Finite Group Databasebeta

← C43×#18296 #24938313

Subgroups — C43×#18296 #24938313

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#538C211yesmaximal, characteristic, complemented
2C43×#3187C211yesmaximal, characteristic, complemented
3C43×#3186C211yesmaximal, characteristic, complemented
4C43×#2617C211yesmaximal, characteristic, complemented
5C43×#1612C214yesmaximal, complemented
6C43×#1600C214yesmaximal, complemented
7C43×#1520C211yesmaximal, characteristic, complemented
8C43×#1519C211yesmaximal, characteristic, complemented
9C2×C43×#323C211yesmaximal, characteristic, complemented
10C43×#538—22no—
11C43×#538—22no—
12C43×#538—22no—
13C43×#538C2214yes—
14C2×#126×C43—21no—
15C2×#124×C43—21no—
16C2×#123×C43—21no—
17C2×C22⋊Q8×C43C2211yescharacteristic
18C2×#121×C43—21no—
19C2×#121×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#120×C43—21no—
22C2×#120×C43—21no—
23C2×C4×D4×C43—21no—
24C22×C22⋊C4×C43C2211yescharacteristic
25C43×#483C2212yescomplemented
26C43×#481—21no—
27C43×#480—21no—
28C43×#480C2212yescomplemented
29C43×#466—22no—
30C43×#465—22no—
31C43×#450C2212yescomplemented
32C43×#448—21no—
33C43×#447—21no—
34C43×#447C2212yescomplemented
35C2×C22⋊C8×C43C2211yescharacteristic
36C2×C22⋊C8×C43C2211yescharacteristic
37C43×#397C2212yescomplemented
38C43×#394—22no—
39C43×#392C2212yescomplemented
40C43×#386—21no—
41C43×#380C2211yescharacteristic
42C43×#328C2214yescomplemented
43C43×#327C2214yescomplemented
44C43×#323C2214yescomplemented
45C25×C43D411yescharacteristic
46C22×Q8×C43D411yescharacteristic, complemented
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C22×D4×C43—22no—
52C22×D4×C43D411yescharacteristic, complemented
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43—21no—
55C23×C4×C43D411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×SD16×C43—22no—
58C2×D8×C43—22no—
59C22×C8×C43—21no—
60C22×C8×C43—21no—
61#126×C43—24no—
62#126×C43—24no—
63#124×C43—24no—
64#124×C43—24no—
65#123×C43—24no—
66#123×C43—24no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43D412yescomplemented
70C22⋊Q8×C43C2312yes—
71#121×C43—24no—
72#121×C43—24no—
73#121×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77#121×C43—21no—
78#121×C43—21no—
79#121×C43D412yescomplemented
80#121×C43C2312yes—
81#120×C43—24no—
82#120×C43—24no—
83#120×C43—44no—
84C4×D4×C43—24no—
85C4×D4×C43—24no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43D411yescharacteristic, complemented
90C2×C4⋊C4×C43D411yescharacteristic, complemented
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43D412yes—
106C2×C22⋊C4×C43C2312yes—
107C2×C42×C43—21no—
108#107×C43—22no—
109#106×C43—22no—
110#103×C43—22no—
111#102×C43—22no—
112#102×C43—22no—
113#102×C43—22no—
114C22⋊C8×C43—21no—
115C22⋊C8×C43—21no—
116C22⋊C8×C43C2312yes—
117C22⋊C8×C43C2312yes—
118#95×C43—22no—
119#95×C43C2312yes—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43—21no—
123C24×C43—22no—
124C24×C43—22no—
125C24×C43—21no—
126C24×C43—81no—
127C24×C43—81no—
128C24×C43C2×D412yes—
129C24×C43C2×D411yescharacteristic
130C2×Q8×C43—21no—
131C2×Q8×C43—81no—
132C2×Q8×C43C2×D412yes—
133C2×D4×C43—24no—
134C2×D4×C43—24no—
135C2×D4×C43—21no—
136C2×D4×C43—22no—
137C2×D4×C43—22no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—44no—
141C2×D4×C43—41no—
142C2×D4×C43—41no—
143C2×D4×C43—42no—
144C2×D4×C43—42no—
145C2×D4×C43—42no—
146C2×D4×C43—42no—
147C2×D4×C43—81no—
148C2×D4×C43—81no—
149C2×D4×C43—82no—
150C2×D4×C43—82no—
151C2×D4×C43—82no—
152C2×D4×C43—82no—
153C2×D4×C43C2×D412yes—
154C22×C4×C43—24no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—22no—
162C22×C4×C43—81no—
163C22×C4×C43—81no—
164C22×C4×C43—82no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172SD16×C43—82no—
173D8×C43—82no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C2×C8×C43—81no—
177C2×C8×C43—81no—
178C4⋊C4×C43—24no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—81no—
186C4⋊C4×C43C2×D412yes—
