Finite Group Databasebeta

← C43×#61824 #24981841

Subgroups — C43×#61824 #24981841

Order 11008.

1694 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3523C211yesmaximal, characteristic, complemented
2Q8×#41×C43C211yesmaximal, characteristic, complemented
3C43×#3383C213yesmaximal, complemented
4C43×#3381C213yesmaximal, complemented
5Q8×SD16×C43C211yesmaximal, characteristic, complemented
6Q8×D8×C43C211yesmaximal, characteristic, complemented
7C43×#3364C213yesmaximal, complemented
8C43×#3363C211yesmaximal, characteristic, complemented
9C43×#3360C213yesmaximal, complemented
10C43×#3359C211yesmaximal, characteristic, complemented
11C43×#3233C213yesmaximal, complemented
12C43×#3231C213yesmaximal, complemented
13C43×#3107C213yesmaximal, complemented
14C43×#3102C213yesmaximal
15C43×#2982C211yesmaximal, characteristic, complemented
16Q82×C43C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#557C2213yes—
19C43×#557C2213yes—
20C43×#556C2213yes—
21C43×#554—23no—
22C43×#554C2213yes—
23C43×#552—23no—
24D4×Q8×C43—21no—
25D4×Q8×C43—21no—
26D4×Q8×C43C2211yescharacteristic
27D4×Q8×C43C2211yescharacteristic
28C43×#541—23no—
29C43×#533—23no—
30C43×#533C2213yes—
31C43×#533C2213yes—
32C43×#529C2213yes—
33C43×#519—21no—
34C4×#41×C43C2213yes—
35C2×C4×Q8×C43—21no—
36C2×C4×Q8×C43C2211yescharacteristic
37C43×#500C2213yes—
38C43×#499C2216yes—
39C43×#498C2213yes—
40C43×#488C2216yes—
41C43×#487C2213yes—
42C43×#487C2213yes—
43C43×#485C2213yes—
44C43×#485C2216yes—
45C43×#482C2213yes—
46C43×#479C2213yes—
47C43×#479C2216yes—
48C43×#479C2216yes—
49C43×#478C2213yes—
50C43×#477C2213yes—
51C43×#476C2213yes—
52C43×#475C2213yes—
53C43×#475C2213yes—
54C43×#474C2213yes—
55C43×#474C2213yes—
56C43×#464C2213yes—
57C43×#463C2213yes—
58C43×#462C2213yes—
59C43×#461C2213yes—
60C43×#452C2213yes—
61C43×#449C2211yescharacteristic
62C8×Q8×C43C2211yescharacteristic
63C8×Q8×C43C2213yes—
64C8×Q8×C43C2211yescharacteristic
65C8×Q8×C43C2213yes—
66C4×Q16×C43C2213yes—
67C4×Q16×C43C2216yes—
68C4×SD16×C43C2213yes—
69C4×SD16×C43C2213yes—
70C4×SD16×C43C2216yes—
71C4×D8×C43C2213yes—
72C43×#431C2213yes—
73C43×#431C2213yes—
74C2×#41×C43C2311yescharacteristic
75C22×Q8×C43—21no—
76C22×Q8×C43—21no—
77C22×Q8×C43D411yescharacteristic
78C2×Q16×C43C2313yes—
79C2×SD16×C43C2311yescharacteristic
80C2×SD16×C43C2313yes—
81C2×D8×C43C2311yescharacteristic
82C4⋊Q8×C43—23no—
83C4⋊Q8×C43—23no—
84C4⋊Q8×C43—23no—
85C4⋊Q8×C43C2313yes—
86C4⋊Q8×C43C2313yes—
87C4⋊Q8×C43C2313yes—
88C4⋊Q8×C43C2313yes—
89#126×C43—26no—
90#126×C43—23no—
91#125×C43—26no—
92#125×C43—26no—
93#125×C43—23no—
94#125×C43—23no—
95#125×C43C2313yes—
96#125×C43C2316yes—
97#124×C43C2313yes—
98#123×C43—23no—
99C22⋊Q8×C43—23no—
100C22⋊Q8×C43—23no—
101C22⋊Q8×C43—23no—
102C22⋊Q8×C43—23no—
103C22⋊Q8×C43—23no—
104C22⋊Q8×C43—23no—
105C22⋊Q8×C43—26no—
106C22⋊Q8×C43—23no—
107C22⋊Q8×C43C2313yes—
108#121×C43C2311yescharacteristic
109C4×Q8×C43—21no—
