Finite Group Databasebeta

← C43×#60499 #24980516

Subgroups — C43×#60499 #24980516

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3504C211yesmaximal, characteristic, complemented
2C4×2−1+4×C43C211yesmaximal, characteristic
3C43×#3084C213yesmaximal, complemented
4C43×#3083C213yesmaximal, complemented
5C43×#3082C213yesmaximal, complemented
6C43×#3082C213yesmaximal, complemented
7C43×#3080C213yesmaximal, complemented
8C43×#3078C213yesmaximal, complemented
9C43×#3076C213yesmaximal, complemented
10C2×C43×#479C213yesmaximal, complemented
11C43×#2913C211yesmaximal, characteristic, complemented
12C43×#2912C211yesmaximal, characteristic, complemented
13C43×#2906C211yesmaximal, characteristic, complemented
14C43×#2898C211yesmaximal, characteristic
15C43×#2898C211yesmaximal, characteristic
16C2×2−1+4×C43C2211yescharacteristic
17C2×#131×C43C2211yescharacteristic
18C2×#131×C43C2211yescharacteristic
19C43×#557—21no—
20C43×#557—21no—
21C43×#554—23no—
22C43×#554—23no—
23C43×#544C2213yes—
24C43×#544C2213yes—
25C43×#533C2213yes—
26C2×#125×C43C2213yes—
27C43×#520—23no—
28C43×#520C2213yes—
29C43×#520C2211yescharacteristic
30C43×#520C2211yescharacteristic
31C43×#520C2211yescharacteristic
32C43×#519—21no—
33C43×#519C2213yes—
34C4×#41×C43—23no—
35C4×#41×C43C2213yes—
36C4×#41×C43C2211yescharacteristic
37C2×C4×Q8×C43—21no—
38C2×C4×Q8×C43C2213yes—
39C43×#479C2213yes—
40C43×#479C2216yes—
41C43×#479C2216yes—
42C43×#479C2216yes—
43C43×#479C2213yes—
44C43×#479C2216yes—
45C43×#478C2211yescharacteristic
46C43×#478C2213yes—
47C43×#478C2216yes—
48C43×#477C2213yes—
49C43×#477C2216yes—
50C43×#476C2213yes—
51C43×#475C2213yes—
52C43×#475C2216yes—
53C43×#474C2213yes—
54C43×#428C2213yes—
55C43×#428C2213yes—
56C43×#428C2213yes—
57C43×#428C2213yes—
58C43×#427C2213yes—
59C43×#427C2213yes—
60C2×#107×C43C2213yes—
61C2×#106×C43C2213yes—
62C43×#424C2213yes—
63C43×#424C2213yes—
64C43×#423C2213yes—
65C2×C4⋊C8×C43C2213yes—
66C43×#419C2213yes—
67C43×#419C2213yes—
68C43×#417C2213yes—
69C43×#417C2213yes—
70C43×#416C2213yes—
71C43×#416C2213yes—
72C2×#103×C43C2213yes—
73C2×#103×C43C2213yes—
742−1+4×C43—24no—
752−1+4×C43Q818yescomplemented
76C2×#41×C43—23no—
77C2×#41×C43C2313yes—
78C2×#41×C43C2311yescharacteristic
79C22×Q8×C43—21no—
80C22×Q8×C43C2313yes—
81#131×C43—24no—
82#131×C43—24no—
83C2×M16×C43C2313yes—
84C2×M16×C43C2313yes—
85C22×C8×C43C2313yes—
86C22×C8×C43C2313yes—
87C4⋊Q8×C43—23no—
88C4⋊Q8×C43—23no—
89C4⋊Q8×C43C2313yes—
90C4⋊Q8×C43C2313yes—
91#125×C43—23no—
92#125×C43—23no—
93#125×C43—23no—
94#125×C43—23no—
95#125×C43C2313yes—
96#125×C43C2316yes—
97#125×C43C2311yescharacteristic
98C22⋊Q8×C43—23no—
99C22⋊Q8×C43—23no—
100C22⋊Q8×C43—26no—
101C22⋊Q8×C43—26no—
102C4×Q8×C43—21no—
103C4×Q8×C43—21no—
104C4×Q8×C43—21no—
105C4×Q8×C43—23no—
106C4×Q8×C43—23no—
107C4×Q8×C43—23no—
108C4×Q8×C43—23no—
109C4×Q8×C43—23no—
110C4×Q8×C43—23no—
111C4×Q8×C43D411yescharacteristic
