Finite Group Databasebeta

← C43×#24725 #24944742

Subgroups — C43×#24725 #24944742

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3080C211yesmaximal, characteristic
2C2×C43×#479C211yesmaximal, characteristic, complemented
3C4×#137×C43C211yesmaximal, characteristic
4C43×#2925C211yesmaximal, characteristic
5C43×#2079C211yesmaximal, characteristic
6C43×#2078C211yesmaximal, characteristic
7C43×#2052C211yesmaximal, characteristic
8C43×#2052C211yesmaximal, characteristic
9C43×#1998C211yesmaximal, characteristic, complemented
10C43×#1952C211yesmaximal, characteristic, complemented
11C43×#1951C211yesmaximal, characteristic, complemented
12C43×#1950C211yesmaximal, characteristic, complemented
13C43×#1930C211yesmaximal, characteristic, complemented
14C43×#1930C211yesmaximal, characteristic, complemented
15C43×#1801C211yesmaximal, characteristic, complemented
16C2×#137×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C4×#41×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#479—21no—
21C43×#479—21no—
22C43×#479—21no—
23C43×#479—21no—
24C43×#479—21no—
25C43×#479—21no—
26C43×#478—21no—
27C43×#478—21no—
28C43×#441—21no—
29C43×#440—21no—
30C4×Q16×C43—21no—
31C4×SD16×C43—21no—
32C43×#433—21no—
33C43×#433—21no—
34C43×#432—21no—
35C43×#431—21no—
36C2×#108×C43C2211yescharacteristic
37C2×#108×C43C2211yescharacteristic
38C43×#428C2211yescharacteristic
39C43×#428C2211yescharacteristic
40C43×#428C2211yescharacteristic
41C2×#107×C43C2211yescharacteristic
42C2×#106×C43C2211yescharacteristic
43C43×#423C2211yescharacteristic
44C43×#423C2211yescharacteristic
45C2×C4⋊C8×C43C2211yescharacteristic
46C43×#419C2211yescharacteristic
47C43×#417C2211yescharacteristic
48C43×#417C2211yescharacteristic
49C43×#417C2211yescharacteristic
50C2×#103×C43C2211yescharacteristic
51C2×#103×C43C2211yescharacteristic
52C2×#101×C43C2211yescharacteristic
53C2×#101×C43C2211yescharacteristic
54C43×#408C2211yescharacteristic
55C43×#408C2211yescharacteristic
56C43×#405C2211yescharacteristic
57C43×#405C2211yescharacteristic
58C4×M16×C43C2211yescharacteristic
59C43×#343C2211yescharacteristic
60C43×#343C2211yescharacteristic
61C43×#343C2211yescharacteristic
62C43×#343C2211yescharacteristic
63C43×#343C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#41×C43C2311yescharacteristic
68C22×Q8×C43C2311yescharacteristic
69#137×C43—22no—
70#137×C43—22no—
71C2×Q16×C43—21no—
72C2×SD16×C43—21no—
73C2×M16×C43C2311yescharacteristic
74C2×M16×C43C2311yescharacteristic
75C2×M16×C43C2311yescharacteristic
76C2×M16×C43C2311yescharacteristic
77C2×M16×C43C2311yescharacteristic
78C2×M16×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81#125×C43—21no—
82#125×C43—21no—
83#125×C43—21no—
84#125×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43D411yescharacteristic
90C4×Q8×C43D411yescharacteristic
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43D411yescharacteristic
94C4×D4×C43D411yescharacteristic
95#117×C43—21no—
96#117×C43C2311yescharacteristic
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C42×C43—21no—
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#108×C43—22no—
107#108×C43—22no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#107×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117#106×C43—21no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43—21no—
120C4⋊C8×C43—21no—
121C4⋊C8×C43—21no—
122C4⋊C8×C43D411yescharacteristic
123C4⋊C8×C43D411yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125C4⋊C8×C43D411yescharacteristic
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—21no—
129#103×C43—21no—
130#103×C43—21no—
131#103×C43—21no—
132#103×C43—21no—
133#103×C43—21no—
134#103×C43—21no—
135#102×C43—21no—
136#102×C43—21no—
137#102×C43—21no—
138#101×C43—22no—
139#101×C43—22no—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43—21no—
144#97×C43—21no—
145#97×C43—21no—
146#97×C43—21no—
