Finite Group Databasebeta

← C43×#62105 #24982122

Subgroups — C43×#62105 #24982122

Order 11008.

1728 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3518C211yesmaximal, characteristic, complemented
2C43×#3482C211yesmaximal, characteristic, complemented
3Q8×SD16×C43C211yesmaximal, characteristic, complemented
4Q8×D8×C43C211yesmaximal, characteristic, complemented
5C43×#3363C211yesmaximal, characteristic, complemented
6C43×#3359C211yesmaximal, characteristic, complemented
7C43×#3342C213yesmaximal, complemented
8C43×#3340C213yesmaximal, complemented
9C43×#3303C213yesmaximal, complemented
10C43×#3302C213yesmaximal, complemented
11C43×#3248C213yesmaximal, complemented
12C43×#3231C213yesmaximal, complemented
13C43×#3102C213yesmaximal, complemented
14C43×#3076C213yesmaximal, complemented
15C43×#2988C211yesmaximal, characteristic, complemented
16Q82×C43C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#556—23no—
19C43×#556C2213yes—
20C43×#556C2213yes—
21C43×#555C2213yes—
22C43×#552—23no—
23D4×Q8×C43C2211yescharacteristic
24D4×Q8×C43C2211yescharacteristic
25C43×#548—21no—
26C43×#548—21no—
27C43×#547C2213yes—
28C43×#542—23no—
29C43×#533C2213yes—
30C43×#533C2213yes—
31C43×#529—23no—
32C43×#529C2213yes—
33C43×#519—21no—
34C4×#41×C43C2213yes—
35C4×#41×C43C2211yescharacteristic
36C2×C4×Q8×C43—21no—
37C43×#500C2213yes—
38C43×#498C2213yes—
39C43×#487C2213yes—
40C43×#487C2213yes—
41C43×#485C2213yes—
42C43×#485C2216yes—
43C43×#485C2216yes—
44C43×#482C2213yes—
45C43×#479C2213yes—
46C43×#479C2216yes—
47C43×#478C2213yes—
48C43×#477C2213yes—
49C43×#476C2213yes—
50C43×#475C2213yes—
51C43×#475C2213yes—
52C43×#474C2213yes—
53C43×#474C2213yes—
54C43×#467C2216yes—
55C43×#465C2216yes—
56C43×#464C2213yes—
57C43×#463C2211yescharacteristic
58C43×#462C2213yes—
59C43×#461C2213yes—
60C43×#452C2213yes—
61C43×#449C2213yes—
62C8×Q8×C43C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C4×Q16×C43C2213yes—
65C4×SD16×C43C2213yes—
66C4×SD16×C43C2213yes—
67C4×D8×C43C2213yes—
68C8×D4×C43C2213yes—
69C8×D4×C43C2213yes—
70C43×#431C2213yes—
71C43×#427C2216yes—
72C2×C4⋊C8×C43C2213yes—
73C43×#416C2216yes—
74C2×#41×C43D411yescharacteristic
75C2×#41×C43C2313yes—
76C22×Q8×C43—21no—
77C22×Q8×C43—21no—
78C2×Q16×C43C2313yes—
79C2×SD16×C43C2311yescharacteristic
80C2×SD16×C43C2313yes—
81C2×D8×C43C2311yescharacteristic
82C22×C8×C43C2316yes—
83C4⋊Q8×C43—23no—
84C4⋊Q8×C43C2313yes—
85C4⋊Q8×C43C2313yes—
86C4⋊Q8×C43C2313yes—
87C4⋊Q8×C43C2313yes—
88#126×C43—26no—
89#126×C43—26no—
90#126×C43—23no—
91#125×C43—23no—
92#125×C43—23no—
93#125×C43C2313yes—
94#124×C43—23no—
95#124×C43—23no—
96#124×C43—26no—
97#124×C43C2311yescharacteristic
98#123×C43—23no—
99#123×C43—26no—
100C22⋊Q8×C43—23no—
101C22⋊Q8×C43—23no—
102C22⋊Q8×C43—23no—
103C22⋊Q8×C43—23no—
104C22⋊Q8×C43—23no—
105C22⋊Q8×C43C2313yes—
106C22⋊Q8×C43C2316yes—
107#121×C43—23no—
108#121×C43—23no—
109#121×C43C2313yes—
110C4×Q8×C43—21no—
111C4×Q8×C43—21no—
112C4×Q8×C43—23no—
113C4×Q8×C43—23no—
114C4×Q8×C43—23no—
115C4×Q8×C43—23no—
116C4×Q8×C43—23no—
117C4×Q8×C43D411yescharacteristic
118C4×Q8×C43C2313yes—
119C4×Q8×C43C2313yes—
120C4×Q8×C43C2313yes—
121C4×Q8×C43C2311yescharacteristic
122C4×D4×C43—23no—
123C4×D4×C43—23no—
124C4×D4×C43—23no—
125C4×D4×C43D413yes—
126C4×D4×C43C2311yescharacteristic
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×C43D413yes—