110C4×Q8×C43—21no—
111C4×Q8×C43—23no—
112C4×Q8×C43—23no—
113C4×Q8×C43—23no—
114C4×Q8×C43—23no—
115C4×Q8×C43—23no—
116C4×Q8×C43D411yescharacteristic
117C4×Q8×C43D413yes—
118C4×Q8×C43C2313yes—
119C4×Q8×C43C2313yes—
120C4×Q8×C43C2313yes—
121C4×Q8×C43C2316yes—
122C4×Q8×C43C2311yescharacteristic
123C4×Q8×C43C2313yes—
124C4×D4×C43—23no—
125C4×D4×C43—23no—
126C4×D4×C43—23no—
127C4×D4×C43C2313yes—
128C4×D4×C43C2313yes—
129C4×D4×C43C2313yes—
130#117×C43—23no—
131#117×C43—23no—
132#117×C43—23no—
133#117×C43—23no—
134#117×C43C2313yes—
135C2×C4⋊C4×C43—23no—
136C2×C4⋊C4×C43D413yes—
137C2×C42×C43—23no—
138C2×C42×C43C2313yes—
139#107×C43C2313yes—
140#107×C43C2316yes—
141#107×C43C2313yes—
142#106×C43C2313yes—
143#106×C43C2316yes—
144#106×C43C2313yes—
145C4⋊C8×C43C2313yes—
146C4⋊C8×C43C2313yes—
147C4⋊C8×C43C2313yes—
148C4⋊C8×C43C2313yes—
149#103×C43C2313yes—
150#103×C43C2316yes—
151#103×C43C2313yes—
152#103×C43C2311yescharacteristic
153#103×C43C2316yes—
154#103×C43C2313yes—
155#102×C43C2313yes—
156#102×C43C2313yes—
157#102×C43C2311yescharacteristic
158#102×C43C2313yes—
159C22⋊C8×C43C2311yescharacteristic
160C22⋊C8×C43C2313yes—
161C4×C8×C43C2313yes—
162C4×C8×C43C2316yes—
163C4×C8×C43C2313yes—
164#41×C43—22no—
165#41×C43—22no—
166C2×Q8×C43—24no—
167C2×Q8×C43—23no—
168C2×Q8×C43—23no—
169C2×Q8×C43—23no—
170C2×Q8×C43—44no—
171C2×Q8×C43—44no—
172C2×Q8×C43C2×D413yes—
173C2×Q8×C43C2×D411yescharacteristic
174C2×Q8×C43C2413yes—
175C2×Q8×C43C2411yescharacteristic
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43C2411yescharacteristic
179C2×D4×C43C2411yescharacteristic
180C22×C4×C43—21no—
181C22×C4×C43—23no—
182C22×C4×C43—23no—
183C22×C4×C43—23no—
184C22×C4×C43C2×D413yes—
185C22×C4×C43C2×D413yes—
186C22×C4×C43C2411yescharacteristic
187Q16×C43—26no—
188SD16×C43—22no—
189SD16×C43—26no—
190D8×C43—22no—
191C2×C8×C43C2413yes—
192C2×C8×C43C2411yescharacteristic
193C2×C8×C43C2413yes—
194C2×C8×C43C2411yescharacteristic
195C4⋊C4×C43—26no—
196C4⋊C4×C43—23no—
197C4⋊C4×C43—23no—
198C4⋊C4×C43—23no—
199C4⋊C4×C43—23no—
200C4⋊C4×C43—23no—
201C4⋊C4×C43—23no—
202C4⋊C4×C43—23no—
203C4⋊C4×C43—23no—
204C4⋊C4×C43—23no—
205C4⋊C4×C43—23no—
206C4⋊C4×C43—26no—
207C4⋊C4×C43—26no—
208C4⋊C4×C43—23no—
209C4⋊C4×C43C2×D413yes—
210C4⋊C4×C43C2×D413yes—
211C4⋊C4×C43C2×D416yes—
212C4⋊C4×C43C2413yes—
213C4⋊C4×C43C2413yes—
214C4⋊C4×C43C2413yes—
215C4⋊C4×C43C2411yescharacteristic
216C22⋊C4×C43—21no—
217C22⋊C4×C43—23no—
218C22⋊C4×C43—23no—
219C22⋊C4×C43—23no—
220C22⋊C4×C43—23no—
221C22⋊C4×C43—23no—
222C22⋊C4×C43—23no—
223C22⋊C4×C43—23no—
224C42×C43—23no—
225C42×C43—23no—
226C42×C43—23no—
227C42×C43—26no—
228C42×C43—23no—
229C42×C43C2×D413yes—
230C42×C43C2×D413yes—
231C42×C43C2413yes—
232C42×C43C2413yes—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43C22×D411yescharacteristic
236Q8×C43—26no—
237Q8×C43—21no—
238Q8×C43—23no—
239Q8×C43—23no—
240Q8×C43—46no—
241Q8×C43—46no—
