Finite Group Databasebeta

← C43×#23901 #24943918

Subgroups — C43×#23901 #24943918

Order 11008.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3484C211yesmaximal, characteristic
2C22×#123×C43C211yesmaximal, characteristic, complemented
3C2×C43×#458C212yesmaximal, complemented
4C43×#2849C212yesmaximal, complemented
5C43×#2022C214yesmaximal, complemented
6C43×#1898C212yesmaximal, complemented
7C43×#1890C212yesmaximal, complemented
8C43×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C43C2211yescharacteristic
10C23×D4×C43C2211yescharacteristic
11C24×C4×C43C2211yescharacteristic, complemented
12C43×#546—24no—
13D42×C43—24no—
14C43×#535—21no—
15C43×#534—21no—
16C43×#534C2212yes—
17C43×#525—21no—
18C2×#123×C43—21no—
19C2×#123×C43—21no—
20C2×#123×C43—28no—
21C2×#123×C43C2212yes—
22C2×#123×C43C2212yescomplemented
23C2×#123×C43C2214yescomplemented
24C2×#120×C43—21no—
25C2×#120×C43C2212yes—
26C43×#518C2211yescharacteristic
27C22×C4⋊C4×C43—21no—
28C22×C22⋊C4×C43—21no—
29C22×C22⋊C4×C43C2211yescharacteristic, complemented
30C43×#458—28no—
31C2×#99×C43C2212yes—
32C2×#99×C43C2214yescomplemented
33C2×#99×C43C2212yescomplemented
34C43×#386—24no—
35C43×#385—24no—
36C43×#381C2214yescomplemented
37C43×#379C2212yescomplemented
38C43×#342C2214yescomplemented
39C25×C43D411yescharacteristic
40C25×C43C2311yescharacteristic
41H(5,𝔽2)×C43—24no—
42H(5,𝔽2)×C43—42no—
43C2×#41×C43—21no—
44C2×#41×C43—22no—
45C22×D4×C43—21no—
46C22×D4×C43—22no—
47C22×D4×C43—24no—
48C22×D4×C43—22no—
49C22×D4×C43—24no—
50C22×D4×C43—42no—
51C22×D4×C43D411yescharacteristic
52C22×D4×C43D411yescharacteristic
53C22×D4×C43D414yes—
54C22×D4×C43C2312yes—
55C22×D4×C43C2311yescharacteristic
56C22×D4×C43C2311yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43—21no—
59C23×C4×C43—21no—
60C23×C4×C43—24no—
61C23×C4×C43—24no—
62C23×C4×C43—42no—
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2312yes—
65#127×C43—22no—
66#124×C43—22no—
67#123×C43—28no—
68#123×C43—28no—
69#123×C43—22no—
70#123×C43—24no—
71#123×C43—22no—
72#123×C43—22no—
73#123×C43—24no—
74#123×C43—24no—
75#123×C43—28no—
76#123×C43—44no—
77#123×C43D418yescomplemented
78C22⋊Q8×C43—22no—
79#121×C43—22no—
80#121×C43—24no—
81#121×C43—24no—
82#121×C43—24no—
83#120×C43—24no—
84#120×C43—22no—
85#120×C43—22no—
86#120×C43—22no—
87#120×C43—22no—
88#120×C43—24no—
89#120×C43—22no—
90C4×D4×C43—24no—
91C4×D4×C43—24no—
92#117×C43—21no—
93C2×C4⋊C4×C43—28no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—24no—
97C2×C22⋊C4×C43—28no—
98C2×C22⋊C4×C43—22no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—24no—
106C2×C22⋊C4×C43D414yes—
107C2×C22⋊C4×C43C2314yes—
108C2×C22⋊C4×C43C2312yes—
109C2×C22⋊C4×C43C2312yes—
110#99×C43—24no—
111#99×C43—28no—
112#99×C43—42no—
113#95×C43—28no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—21no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—44no—
120C24×C43—41no—
121C24×C43—44no—
122C24×C43C2×D411yescharacteristic
123C24×C43C2×D414yes—
124C24×C43C2×D411yescharacteristic
125C24×C43C2×D412yes—
126C24×C43C2×D411yescharacteristic
127C24×C43C2×D411yescharacteristic
128C24×C43C2411yescharacteristic
129#41×C43—48no—
130#41×C43—42no—
131#41×C43—42no—
132C2×Q8×C43—21no—
133C2×D4×C43—22no—
134C2×D4×C43—21no—
135C2×D4×C43—24no—
136C2×D4×C43—22no—
137C2×D4×C43—24no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—24no—
142C2×D4×C43—22no—
143C2×D4×C43—24no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—22no—
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—24no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—416no—
154C2×D4×C43—48no—
155C2×D4×C43—42no—
156C2×D4×C43—48no—
157C2×D4×C43—42no—
158C2×D4×C43—84no—
159C2×D4×C43C2×D414yes—
160C22×C4×C43—24no—
161C22×C4×C43—24no—
162C22×C4×C43—21no—
163C22×C4×C43—22no—
164C22×C4×C43—24no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—24no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—24no—