187C4⋊C4×C43C2×D412yes—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—24no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—44no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—82no—
204C42×C43—24no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43—84no—
228C23×C43—84no—
229C23×C43#12011yescharacteristic
230C23×C43#12011yescharacteristic
231C23×C43#13512yes—
232C23×C43AGL(1,ℤ/8)12yes—
233C23×C43C22×D411yescharacteristic
234Q8×C43—42no—
235Q8×C43—81no—
236D4×C43—42no—
237D4×C43—42no—
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—44no—
242D4×C43—81no—
243D4×C43—84no—
244D4×C43—84no—
245D4×C43—88no—
246D4×C43—82no—
247D4×C43—82no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
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—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—41no—
269C2×C4×C43—81no—
270C2×C4×C43—84no—
271C2×C4×C43#12011yescharacteristic
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C8×C43—42no—
276C8×C43—42no—
277#18296C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—44no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—82no—
294C22×C43—84no—
295C22×C43—84no—
296C22×C43—84no—
297C22×C43—82no—
298C22×C43—82no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43#44912yes—
303C22×C43#44912yes—
304C22×C43C2×#12011yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—82no—
316C4×C43—81no—
317C2×#538C2×C4311yescharacteristic, complemented
318#3187C2×C4311yescharacteristic, complemented
319#3186C2×C4311yescharacteristic, complemented
320#2617C2×C4311yescharacteristic, complemented
321#1612C2×C4314yescomplemented
322#1600C2×C4314yescomplemented
323#1520C2×C4311yescharacteristic, complemented
324#1519C2×C4311yescharacteristic, complemented
325C2×#323C2×C4311yescharacteristic, complemented
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—22no—
329C2×C43—22no—
330C2×C43—82no—
331C2×C43—82no—
332C2×C43—161no—
333C2×C43C2×#44911yescharacteristic
334C2×C43#301911yescharacteristic
335C2×C43#302611yescharacteristic
336#538—22no—
337#538—22no—
338#538—22no—
339#538C22×C4314yes—
340C2×#126—21no—
341C2×#124—21no—
342C2×#123—21no—
343C2×C22⋊Q8C22×C4311yescharacteristic
344C2×#121—21no—
345C2×#121C22×C4311yescharacteristic
346C2×#121C22×C4311yescharacteristic
347C2×#120—21no—
348C2×#120—21no—
349C2×C4×D4—21no—
350C22×C22⋊C4C22×C4311yescharacteristic
351#483C22×C4312yescomplemented
352#481—21no—
353#480—21no—
354#480C22×C4312yescomplemented
355#466—22no—
356#465—22no—
357#450C22×C4312yescomplemented
358#448—21no—
359#447—21no—
360#447C22×C4312yescomplemented
361C2×C22⋊C8C22×C4311yescharacteristic
362C2×C22⋊C8C22×C4311yescharacteristic
363#397C22×C4312yescomplemented
364#394—22no—
365#392C22×C4312yescomplemented
366#386—21no—
367#380C22×C4311yescharacteristic
368#328C22×C4314yescomplemented
369#327C22×C4314yescomplemented
370#323C22×C4314yescomplemented
371C43#1829611yescharacteristic, direct product factor, Sylow
372C25D4×C4311yescharacteristic
373C22×Q8D4×C4311yescharacteristic, complemented
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4D4×C4311yescharacteristic, complemented
380C22×D4C23×C4311yescharacteristic
381C23×C4—21no—
382C23×C4D4×C4311yescharacteristic
383C23×C4C23×C4311yescharacteristic
384C2×SD16—22no—
385C2×D8—22no—
386C22×C8—21no—
387C22×C8—21no—
388#126—24no—
389#126—24no—
390#124—24no—
391#124—24no—
392#123—24no—
393#123—24no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8D4×C4312yescomplemented
397C22⋊Q8C23×C4312yes—
398#121—24no—
399#121—24no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121D4×C4312yescomplemented
407#121C23×C4312yes—
408#120—24no—
409#120—24no—
410#120—44no—
411C4×D4—24no—
412C4×D4—24no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4D4×C4311yescharacteristic, complemented
417C2×C4⋊C4D4×C4311yescharacteristic, complemented
418C2×C4⋊C4C23×C4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4D4×C4312yes—
433C2×C22⋊C4C23×C4312yes—
434C2×C42—21no—
435#107—22no—
436#106—22no—
