Finite Group Databasebeta

← C43×#9113 #24929130

Subgroups — C43×#9113 #24929130

Order 11008.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C43C211yesmaximal, characteristic, complemented
2C43×#2847C211yesmaximal, characteristic
3C2×C43×#327C212yesmaximal, complemented
4C43×C22⋊#95C211yesmaximal, characteristic, complemented
5C43×#1294C212yesmaximal, complemented
6C24×C4×C43C2211yescharacteristic
7C23×C8×C43—21no—
8C2×#121×C43C411yescharacteristic, complemented
9C2×#121×C43C411yescharacteristic, complemented
10C2×#121×C43C2211yescharacteristic
11C2×#120×C43—21no—
12C22×C22⋊C4×C43—21no—
13C2×C22⋊C8×C43—21no—
14C2×C22⋊C8×C43—24no—
15C2×C22⋊C8×C43C2212yes—
16C43×#386—21no—
17C43×#386—21no—
18C43×#386—21no—
19C43×#380C411yescharacteristic, complemented
20C43×#380C411yescharacteristic, complemented
21C43×#380C2211yescharacteristic
22C2×#95×C43—21no—
23C2×#95×C43C2212yes—
24C43×#327—24no—
25C25×C43D411yescharacteristic
26C22×D4×C43—21no—
27C22×D4×C43—21no—
28C22×D4×C43—21no—
29C22×D4×C43C2×C411yescharacteristic
30C23×C4×C43—22no—
31C23×C4×C43—22no—
32C23×C4×C43—22no—
33C23×C4×C43—42no—
34C23×C4×C43—42no—
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C23×C4×C43C2311yescharacteristic
41C22×C8×C43—24no—
42C22×C8×C43—22no—
43C22×C8×C43—42no—
44C22×C8×C43—42no—
45#121×C43—22no—
46#121×C43—22no—
47#121×C43—42no—
48#121×C43—42no—
49#120×C43—42no—
50#120×C43—42no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43—24no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—42no—
62C2×C22⋊C4×C43—42no—
63C22⋊C8×C43—24no—
64C22⋊C8×C43—22no—
65C22⋊C8×C43D414yescomplemented
66#95×C43—21no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43—42no—
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—22no—
75C24×C43—22no—
76C24×C43—21no—
77C24×C43—41no—
78C24×C43—41no—
79C24×C43C22⋊C411yescharacteristic
80C24×C43C22⋊C411yescharacteristic
81C24×C43D812yes—
82C24×C43SD1612yes—
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—22no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43—42no—
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—42no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—24no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—48no—
124C22×C4×C43—48no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C22⋊C411yescharacteristic
129C22×C4×C43C22⋊C411yescharacteristic
130C22×C4×C43C22×C411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D412yes—
133C22×C4×C43#4112yes—
134C2×C8×C43—24no—
135C2×C8×C43—48no—
136C2×C8×C43—42no—
137C2×C8×C43—42no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—48no—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—42no—
147C22⋊C4×C43—42no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—24no—
159C23×C43—24no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—24no—
167C23×C43—24no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—44no—
171C23×C43—44no—
172C23×C43—44no—
173C23×C43—44no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43#9912yes—
182C23×C43#10212yes—
183C23×C43#10212yes—
184C23×C43#10412yes—
185C23×C43C2×C22⋊C411yescharacteristic
186C23×C43#12112yes—
187C23×C43C2×D811yescharacteristic
188C23×C43C2×SD1611yescharacteristic
189C23×C43#13512yes—
190D4×C43—82no—
191D4×C43—84no—
192D4×C43—84no—
193D4×C43—82no—
194D4×C43—82no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—44no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—44no—
214C2×C4×C43—44no—
215C2×C4×C43—44no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—82no—
226C2×C4×C43—82no—
227C2×C4×C43—82no—
228C2×C4×C43—82no—
229C2×C4×C43#9912yes—
230C2×C4×C43C4×D412yes—
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C8×C43—44no—
234#9113C4311yesmaximal, characteristic, direct product factor, Sylow
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—48no—
253C22×C43—48no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43#32714yescomplemented
266C22×C43#38611yescharacteristic
267C22×C43C2×#9911yescharacteristic
268C22×C43C2×#9911yescharacteristic
269C22×C43C2×#10211yescharacteristic
270C22×C43#41611yescharacteristic
271C22×C43C2×#10411yescharacteristic
272C22×C43#42111yescharacteristic
273C22×C43#46512yes—
