Finite Group Databasebeta

← C43×#9083 #24929100

Subgroups — C43×#9083 #24929100

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#407C211yesmaximal, characteristic, complemented
2C2×C43×#386C211yesmaximal, characteristic
3C43×#1779C211yesmaximal, characteristic, complemented
4C2×C43×#323C212yesmaximal, complemented
5C43×#1280C212yesmaximal, complemented
6C23×D4×C43C411yescharacteristic
7C24×C4×C43C2211yescharacteristic
8C22×M16×C43—21no—
9C22×C22⋊C4×C43C411yescharacteristic
10C22×C22⋊C4×C43C411yescharacteristic
11C22×C22⋊C4×C43C2211yescharacteristic
12C43×#407—24no—
13C2×C22⋊C8×C43—21no—
14C2×C22⋊C8×C43—21no—
15C2×C22⋊C8×C43—21no—
16C2×C22⋊C8×C43C2212yes—
17C2×C22⋊C8×C43C2212yes—
18C43×#386—21no—
19C43×#386—21no—
20C43×#386—21no—
21C43×#386—21no—
22C2×#95×C43C411yescharacteristic
23C2×#95×C43C2211yescharacteristic
24C43×#323—24no—
25C25×C43C2×C411yescharacteristic
26C25×C43C2×C411yescharacteristic
27C22×D4×C43—21no—
28C22×D4×C43—21no—
29C22×D4×C43—22no—
30C22×D4×C43—22no—
31C22×D4×C43—42no—
32C22×D4×C43—42no—
33C23×C4×C43—22no—
34C23×C4×C43—22no—
35C23×C4×C43—42no—
36C23×C4×C43—42no—
37C23×C4×C43C2×C411yescharacteristic
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43C2×C411yescharacteristic
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C2×M16×C43—24no—
47C2×M16×C43—42no—
48C2×M16×C43—42no—
49C22×C8×C43—22no—
50C22×C8×C43—22no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—22no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43—42no—
60C2×C22⋊C4×C43—42no—
61C22⋊C8×C43—24no—
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64C22⋊C8×C43—22no—
65C22⋊C8×C43—42no—
66C22⋊C8×C43—42no—
67C22⋊C8×C43D414yescomplemented
68#95×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—21no—
75C24×C43—21no—
76C24×C43—21no—
77C24×C43—22no—
78C24×C43—21no—
79C24×C43—22no—
80C24×C43—22no—
81C24×C43—22no—
82C24×C43—41no—
83C24×C43—41no—
84C24×C43—41no—
85C24×C43—41no—
86C24×C43—41no—
87C24×C43—41no—
88C24×C43C22⋊C411yescharacteristic
89C24×C43C22⋊C411yescharacteristic
90C24×C43M1612yescomplemented
91C24×C43C22×C411yescharacteristic
92C2×D4×C43—24no—
93C2×D4×C43—24no—
94C2×D4×C43—48no—
95C2×D4×C43—48no—
96C2×D4×C43—42no—
97C2×D4×C43—42no—
98C2×D4×C43—42no—
99C2×D4×C43—42no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43—48no—
132C22×C4×C43—48no—
133C22×C4×C43C22⋊C411yescharacteristic
134C22×C4×C43C22⋊C411yescharacteristic
135C22×C4×C43M1612yescomplemented
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D412yes—
139C22×C4×C43#4112yes—
140M16×C43—48no—
141C2×C8×C43—24no—
142C2×C8×C43—42no—
143C2×C8×C43—42no—
144C2×C8×C43—42no—
145C2×C8×C43—42no—
146C2×C8×C43—42no—
147C22⋊C4×C43—42no—
148C22⋊C4×C43—42no—
149C22⋊C4×C43—42no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—42no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—42no—
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—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—22no—
173C23×C43—24no—
174C23×C43—44no—
175C23×C43—44no—
176C23×C43—44no—
177C23×C43—44no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—42no—
193C23×C43—82no—
194C23×C43—82no—
195C23×C43—82no—
196C23×C43—82no—
197C23×C43#9912yes—
198C23×C43#10012yes—
199C23×C43C2×C22⋊C411yescharacteristic
200C23×C43C4×D412yes—
201C23×C43C2×M1611yescharacteristic
202C23×C43C2×M1611yescharacteristic
203C23×C43#13112yes—
204D4×C43—48no—
205D4×C43—48no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—44no—
221C2×C4×C43—44no—
222C2×C4×C43—44no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43—82no—
237C2×C4×C43#9912yes—
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12112yes—
240C2×C4×C43#12311yescharacteristic
241C8×C43—44no—
242C8×C43—82no—
243#9083C4311yesmaximal, characteristic, direct product factor, Sylow
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—48no—
259C22×C43—48no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—84no—
272C22×C43—84no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43#38611yescharacteristic
278C22×C43#40711yescharacteristic
279C22×C43#40811yescharacteristic
280C22×C43C2×#9911yescharacteristic
281C22×C43C2×#9911yescharacteristic
282C22×C43C2×#10011yescharacteristic
283C22×C43#41311yescharacteristic
284C22×C43#43512yes—
