Finite Group Databasebeta

← C43×#25493 #24945510

Subgroups — C43×#25493 #24945510

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3166C211yesmaximal, characteristic, complemented
2C43×#3077C211yesmaximal, characteristic
3C2×C43×#478C211yesmaximal, characteristic
4C43×#2962C211yesmaximal, characteristic, complemented
5C43×#2090C211yesmaximal, characteristic, complemented
6C43×#2089C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic
8C43×#2063C211yesmaximal, characteristic
9C43×#1998C211yesmaximal, characteristic, complemented
10C43×#1952C211yesmaximal, characteristic, complemented
11C43×#1951C211yesmaximal, characteristic, complemented
12C43×#1950C211yesmaximal, characteristic, complemented
13C43×#1931C211yesmaximal, characteristic
14C43×#1931C211yesmaximal, characteristic
15C4×#100×C43C211yesmaximal, characteristic
16C43×#533C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C43×#501—21no—
20C43×#501—21no—
21C43×#499—21no—
22C43×#499—21no—
23C43×#478—21no—
24C43×#478—21no—
25C43×#478—21no—
26C43×#478—21no—
27C43×#478—21no—
28C43×#478—21no—
29C43×#476—21no—
30C43×#474—21no—
31C43×#446—21no—
32C43×#446—21no—
33C43×#446—21no—
34C8×Q8×C43—21no—
35C2×#108×C43C2211yescharacteristic
36C2×#108×C43C2211yescharacteristic
37C43×#428C2211yescharacteristic
38C43×#428C2211yescharacteristic
39C43×#428C2211yescharacteristic
40C43×#428C2211yescharacteristic
41C43×#428C2211yescharacteristic
42C43×#428C2211yescharacteristic
43C2×#107×C43C2211yescharacteristic
44C2×#106×C43C2211yescharacteristic
45C43×#424C2211yescharacteristic
46C43×#424C2211yescharacteristic
47C43×#423C2211yescharacteristic
48C2×C4⋊C8×C43C2211yescharacteristic
49C43×#418C2211yescharacteristic
50C43×#418C2211yescharacteristic
51C2×#102×C43C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#100×C43C2211yescharacteristic
54C2×#100×C43C2211yescharacteristic
55C43×#405C2211yescharacteristic
56C43×#405C2211yescharacteristic
57C4×M16×C43C2211yescharacteristic
58C4×M16×C43C2211yescharacteristic
59C43×#343C2211yescharacteristic
60C43×#343C2211yescharacteristic
61C43×#343C2211yescharacteristic
62C43×#343C2211yescharacteristic
63C43×#343C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C2×M16×C43C2311yescharacteristic
70C2×M16×C43C2311yescharacteristic
71C2×M16×C43C2311yescharacteristic
72C2×M16×C43C2311yescharacteristic
73C2×M16×C43C2311yescharacteristic
74C2×M16×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77C4⋊Q8×C43D411yescharacteristic
78C4⋊Q8×C43D411yescharacteristic
79#125×C43—21no—
80#125×C43—21no—
81#125×C43—21no—
82#125×C43—21no—
83#125×C43D411yescharacteristic
84#125×C43D411yescharacteristic
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93#117×C43C2311yescharacteristic
94#117×C43C2311yescharacteristic
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#108×C43—22no—
103#108×C43—22no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117#106×C43—21no—
118#106×C43—21no—
119#106×C43—21no—
120C4⋊C8×C43—21no—
121C4⋊C8×C43—21no—
122C4⋊C8×C43—21no—
123C4⋊C8×C43—21no—
124C4⋊C8×C43—21no—
125C4⋊C8×C43—21no—
126C4⋊C8×C43D411yescharacteristic
127C4⋊C8×C43D411yescharacteristic
128C4⋊C8×C43D411yescharacteristic
129C4⋊C8×C43D411yescharacteristic
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136#102×C43—21no—
137#102×C43—21no—
138#100×C43—22no—
139#100×C43Q814yescomplemented
140#97×C43—21no—
141#97×C43—21no—
142#97×C43—21no—
143#97×C43—21no—
144C4×C8×C43—21no—
145C4×C8×C43—21no—
146C4×C8×C43—21no—
147C4×C8×C43—21no—
148C24×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C2×Q812yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—82no—
163C22×C4×C43#4111yescharacteristic
164C22×C4×C43#4111yescharacteristic
