Finite Group Databasebeta

← C43×#14589 #24934606

Subgroups — C43×#14589 #24934606

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#394C211yesmaximal, characteristic
2C2×C43×#388C212yesmaximal, complemented
3C43×#1441C211yesmaximal, characteristic, complemented
4C43×#1439C212yesmaximal, complemented
5C43×#1438C212yesmaximal
6C43×#1437C212yesmaximal, complemented
7C43×#1437C212yesmaximal, complemented
8C43×C4⋊#95C211yesmaximal, characteristic, complemented
9C43×#1434C212yesmaximal, complemented
10C23×D4×C43C2211yescharacteristic
11C22×C4⋊C4×C43C2211yescharacteristic
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C4⋊C4×C43C2211yescharacteristic
14C22×C22⋊C4×C43C2212yes—
15C22×C22⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C22⋊C4×C43C2212yes—
20C22×C42×C43C2212yes—
21C22×C42×C43C2211yescharacteristic
22C43×#394C418yescomplemented
23C43×#388—28no—
24C2×#95×C43C2212yes—
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2212yes—
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2211yescharacteristic
33C25×C43C2312yes—
34C22×D4×C43—42no—
35C22×D4×C43—42no—
36C22×D4×C43—41no—
37C22×D4×C43—41no—
38C22×D4×C43C2×C414yes—
39C23×C4×C43C2312yes—
40C23×C4×C43C2312yes—
41C23×C4×C43C2311yescharacteristic
42C23×C4×C43C2311yescharacteristic
43C23×C4×C43C2312yes—
44C23×C4×C43C2312yes—
45C23×C4×C43C2312yes—
46C23×C4×C43C2311yescharacteristic
47C2×C4⋊C4×C43—41no—
48C2×C4⋊C4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43—41no—
51C2×C4⋊C4×C43—42no—
52C2×C4⋊C4×C43—41no—
53C2×C4⋊C4×C43C2×C414yes—
54C2×C4⋊C4×C43D414yescomplemented
55C2×C22⋊C4×C43—24no—
56C2×C22⋊C4×C43—24no—
57C2×C22⋊C4×C43—24no—
58C2×C22⋊C4×C43—24no—
59C2×C22⋊C4×C43—24no—
60C2×C22⋊C4×C43—24no—
61C2×C22⋊C4×C43—24no—
62C2×C22⋊C4×C43—24no—
63C2×C22⋊C4×C43—42no—
64C2×C22⋊C4×C43—42no—
65C2×C22⋊C4×C43—42no—
66C2×C22⋊C4×C43—42no—
67C2×C22⋊C4×C43—42no—
68C2×C22⋊C4×C43—42no—
69C2×C22⋊C4×C43—42no—
70C2×C22⋊C4×C43—42no—
71C2×C22⋊C4×C43C2×C418yes—
72C2×C22⋊C4×C43C2×C418yes—
73C2×C42×C43—24no—
74C2×C42×C43—24no—
75C2×C42×C43—22no—
76C2×C42×C43—42no—
77C2×C42×C43—41no—
78C2×C42×C43—41no—
79#95×C43—24no—
80#95×C43—24no—
81#95×C43—24no—
82#95×C43—42no—
83#95×C43—42no—
84#95×C43—42no—
85#95×C43—42no—
86#95×C43—41no—
87#95×C43C2×C414yes—
88C24×C43—22no—
89C24×C43—22no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43C22×C414yes—
103C24×C43C2411yescharacteristic
104C2×D4×C43—48no—
105C2×D4×C43—44no—
106C2×D4×C43—44no—
107C2×D4×C43—48no—
108C2×D4×C43—44no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—21no—
151C22×C4×C43—22no—
152C22×C4×C43C22×C414yes—
153C22×C4×C43C22×C412yes—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D414yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43#4114yes—
159C22×C4×C43#4114yes—
160C22×C4×C43#4112yes—
161C4⋊C4×C43—44no—
162C4⋊C4×C43—44no—
163C4⋊C4×C43—44no—
164C22⋊C4×C43—216no—
165C22⋊C4×C43—48no—
166C22⋊C4×C43—48no—
167C22⋊C4×C43—48no—
168C22⋊C4×C43—48no—
169C22⋊C4×C43—48no—
170C42×C43—48no—
171C42×C43—44no—
172C23×C43—24no—
173C23×C43—24no—
174C23×C43—24no—
175C23×C43—24no—
176C23×C43—24no—
177C23×C43—24no—
178C23×C43—24no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43C23×C411yescharacteristic
208C23×C43C22×D411yescharacteristic
209C23×C43C2×#4111yescharacteristic