135#117×C43C2313yes—
136#117×C43C2316yes—
137C2×C4⋊C4×C43—23no—
138C2×C42×C43—23no—
139C2×C42×C43C2313yes—
140#107×C43C2313yes—
141#107×C43C2316yes—
142#107×C43C2313yes—
143#106×C43C2313yes—
144#106×C43C2316yes—
145#106×C43C2313yes—
146C4⋊C8×C43C2313yes—
147C4⋊C8×C43C2313yes—
148C4⋊C8×C43C2313yes—
149C4⋊C8×C43C2311yescharacteristic
150#103×C43C2316yes—
151#103×C43C2316yes—
152#103×C43C2313yes—
153#103×C43C2313yes—
154#103×C43C2311yescharacteristic
155#103×C43C2313yes—
156#102×C43C2313yes—
157#102×C43C2313yes—
158#102×C43C2313yes—
159#102×C43C2311yescharacteristic
160C22⋊C8×C43C2313yes—
161C22⋊C8×C43C2313yes—
162C4×C8×C43C2313yes—
163C4×C8×C43C2313yes—
164#41×C43—24no—
165#41×C43—26no—
166#41×C43—43no—
167C2×Q8×C43—23no—
168C2×Q8×C43—23no—
169C2×Q8×C43—23no—
170C2×Q8×C43—44no—
171C2×Q8×C43—44no—
172C2×Q8×C43C2×D411yescharacteristic
173C2×Q8×C43C2413yes—
174C2×Q8×C43C2411yescharacteristic
175C2×D4×C43—23no—
176C2×D4×C43—23no—
177C2×D4×C43C2×D413yes—
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×C43C2413yes—
187Q16×C43—43no—
188SD16×C43—22no—
189SD16×C43—43no—
190D8×C43—22no—
191C2×C8×C43—46no—
192C2×C8×C43C2411yescharacteristic
193C2×C8×C43C2411yescharacteristic
194C2×C8×C43C2413yes—
195C2×C8×C43C2413yes—
196C4⋊C4×C43—23no—
197C4⋊C4×C43—26no—
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—23no—
207C4⋊C4×C43—23no—
208C4⋊C4×C43C2×D413yes—
209C4⋊C4×C43C2×D413yes—
210C4⋊C4×C43C2413yes—
211C4⋊C4×C43C2413yes—
212C4⋊C4×C43C2411yescharacteristic
213C4⋊C4×C43C2413yes—
214C22⋊C4×C43—21no—
215C22⋊C4×C43—23no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—23no—
218C22⋊C4×C43—21no—
219C22⋊C4×C43—23no—
220C22⋊C4×C43—26no—
221C22⋊C4×C43—23no—
222C22⋊C4×C43—26no—
223C22⋊C4×C43—23no—
224C22⋊C4×C43C2×D416yes—
225C42×C43—23no—
226C42×C43—23no—
227C42×C43—23no—
228C42×C43—26no—
229C42×C43—23no—
230C42×C43C2×D413yes—
231C42×C43C2×D413yes—
232C42×C43C2413yes—
233C42×C43C2411yescharacteristic
234C23×C43—21no—
235C23×C43—21no—
236C23×C43C22×D413yes—
237Q8×C43—21no—
238Q8×C43—23no—
239Q8×C43—23no—
240Q8×C43—21no—
241Q8×C43—46no—
242Q8×C43—46no—
243Q8×C43—83no—
244Q8×C43#13514yes—
245D4×C43—26no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—21no—
249D4×C43—46no—
250D4×C43—83no—
251D4×C432−1+412yes—
252C2×C4×C43—26no—
253C2×C4×C43—23no—
254C2×C4×C43—23no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—23no—
258C2×C4×C43—23no—
259C2×C4×C43—23no—
260C2×C4×C43—23no—
261C2×C4×C43—43no—
262C2×C4×C43—46no—
263C2×C4×C43—42no—
264C2×C4×C43—46no—
265C2×C4×C43—46no—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D413yes—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×D413yes—
270C2×C4×C43C22×D413yes—
271C2×C4×C43C2511yescharacteristic
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—23no—
275C8×C43—23no—
276#62105C4311yesmaximal, characteristic, direct product factor, Sylow
277C22×C43—23no—
278C22×C43—22no—
279C22×C43—23no—
280C22×C43—23no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43C23×D411yescharacteristic
287C4×C43—21no—
288C4×C43—23no—
289C4×C43—23no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—43no—
293C4×C43—43no—
294C4×C43—41no—
295C4×C43—43no—
296C4×C43—43no—
297C4×C43C2×#13516yes—
298C4×C43C2×2−1+411yescharacteristic
299C4×C43#58511yescharacteristic