173C22×C4×C43—24no—
174C22×C4×C43—41no—
175C22×C4×C43—416no—
176C22×C4×C43—44no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43C2×D412yes—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D414yes—
185C22×C4×C43C2×D414yescomplemented
186C4⋊C4×C43—28no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—28no—
190C4⋊C4×C43—48no—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—28no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—24no—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—28no—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—24no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—24no—
203C22⋊C4×C43—24no—
204C22⋊C4×C43—48no—
205C22⋊C4×C43—48no—
206C22⋊C4×C43C2×D414yescomplemented
207C42×C43—22no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—24no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—28no—
215C23×C43—28no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—22no—
220C23×C43—21no—
221C23×C43—24no—
222C23×C43—42no—
223C23×C43—44no—
224C23×C43—42no—
225C23×C43—44no—
226C23×C43—48no—
227C23×C43—48no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—48no—
231C23×C43—42no—
232C23×C43—44no—
233C23×C43—44no—
234C23×C43—82no—
235C23×C43—84no—
236C23×C43—82no—
237C23×C43#12012yes—
238C23×C43#12012yes—
239C23×C43#12012yes—
240C23×C43C22×D411yescharacteristic
241C23×C43C22×D412yes—
242C23×C43C22×D412yes—
243C23×C43H(5,𝔽2)12yes—
244Q8×C43—42no—
245D4×C43—28no—
246D4×C43—44no—
247D4×C43—42no—
248D4×C43—44no—
249D4×C43—44no—
250D4×C43—42no—
251D4×C43—42no—
252D4×C43—44no—
253D4×C43—44no—
254D4×C43—48no—
255D4×C43—84no—
256D4×C43—84no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—21no—
262C2×C4×C43—24no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—28no—
267C2×C4×C43—24no—
268C2×C4×C43—44no—
269C2×C4×C43—44no—
270C2×C4×C43—48no—
271C2×C4×C43—44no—
272C2×C4×C43—48no—
273C2×C4×C43—48no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—44no—
278C2×C4×C43—44no—
279C2×C4×C43—48no—
280C2×C4×C43—44no—
281C2×C4×C43—82no—
282C2×C4×C43#12012yes—
283#23901C4311yesmaximal, characteristic, direct product factor, Sylow
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—24no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—24no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—416no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—44no—
305C22×C43—81no—
306C22×C43—88no—
307C22×C43—84no—
308C22×C43—81no—
309C22×C43—162no—
310C22×C43#45814yescomplemented
311C22×C43C2×#12011yescharacteristic
312C22×C43C2×#12011yescharacteristic
313C22×C43#53411yescharacteristic
314C22×C43D4214yes—
315C4×C43—22no—
316C4×C43—44no—
317C4×C43—44no—
318C4×C43—41no—
319C4×C43—42no—
320C4×C43—44no—
321C4×C43—84no—
322#3484C2×C4311yescharacteristic
323C22×#123C2×C4311yescharacteristic, complemented
324C2×#458C2×C4312yescomplemented
325#2849C2×C4312yescomplemented
326#2022C2×C4314yescomplemented
327#1898C2×C4312yescomplemented
328#1890C2×C4312yescomplemented
329#1781C2×C4311yescharacteristic, complemented
330C2×C43—21no—
331C2×C43—24no—
332C2×C43—21no—
333C2×C43—24no—
334C2×C43—42no—
335C2×C43—42no—
336C2×C43—81no—
337C2×C43—82no—
338C2×C43#240311yescharacteristic
339C2×C43C2×#45812yes—
340C2×H(5,𝔽2)C22×C4311yescharacteristic
341C23×D4C22×C4311yescharacteristic
342C24×C4C22×C4311yescharacteristic, complemented
343#546—24no—
344D42—24no—
345#535—21no—
346#534—21no—
347#534C22×C4312yes—
348#525—21no—
349C2×#123—21no—
350C2×#123—21no—
351C2×#123—28no—
352C2×#123C22×C4312yes—
353C2×#123C22×C4312yescomplemented
354C2×#123C22×C4314yescomplemented
355C2×#120—21no—
356C2×#120C22×C4312yes—
357#518C22×C4311yescharacteristic
358C22×C4⋊C4—21no—
359C22×C22⋊C4—21no—
360C22×C22⋊C4C22×C4311yescharacteristic, complemented
361#458—28no—
362C2×#99C22×C4312yes—
363C2×#99C22×C4314yescomplemented
364C2×#99C22×C4312yescomplemented
365#386—24no—
366#385—24no—