210C23×C43C2×#4112yes—
211C23×C43C2×#4112yes—
212C23×C43H(5,𝔽2)11yescharacteristic
213C23×C43H(5,𝔽2)11yescharacteristic
214C23×C43H(5,𝔽2)12yes—
215C23×C43H(5,𝔽2)12yes—
216C23×C43H(5,𝔽2)11yescharacteristic
217C23×C432−1+411yescharacteristic
218D4×C43—416no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—24no—
239C2×C4×C43—24no—
240C2×C4×C43—24no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—41no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—41no—
260C2×C4×C43—42no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43C4×D414yes—
271#14589C4311yesmaximal, characteristic, direct product factor, Sylow
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—44no—
276C22×C43—44no—
277C22×C43—44no—
278C22×C43—44no—
279C22×C43—82no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43—82no—
284C22×C43—82no—
285C22×C43—82no—
286C22×C43—82no—
287C22×C43C2×C4×D411yescharacteristic
288C22×C43C4×#4112yes—
289C22×C43#51811yescharacteristic
290C22×C43#51812yes—
291C22×C43#52011yescharacteristic
292C22×C43#53411yescharacteristic
293C22×C43#53711yescharacteristic
294C22×C43#53811yescharacteristic
295C22×C43#53812yes—
296C22×C43#53911yescharacteristic
297C22×C43#53912yes—
298C22×C43#54012yes—
299C22×C43#54212yes—
300C22×C43#54612yes—
301C22×C43#55012yes—
302C22×C43#55112yes—
303C22×C43#55312yes—
304C22×C43#55512yes—
305C22×C43#55511yescharacteristic
306C22×C43#55511yescharacteristic
307C22×C43#56011yescharacteristic
308C22×C43#56012yes—
309C22×C43H(3,𝔽4)11yescharacteristic
310C4×C43—24no—
311C4×C43—44no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—44no—
315C4×C43—44no—
316C4×C43—44no—
317C4×C43—82no—
318C2×#394C2×C4311yescharacteristic
319C2×#388C2×C4312yescomplemented
320#1441C2×C4311yescharacteristic, complemented
321#1439C2×C4312yescomplemented
322#1438C2×C4312yes—
323#1437C2×C4312yescomplemented
324#1437C2×C4312yescomplemented
325C4⋊#95C2×C4311yescharacteristic, complemented
326#1434C2×C4312yescomplemented
327C2×C43—84no—
328C2×C43#232511yescharacteristic
329C2×C43#233512yes—
330C2×C43#236312yes—
331C2×C43#237211yescharacteristic
332C2×C43#237511yescharacteristic
333C2×C43#269911yescharacteristic
334C2×C43#270512yes—
335C2×C43#273311yescharacteristic
336C2×C43#275612yes—
337C2×C43#278511yescharacteristic
338C2×C43#279511yescharacteristic
339C23×D4C22×C4311yescharacteristic
340C22×C4⋊C4C22×C4311yescharacteristic
341C22×C4⋊C4C22×C4311yescharacteristic
342C22×C4⋊C4C22×C4311yescharacteristic
343C22×C22⋊C4C22×C4312yes—
344C22×C22⋊C4C22×C4312yes—
345C22×C22⋊C4C22×C4312yes—
346C22×C22⋊C4C22×C4312yes—
347C22×C22⋊C4C22×C4312yes—
348C22×C22⋊C4C22×C4312yes—
349C22×C42C22×C4312yes—
350C22×C42C22×C4311yescharacteristic
351#394C4×C4318yescomplemented
352#388—28no—
353C2×#95C22×C4312yes—
354C2×#95C22×C4312yes—
355C2×#95C22×C4312yes—
356C2×#95C22×C4312yes—
357C2×#95C22×C4312yes—
358C2×#95C22×C4312yes—
359C2×#95C22×C4312yes—
360C2×#95C22×C4311yescharacteristic
361C2×#95C22×C4311yescharacteristic
362C43#1458911yescharacteristic, direct product factor, Sylow
363C25C23×C4312yes—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4C2×C4×C4314yes—
369C23×C4C23×C4312yes—
370C23×C4C23×C4311yescharacteristic
371C23×C4C23×C4312yes—
372C23×C4C23×C4311yescharacteristic
373C23×C4C23×C4312yes—
374C23×C4C23×C4312yes—