147C4×C8×C43—21no—
148C4×C8×C43—21no—
149C4×C8×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C2×D411yescharacteristic
160C2×Q8×C43#4112yes—
161C2×D4×C43—21no—
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43#4111yescharacteristic
171C22×C4×C43#4111yescharacteristic
172C22×C4×C43C2411yescharacteristic
173Q16×C43—24no—
174SD16×C43—24no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C2×C8×C43C2×D411yescharacteristic
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—41no—
210C4⋊C4×C43—41no—
211C4⋊C4×C43—41no—
212C4⋊C4×C43—41no—
213C4⋊C4×C43—41no—
214C4⋊C4×C43—41no—
215C4⋊C4×C43C2×D411yescharacteristic
216C4⋊C4×C43C2×D411yescharacteristic
217C22⋊C4×C43—21no—
218C22⋊C4×C43—21no—
219C22⋊C4×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—41no—
224C42×C43—41no—
225C42×C43C2×D411yescharacteristic
226C42×C43C2×D411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C23×C43—21no—
230C23×C43C2×#4111yescharacteristic
231Q8×C43—22no—
232Q8×C43—21no—
233Q8×C43—21no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
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—81no—
256C2×C4×C43—81no—
257C2×C4×C43—81no—
258C2×C4×C43—81no—
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C8×C43—22no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279#24725C4311yesmaximal, characteristic, direct product factor, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#52511yescharacteristic
300C4×C43#53611yescharacteristic
301C4×C43#54711yescharacteristic
302C4×C43#54811yescharacteristic
303#3080C2×C4311yescharacteristic
304C2×#479C2×C4311yescharacteristic, complemented
305C4×#137C2×C4311yescharacteristic
306#2925C2×C4311yescharacteristic
307#2079C2×C4311yescharacteristic
308#2078C2×C4311yescharacteristic
309#2052C2×C4311yescharacteristic
310#2052C2×C4311yescharacteristic
311#1998C2×C4311yescharacteristic, complemented
312#1952C2×C4311yescharacteristic, complemented
313#1951C2×C4311yescharacteristic, complemented
314#1950C2×C4311yescharacteristic, complemented
315#1930C2×C4311yescharacteristic, complemented
316#1930C2×C4311yescharacteristic, complemented
317#1801C2×C4311yescharacteristic, complemented
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#241511yescharacteristic
322C2×C43#306711yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137C22×C4311yescharacteristic
325C2×#125C22×C4311yescharacteristic
326C4×#41C22×C4311yescharacteristic
327C2×C4×Q8C22×C4311yescharacteristic
328#479—21no—
329#479—21no—
330#479—21no—
331#479—21no—
332#479—21no—
333#479—21no—
334#478—21no—
335#478—21no—
336#441—21no—
337#440—21no—
338C4×Q16—21no—
339C4×SD16—21no—
340#433—21no—
341#433—21no—
342#432—21no—
343#431—21no—
344C2×#108C22×C4311yescharacteristic
345C2×#108C22×C4311yescharacteristic
346#428C22×C4311yescharacteristic
347#428C22×C4311yescharacteristic
348#428C22×C4311yescharacteristic
349C2×#107C22×C4311yescharacteristic
350C2×#106C22×C4311yescharacteristic
351#423C22×C4311yescharacteristic
352#423C22×C4311yescharacteristic
353C2×C4⋊C8C22×C4311yescharacteristic
354#419C22×C4311yescharacteristic
355#417C22×C4311yescharacteristic
356#417C22×C4311yescharacteristic
357#417C22×C4311yescharacteristic
358C2×#103C22×C4311yescharacteristic
359C2×#103C22×C4311yescharacteristic
360C2×#101C22×C4311yescharacteristic
361C2×#101C22×C4311yescharacteristic
362#408C22×C4311yescharacteristic
363#408C22×C4311yescharacteristic
364#405C22×C4311yescharacteristic
365#405C22×C4311yescharacteristic
366C4×M16C22×C4311yescharacteristic
367#343C22×C4311yescharacteristic
368#343C22×C4311yescharacteristic
369#343C22×C4311yescharacteristic
370#343C22×C4311yescharacteristic
371#343C22×C4311yescharacteristic
372#343C22×C4311yescharacteristic
373#341C22×C4311yescharacteristic
374#341C22×C4311yescharacteristic
375C43#2472511yescharacteristic, direct product factor, Sylow
376C2×#41C23×C4311yescharacteristic