242Q8×C43—83no—
243Q8×C43#13514yes—
244Q8×C432−1+412yes—
245D4×C43—24no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—21no—
249D4×C43—42no—
250D4×C432−1+412yes—
251C2×C4×C43—24no—
252C2×C4×C43—21no—
253C2×C4×C43—26no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—23no—
257C2×C4×C43—21no—
258C2×C4×C43—23no—
259C2×C4×C43—23no—
260C2×C4×C43—23no—
261C2×C4×C43—43no—
262C2×C4×C43—46no—
263C2×C4×C43—46no—
264C2×C4×C43—83no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D413yes—
267C2×C4×C43C22×D413yes—
268C2×C4×C43C22×D413yes—
269C2×C4×C43C22×D413yes—
270C2×C4×C43C2511yescharacteristic
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—23no—
274C8×C43—23no—
275#61824C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—21no—
277C22×C43—22no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C23×D411yescharacteristic
286C4×C43—23no—
287C4×C43—23no—
288C4×C43—21no—
289C4×C43—22no—
290C4×C43—23no—
291C4×C43—43no—
292C4×C43—41no—
293C4×C43—43no—
294C4×C43—43no—
295C4×C43—43no—
296C4×C43C2×#13516yes—
297C4×C43C2×2−1+411yescharacteristic
298C4×C43C2×2−1+411yescharacteristic
299#3523C2×C4311yescharacteristic, complemented
300Q8×#41C2×C4311yescharacteristic, complemented
301#3383C2×C4313yescomplemented
302#3381C2×C4313yescomplemented
303Q8×SD16C2×C4311yescharacteristic, complemented
304Q8×D8C2×C4311yescharacteristic, complemented
305#3364C2×C4313yescomplemented
306#3363C2×C4311yescharacteristic, complemented
307#3360C2×C4313yescomplemented
308#3359C2×C4311yescharacteristic, complemented
309#3233C2×C4313yescomplemented
310#3231C2×C4313yescomplemented
311#3107C2×C4313yescomplemented
312#3102C2×C4313yes—
313#2982C2×C4311yescharacteristic, complemented
314C2×C43—41no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43#348611yescharacteristic
318C2×C43C22×#13511yescharacteristic
319C2×C43#358611yescharacteristic
320Q82C22×C4311yescharacteristic
321#557C22×C4311yescharacteristic
322#557C22×C4313yes—
323#557C22×C4313yes—
324#556C22×C4313yes—
325#554—23no—
326#554C22×C4313yes—
327#552—23no—
328D4×Q8—21no—
329D4×Q8—21no—
330D4×Q8C22×C4311yescharacteristic
331D4×Q8C22×C4311yescharacteristic
332#541—23no—
333#533—23no—
334#533C22×C4313yes—
335#533C22×C4313yes—
336#529C22×C4313yes—
337#519—21no—
338C4×#41C22×C4313yes—
339C2×C4×Q8—21no—
340C2×C4×Q8C22×C4311yescharacteristic
341#500C22×C4313yes—
342#499C22×C4316yes—
343#498C22×C4313yes—
344#488C22×C4316yes—
345#487C22×C4313yes—
346#487C22×C4313yes—
347#485C22×C4313yes—
348#485C22×C4316yes—
349#482C22×C4313yes—
350#479C22×C4313yes—
351#479C22×C4316yes—
352#479C22×C4316yes—
353#478C22×C4313yes—
354#477C22×C4313yes—
355#476C22×C4313yes—
356#475C22×C4313yes—
357#475C22×C4313yes—
358#474C22×C4313yes—
359#474C22×C4313yes—
360#464C22×C4313yes—
361#463C22×C4313yes—
362#462C22×C4313yes—
363#461C22×C4313yes—
364#452C22×C4313yes—
365#449C22×C4311yescharacteristic