285C22×C43#43612yes—
286C4×C43—21no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C2×#407C2×C4311yescharacteristic, complemented
295C2×#386C2×C4311yescharacteristic
296#1779C2×C4311yescharacteristic, complemented
297C2×#323C2×C4312yescomplemented
298#1280C2×C4312yescomplemented
299C2×C43—22no—
300C2×C43—22no—
301C2×C43—42no—
302C2×C43—42no—
303C2×C43—82no—
304C2×C43#146211yescharacteristic
305C2×C43#146511yescharacteristic
306C2×C43#146811yescharacteristic
307C2×C43#147111yescharacteristic
308C2×C43#187011yescharacteristic
309C2×C43#189811yescharacteristic
310C2×C43#190011yescharacteristic
311C23×D4C4×C4311yescharacteristic
312C24×C4C22×C4311yescharacteristic
313C22×M16—21no—
314C22×C22⋊C4C4×C4311yescharacteristic
315C22×C22⋊C4C4×C4311yescharacteristic
316C22×C22⋊C4C22×C4311yescharacteristic
317#407—24no—
318C2×C22⋊C8—21no—
319C2×C22⋊C8—21no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8C22×C4312yes—
322C2×C22⋊C8C22×C4312yes—
323#386—21no—
324#386—21no—
325#386—21no—
326#386—21no—
327C2×#95C4×C4311yescharacteristic
328C2×#95C22×C4311yescharacteristic
329#323—24no—
330C43#908311yescharacteristic, direct product factor, Sylow
331C25C2×C4×C4311yescharacteristic
332C25C2×C4×C4311yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C4311yescharacteristic
344C23×C4C2×C4×C4311yescharacteristic
345C23×C4C2×C4×C4311yescharacteristic
346C23×C4C2×C4×C4311yescharacteristic
347C23×C4D4×C4311yescharacteristic
348C23×C4D4×C4311yescharacteristic
349C23×C4D4×C4311yescharacteristic
350C23×C4D4×C4311yescharacteristic
351C23×C4C23×C4311yescharacteristic
352C2×M16—24no—
353C2×M16—42no—
354C2×M16—42no—
355C22×C8—22no—
356C22×C8—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C4314yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24C22⋊C4×C4311yescharacteristic
395C24C22⋊C4×C4311yescharacteristic
396C24M16×C4312yescomplemented
397C24C22×C4×C4311yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—48no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C4311yescharacteristic
440C22×C4C22⋊C4×C4311yescharacteristic
441C22×C4M16×C4312yescomplemented
442C22×C4C2×D4×C4311yescharacteristic
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4312yes—
445C22×C4#41×C4312yes—
446M16—48no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—24no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—42no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23#99×C4312yes—
504C23#100×C4312yes—
505C23C2×C22⋊C4×C4311yescharacteristic
506C23C4×D4×C4312yes—
507C23C2×M16×C4311yescharacteristic
508C23C2×M16×C4311yescharacteristic
509C23#131×C4312yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C4312yes—
544C2×C4#120×C4311yescharacteristic
545C2×C4#121×C4312yes—
546C2×C4#123×C4311yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—48no—
564C22—48no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—84no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22C43×#38611yescharacteristic
583C22C43×#40711yescharacteristic
584C22C43×#40811yescharacteristic
585C22C2×#99×C4311yescharacteristic
586C22C2×#99×C4311yescharacteristic
587C22C2×#100×C4311yescharacteristic
588C22C43×#41311yescharacteristic
589C22C43×#43512yes—
590C22C43×#43612yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—42no—
602C2—42no—
603C2—82no—
604C2C43×#146211yescharacteristic
605C2C43×#146511yescharacteristic
606C2C43×#146811yescharacteristic
607C2C43×#147111yescharacteristic
608C2C43×#187011yescharacteristic
609C2C43×#189811yescharacteristic
610C2C43×#190011yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC24C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC23×D4×C43C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#407C2semidirect
3. C43×#1779C2semidirect
4. C2×C43×#323C2semidirect
5. C43×#1280C2semidirect
67. C22⋊C8×C43D4semidirect
90. C24×C43M16semidirect
135. C22×C4×C43M16semidirect
243. #9083C43direct (N × H)
294. C2×#407C2×C43semidirect
296. #1779C2×C43semidirect
297. C2×#323C2×C43semidirect
298. #1280C2×C43semidirect
330. C43#9083direct (N × H)
373. C22⋊C8D4×C43semidirect
396. C24M16×C43semidirect
441. C22×C4M16×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4072
C2×C43×#3862
C43×#17792
C2×C43×#3232
C43×#12802
#908343