437#103—22no—
438#102—22no—
439#102—22no—
440#102—22no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8C23×C4312yes—
444C22⋊C8C23×C4312yes—
445#95—22no—
446#95C23×C4312yes—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—81no—
454C24—81no—
455C24C2×D4×C4312yes—
456C24C2×D4×C4311yescharacteristic
457C2×Q8—21no—
458C2×Q8—81no—
459C2×Q8C2×D4×C4312yes—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4—82no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4—82no—
480C2×D4C2×D4×C4312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—82no—
492C22×C4C2×D4×C4312yes—
493C22×C4C2×D4×C4311yescharacteristic
494C22×C4C2×D4×C4311yescharacteristic
495C22×C4C2×D4×C4311yescharacteristic
496C22×C4C2×D4×C4311yescharacteristic
497C22×C4C2×D4×C4311yescharacteristic
498C22×C4C24×C4311yescharacteristic
499SD16—82no—
500D8—82no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—81no—
504C2×C8—81no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—81no—
513C4⋊C4C2×D4×C4312yes—
514C4⋊C4C2×D4×C4312yes—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—44no—
527C22⋊C4—42no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—82no—
531C42—24no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—81no—
553C23—81no—
554C23—84no—
555C23—84no—
556C23#120×C4311yescharacteristic
557C23#120×C4311yescharacteristic
558C23#135×C4312yes—
559C23AGL(1,ℤ/8)×C4312yes—
560C23C22×D4×C4311yescharacteristic
561Q8—42no—
562Q8—81no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—44no—
569D4—81no—
570D4—84no—
571D4—84no—
572D4—88no—
573D4—82no—
574D4—82no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—81no—
597C2×C4—84no—
598C2×C4#120×C4311yescharacteristic
599C2×C4#120×C4311yescharacteristic
600C2×C4C22×D4×C4311yescharacteristic
601C2×C4C22×D4×C4311yescharacteristic
602C8—42no—
603C8—42no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—82no—
620C22—84no—
621C22—84no—
622C22—84no—
623C22—82no—
624C22—82no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22C43×#44912yes—
629C22C43×#44912yes—
630C22C2×#120×C4311yescharacteristic
631C22C2×#135×C4311yescharacteristic
632C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—82no—
642C4—81no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—22no—
647C2—82no—
648C2—82no—
649C2—161no—
650C2C2×C43×#44911yescharacteristic
651C2C43×#301911yescharacteristic
652C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×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. C2×C43×#538C2semidirect
2. C43×#3187C2semidirect
3. C43×#3186C2semidirect
4. C43×#2617C2semidirect
5. C43×#1612C2semidirect
6. C43×#1600C2semidirect
7. C43×#1520C2semidirect
8. C43×#1519C2semidirect
9. C2×C43×#323C2semidirect
25. C43×#483C22semidirect
28. C43×#480C22semidirect
31. C43×#450C22semidirect
34. C43×#447C22semidirect
37. C43×#397C22semidirect
39. C43×#392C22semidirect
42. C43×#328C22semidirect
43. C43×#327C22semidirect
44. C43×#323C22semidirect
46. C22×Q8×C43D4semidirect
52. C22×D4×C43D4semidirect
69. C22⋊Q8×C43D4semidirect
79. #121×C43D4semidirect
89. C2×C4⋊C4×C43D4semidirect
90. C2×C4⋊C4×C43D4semidirect
277. #18296C43direct (N × H)
317. C2×#538C2×C43semidirect
318. #3187C2×C43semidirect
319. #3186C2×C43semidirect
320. #2617C2×C43semidirect
321. #1612C2×C43semidirect
322. #1600C2×C43semidirect
323. #1520C2×C43semidirect
324. #1519C2×C43semidirect
325. C2×#323C2×C43semidirect
351. #483C22×C43semidirect
354. #480C22×C43semidirect
357. #450C22×C43semidirect
360. #447C22×C43semidirect
363. #397C22×C43semidirect
365. #392C22×C43semidirect
368. #328C22×C43semidirect
369. #327C22×C43semidirect
370. #323C22×C43semidirect
371. C43#18296direct (N × H)
373. C22×Q8D4×C43semidirect
379. C22×D4D4×C43semidirect
396. C22⋊Q8D4×C43semidirect
406. #121D4×C43semidirect
416. C2×C4⋊C4D4×C43semidirect
417. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5382
C43×#31872
C43×#31862
C43×#26172
C43×#16122
C43×#16002
C43×#15202
C43×#15192
C2×C43×#3232
#1829643