112C4×Q8×C43D411yescharacteristic
113C4×Q8×C43C2313yes—
114C4×Q8×C43C2316yes—
115C4×Q8×C43C2313yes—
116C4×D4×C43—23no—
117C4×D4×C43—23no—
118C4×D4×C43—23no—
119C4×D4×C43—23no—
120C4×D4×C43—23no—
121C4×D4×C43—26no—
122C4×D4×C43D413yes—
123C4×D4×C43D413yes—
124C4×D4×C43C2311yescharacteristic
125C4×D4×C43C2313yes—
126#117×C43—23no—
127#117×C43—26no—
128#117×C43—23no—
129#117×C43C2313yes—
130#117×C43C2313yes—
131#117×C43C2313yes—
132#117×C43C2313yes—
133C2×C4⋊C4×C43—23no—
134C2×C4⋊C4×C43—23no—
135C2×C4⋊C4×C43—23no—
136C2×C4⋊C4×C43—23no—
137C2×C4⋊C4×C43C2313yes—
138C2×C4⋊C4×C43C2313yes—
139C2×C4⋊C4×C43C2313yes—
140C2×C42×C43—23no—
141C2×C42×C43—23no—
142C2×C42×C43C2313yes—
143#107×C43C2313yes—
144#107×C43C2316yes—
145#107×C43C2311yescharacteristic
146#107×C43C2313yes—
147#107×C43C2313yes—
148#106×C43C2313yes—
149#106×C43C2316yes—
150#106×C43C2311yescharacteristic
151#106×C43C2313yes—
152#106×C43C2313yes—
153C4⋊C8×C43C2311yescharacteristic
154C4⋊C8×C43C2313yes—
155C4⋊C8×C43C2313yes—
156C4⋊C8×C43C2313yes—
157C4⋊C8×C43C2316yes—
158#103×C43C2313yes—
159#103×C43C2313yes—
160#103×C43C2316yes—
161#103×C43C2316yes—
162#103×C43C2313yes—
163#103×C43C2313yes—
164#102×C43C2311yescharacteristic
165#102×C43C2311yescharacteristic
166#102×C43C2313yes—
167#102×C43C2313yes—
168#41×C43—224no—
169#41×C43—26no—
170#41×C43C2×Q8112yes—
171#41×C43C2×Q814yes—
172#41×C43#4114yes—
173C2×Q8×C43—28no—
174C2×Q8×C43—23no—
175C2×Q8×C43—23no—
176C2×Q8×C43—23no—
177C2×Q8×C43—26no—
178C2×Q8×C43C2×D411yescharacteristic
179C2×Q8×C43C2×Q8112yes—
180C2×Q8×C43C2413yes—
181C2×D4×C43—23no—
182C2×D4×C43C2×D413yes—
183C2×D4×C43C2411yescharacteristic
184C22×C4×C43—23no—
185C22×C4×C43—21no—
186C22×C4×C43—23no—
187C22×C4×C43—23no—
188C22×C4×C43—23no—
189C22×C4×C43—23no—
190C22×C4×C43—23no—
191C22×C4×C43C2×D413yes—
192C22×C4×C43C2×D413yes—
193C22×C4×C43C2413yes—
194M16×C43—26no—
195M16×C43—26no—
196C2×C8×C43—26no—
197C2×C8×C43—26no—
198C2×C8×C43C2411yescharacteristic
199C2×C8×C43C2413yes—
200C2×C8×C43C2413yes—
201C2×C8×C43C2411yescharacteristic
202C4⋊C4×C43—26no—
203C4⋊C4×C43—23no—
204C4⋊C4×C43—23no—
205C4⋊C4×C43—23no—
206C4⋊C4×C43—23no—
207C4⋊C4×C43—26no—
208C4⋊C4×C43—26no—
209C4⋊C4×C43—23no—
210C4⋊C4×C43—23no—
211C4⋊C4×C43—23no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—23no—
215C4⋊C4×C43—23no—
216C4⋊C4×C43C2×D413yes—
217C4⋊C4×C43C2×D413yes—
218C4⋊C4×C43C2413yes—
219C4⋊C4×C43C2411yescharacteristic
220C4⋊C4×C43C2413yes—
221C4⋊C4×C43C2411yescharacteristic
222C4⋊C4×C43C2413yes—
223C4⋊C4×C43C2411yescharacteristic
224C22⋊C4×C43—21no—
225C22⋊C4×C43—23no—
226C22⋊C4×C43—23no—
227C22⋊C4×C43—23no—
228C22⋊C4×C43—23no—
229C22⋊C4×C43C2×D416yes—
230C42×C43—23no—
231C42×C43—23no—
232C42×C43—26no—
233C42×C43—23no—
234C42×C43—23no—
235C42×C43—23no—
236C42×C43C2×D413yes—
237C42×C43C2×D413yes—
238C42×C43C2411yescharacteristic
239C42×C43C2413yes—
240C23×C43—21no—
241C23×C43C22×D413yes—
242Q8×C43—212no—
