Finite Group Databasebeta

← C43×#24854 #24944871

Subgroups — C43×#24854 #24944871

Order 11008.

788 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#479C211yesmaximal, characteristic, complemented
2C2×C43×#424C211yesmaximal, characteristic
3C43×#2629C211yesmaximal, characteristic
4C43×#2323C211yesmaximal, characteristic
5C43×#2088C211yesmaximal, characteristic, complemented
6C43×#2087C211yesmaximal, characteristic, complemented
7C43×#2066C211yesmaximal, characteristic, complemented
8C43×#2066C211yesmaximal, characteristic, complemented
9C43×#1989C211yesmaximal, characteristic, complemented
10C43×#1948C211yesmaximal, characteristic, complemented
11C43×#1894C211yesmaximal, characteristic
12C43×#1892C211yesmaximal, characteristic
13C43×#1809C211yesmaximal, characteristic
14C43×#1807C211yesmaximal, characteristic
15C43×#1803C211yesmaximal, characteristic, complemented
16C22×M16×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×#125×C43C2211yescharacteristic
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×C4×Q8×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C43×#479—24no—
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C43×#424—24no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×#103×C43C2211yescharacteristic
36C43×#398—21no—
37C43×#398—21no—
38C43×#396—21no—
39C43×#396—21no—
40C43×#391C2211yescharacteristic
41C43×#389—21no—
42C43×#389C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#389C2211yescharacteristic
45C43×#388—21no—
46C43×#388—21no—
47C43×#387—21no—
48C43×#384C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C2×M16×C43—22no—
64C2×M16×C43—22no—
65C2×M16×C43—41no—
66C22×C8×C43—22no—
67C22×C8×C43—22no—
68C22×C8×C43—41no—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#125×C43—22no—
74#125×C43—22no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43Q814yes—
77C4×Q8×C43—22no—
78C4×Q8×C43—22no—
79#117×C43—22no—
80#117×C43—22no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#107×C43—22no—
110#106×C43—22no—
111#106×C43—41no—
112#106×C43—41no—
113C4⋊C8×C43—22no—
114C4⋊C8×C43—22no—
115C4⋊C8×C43—22no—
116C4⋊C8×C43D414yes—
117#103×C43—22no—
118#103×C43—22no—
119#103×C43—41no—
120#103×C43—41no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130C24×C43C2×D411yescharacteristic
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×Q812yes—
155C22×C4×C43#4112yes—
156C22×C4×C43C2411yescharacteristic
157M16×C43—44no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—44no—
169C2×C8×C43C2×D412yes—
170C2×C8×C43C2×D412yes—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43—81no—
191C4⋊C4×C43—81no—
192C4⋊C4×C43—81no—
193C4⋊C4×C43—81no—
194C4⋊C4×C43—81no—
195C4⋊C4×C43C2×Q812yes—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—24no—
199C22⋊C4×C43—81no—
200C22⋊C4×C43—81no—
201C22⋊C4×C43—81no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—42no—
205C42×C43—81no—
206C42×C43C2×D412yes—
207C42×C43#4112yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C22⋊Q812yes—
215C23×C43C22×D411yescharacteristic
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43#12112yes—
261C2×C4×C43#12112yes—
262C2×C4×C43C22⋊Q812yes—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×Q811yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C8×C43—22no—
270C8×C43—22no—
271C8×C43—41no—
272C8×C43—41no—
273#24854C4311yesmaximal, characteristic, direct product factor, Sylow
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×#12111yescharacteristic
282C22×C43C2×C22⋊Q811yescharacteristic
283C22×C43#53711yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57811yescharacteristic
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43#54611yescharacteristic
302C4×C43D4×Q811yescharacteristic
303C4×C43#55211yescharacteristic
304C4×C43#55411yescharacteristic
305C2×#479C2×C4311yescharacteristic, complemented
306C2×#424C2×C4311yescharacteristic
307#2629C2×C4311yescharacteristic
308#2323C2×C4311yescharacteristic
309#2088C2×C4311yescharacteristic, complemented
310#2087C2×C4311yescharacteristic, complemented
311#2066C2×C4311yescharacteristic, complemented
312#2066C2×C4311yescharacteristic, complemented
313#1989C2×C4311yescharacteristic, complemented
314#1948C2×C4311yescharacteristic, complemented
315#1894C2×C4311yescharacteristic
316#1892C2×C4311yescharacteristic
317#1809C2×C4311yescharacteristic
318#1807C2×C4311yescharacteristic
319#1803C2×C4311yescharacteristic, complemented
320C2×C43—42no—
321C2×C43#241711yescharacteristic
322C2×C43#306011yescharacteristic
323C2×C43#306311yescharacteristic
324C2×C43#308211yescharacteristic
325C2×C43#308411yescharacteristic
326C2×C43#325811yescharacteristic
327C2×C43#326011yescharacteristic
328C22×M16C22×C4311yescharacteristic
329C23×C8C22×C4311yescharacteristic
330C2×#125C22×C4311yescharacteristic
331C2×C22⋊Q8C22×C4311yescharacteristic
332C2×C4×Q8C22×C4311yescharacteristic
333C2×#117C22×C4311yescharacteristic
334#479—24no—
335C2×#107C22×C4311yescharacteristic
336C2×#106C22×C4311yescharacteristic
337C2×#106C22×C4311yescharacteristic