165C22×C4×C43C2411yescharacteristic
166M16×C43—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43C2×Q812yes—
176M16×C43C2×Q812yes—
177M16×C43#4112yes—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C4⋊C4×C43C2×D411yescharacteristic
211C4⋊C4×C43C2×D411yescharacteristic
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221C42×C43C2×D411yescharacteristic
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43C2×#4111yescharacteristic
228Q8×C43—42no—
229Q8×C43—81no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
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—82no—
244C2×C4×C43—82no—
245C2×C4×C43—81no—
246C2×C4×C43—81no—
247C2×C4×C43—81no—
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43#12111yescharacteristic
251C2×C4×C43#12111yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—22no—
263C8×C43—22no—
264C8×C43—22no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268#25493C4311yesmaximal, characteristic, direct product factor, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12111yescharacteristic
277C22×C43#53311yescharacteristic
278C22×C43#54111yescharacteristic
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43#54711yescharacteristic
291C4×C43#54811yescharacteristic
292C4×C43D4×Q811yescharacteristic
293C4×C43D4×Q811yescharacteristic
294#3166C2×C4311yescharacteristic, complemented
295#3077C2×C4311yescharacteristic
296C2×#478C2×C4311yescharacteristic
297#2962C2×C4311yescharacteristic, complemented
298#2090C2×C4311yescharacteristic, complemented
299#2089C2×C4311yescharacteristic, complemented
300#2063C2×C4311yescharacteristic
301#2063C2×C4311yescharacteristic
302#1998C2×C4311yescharacteristic, complemented
303#1952C2×C4311yescharacteristic, complemented
304#1951C2×C4311yescharacteristic, complemented
305#1950C2×C4311yescharacteristic, complemented
306#1931C2×C4311yescharacteristic
307#1931C2×C4311yescharacteristic
308C4×#100C2×C4311yescharacteristic
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—82no—
312C2×C43#242911yescharacteristic
313C2×C43#306711yescharacteristic
314C2×C43#306811yescharacteristic
315#533C22×C4311yescharacteristic
316C2×#125C22×C4311yescharacteristic
317C2×C4×D4C22×C4311yescharacteristic
318#501—21no—
319#501—21no—
320#499—21no—
321#499—21no—
322#478—21no—
323#478—21no—
324#478—21no—
325#478—21no—
326#478—21no—
327#478—21no—
328#476—21no—
329#474—21no—
330#446—21no—
331#446—21no—
332#446—21no—
333C8×Q8—21no—
334C2×#108C22×C4311yescharacteristic
335C2×#108C22×C4311yescharacteristic
336#428C22×C4311yescharacteristic
337#428C22×C4311yescharacteristic
338#428C22×C4311yescharacteristic
339#428C22×C4311yescharacteristic
340#428C22×C4311yescharacteristic
341#428C22×C4311yescharacteristic
342C2×#107C22×C4311yescharacteristic
343C2×#106C22×C4311yescharacteristic
344#424C22×C4311yescharacteristic
345#424C22×C4311yescharacteristic
346#423C22×C4311yescharacteristic
347C2×C4⋊C8C22×C4311yescharacteristic
348#418C22×C4311yescharacteristic
349#418C22×C4311yescharacteristic
350C2×#102C22×C4311yescharacteristic
351C2×#102C22×C4311yescharacteristic
352C2×#100C22×C4311yescharacteristic
353C2×#100C22×C4311yescharacteristic
354#405C22×C4311yescharacteristic
355#405C22×C4311yescharacteristic
356C4×M16C22×C4311yescharacteristic
357C4×M16C22×C4311yescharacteristic
358#343C22×C4311yescharacteristic
359#343C22×C4311yescharacteristic
360#343C22×C4311yescharacteristic
361#343C22×C4311yescharacteristic
362#343C22×C4311yescharacteristic
363#343C22×C4311yescharacteristic
364#341C22×C4311yescharacteristic
365#341C22×C4311yescharacteristic
366C43#2549311yescharacteristic, direct product factor, Sylow
367C22×D4C23×C4311yescharacteristic
368C23×C4—21no—
369C2×M16C23×C4311yescharacteristic