366C8×Q8C22×C4311yescharacteristic
367C8×Q8C22×C4313yes—
368C8×Q8C22×C4311yescharacteristic
369C8×Q8C22×C4313yes—
370C4×Q16C22×C4313yes—
371C4×Q16C22×C4316yes—
372C4×SD16C22×C4313yes—
373C4×SD16C22×C4313yes—
374C4×SD16C22×C4316yes—
375C4×D8C22×C4313yes—
376#431C22×C4313yes—
377#431C22×C4313yes—
378C43#6182411yescharacteristic, direct product factor, Sylow
379C2×#41C23×C4311yescharacteristic
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8D4×C4311yescharacteristic
383C2×Q16C23×C4313yes—
384C2×SD16C23×C4311yescharacteristic
385C2×SD16C23×C4313yes—
386C2×D8C23×C4311yescharacteristic
387C4⋊Q8—23no—
388C4⋊Q8—23no—
389C4⋊Q8—23no—
390C4⋊Q8C23×C4313yes—
391C4⋊Q8C23×C4313yes—
392C4⋊Q8C23×C4313yes—
393C4⋊Q8C23×C4313yes—
394#126—26no—
395#126—23no—
396#125—26no—
397#125—26no—
398#125—23no—
399#125—23no—
400#125C23×C4313yes—
401#125C23×C4316yes—
402#124C23×C4313yes—
403#123—23no—
404C22⋊Q8—23no—
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8—26no—
411C22⋊Q8—23no—
412C22⋊Q8C23×C4313yes—
413#121C23×C4311yescharacteristic
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8—23no—
421C4×Q8D4×C4311yescharacteristic
422C4×Q8D4×C4313yes—
423C4×Q8C23×C4313yes—
424C4×Q8C23×C4313yes—
425C4×Q8C23×C4313yes—
426C4×Q8C23×C4316yes—
427C4×Q8C23×C4311yescharacteristic
428C4×Q8C23×C4313yes—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4C23×C4313yes—
433C4×D4C23×C4313yes—
434C4×D4C23×C4313yes—
435#117—23no—
436#117—23no—
437#117—23no—
438#117—23no—
439#117C23×C4313yes—
440C2×C4⋊C4—23no—
441C2×C4⋊C4D4×C4313yes—
442C2×C42—23no—
443C2×C42C23×C4313yes—
444#107C23×C4313yes—
445#107C23×C4316yes—
446#107C23×C4313yes—
447#106C23×C4313yes—
448#106C23×C4316yes—
449#106C23×C4313yes—
450C4⋊C8C23×C4313yes—
451C4⋊C8C23×C4313yes—
452C4⋊C8C23×C4313yes—
453C4⋊C8C23×C4313yes—
454#103C23×C4313yes—
455#103C23×C4316yes—
456#103C23×C4313yes—
457#103C23×C4311yescharacteristic
458#103C23×C4316yes—
459#103C23×C4313yes—
460#102C23×C4313yes—
461#102C23×C4313yes—
462#102C23×C4311yescharacteristic
463#102C23×C4313yes—
464C22⋊C8C23×C4311yescharacteristic
465C22⋊C8C23×C4313yes—
466C4×C8C23×C4313yes—
467C4×C8C23×C4313yes—
468C4×C8C23×C4316yes—
469#41—22no—
470#41—22no—
471C2×Q8—24no—
472C2×Q8—23no—
473C2×Q8—23no—
474C2×Q8—23no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8C2×D4×C4313yes—
478C2×Q8C2×D4×C4311yescharacteristic
479C2×Q8C24×C4313yes—
480C2×Q8C24×C4311yescharacteristic
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C24×C4311yescharacteristic
484C2×D4C24×C4311yescharacteristic
485C22×C4—21no—
486C22×C4—23no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4C2×D4×C4313yes—
490C22×C4C2×D4×C4313yes—
491C22×C4C24×C4311yescharacteristic
492Q16—26no—
493SD16—22no—
494SD16—26no—
495D8—22no—
496C2×C8C24×C4313yes—
497C2×C8C24×C4311yescharacteristic
498C2×C8C24×C4313yes—
499C2×C8C24×C4311yescharacteristic
500C4⋊C4—26no—
501C4⋊C4—23no—
502C4⋊C4—23no—