243Q8×C43—23no—
244Q8×C43—83no—
245Q8×C43—83no—
246Q8×C43C22⋊Q814yes—
247Q8×C43C22×Q816yes—
248D4×C43—212no—
249D4×C43—21no—
250D4×C43C22⋊Q8112yes—
251D4×C43C22×Q812yes—
252C2×C4×C43—212no—
253C2×C4×C43—23no—
254C2×C4×C43—212no—
255C2×C4×C43—21no—
256C2×C4×C43—23no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—23no—
260C2×C4×C43—23no—
261C2×C4×C43—43no—
262C2×C4×C43—43no—
263C2×C4×C43—42no—
264C2×C4×C43—83no—
265C2×C4×C43—83no—
266C2×C4×C43—83no—
267C2×C4×C43—83no—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×D413yes—
270C2×C4×C43C22×D413yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D413yes—
273C2×C4×C43C22×Q816yes—
274C2×C4×C43C2×#4116yes—
275C2×C4×C43C2511yescharacteristic
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—23no—
279C8×C43—23no—
280#60499C4311yesmaximal, characteristic, direct product factor, Sylow
281C22×C43—23no—
282C22×C43—23no—
283C22×C43—22no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43C2×C22⋊Q816yes—
287C22×C43C23×D411yescharacteristic
288C4×C43—21no—
289C4×C43—23no—
290C4×C43—21no—
291C4×C43—23no—
292C4×C43—26no—
293C4×C43—43no—
294C4×C43—43no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—43no—
298C4×C43—41no—
299C4×C43C2×C22⋊Q816yes—
300C4×C43C23×Q811yescharacteristic
301C4×C43C22×#4111yescharacteristic
302#3504C2×C4311yescharacteristic, complemented
303C4×2−1+4C2×C4311yescharacteristic
304#3084C2×C4313yescomplemented
305#3083C2×C4313yescomplemented
306#3082C2×C4313yescomplemented
307#3082C2×C4313yescomplemented
308#3080C2×C4313yescomplemented
309#3078C2×C4313yescomplemented
310#3076C2×C4313yescomplemented
311C2×#479C2×C4313yescomplemented
312#2913C2×C4311yescharacteristic, complemented
313#2912C2×C4311yescharacteristic, complemented
314#2906C2×C4311yescharacteristic, complemented
315#2898C2×C4311yescharacteristic
316#2898C2×C4311yescharacteristic
317C2×C43—26no—
318C2×C43—42no—
319C2×C43C22×C22⋊Q811yescharacteristic
320C2×C43#358411yescharacteristic
321C2×C43#358611yescharacteristic
322C2×2−1+4C22×C4311yescharacteristic
323C2×#131C22×C4311yescharacteristic
324C2×#131C22×C4311yescharacteristic
325#557—21no—
326#557—21no—
327#554—23no—
328#554—23no—
329#544C22×C4313yes—
330#544C22×C4313yes—
331#533C22×C4313yes—
332C2×#125C22×C4313yes—
333#520—23no—
334#520C22×C4313yes—
335#520C22×C4311yescharacteristic
336#520C22×C4311yescharacteristic
337#520C22×C4311yescharacteristic
338#519—21no—
339#519C22×C4313yes—
340C4×#41—23no—
341C4×#41C22×C4313yes—
342C4×#41C22×C4311yescharacteristic
343C2×C4×Q8—21no—
344C2×C4×Q8C22×C4313yes—
345#479C22×C4313yes—
346#479C22×C4316yes—
347#479C22×C4316yes—
348#479C22×C4316yes—
349#479C22×C4313yes—
350#479C22×C4316yes—
351#478C22×C4311yescharacteristic
352#478C22×C4313yes—
353#478C22×C4316yes—
354#477C22×C4313yes—
355#477C22×C4316yes—
356#476C22×C4313yes—
357#475C22×C4313yes—
358#475C22×C4316yes—
359#474C22×C4313yes—
360#428C22×C4313yes—