370C2×M16C23×C4311yescharacteristic
371C2×M16C23×C4311yescharacteristic
372C2×M16C23×C4311yescharacteristic
373C2×M16C23×C4311yescharacteristic
374C2×M16C23×C4311yescharacteristic
375C22×C8C23×C4311yescharacteristic
376C22×C8C23×C4311yescharacteristic
377C4⋊Q8D4×C4311yescharacteristic
378C4⋊Q8D4×C4311yescharacteristic
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C4311yescharacteristic
384#125D4×C4311yescharacteristic
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117C23×C4311yescharacteristic
394#117C23×C4311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C23×C4311yescharacteristic
402#108—22no—
403#108—22no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8D4×C4311yescharacteristic
427C4⋊C8D4×C4311yescharacteristic
428C4⋊C8D4×C4311yescharacteristic
429C4⋊C8D4×C4311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#100—22no—
439#100Q8×C4314yescomplemented
440#97—21no—
441#97—21no—
442#97—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8—21no—
447C4×C8—21no—
448C24—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C2×Q8×C4312yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4#41×C4311yescharacteristic
464C22×C4#41×C4311yescharacteristic
465C22×C4C24×C4311yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—21no—
474M16—21no—
475M16C2×Q8×C4312yes—
476M16C2×Q8×C4312yes—
477M16#41×C4312yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C2×D4×C4311yescharacteristic
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C2×C8C2×D4×C4311yescharacteristic
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—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C4311yescharacteristic
509C4⋊C4C2×D4×C4311yescharacteristic
510C4⋊C4C2×D4×C4311yescharacteristic
511C4⋊C4C2×D4×C4311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—21no—
517C42—21no—
518C42C2×D4×C4311yescharacteristic
519C42C2×D4×C4311yescharacteristic
520C42C2×D4×C4311yescharacteristic
521C42C2×D4×C4311yescharacteristic
522C23—22no—
523C23—41no—
524C23—41no—
525C23—81no—
526C23—81no—
527C23C2×#41×C4311yescharacteristic
528Q8—42no—
529Q8—81no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4#121×C4311yescharacteristic
549C2×C4#121×C4311yescharacteristic
550C2×C4#121×C4311yescharacteristic
551C2×C4#121×C4311yescharacteristic
552C2×C4C22×D4×C4311yescharacteristic
553C2×C4C22×D4×C4311yescharacteristic
554C2×C4C22×Q8×C4311yescharacteristic
555C2×C4C2×#41×C4311yescharacteristic
556C2×C42−1+4×C4311yescharacteristic
557C2×C42−1+4×C4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22C2×#121×C4311yescharacteristic
576C22C43×#53311yescharacteristic
577C22C43×#54111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C43×#54711yescharacteristic
590C4C43×#54811yescharacteristic
591C4D4×Q8×C4311yescharacteristic
592C4D4×Q8×C4311yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2C43×#242911yescharacteristic
597C2C43×#306711yescharacteristic
598C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3166C2semidirect
4. C43×#2962C2semidirect
5. C43×#2090C2semidirect
6. C43×#2089C2semidirect
9. C43×#1998C2semidirect
10. C43×#1952C2semidirect
11. C43×#1951C2semidirect
12. C43×#1950C2semidirect
139. #100×C43Q8semidirect
268. #25493C43direct (N × H)
294. #3166C2×C43semidirect
297. #2962C2×C43semidirect
298. #2090C2×C43semidirect
299. #2089C2×C43semidirect
302. #1998C2×C43semidirect
303. #1952C2×C43semidirect
304. #1951C2×C43semidirect
305. #1950C2×C43semidirect
366. C43#25493direct (N × H)
439. #100Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31662
C43×#30772
C2×C43×#4782
C43×#29622
C43×#20902
C43×#20892
C43×#20632
C43×#19982
C43×#19522
C43×#19512
C43×#19502
C43×#19312
C4×#100×C432
#2549343