338C2×#106C22×C4311yescharacteristic
339#424—24no—
340C2×C4⋊C8C22×C4311yescharacteristic
341C2×C4⋊C8C22×C4311yescharacteristic
342C2×C4⋊C8C22×C4311yescharacteristic
343C2×C4⋊C8C22×C4311yescharacteristic
344C2×#103C22×C4311yescharacteristic
345C2×#103C22×C4311yescharacteristic
346C2×#103C22×C4311yescharacteristic
347C2×#103C22×C4311yescharacteristic
348#398—21no—
349#398—21no—
350#396—21no—
351#396—21no—
352#391C22×C4311yescharacteristic
353#389—21no—
354#389C22×C4311yescharacteristic
355#389C22×C4311yescharacteristic
356#389C22×C4311yescharacteristic
357#388—21no—
358#388—21no—
359#387—21no—
360#384C22×C4311yescharacteristic
361#380C22×C4311yescharacteristic
362#380C22×C4311yescharacteristic
363#380C22×C4311yescharacteristic
364C4×C4⋊C4C22×C4311yescharacteristic
365#340C22×C4311yescharacteristic
366#340C22×C4311yescharacteristic
367#340C22×C4311yescharacteristic
368#340C22×C4311yescharacteristic
369#340C22×C4311yescharacteristic
370#340C22×C4311yescharacteristic
371#340C22×C4311yescharacteristic
372#340C22×C4311yescharacteristic
373C43#2485411yescharacteristic, direct product factor, Sylow
374C22×Q8C23×C4311yescharacteristic
375C23×C4C23×C4311yescharacteristic
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—41no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—41no—
382C22×C8C23×C4311yescharacteristic
383C22×C8C23×C4311yescharacteristic
384C22×C8C23×C4311yescharacteristic
385C22×C8C23×C4311yescharacteristic
386#125—22no—
387#125—22no—
388C22⋊Q8—22no—
389C22⋊Q8Q8×C4314yes—
390C4×Q8—22no—
391C4×Q8—22no—
392#117—22no—
393#117—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4D4×C4311yescharacteristic
404C2×C4⋊C4D4×C4311yescharacteristic
405C2×C4⋊C4C23×C4311yescharacteristic
406C2×C4⋊C4C23×C4311yescharacteristic
407C2×C4⋊C4C23×C4311yescharacteristic
408C2×C4⋊C4C23×C4311yescharacteristic
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C4⋊C4C23×C4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4D4×C4311yescharacteristic
417C2×C22⋊C4D4×C4311yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42C23×C4311yescharacteristic
421C2×C42C23×C4311yescharacteristic
422#107—22no—
423#106—22no—
424#106—41no—
425#106—41no—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8D4×C4314yes—
430#103—22no—
431#103—22no—
432#103—41no—
433#103—41no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443C24C2×D4×C4311yescharacteristic
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×Q8×C4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4C2×D4×C4311yescharacteristic
463C22×C4C2×D4×C4311yescharacteristic
464C22×C4C2×D4×C4311yescharacteristic
465C22×C4C2×D4×C4311yescharacteristic
466C22×C4C2×D4×C4311yescharacteristic
467C22×C4C2×Q8×C4312yes—
468C22×C4#41×C4312yes—
469C22×C4C24×C4311yescharacteristic
470M16—44no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—44no—
482C2×C8C2×D4×C4312yes—
483C2×C8C2×D4×C4312yes—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4—81no—
508C4⋊C4C2×Q8×C4312yes—
509C22⋊C4—24no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—81no—
519C42C2×D4×C4312yes—
520C42#41×C4312yes—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C22⋊Q8×C4312yes—
528C23C22×D4×C4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4#121×C4312yes—
574C2×C4#121×C4312yes—
575C2×C4C22⋊Q8×C4312yes—
576C2×C4C22×D4×C4311yescharacteristic
577C2×C4C22×Q8×C4311yescharacteristic
578C2×C4C2×#41×C4311yescharacteristic
579C2×C4C2×#41×C4311yescharacteristic
580C2×C4H(5,𝔽2)×C4311yescharacteristic
581C2×C42−1+4×C4311yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#121×C4311yescharacteristic
594C22C2×C22⋊Q8×C4311yescharacteristic
595C22C43×#53711yescharacteristic
596C22C43×#57711yescharacteristic
597C22C43×#57711yescharacteristic
598C22C43×#57711yescharacteristic
599C22C43×#57811yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—42no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C43×#54611yescharacteristic
614C4D4×Q8×C4311yescharacteristic
615C4C43×#55211yescharacteristic
616C4C43×#55411yescharacteristic
617C2—42no—
618C2C43×#241711yescharacteristic
619C2C43×#306011yescharacteristic
620C2C43×#306311yescharacteristic
621C2C43×#308211yescharacteristic
622C2C43×#308411yescharacteristic
623C2C43×#325811yescharacteristic
624C2C43×#326011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#479C2semidirect
5. C43×#2088C2semidirect
6. C43×#2087C2semidirect
7. C43×#2066C2semidirect
8. C43×#2066C2semidirect
9. C43×#1989C2semidirect
10. C43×#1948C2semidirect
15. C43×#1803C2semidirect
273. #24854C43direct (N × H)
305. C2×#479C2×C43semidirect
309. #2088C2×C43semidirect
310. #2087C2×C43semidirect
311. #2066C2×C43semidirect
312. #2066C2×C43semidirect
313. #1989C2×C43semidirect
314. #1948C2×C43semidirect
319. #1803C2×C43semidirect
373. C43#24854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4792
C2×C43×#4242
C43×#26292
C43×#23232
C43×#20882
C43×#20872
C43×#20662
C43×#19892
C43×#19482
C43×#18942
C43×#18922
C43×#18092
C43×#18072
C43×#18032
#2485443