Finite Group Databasebeta

← C43×#29894 #24949911

Subgroups — C43×#29894 #24949911

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2848C211yesmaximal, characteristic
2C2×C43×#380C211yesmaximal, characteristic
3C43×#2077C212yesmaximal, complemented
4C43×#2075C212yesmaximal, complemented
5C43×#2036C212yesmaximal, complemented
6C43×#2035C212yesmaximal, complemented
7C43×#1872C211yesmaximal, characteristic, complemented
8C43×#1872C211yesmaximal, characteristic, complemented
9C43×#1853C211yesmaximal, characteristic, complemented
10C43×#1852C211yesmaximal, characteristic, complemented
11C43×#1779C211yesmaximal, characteristic
12C24×C4×C43C2211yescharacteristic
13C2×C22⋊Q8×C43C2211yescharacteristic
14C2×C22⋊Q8×C43C2211yescharacteristic
15C2×C22⋊Q8×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2211yescharacteristic
17C22×C4⋊C4×C43C2211yescharacteristic
18C22×C22⋊C4×C43—21no—
19C2×#107×C43C2212yescomplemented
20C2×#106×C43C2212yescomplemented
21C2×#103×C43C2212yescomplemented
22C2×#103×C43C2212yescomplemented
23C2×C22⋊C8×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C2×C22⋊C8×C43C2212yes—
26C2×C22⋊C8×C43C2212yes—
27C43×#385—21no—
28C43×#385—21no—
29C43×#385—21no—
30C43×#380—21no—
31C43×#380—21no—
32C43×#380C2211yescharacteristic
33C43×#380C2212yes—
34C43×#380C2211yescharacteristic
35C43×#380C2212yes—
36C43×#380C2211yescharacteristic
37C43×#379—21no—
38C2×#95×C43—21no—
39C43×#340C2212yescomplemented
40C43×#340C2212yescomplemented
41C43×#340C2212yescomplemented
42C43×#340C2212yescomplemented
43C25×C43D411yescharacteristic
44C22×Q8×C43C2311yescharacteristic
45C23×C4×C43—22no—
46C23×C4×C43—22no—
47C23×C4×C43—21no—
48C23×C4×C43—21no—
49C23×C4×C43—42no—
50C23×C4×C43—42no—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43C2311yescharacteristic
55C23×C4×C43C2311yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C22×C8×C43C2312yes—
58C22×C8×C43C2312yes—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—42no—
62C22⋊Q8×C43—42no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—42no—
69C2×C4⋊C4×C43—42no—
70C2×C4⋊C4×C43C2312yes—
71C2×C4⋊C4×C43C2312yes—
72C2×C4⋊C4×C43C2311yescharacteristic
73C2×C4⋊C4×C43C2311yescharacteristic
74C2×C4⋊C4×C43C2311yescharacteristic
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—44no—
84#107×C43—42no—
85#106×C43—42no—
86#103×C43—42no—
87#103×C43—42no—
88C22⋊C8×C43—22no—
89C22⋊C8×C43—22no—
90C22⋊C8×C43—42no—
91C22⋊C8×C43—42no—
92#95×C43—22no—
93#95×C43—22no—
94#95×C43—21no—
95#95×C43—21no—
96#95×C43—21no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—41no—
103C24×C43—41no—
104C24×C43C2×D411yescharacteristic
105C24×C43C2×D411yescharacteristic
106C24×C43C2×D411yescharacteristic
107C2×Q8×C43—21no—
108C2×Q8×C43—21no—
109C2×Q8×C43—22no—
110C2×Q8×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—48no—
141C22×C4×C43—48no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43#4112yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C2×C8×C43—22no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—42no—
169C22⋊C4×C43—44no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—44no—
176C22⋊C4×C43—42no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—28no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—44no—
195C23×C43—44no—
196C23×C43—44no—
197C23×C43—44no—
198C23×C43—44no—
199C23×C43—44no—
200C23×C43#12312yes—
201C23×C43#13512yes—
202C23×C43AGL(1,ℤ/8)12yes—
203C23×C43#13712yes—
204C23×C43#13712yes—
205C23×C43C22×D411yescharacteristic
206Q8×C43—42no—
207Q8×C43—42no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—44no—
219C2×C4×C43—44no—
220C2×C4×C43—44no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—84no—
244C2×C4×C43—84no—
245C2×C4×C43#12312yes—
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)12yes—
249C2×C4×C43H(5,𝔽2)12yes—
250C8×C43—42no—
251C8×C43—42no—
252#29894C4311yesmaximal, characteristic, direct product factor, Sylow
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—416no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43#48514yes—
275C22×C43C2×#12311yescharacteristic
276C22×C43#53411yescharacteristic
277C22×C43#53411yescharacteristic
278C22×C43C2×#13511yescharacteristic
279C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C43C2×#13711yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C4×C43—22no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—82no—
289C4×C43—81no—
290C4×C43—82no—
291C4×C43#53812yes—
292C4×C43#53812yes—
293#2848C2×C4311yescharacteristic
294C2×#380C2×C4311yescharacteristic
295#2077C2×C4312yescomplemented
296#2075C2×C4312yescomplemented
297#2036C2×C4312yescomplemented
298#2035C2×C4312yescomplemented
299#1872C2×C4311yescharacteristic, complemented
300#1872C2×C4311yescharacteristic, complemented
301#1853C2×C4311yescharacteristic, complemented
302#1852C2×C4311yescharacteristic, complemented
303#1779C2×C4311yescharacteristic
304C2×C43—24no—
305C2×C43—42no—
306C2×C43—42no—