274C22×C43#46612yes—
275C4×C43—21no—
276C4×C43—22no—
277C4×C43—21no—
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—84no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C22×C22⋊C8C2×C4311yescharacteristic, complemented
285#2847C2×C4311yescharacteristic
286C2×#327C2×C4312yescomplemented
287C22⋊#95C2×C4311yescharacteristic, complemented
288#1294C2×C4312yescomplemented
289C2×C43—22no—
290C2×C43—24no—
291C2×C43—22no—
292C2×C43—42no—
293C2×C43—161no—
294C2×C43C2×#32711yescharacteristic
295C2×C43#150111yescharacteristic
296C2×C43#151611yescharacteristic
297C2×C43#151911yescharacteristic
298C2×C43#187111yescharacteristic
299C2×C43#189311yescharacteristic
300C2×C43#189811yescharacteristic
301C24×C4C22×C4311yescharacteristic
302C23×C8—21no—
303C2×#121C4×C4311yescharacteristic, complemented
304C2×#121C4×C4311yescharacteristic, complemented
305C2×#121C22×C4311yescharacteristic
306C2×#120—21no—
307C22×C22⋊C4—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8—24no—
310C2×C22⋊C8C22×C4312yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#380C4×C4311yescharacteristic, complemented
315#380C4×C4311yescharacteristic, complemented
316#380C22×C4311yescharacteristic
317C2×#95—21no—
318C2×#95C22×C4312yes—
319#327—24no—
320C43#911311yescharacteristic, direct product factor, Sylow
321C25D4×C4311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C4311yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C4311yescharacteristic
332C23×C4C2×C4×C4311yescharacteristic
333C23×C4D4×C4311yescharacteristic
334C23×C4D4×C4311yescharacteristic
335C23×C4D4×C4311yescharacteristic
336C23×C4C23×C4311yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C4311yescharacteristic
348C2×C4⋊C4C2×C4×C4311yescharacteristic
349C2×C4⋊C4C2×C4×C4311yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C4314yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C4311yescharacteristic
376C24C22⋊C4×C4311yescharacteristic
377C24D8×C4312yes—
378C24SD16×C4312yes—
379C24C2×D4×C4311yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C4311yescharacteristic
425C22×C4C22⋊C4×C4311yescharacteristic
426C22×C4C22×C4×C4311yescharacteristic
427C22×C4C2×D4×C4311yescharacteristic
428C22×C4C2×D4×C4312yes—
429C22×C4#41×C4312yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C4312yes—
478C23#102×C4312yes—
479C23#102×C4312yes—
480C23#104×C4312yes—
481C23C2×C22⋊C4×C4311yescharacteristic
482C23#121×C4312yes—
483C23C2×D8×C4311yescharacteristic
484C23C2×SD16×C4311yescharacteristic
485C23#135×C4312yes—
486D4—82no—
487D4—84no—
488D4—84no—
489D4—82no—
490D4—82no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C4312yes—
526C2×C4C4×D4×C4312yes—
527C2×C4#120×C4311yescharacteristic
528C2×C4#123×C4311yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C43×#32714yescomplemented
561C22C43×#38611yescharacteristic
562C22C2×#99×C4311yescharacteristic
563C22C2×#99×C4311yescharacteristic
564C22C2×#102×C4311yescharacteristic
565C22C43×#41611yescharacteristic
566C22C2×#104×C4311yescharacteristic
567C22C43×#42111yescharacteristic
568C22C43×#46512yes—
569C22C43×#46612yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—42no—
583C2—161no—
584C2C2×C43×#32711yescharacteristic
585C2C43×#150111yescharacteristic
586C2C43×#151611yescharacteristic
587C2C43×#151911yescharacteristic
588C2C43×#187111yescharacteristic
589C2C43×#189311yescharacteristic
590C2C43×#189811yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC43×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C43C2semidirect
3. C2×C43×#327C2semidirect
4. C43×C22⋊#95C2semidirect
5. C43×#1294C2semidirect
8. C2×#121×C43C4semidirect
9. C2×#121×C43C4semidirect
19. C43×#380C4semidirect
20. C43×#380C4semidirect
65. C22⋊C8×C43D4semidirect
234. #9113C43direct (N × H)
265. C22×C43#327semidirect
284. C22×C22⋊C8C2×C43semidirect
286. C2×#327C2×C43semidirect
287. C22⋊#95C2×C43semidirect
288. #1294C2×C43semidirect
303. C2×#121C4×C43semidirect
304. C2×#121C4×C43semidirect
314. #380C4×C43semidirect
315. #380C4×C43semidirect
320. C43#9113direct (N × H)
361. C22⋊C8D4×C43semidirect
560. C22C43×#327semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C432
C43×#28472
C2×C43×#3272
C43×C22⋊#952
C43×#12942
#911343