—21no—
262C22×C43—22no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×#12111yescharacteristic
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13511yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57511yescharacteristic
285#3131C2×C4311yescharacteristic, complemented
286#3116C2×C4311yescharacteristic, complemented
287#3115C2×C4311yescharacteristic
288C8×#41C2×C4311yescharacteristic, complemented
289#1684C2×C4311yescharacteristic, complemented
290#1683C2×C4311yescharacteristic, complemented
291#1682C2×C4311yescharacteristic, complemented
292#1681C2×C4311yescharacteristic, complemented
293#1680C2×C4311yescharacteristic, complemented
294#1679C2×C4311yescharacteristic, complemented
295#1678C2×C4311yescharacteristic, complemented
296#1677C2×C4311yescharacteristic, complemented
297#1568C2×C4311yescharacteristic, complemented
298#1554C2×C4311yescharacteristic, complemented
299#1553C2×C4311yescharacteristic, complemented
300C2×C43—41no—
301C2×C43—42no—
302C2×C43—161no—
303C2×C43#304011yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43#306711yescharacteristic
306#533C22×C4311yescharacteristic
307#532C22×C4311yescharacteristic
308C4×#41C22×C4311yescharacteristic
309#488—21no—
310#488—21no—
311#487C22×C4311yescharacteristic
312#487C22×C4311yescharacteristic
313#486C22×C4311yescharacteristic
314#486C22×C4311yescharacteristic
315#485—21no—
316#482—21no—
317#477C22×C4311yescharacteristic
318#476C22×C4311yescharacteristic
319#475C22×C4311yescharacteristic
320#474C22×C4311yescharacteristic
321#462C22×C4311yescharacteristic
322#461C22×C4311yescharacteristic
323#460C22×C4311yescharacteristic
324#459C22×C4311yescharacteristic
325#452—21no—
326#449—21no—
327C8×Q8C22×C4311yescharacteristic
328C8×Q8C22×C4311yescharacteristic
329#442—21no—
330#441—21no—
331#440—21no—
332#440—21no—
333C8×D4—21no—
334C8×D4—21no—
335C8×D4C22×C4311yescharacteristic
336C8×D4C22×C4311yescharacteristic
337#432C22×C4311yescharacteristic
338#432C22×C4311yescharacteristic
339#431—21no—
340#431C22×C4311yescharacteristic
341#416—21no—
342#416—21no—
343C2×C4×C8—21no—
344C2×C4×C8C22×C4311yescharacteristic
345#335C22×C4311yescharacteristic
346#335C22×C4311yescharacteristic
347#334C22×C4311yescharacteristic
348#334C22×C4311yescharacteristic
349#333C22×C4311yescharacteristic
350#333C22×C4311yescharacteristic
351#332C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355#331C22×C4311yescharacteristic
356#331C22×C4311yescharacteristic
357C43#1927811yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C2×#41D4×C4311yescharacteristic
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×D8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8D4×C4311yescharacteristic
367C22×C8D4×C4311yescharacteristic
368C4⋊Q8C23×C4311yescharacteristic
369C4⋊Q8C23×C4311yescharacteristic
370C4⋊Q8C23×C4311yescharacteristic
371#127C23×C4311yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C4311yescharacteristic
381C4×Q8C23×C4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C4311yescharacteristic
387C4×D4C23×C4311yescharacteristic
388#117—21no—
389#117—21no—
390#117D4×C4311yescharacteristic
391C2×C42—21no—
392C2×C42C23×C4311yescharacteristic
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C4311yescharacteristic
400C4⋊C8C23×C4311yescharacteristic
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#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8D4×C4311yescharacteristic
432C4×C8D4×C4311yescharacteristic
433C4×C8C23×C4311yescharacteristic
434C4×C8C23×C4311yescharacteristic
435#41—22no—
436#41—22no—
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4#41×C4311yescharacteristic
456Q16—42no—
457SD16—42no—
458SD16—42no—
459D8—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—42no—
469C2×C8—42no—
470C2×C8C2×D4×C4311yescharacteristic
471C2×C8C2×D4×C4311yescharacteristic
472C2×C8C2×D4×C4311yescharacteristic
473C2×C8C2×D4×C4311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C4311yescharacteristic
485C4⋊C4C2×D4×C4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C2×D4×C4311yescharacteristic
497C42C2×D4×C4311yescharacteristic
498C42#41×C4311yescharacteristic
499C42C24×C4311yescharacteristic
500C23—21no—
501C23—41no—
502C23#121×C4311yescharacteristic
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8#135×C4312yes—
510D4—24no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4#135×C4312yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4#121×C4311yescharacteristic
536C2×C4#121×C4311yescharacteristic
537C2×C4#121×C4311yescharacteristic
538C2×C4C22×D4×C4311yescharacteristic
539C2×C4C22×D4×C4311yescharacteristic
540C2×C4C2×#41×C4311yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C2×#121×C4311yescharacteristic
561C4—21no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#135×C4311yescharacteristic
572C4C2×#135×C4311yescharacteristic
573C4C43×#57511yescharacteristic
574C4C43×#57511yescharacteristic
575C2—41no—
576C2—42no—
577C2—161no—
578C2C43×#304011yescharacteristic
579C2C43×#305011yescharacteristic
580C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3115C2
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
1. C43×#3131C2semidirect
2. C43×#3116C2semidirect
4. C8×#41×C43C2semidirect
5. C43×#1684C2semidirect
6. C43×#1683C2semidirect
7. C43×#1682C2semidirect
8. C43×#1681C2semidirect
9. C43×#1680C2semidirect
10. C43×#1679C2semidirect
11. C43×#1678C2semidirect
12. C43×#1677C2semidirect
13. C43×#1568C2semidirect
14. C43×#1554C2semidirect
15. C43×#1553C2semidirect
260. #19278C43direct (N × H)
285. #3131C2×C43semidirect
286. #3116C2×C43semidirect
288. C8×#41C2×C43semidirect
289. #1684C2×C43semidirect
290. #1683C2×C43semidirect
291. #1682C2×C43semidirect
292. #1681C2×C43semidirect
293. #1680C2×C43semidirect
294. #1679C2×C43semidirect
295. #1678C2×C43semidirect
296. #1677C2×C43semidirect
297. #1568C2×C43semidirect
298. #1554C2×C43semidirect
299. #1553C2×C43semidirect
357. C43#19278direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31312
C43×#31162
C43×#31152
C8×#41×C432
C43×#16842
C43×#16832
C43×#16822
C43×#16812
C43×#16802
C43×#16792
C43×#16782
C43×#16772
C43×#15682
C43×#15542
C43×#15532
#1927843