307C2×C43#262211yescharacteristic
308C2×C43C2×#48511yescharacteristic
309C2×C43#309211yescharacteristic
310C2×C43#318811yescharacteristic
311C2×C43#319011yescharacteristic
312C2×C43#319311yescharacteristic
313C2×C43#319511yescharacteristic
314C24×C4C22×C4311yescharacteristic
315C2×C22⋊Q8C22×C4311yescharacteristic
316C2×C22⋊Q8C22×C4311yescharacteristic
317C2×C22⋊Q8C22×C4311yescharacteristic
318C22×C4⋊C4C22×C4311yescharacteristic
319C22×C4⋊C4C22×C4311yescharacteristic
320C22×C22⋊C4—21no—
321C2×#107C22×C4312yescomplemented
322C2×#106C22×C4312yescomplemented
323C2×#103C22×C4312yescomplemented
324C2×#103C22×C4312yescomplemented
325C2×C22⋊C8C22×C4311yescharacteristic
326C2×C22⋊C8C22×C4311yescharacteristic
327C2×C22⋊C8C22×C4312yes—
328C2×C22⋊C8C22×C4312yes—
329#385—21no—
330#385—21no—
331#385—21no—
332#380—21no—
333#380—21no—
334#380C22×C4311yescharacteristic
335#380C22×C4312yes—
336#380C22×C4311yescharacteristic
337#380C22×C4312yes—
338#380C22×C4311yescharacteristic
339#379—21no—
340C2×#95—21no—
341#340C22×C4312yescomplemented
342#340C22×C4312yescomplemented
343#340C22×C4312yescomplemented
344#340C22×C4312yescomplemented
345C43#2989411yescharacteristic, direct product factor, Sylow
346C25D4×C4311yescharacteristic
347C22×Q8C23×C4311yescharacteristic
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4D4×C4311yescharacteristic
355C23×C4D4×C4311yescharacteristic
356C23×C4D4×C4311yescharacteristic
357C23×C4C23×C4311yescharacteristic
358C23×C4C23×C4311yescharacteristic
359C23×C4C23×C4311yescharacteristic
360C22×C8C23×C4312yes—
361C22×C8C23×C4312yes—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—42no—
365C22⋊Q8—42no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C23×C4312yes—
374C2×C4⋊C4C23×C4312yes—
375C2×C4⋊C4C23×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—44no—
387#107—42no—
388#106—42no—
389#103—42no—
390#103—42no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393C22⋊C8—42no—
394C22⋊C8—42no—
395#95—22no—
396#95—22no—
397#95—21no—
398#95—21no—
399#95—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—41no—
406C24—41no—
407C24C2×D4×C4311yescharacteristic
408C24C2×D4×C4311yescharacteristic
409C24C2×D4×C4311yescharacteristic
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4#41×C4312yes—
451C22×C4#41×C4312yes—
452C22×C4C24×C4311yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C22⋊C4—44no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—44no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—28no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—44no—
502C23—44no—
503C23#123×C4312yes—
504C23#135×C4312yes—
505C23AGL(1,ℤ/8)×C4312yes—
506C23#137×C4312yes—
507C23#137×C4312yes—
508C23C22×D4×C4311yescharacteristic
509Q8—42no—
510Q8—42no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4#123×C4312yes—
549C2×C4C2×#41×C4311yescharacteristic
550C2×C4C2×#41×C4311yescharacteristic
551C2×C4H(5,𝔽2)×C4312yes—
552C2×C4H(5,𝔽2)×C4312yes—
553C8—42no—
554C8—42no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—416no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22C43×#48514yes—
577C22C2×#123×C4311yescharacteristic
578C22C43×#53411yescharacteristic
579C22C43×#53411yescharacteristic
580C22C2×#135×C4311yescharacteristic
581C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
582C22C2×#137×C4311yescharacteristic
583C22C2×#137×C4311yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—82no—
593C4C43×#53812yes—
594C4C43×#53812yes—
595C2—24no—
596C2—42no—
597C2—42no—
598C2C43×#262211yescharacteristic
599C2C2×C43×#48511yescharacteristic
600C2C43×#309211yescharacteristic
601C2C43×#318811yescharacteristic
602C2C43×#319011yescharacteristic
603C2C43×#319311yescharacteristic
604C2C43×#319511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC25×C43D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2077C2semidirect
4. C43×#2075C2semidirect
5. C43×#2036C2semidirect
6. C43×#2035C2semidirect
7. C43×#1872C2semidirect
8. C43×#1872C2semidirect
9. C43×#1853C2semidirect
10. C43×#1852C2semidirect
19. C2×#107×C43C22semidirect
20. C2×#106×C43C22semidirect
21. C2×#103×C43C22semidirect
22. C2×#103×C43C22semidirect
39. C43×#340C22semidirect
40. C43×#340C22semidirect
41. C43×#340C22semidirect
42. C43×#340C22semidirect
252. #29894C43direct (N × H)
295. #2077C2×C43semidirect
296. #2075C2×C43semidirect
297. #2036C2×C43semidirect
298. #2035C2×C43semidirect
299. #1872C2×C43semidirect
300. #1872C2×C43semidirect
301. #1853C2×C43semidirect
302. #1852C2×C43semidirect
321. C2×#107C22×C43semidirect
322. C2×#106C22×C43semidirect
323. C2×#103C22×C43semidirect
324. C2×#103C22×C43semidirect
341. #340C22×C43semidirect
342. #340C22×C43semidirect
343. #340C22×C43semidirect
344. #340C22×C43semidirect
345. C43#29894direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28482
C2×C43×#3802
C43×#20772
C43×#20752
C43×#20362
C43×#20352
C43×#18722
C43×#18532
C43×#18522
C43×#17792
#2989443