Finite Group Databasebeta

← C43×#29719 #24949736

Subgroups — C43×#29719 #24949736

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#451C211yesmaximal, characteristic, complemented
2C2×C43×#448C211yesmaximal, characteristic
3C43×#2850C211yesmaximal, characteristic
4C2×C43×#391C211yesmaximal, characteristic, complemented
5C43×#2074C212yesmaximal, complemented
6C43×#2056C212yesmaximal, complemented
7C43×#2055C212yesmaximal, complemented
8C43×#2015C212yesmaximal, complemented
9C43×#1874C211yesmaximal, characteristic
10C43×#1872C211yesmaximal, characteristic, complemented
11C43×#1797C211yesmaximal, characteristic, complemented
12C23×Q8×C43C2211yescharacteristic
13C22×Q16×C43C2212yes—
14C22×SD16×C43C2212yes—
15C2×#124×C43C2211yescharacteristic
16C2×C22⋊Q8×C43C2211yescharacteristic
17C2×#121×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C42×C43C2211yescharacteristic
20C43×#451—24no—
21C43×#448—24no—
22C2×C4⋊C8×C43C2212yes—
23C2×#103×C43C2212yes—
24C2×#103×C43C2212yes—
25C2×#103×C43C2212yes—
26C2×#102×C43C2212yes—
27C2×C22⋊C8×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#391—21no—
30C43×#391—21no—
31C43×#391C2212yes—
32C43×#391C2211yescharacteristic
33C43×#391C2212yes—
34C43×#390C2211yescharacteristic
35C43×#388—21no—
36C43×#388—21no—
37C43×#386—21no—
38C43×#386—21no—
39C43×#382C2211yescharacteristic
40C2×#95×C43—21no—
41C2×#95×C43—21no—
42C43×#340C2212yes—
43C43×#340C2212yes—
44C43×#336C2212yes—
45C22×Q8×C43—21no—
46C22×Q8×C43—22no—
47C22×Q8×C43—42no—
48C22×Q8×C43—42no—
49C22×Q8×C43D414yes—
50C22×Q8×C43C2311yescharacteristic
51C22×Q8×C43C2312yes—
52C22×D4×C43—21no—
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43—21no—
55C23×C4×C43—21no—
56C23×C4×C43D411yescharacteristic
57C23×C4×C43D411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C2×Q16×C43—24no—
60C2×Q16×C43—42no—
61C2×Q16×C43—42no—
62C2×SD16×C43—24no—
63C2×SD16×C43—42no—
64C2×SD16×C43—42no—
65C22×C8×C43C2312yes—
66C22×C8×C43C2312yes—
67#124×C43—42no—
68C22⋊Q8×C43—22no—
69C22⋊Q8×C43—22no—
70#121×C43—22no—
71#121×C43—22no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—42no—
75C2×C4⋊C4×C43C2312yes—
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C42×C43—42no—
85C2×C42×C43D411yescharacteristic
86C2×C42×C43D411yescharacteristic
87C2×C42×C43C2311yescharacteristic
88C2×C42×C43C2311yescharacteristic
89C4⋊C8×C43—42no—
90#103×C43—24no—
91#103×C43—24no—
92#103×C43—42no—
93#102×C43—42no—
94C22⋊C8×C43—22no—
95C22⋊C8×C43—22no—
96#95×C43—22no—
97#95×C43—22no—
98#95×C43—22no—
99#95×C43—22no—
100#95×C43—21no—
101#95×C43—21no—
102#95×C43—21no—
103#95×C43—21no—
104C24×C43—21no—
105C24×C43C2×D411yescharacteristic
106C2×Q8×C43—24no—
107C2×Q8×C43—22no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—48no—
117C2×Q8×C43—42no—
118C2×Q8×C43—42no—
119C2×Q8×C43—48no—
120C2×Q8×C43C2×D414yes—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—42no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—24no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43—41no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4112yes—
154C22×C4×C43C2411yescharacteristic
155Q16×C43—48no—
156SD16×C43—48no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—41no—
180C42×C43—41no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43#12112yes—
193C23×C43#13512yes—
194C23×C43#13712yes—
195C23×C43C22×D411yescharacteristic
196Q8×C43—24no—
197Q8×C43—24no—
198Q8×C43—48no—
199Q8×C43—42no—
200Q8×C43—42no—
201Q8×C43—42no—
202Q8×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—84no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—48no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—84no—
240C2×C4×C43#12112yes—
241C2×C4×C43#13712yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)12yes—
245C2×C4×C43H(5,𝔽2)12yes—
246C8×C43—42no—
247C8×C43—42no—
248#29719C4311yesmaximal, characteristic, direct product factor, Sylow
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43#46414yes—
263C22×C43C2×#12111yescharacteristic
264C22×C43#53411yescharacteristic
265C22×C43#53511yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43C2×#13711yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C22×C43#57511yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—44no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—82no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43#53412yes—
281C4×C43#53812yes—
282C2×#451C2×C4311yescharacteristic, complemented
283C2×#448C2×C4311yescharacteristic
284#2850C2×C4311yescharacteristic
285C2×#391C2×C4311yescharacteristic, complemented
286#2074C2×C4312yescomplemented
287#2056C2×C4312yescomplemented
288#2055C2×C4312yescomplemented
289#2015C2×C4312yescomplemented
290#1874C2×C4311yescharacteristic
291#1872C2×C4311yescharacteristic, complemented
292#1797C2×C4311yescharacteristic, complemented
293C2×C43—24no—
294C2×C43—161no—