367#381C22×C4314yescomplemented
368#379C22×C4312yescomplemented
369#342C22×C4314yescomplemented
370C43#2390111yescharacteristic, direct product factor, Sylow
371C25D4×C4311yescharacteristic
372C25C23×C4311yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C4311yescharacteristic
384C22×D4D4×C4311yescharacteristic
385C22×D4D4×C4314yes—
386C22×D4C23×C4312yes—
387C22×D4C23×C4311yescharacteristic
388C22×D4C23×C4311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C4311yescharacteristic
396C23×C4C23×C4312yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C4318yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C4314yes—
439C2×C22⋊C4C23×C4314yes—
440C2×C22⋊C4C23×C4312yes—
441C2×C22⋊C4C23×C4312yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C4311yescharacteristic
455C24C2×D4×C4314yes—
456C24C2×D4×C4311yescharacteristic
457C24C2×D4×C4312yes—
458C24C2×D4×C4311yescharacteristic
459C24C2×D4×C4311yescharacteristic
460C24C24×C4311yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C4314yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—44no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C4312yes—
514C22×C4C2×D4×C4311yescharacteristic
515C22×C4C2×D4×C4311yescharacteristic
516C22×C4C2×D4×C4314yes—
517C22×C4C2×D4×C4314yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C4314yescomplemented
539C42—22no—
540C23—21no—
541C23—21no—
542C23—24no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—28no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C4312yes—
570C23#120×C4312yes—
571C23#120×C4312yes—
572C23C22×D4×C4311yescharacteristic
573C23C22×D4×C4312yes—
574C23C22×D4×C4312yes—
575C23H(5,𝔽2)×C4312yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—42no—
583D4—42no—
584D4—44no—
585D4—44no—
586D4—48no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C4312yes—
615C22—24no—
616C22—24no—
617C22—22no—
618C22—24no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—41no—
634C22—44no—
635C22—42no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22C43×#45814yescomplemented
642C22C2×#120×C4311yescharacteristic
643C22C2×#120×C4311yescharacteristic
644C22C43×#53411yescharacteristic
645C22D42×C4314yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—44no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—21no—
656C2—24no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C43×#240311yescharacteristic
662C2C2×C43×#45812yes—
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
prime radicalC43×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C43C2semidirect
3. C2×C43×#458C2semidirect
4. C43×#2849C2semidirect
5. C43×#2022C2semidirect
6. C43×#1898C2semidirect
7. C43×#1890C2semidirect
8. C43×#1781C2semidirect
11. C24×C4×C43C22semidirect
22. C2×#123×C43C22semidirect
23. C2×#123×C43C22semidirect
29. C22×C22⋊C4×C43C22semidirect
32. C2×#99×C43C22semidirect
33. C2×#99×C43C22semidirect
36. C43×#381C22semidirect
37. C43×#379C22semidirect
38. C43×#342C22semidirect
77. #123×C43D4semidirect
185. C22×C4×C43C2×D4semidirect
206. C22⋊C4×C43C2×D4semidirect
283. #23901C43direct (N × H)
310. C22×C43#458semidirect
323. C22×#123C2×C43semidirect
324. C2×#458C2×C43semidirect
325. #2849C2×C43semidirect
326. #2022C2×C43semidirect
327. #1898C2×C43semidirect
328. #1890C2×C43semidirect
329. #1781C2×C43semidirect
342. C24×C4C22×C43semidirect
353. C2×#123C22×C43semidirect
354. C2×#123C22×C43semidirect
360. C22×C22⋊C4C22×C43semidirect
363. C2×#99C22×C43semidirect
364. C2×#99C22×C43semidirect
367. #381C22×C43semidirect
368. #379C22×C43semidirect
369. #342C22×C43semidirect
370. C43#23901direct (N × H)
409. #123D4×C43semidirect
517. C22×C4C2×D4×C43semidirect
538. C22⋊C4C2×D4×C43semidirect
641. C22C43×#458semidirect

Maximal subgroups

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

subgroupindex
C43×#34842
C22×#123×C432
C2×C43×#4582
C43×#28492
C43×#20222
C43×#18982
C43×#18902
C43×#17812
#2390143