361#428C22×C4313yes—
362#428C22×C4313yes—
363#428C22×C4313yes—
364#427C22×C4313yes—
365#427C22×C4313yes—
366C2×#107C22×C4313yes—
367C2×#106C22×C4313yes—
368#424C22×C4313yes—
369#424C22×C4313yes—
370#423C22×C4313yes—
371C2×C4⋊C8C22×C4313yes—
372#419C22×C4313yes—
373#419C22×C4313yes—
374#417C22×C4313yes—
375#417C22×C4313yes—
376#416C22×C4313yes—
377#416C22×C4313yes—
378C2×#103C22×C4313yes—
379C2×#103C22×C4313yes—
380C43#6049911yescharacteristic, direct product factor, Sylow
3812−1+4—24no—
3822−1+4Q8×C4318yescomplemented
383C2×#41—23no—
384C2×#41C23×C4313yes—
385C2×#41C23×C4311yescharacteristic
386C22×Q8—21no—
387C22×Q8C23×C4313yes—
388#131—24no—
389#131—24no—
390C2×M16C23×C4313yes—
391C2×M16C23×C4313yes—
392C22×C8C23×C4313yes—
393C22×C8C23×C4313yes—
394C4⋊Q8—23no—
395C4⋊Q8—23no—
396C4⋊Q8C23×C4313yes—
397C4⋊Q8C23×C4313yes—
398#125—23no—
399#125—23no—
400#125—23no—
401#125—23no—
402#125C23×C4313yes—
403#125C23×C4316yes—
404#125C23×C4311yescharacteristic
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—26no—
408C22⋊Q8—26no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8D4×C4311yescharacteristic
419C4×Q8D4×C4311yescharacteristic
420C4×Q8C23×C4313yes—
421C4×Q8C23×C4316yes—
422C4×Q8C23×C4313yes—
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—26no—
429C4×D4D4×C4313yes—
430C4×D4D4×C4313yes—
431C4×D4C23×C4311yescharacteristic
432C4×D4C23×C4313yes—
433#117—23no—
434#117—26no—
435#117—23no—
436#117C23×C4313yes—
437#117C23×C4313yes—
438#117C23×C4313yes—
439#117C23×C4313yes—
440C2×C4⋊C4—23no—
441C2×C4⋊C4—23no—
442C2×C4⋊C4—23no—
443C2×C4⋊C4—23no—
444C2×C4⋊C4C23×C4313yes—
445C2×C4⋊C4C23×C4313yes—
446C2×C4⋊C4C23×C4313yes—
447C2×C42—23no—
448C2×C42—23no—
449C2×C42C23×C4313yes—
450#107C23×C4313yes—
451#107C23×C4316yes—
452#107C23×C4311yescharacteristic
453#107C23×C4313yes—
454#107C23×C4313yes—
455#106C23×C4313yes—
456#106C23×C4316yes—
457#106C23×C4311yescharacteristic
458#106C23×C4313yes—
459#106C23×C4313yes—
460C4⋊C8C23×C4311yescharacteristic
461C4⋊C8C23×C4313yes—
462C4⋊C8C23×C4313yes—
463C4⋊C8C23×C4313yes—
464C4⋊C8C23×C4316yes—
465#103C23×C4313yes—
466#103C23×C4313yes—
467#103C23×C4316yes—
468#103C23×C4316yes—
469#103C23×C4313yes—
470#103C23×C4313yes—
471#102C23×C4311yescharacteristic
472#102C23×C4311yescharacteristic
473#102C23×C4313yes—
474#102C23×C4313yes—
475#41—224no—
476#41—26no—
477#41C2×Q8×C43112yes—
478#41C2×Q8×C4314yes—
479#41#41×C4314yes—
480C2×Q8—28no—
481C2×Q8—23no—
482C2×Q8—23no—
483C2×Q8—23no—
484C2×Q8—26no—
485C2×Q8C2×D4×C4311yescharacteristic
486C2×Q8C2×Q8×C43112yes—
487C2×Q8C24×C4313yes—
488C2×D4—23no—
489C2×D4C2×D4×C4313yes—
490C2×D4C24×C4311yescharacteristic
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—21no—
497C22×C4—23no—
498C22×C4C2×D4×C4313yes—
499C22×C4C2×D4×C4313yes—
500C22×C4C24×C4313yes—
501M16—26no—
502M16—26no—
503C2×C8—26no—
504C2×C8—26no—
505C2×C8C24×C4311yescharacteristic
506C2×C8C24×C4313yes—