295C2×C43#261711yescharacteristic
296C2×C43C2×#46411yescharacteristic
297C2×C43#303711yescharacteristic
298C2×C43#319011yescharacteristic
299C2×C43#319611yescharacteristic
300C2×C43#321111yescharacteristic
301C2×C43#321811yescharacteristic
302C23×Q8C22×C4311yescharacteristic
303C22×Q16C22×C4312yes—
304C22×SD16C22×C4312yes—
305C2×#124C22×C4311yescharacteristic
306C2×C22⋊Q8C22×C4311yescharacteristic
307C2×#121C22×C4311yescharacteristic
308C22×C4⋊C4C22×C4311yescharacteristic
309C22×C42C22×C4311yescharacteristic
310#451—24no—
311#448—24no—
312C2×C4⋊C8C22×C4312yes—
313C2×#103C22×C4312yes—
314C2×#103C22×C4312yes—
315C2×#103C22×C4312yes—
316C2×#102C22×C4312yes—
317C2×C22⋊C8C22×C4311yescharacteristic
318C2×C22⋊C8C22×C4311yescharacteristic
319#391—21no—
320#391—21no—
321#391C22×C4312yes—
322#391C22×C4311yescharacteristic
323#391C22×C4312yes—
324#390C22×C4311yescharacteristic
325#388—21no—
326#388—21no—
327#386—21no—
328#386—21no—
329#382C22×C4311yescharacteristic
330C2×#95—21no—
331C2×#95—21no—
332#340C22×C4312yes—
333#340C22×C4312yes—
334#336C22×C4312yes—
335C43#2971911yescharacteristic, direct product factor, Sylow
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8D4×C4314yes—
341C22×Q8C23×C4311yescharacteristic
342C22×Q8C23×C4312yes—
343C22×D4—21no—
344C22×D4C23×C4311yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4D4×C4311yescharacteristic
348C23×C4D4×C4311yescharacteristic
349C23×C4C23×C4311yescharacteristic
350C2×Q16—24no—
351C2×Q16—42no—
352C2×Q16—42no—
353C2×SD16—24no—
354C2×SD16—42no—
355C2×SD16—42no—
356C22×C8C23×C4312yes—
357C22×C8C23×C4312yes—
358#124—42no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361#121—22no—
362#121—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C23×C4312yes—
367C2×C4⋊C4C23×C4311yescharacteristic
368C2×C4⋊C4C23×C4311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—42no—
376C2×C42D4×C4311yescharacteristic
377C2×C42D4×C4311yescharacteristic
378C2×C42C23×C4311yescharacteristic
379C2×C42C23×C4311yescharacteristic
380C4⋊C8—42no—
381#103—24no—
382#103—24no—
383#103—42no—
384#102—42no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395C24—21no—
396C24C2×D4×C4311yescharacteristic
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—48no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8—48no—
411C2×Q8C2×D4×C4314yes—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4311yescharacteristic
440C22×C4C2×D4×C4311yescharacteristic
441C22×C4C2×D4×C4311yescharacteristic
442C22×C4C2×D4×C4312yes—
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4#41×C4312yes—
445C22×C4C24×C4311yescharacteristic
446Q16—48no—
447SD16—48no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C42—22no—
469C42—22no—
470C42—41no—
471C42—41no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23#121×C4312yes—
484C23#135×C4312yes—
485C23#137×C4312yes—
486C23C22×D4×C4311yescharacteristic
487Q8—24no—
488Q8—24no—
489Q8—48no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—42no—
494D4—42no—
495D4—42no—
496D4—84no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—44no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—84no—
531C2×C4#121×C4312yes—
532C2×C4#137×C4312yes—
533C2×C4C22×D4×C4311yescharacteristic
534C2×C4C2×#41×C4311yescharacteristic
535C2×C4H(5,𝔽2)×C4312yes—
536C2×C4H(5,𝔽2)×C4312yes—
537C8—42no—
538C8—42no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22C43×#46414yes—
553C22C2×#121×C4311yescharacteristic
554C22C43×#53411yescharacteristic
555C22C43×#53511yescharacteristic
556C22C2×#135×C4311yescharacteristic
557C22C2×#137×C4311yescharacteristic
558C22C2×#137×C4311yescharacteristic
559C22C43×#57511yescharacteristic
560C4—22no—
561C4—22no—
562C4—44no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—82no—
568C4—81no—
569C4—81no—
570C4C43×#53412yes—
571C4C43×#53812yes—
572C2—24no—
573C2—161no—
574C2C43×#261711yescharacteristic
575C2C2×C43×#46411yescharacteristic
576C2C43×#303711yescharacteristic
577C2C43×#319011yescharacteristic
578C2C43×#319611yescharacteristic
579C2C43×#321111yescharacteristic
580C2C43×#321811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#121×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#451C2semidirect
4. C2×C43×#391C2semidirect
5. C43×#2074C2semidirect
6. C43×#2056C2semidirect
7. C43×#2055C2semidirect
8. C43×#2015C2semidirect
10. C43×#1872C2semidirect
11. C43×#1797C2semidirect
248. #29719C43direct (N × H)
282. C2×#451C2×C43semidirect
285. C2×#391C2×C43semidirect
286. #2074C2×C43semidirect
287. #2056C2×C43semidirect
288. #2055C2×C43semidirect
289. #2015C2×C43semidirect
291. #1872C2×C43semidirect
292. #1797C2×C43semidirect
335. C43#29719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4512
C2×C43×#4482
C43×#28502
C2×C43×#3912
C43×#20742
C43×#20562
C43×#20552
C43×#20152
C43×#18742
C43×#18722
C43×#17972
#2971943