Finite Group Databasebeta

← C43×#10322 #24930339

Subgroups — C43×#10322 #24930339

Order 11008.

988 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
1C43×#3187C211yesmaximal, characteristic, complemented
2C43×#2848C211yesmaximal, characteristic, complemented
3C43×#2847C211yesmaximal, characteristic
4C43×#1779C211yesmaximal, characteristic, complemented
5C43×#1520C211yesmaximal, characteristic, complemented
6C43×#1519C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C43C2211yescharacteristic
9C2×C22⋊Q8×C43—21no—
10C2×C22⋊Q8×C43C2211yescharacteristic
11C2×#121×C43—21no—
12C2×#121×C43C2211yescharacteristic
13C2×#120×C43—21no—
14C43×#483—21no—
15C43×#481—21no—
16C43×#465—22no—
17C43×#450—21no—
18C43×#448—21no—
19C2×C22⋊C8×C43—22no—
20C2×C22⋊C8×C43C2211yescharacteristic
21C2×C22⋊C8×C43C2211yescharacteristic
22C43×#386—21no—
23C43×#386—22no—
24C43×#385—21no—
25C43×#385—22no—
26C43×#380—21no—
27C43×#380—21no—
28C43×#380C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#379—21no—
31C43×#328—22no—
32C43×#327—22no—
33C25×C43D411yescharacteristic
34C22×Q8×C43D411yescharacteristic, complemented
35C22×D4×C43—22no—
36C22×D4×C43—21no—
37C22×D4×C43D411yescharacteristic
38C23×C4×C43—21no—
39C23×C4×C43—21no—
40C23×C4×C43—21no—
41C23×C4×C43—21no—
42C23×C4×C43—21no—
43C23×C4×C43—21no—
44C23×C4×C43—44no—
45C23×C4×C43D411yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C2×SD16×C43—22no—
48C22×C8×C43—21no—
49C22×C8×C43D412yescomplemented
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—44no—
55#121×C43—21no—
56#121×C43—21no—
57#121×C43—21no—
58#121×C43—21no—
59#121×C43—44no—
60#120×C43—42no—
61#120×C43—42no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic, complemented
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76#106×C43—22no—
77#103×C43—22no—
78#102×C43—22no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—44no—
84#95×C43—22no—
85#95×C43—22no—
86#95×C43D412yes—
87#95×C43D412yescomplemented
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—21no—
92C24×C43—21no—
93C24×C43—21no—
94C24×C43—21no—
95C24×C43—42no—
96C24×C43—42no—
97C24×C43SD1612yescomplemented
98C24×C43C2×D411yescharacteristic
99C2×Q8×C43—21no—
100C2×Q8×C43—21no—
101C2×Q8×C43—42no—
102C2×D4×C43—21no—
103C2×D4×C43—21no—
104C2×D4×C43—44no—
105C2×D4×C43—44no—
106C2×D4×C43—44no—
107C2×D4×C43—42no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—41no—
114C22×C4×C43—24no—
115C22×C4×C43—24no—
116C22×C4×C43—24no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43#4111yescharacteristic
146SD16×C43—82no—
147C2×C8×C43—22no—
148C2×C8×C43—42no—
149C2×C8×C43—42no—
150C2×C8×C43—41no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—44no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—41no—
160C22⋊C4×C43—44no—
161C22⋊C4×C43—44no—
162C22⋊C4×C43—44no—
163C22⋊C4×C43—44no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—41no—
182C23×C43—44no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—44no—
191C23×C43—44no—
192C23×C43—44no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43#12011yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43#12111yescharacteristic
205C23×C43C2×SD1611yescharacteristic
206C23×C43#13511yescharacteristic
207C23×C43AGL(1,ℤ/8)11yescharacteristic
208C23×C43#13711yescharacteristic
209Q8×C43—42no—
210Q8×C43—81no—
211D4×C43—42no—
212D4×C43—81no—
213D4×C43—88no—
214D4×C43—81no—
215D4×C43—81no—
216D4×C43—81no—
217D4×C43—81no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—44no—
228C2×C4×C43—44no—
229C2×C4×C43—44no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—44no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43#12011yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43#12111yescharacteristic
251C2×C4×C43#12711yescharacteristic
252C8×C43—42no—
253C8×C43—81no—
254#10322C4311yesmaximal, characteristic, direct product factor, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—24no—
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43#39211yescharacteristic