503C4⋊C4—23no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—26no—
512C4⋊C4—26no—
513C4⋊C4—23no—
514C4⋊C4C2×D4×C4313yes—
515C4⋊C4C2×D4×C4313yes—
516C4⋊C4C2×D4×C4316yes—
517C4⋊C4C24×C4313yes—
518C4⋊C4C24×C4313yes—
519C4⋊C4C24×C4313yes—
520C4⋊C4C24×C4311yescharacteristic
521C22⋊C4—23no—
522C22⋊C4—23no—
523C22⋊C4—21no—
524C22⋊C4—23no—
525C22⋊C4—23no—
526C22⋊C4—23no—
527C22⋊C4—23no—
528C22⋊C4—23no—
529C42—23no—
530C42—23no—
531C42—23no—
532C42—26no—
533C42—23no—
534C42C2×D4×C4313yes—
535C42C2×D4×C4313yes—
536C42C24×C4313yes—
537C42C24×C4313yes—
538C23—21no—
539C23—21no—
540C23C22×D4×C4311yescharacteristic
541Q8—26no—
542Q8—21no—
543Q8—23no—
544Q8—23no—
545Q8—46no—
546Q8—46no—
547Q8—83no—
548Q8#135×C4314yes—
549Q82−1+4×C4312yes—
550D4—24no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—42no—
555D42−1+4×C4312yes—
556C2×C4—24no—
557C2×C4—21no—
558C2×C4—26no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—23no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—43no—
567C2×C4—46no—
568C2×C4—46no—
569C2×C4—83no—
570C2×C4C22×D4×C4311yescharacteristic
571C2×C4C22×D4×C4313yes—
572C2×C4C22×D4×C4313yes—
573C2×C4C22×D4×C4313yes—
574C2×C4C22×D4×C4313yes—
575C2×C4C25×C4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—23no—
579C8—23no—
580C22—21no—
581C22—22no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C23×D4×C4311yescharacteristic
590C4—21no—
591C4—22no—
592C4—23no—
593C4—23no—
594C4—23no—
595C4—43no—
596C4—43no—
597C4—43no—
598C4—43no—
599C4—41no—
600C4C2×#135×C4316yes—
601C4C2×2−1+4×C4311yescharacteristic
602C4C2×2−1+4×C4311yescharacteristic
603C2—41no—
604C2—42no—
605C2—81no—
606C2C43×#348611yescharacteristic
607C2C22×#135×C4311yescharacteristic
608C2C43×#358611yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC43×#449C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C4×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3523C2semidirect
2. Q8×#41×C43C2semidirect
3. C43×#3383C2semidirect
4. C43×#3381C2semidirect
5. Q8×SD16×C43C2semidirect
6. Q8×D8×C43C2semidirect
7. C43×#3364C2semidirect
8. C43×#3363C2semidirect
9. C43×#3360C2semidirect
10. C43×#3359C2semidirect
11. C43×#3233C2semidirect
12. C43×#3231C2semidirect
13. C43×#3107C2semidirect
15. C43×#2982C2semidirect
275. #61824C43direct (N × H)
299. #3523C2×C43semidirect
300. Q8×#41C2×C43semidirect
301. #3383C2×C43semidirect
302. #3381C2×C43semidirect
303. Q8×SD16C2×C43semidirect
304. Q8×D8C2×C43semidirect
305. #3364C2×C43semidirect
306. #3363C2×C43semidirect
307. #3360C2×C43semidirect
308. #3359C2×C43semidirect
309. #3233C2×C43semidirect
310. #3231C2×C43semidirect
311. #3107C2×C43semidirect
313. #2982C2×C43semidirect
378. C43#61824direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35232
Q8×#41×C432
C43×#33832
C43×#33812
Q8×SD16×C432
Q8×D8×C432
C43×#33642
C43×#33632
C43×#33602
C43×#33592
C43×#32332
C43×#32312
C43×#31072
C43×#31022
C43×#29822
#6182443