375C23×C4C23×C4312yes—
376C23×C4C23×C4311yescharacteristic
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4C2×C4×C4314yes—
384C2×C4⋊C4D4×C4314yescomplemented
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4C2×C4×C4318yes—
402C2×C22⋊C4C2×C4×C4318yes—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—42no—
407C2×C42—41no—
408C2×C42—41no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—41no—
417#95C2×C4×C4314yes—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24C22×C4×C4314yes—
433C24C24×C4311yescharacteristic
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—48no—
438C2×D4—44no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4C22×C4×C4314yes—
483C22×C4C22×C4×C4312yes—
484C22×C4C22×C4×C4312yes—
485C22×C4C22×C4×C4312yes—
486C22×C4C2×D4×C4314yes—
487C22×C4C2×D4×C4312yes—
488C22×C4#41×C4314yes—
489C22×C4#41×C4314yes—
490C22×C4#41×C4312yes—
491C4⋊C4—44no—
492C4⋊C4—44no—
493C4⋊C4—44no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C42—48no—
501C42—44no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C23×C4×C4311yescharacteristic
538C23C22×D4×C4311yescharacteristic
539C23C2×#41×C4311yescharacteristic
540C23C2×#41×C4312yes—
541C23C2×#41×C4312yes—
542C23H(5,𝔽2)×C4311yescharacteristic
543C23H(5,𝔽2)×C4311yescharacteristic
544C23H(5,𝔽2)×C4312yes—
545C23H(5,𝔽2)×C4312yes—
546C23H(5,𝔽2)×C4311yescharacteristic
547C232−1+4×C4311yescharacteristic
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4C4×D4×C4314yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×C4×D4×C4311yescharacteristic
617C22C4×#41×C4312yes—
618C22C43×#51811yescharacteristic
619C22C43×#51812yes—
620C22C43×#52011yescharacteristic
621C22C43×#53411yescharacteristic
622C22C43×#53711yescharacteristic
623C22C43×#53811yescharacteristic
624C22C43×#53812yes—
625C22C43×#53911yescharacteristic
626C22C43×#53912yes—
627C22C43×#54012yes—
628C22C43×#54212yes—
629C22C43×#54612yes—
630C22C43×#55012yes—
631C22C43×#55112yes—
632C22C43×#55312yes—
633C22C43×#55512yes—
634C22C43×#55511yescharacteristic
635C22C43×#55511yescharacteristic
636C22C43×#56011yescharacteristic
637C22C43×#56012yes—
638C22C43×H(3,𝔽4)11yescharacteristic
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—44no—
645C4—44no—
646C4—82no—
647C2—84no—
648C2C43×#232511yescharacteristic
649C2C43×#233512yes—
650C2C43×#236312yes—
651C2C43×#237211yescharacteristic
652C2C43×#237511yescharacteristic
653C2C43×#269911yescharacteristic
654C2C43×#270512yes—
655C2C43×#273311yescharacteristic
656C2C43×#275612yes—
657C2C43×#278511yescharacteristic
658C2C43×#279511yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#388C2semidirect
3. C43×#1441C2semidirect
4. C43×#1439C2semidirect
6. C43×#1437C2semidirect
7. C43×#1437C2semidirect
8. C43×C4⋊#95C2semidirect
9. C43×#1434C2semidirect
22. C43×#394C4semidirect
54. C2×C4⋊C4×C43D4semidirect
271. #14589C43direct (N × H)
319. C2×#388C2×C43semidirect
320. #1441C2×C43semidirect
321. #1439C2×C43semidirect
323. #1437C2×C43semidirect
324. #1437C2×C43semidirect
325. C4⋊#95C2×C43semidirect
326. #1434C2×C43semidirect
351. #394C4×C43semidirect
362. C43#14589direct (N × H)
384. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3942
C2×C43×#3882
C43×#14412
C43×#14392
C43×#14382
C43×#14372
C43×C4⋊#952
C43×#14342
#1458943