507C2×C8C24×C4313yes—
508C2×C8C24×C4311yescharacteristic
509C4⋊C4—26no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—26no—
515C4⋊C4—26no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4C2×D4×C4313yes—
524C4⋊C4C2×D4×C4313yes—
525C4⋊C4C24×C4313yes—
526C4⋊C4C24×C4311yescharacteristic
527C4⋊C4C24×C4313yes—
528C4⋊C4C24×C4311yescharacteristic
529C4⋊C4C24×C4313yes—
530C4⋊C4C24×C4311yescharacteristic
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—21no—
535C22⋊C4—23no—
536C22⋊C4C2×D4×C4316yes—
537C42—23no—
538C42—23no—
539C42—26no—
540C42—23no—
541C42—23no—
542C42—23no—
543C42C2×D4×C4313yes—
544C42C2×D4×C4313yes—
545C42C24×C4311yescharacteristic
546C42C24×C4313yes—
547C23—21no—
548C23C22×D4×C4313yes—
549Q8—212no—
550Q8—23no—
551Q8—83no—
552Q8—83no—
553Q8C22⋊Q8×C4314yes—
554Q8C22×Q8×C4316yes—
555D4—212no—
556D4—21no—
557D4C22⋊Q8×C43112yes—
558D4C22×Q8×C4312yes—
559C2×C4—212no—
560C2×C4—23no—
561C2×C4—212no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—43no—
569C2×C4—43no—
570C2×C4—42no—
571C2×C4—83no—
572C2×C4—83no—
573C2×C4—83no—
574C2×C4—83no—
575C2×C4C22×D4×C4311yescharacteristic
576C2×C4C22×D4×C4313yes—
577C2×C4C22×D4×C4313yes—
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4C22×D4×C4313yes—
580C2×C4C22×Q8×C4316yes—
581C2×C4C2×#41×C4316yes—
582C2×C4C25×C4311yescharacteristic
583C8—21no—
584C8—21no—
585C8—23no—
586C8—23no—
587C22—23no—
588C22—23no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22C2×C22⋊Q8×C4316yes—
593C22C23×D4×C4311yescharacteristic
594C4—26no—
595C4—21no—
596C4—23no—
597C4—21no—
598C4—23no—
599C4—43no—
600C4—43no—
601C4—41no—
602C4—41no—
603C4—43no—
604C4—41no—
605C4C2×C22⋊Q8×C4316yes—
606C4C23×Q8×C4311yescharacteristic
607C4C22×#41×C4311yescharacteristic
608C2—26no—
609C2—42no—
610C2C22×C22⋊Q8×C4311yescharacteristic
611C2C43×#358411yescharacteristic
612C2C43×#358611yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×2−1+4×C43C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3504C2semidirect
3. C43×#3084C2semidirect
4. C43×#3083C2semidirect
5. C43×#3082C2semidirect
6. C43×#3082C2semidirect
7. C43×#3080C2semidirect
8. C43×#3078C2semidirect
9. C43×#3076C2semidirect
10. C2×C43×#479C2semidirect
11. C43×#2913C2semidirect
12. C43×#2912C2semidirect
13. C43×#2906C2semidirect
75. 2−1+4×C43Q8semidirect
280. #60499C43direct (N × H)
302. #3504C2×C43semidirect
304. #3084C2×C43semidirect
305. #3083C2×C43semidirect
306. #3082C2×C43semidirect
307. #3082C2×C43semidirect
308. #3080C2×C43semidirect
309. #3078C2×C43semidirect
310. #3076C2×C43semidirect
311. C2×#479C2×C43semidirect
312. #2913C2×C43semidirect
313. #2912C2×C43semidirect
314. #2906C2×C43semidirect
380. C43#60499direct (N × H)
382. 2−1+4Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35042
C4×2−1+4×C432
C43×#30842
C43×#30832
C43×#30822
C43×#30802
C43×#30782
C43×#30762
C2×C43×#4792
C43×#29132
C43×#29122
C43×#29062
C43×#28982
#6049943