286C22×C43#44811yescharacteristic
287C22×C43#44911yescharacteristic
288C22×C43#45011yescharacteristic
289C22×C43#45211yescharacteristic
290C22×C43#46511yescharacteristic
291C22×C43#46811yescharacteristic
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—42no—
296C4×C43—82no—
297C4×C43—82no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43B(4,𝔽2)12yes—
302#3187C2×C4311yescharacteristic, complemented
303#2848C2×C4311yescharacteristic, complemented
304#2847C2×C4311yescharacteristic
305#1779C2×C4311yescharacteristic, complemented
306#1520C2×C4311yescharacteristic, complemented
307#1519C2×C4311yescharacteristic, complemented
308#1289C2×C4311yescharacteristic, complemented
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43—21no—
315C2×C43—44no—
316C2×C43—161no—
317C2×C43#200011yescharacteristic
318C2×C43#201011yescharacteristic
319C2×C43#202111yescharacteristic
320C24×C4C22×C4311yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8C22×C4311yescharacteristic
323C2×#121—21no—
324C2×#121C22×C4311yescharacteristic
325C2×#120—21no—
326#483—21no—
327#481—21no—
328#465—22no—
329#450—21no—
330#448—21no—
331C2×C22⋊C8—22no—
332C2×C22⋊C8C22×C4311yescharacteristic
333C2×C22⋊C8C22×C4311yescharacteristic
334#386—21no—
335#386—22no—
336#385—21no—
337#385—22no—
338#380—21no—
339#380—21no—
340#380C22×C4311yescharacteristic
341#380C22×C4311yescharacteristic
342#379—21no—
343#328—22no—
344#327—22no—
345C43#1032211yescharacteristic, direct product factor, Sylow
346C25D4×C4311yescharacteristic
347C22×Q8D4×C4311yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C4311yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C4311yescharacteristic
359C23×C4C23×C4311yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C4312yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C4311yescharacteristic
380C2×C4⋊C4D4×C4311yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C4312yes—
400#95D4×C4312yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C4312yescomplemented
411C24C2×D4×C4311yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4C2×D4×C4311yescharacteristic
456C22×C4C2×D4×C4311yescharacteristic
457C22×C4C2×D4×C4311yescharacteristic
458C22×C4#41×C4311yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C4311yescharacteristic
516C23#120×C4311yescharacteristic
517C23#121×C4311yescharacteristic
518C23C2×SD16×C4311yescharacteristic
519C23#135×C4311yescharacteristic
520C23AGL(1,ℤ/8)×C4311yescharacteristic
521C23#137×C4311yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C4311yescharacteristic
562C2×C4#121×C4311yescharacteristic
563C2×C4#121×C4311yescharacteristic
564C2×C4#127×C4311yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C43×#39211yescharacteristic
598C22C43×#44811yescharacteristic
599C22C43×#44911yescharacteristic
600C22C43×#45011yescharacteristic
601C22C43×#45211yescharacteristic
602C22C43×#46511yescharacteristic
603C22C43×#46811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C43×B(4,𝔽2)12yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C43×#200011yescharacteristic
623C2C43×#201011yescharacteristic
624C2C43×#202111yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC43×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3187C2semidirect
2. C43×#2848C2semidirect
4. C43×#1779C2semidirect
5. C43×#1520C2semidirect
6. C43×#1519C2semidirect
7. C43×#1289C2semidirect
34. C22×Q8×C43D4semidirect
49. C22×C8×C43D4semidirect
67. C2×C4⋊C4×C43D4semidirect
87. #95×C43D4semidirect
97. C24×C43SD16semidirect
254. #10322C43direct (N × H)
302. #3187C2×C43semidirect
303. #2848C2×C43semidirect
305. #1779C2×C43semidirect
306. #1520C2×C43semidirect
307. #1519C2×C43semidirect
308. #1289C2×C43semidirect
345. C43#10322direct (N × H)
347. C22×Q8D4×C43semidirect
362. C22×C8D4×C43semidirect
380. C2×C4⋊C4D4×C43semidirect
400. #95D4×C43semidirect
410. C24SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31872
C43×#28482
C43×#28472
C43×#17792
C43×#15202
C43×#15192
C43×#12892
#1032243