377C22×Q8C23×C4311yescharacteristic
378#137—22no—
379#137—22no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×M16C23×C4311yescharacteristic
383C2×M16C23×C4311yescharacteristic
384C2×M16C23×C4311yescharacteristic
385C2×M16C23×C4311yescharacteristic
386C2×M16C23×C4311yescharacteristic
387C2×M16C23×C4311yescharacteristic
388C22×C8C23×C4311yescharacteristic
389C22×C8C23×C4311yescharacteristic
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8D4×C4311yescharacteristic
399C4×Q8D4×C4311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D4×C4311yescharacteristic
403C4×D4D4×C4311yescharacteristic
404#117—21no—
405#117C23×C4311yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C4⋊C4C23×C4311yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C4311yescharacteristic
415#108—22no—
416#108—22no—
417#107—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8D4×C4311yescharacteristic
432C4⋊C8D4×C4311yescharacteristic
433C4⋊C8D4×C4311yescharacteristic
434C4⋊C8D4×C4311yescharacteristic
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—21no—
442#103—21no—
443#103—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#101—22no—
448#101—22no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454#97—21no—
455#97—21no—
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×D4×C4311yescharacteristic
469C2×Q8#41×C4312yes—
470C2×D4—21no—
471C2×D4C2×D4×C4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4#41×C4311yescharacteristic
480C22×C4#41×C4311yescharacteristic
481C22×C4C24×C4311yescharacteristic
482Q16—24no—
483SD16—24no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16#41×C4312yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×D4×C4311yescharacteristic
507C2×C8C2×D4×C4311yescharacteristic
508C2×C8C2×D4×C4311yescharacteristic
509C2×C8C2×D4×C4311yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4C2×D4×C4311yescharacteristic
525C4⋊C4C2×D4×C4311yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—41no—
533C42—41no—
534C42C2×D4×C4311yescharacteristic
535C42C2×D4×C4311yescharacteristic
536C42C2×D4×C4311yescharacteristic
537C42C2×D4×C4311yescharacteristic
538C23—21no—
539C23C2×#41×C4311yescharacteristic
540Q8—22no—
541Q8—21no—
542Q8—21no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4#121×C4311yescharacteristic
569C2×C4#121×C4311yescharacteristic
570C2×C4#121×C4311yescharacteristic
571C2×C4#121×C4311yescharacteristic
572C2×C4C22×D4×C4311yescharacteristic
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4C2×#41×C4311yescharacteristic
575C2×C4C2×#41×C4311yescharacteristic
576C2×C42−1+4×C4311yescharacteristic
577C2×C42−1+4×C4311yescharacteristic
578C8—22no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#121×C4311yescharacteristic
594C22C43×#55211yescharacteristic
595C22C43×#55611yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C43×#52511yescharacteristic
608C4C43×#53611yescharacteristic
609C4C43×#54711yescharacteristic
610C4C43×#54811yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2C43×#241511yescharacteristic
615C2C43×#306711yescharacteristic
616C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#41×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
2. C2×C43×#479C2semidirect
9. C43×#1998C2semidirect
10. C43×#1952C2semidirect
11. C43×#1951C2semidirect
12. C43×#1950C2semidirect
13. C43×#1930C2semidirect
14. C43×#1930C2semidirect
15. C43×#1801C2semidirect
279. #24725C43direct (N × H)
304. C2×#479C2×C43semidirect
311. #1998C2×C43semidirect
312. #1952C2×C43semidirect
313. #1951C2×C43semidirect
314. #1950C2×C43semidirect
315. #1930C2×C43semidirect
316. #1930C2×C43semidirect
317. #1801C2×C43semidirect
375. C43#24725direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30802
C2×C43×#4792
C4×#137×C432
C43×#29252
C43×#20792
C43×#20782
C43×#20522
C43×#19982
C43×#19522
C43×#19512
C43×#19502
C43×#19302
C43×#18012
#2472543