300#3518C2×C4311yescharacteristic, complemented
301#3482C2×C4311yescharacteristic, complemented
302Q8×SD16C2×C4311yescharacteristic, complemented
303Q8×D8C2×C4311yescharacteristic, complemented
304#3363C2×C4311yescharacteristic, complemented
305#3359C2×C4311yescharacteristic, complemented
306#3342C2×C4313yescomplemented
307#3340C2×C4313yescomplemented
308#3303C2×C4313yescomplemented
309#3302C2×C4313yescomplemented
310#3248C2×C4313yescomplemented
311#3231C2×C4313yescomplemented
312#3102C2×C4313yescomplemented
313#3076C2×C4313yescomplemented
314#2988C2×C4311yescharacteristic, complemented
315C2×C43—43no—
316C2×C43—42no—
317C2×C43—81no—
318C2×C43#348911yescharacteristic
319C2×C43C22×#13511yescharacteristic
320C2×C43#358611yescharacteristic
321Q82C22×C4311yescharacteristic
322#557C22×C4311yescharacteristic
323#556—23no—
324#556C22×C4313yes—
325#556C22×C4313yes—
326#555C22×C4313yes—
327#552—23no—
328D4×Q8C22×C4311yescharacteristic
329D4×Q8C22×C4311yescharacteristic
330#548—21no—
331#548—21no—
332#547C22×C4313yes—
333#542—23no—
334#533C22×C4313yes—
335#533C22×C4313yes—
336#529—23no—
337#529C22×C4313yes—
338#519—21no—
339C4×#41C22×C4313yes—
340C4×#41C22×C4311yescharacteristic
341C2×C4×Q8—21no—
342#500C22×C4313yes—
343#498C22×C4313yes—
344#487C22×C4313yes—
345#487C22×C4313yes—
346#485C22×C4316yes—
347#485C22×C4313yes—
348#485C22×C4316yes—
349#482C22×C4313yes—
350#479C22×C4316yes—
351#479C22×C4313yes—
352#478C22×C4313yes—
353#477C22×C4313yes—
354#476C22×C4313yes—
355#475C22×C4313yes—
356#475C22×C4313yes—
357#474C22×C4313yes—
358#474C22×C4313yes—
359#467C22×C4316yes—
360#465C22×C4316yes—
361#464C22×C4313yes—
362#463C22×C4311yescharacteristic
363#462C22×C4313yes—
364#461C22×C4313yes—
365#452C22×C4313yes—
366#449C22×C4313yes—
367C8×Q8C22×C4311yescharacteristic
368C8×Q8C22×C4311yescharacteristic
369C4×Q16C22×C4313yes—
370C4×SD16C22×C4313yes—
371C4×SD16C22×C4313yes—
372C4×D8C22×C4313yes—
373C8×D4C22×C4313yes—
374C8×D4C22×C4313yes—
375#431C22×C4313yes—
376#427C22×C4316yes—
377C2×C4⋊C8C22×C4313yes—
378#416C22×C4316yes—
379C43#6210511yescharacteristic, direct product factor, Sylow
380C2×#41D4×C4311yescharacteristic
381C2×#41C23×C4313yes—
382C22×Q8—21no—
383C22×Q8—21no—
384C2×Q16C23×C4313yes—
385C2×SD16C23×C4311yescharacteristic
386C2×SD16C23×C4313yes—
387C2×D8C23×C4311yescharacteristic
388C22×C8C23×C4316yes—
389C4⋊Q8—23no—
390C4⋊Q8C23×C4313yes—
391C4⋊Q8C23×C4313yes—
392C4⋊Q8C23×C4313yes—
393C4⋊Q8C23×C4313yes—
394#126—26no—
395#126—26no—
396#126—23no—
397#125—23no—
398#125—23no—
399#125C23×C4313yes—
400#124—23no—
401#124—23no—
402#124—26no—
403#124C23×C4311yescharacteristic
404#123—23no—
405#123—26no—
406C22⋊Q8—23no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8C23×C4313yes—
412C22⋊Q8C23×C4316yes—
413#121—23no—
414#121—23no—
415#121C23×C4313yes—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8—23no—
421C4×Q8—23no—
422C4×Q8—23no—
423C4×Q8D4×C4311yescharacteristic
424C4×Q8C23×C4313yes—
425C4×Q8C23×C4313yes—
426C4×Q8C23×C4313yes—
427C4×Q8C23×C4311yescharacteristic
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4D4×C4313yes—
432C4×D4C23×C4311yescharacteristic
433C4×D4C23×C4313yes—
434C4×D4C23×C4313yes—
435C4×D4C23×C4313yes—
436#117—23no—
437#117—23no—
438#117—23no—
439#117—23no—
440#117D4×C4313yes—
441#117C23×C4313yes—
442#117C23×C4316yes—
443C2×C4⋊C4—23no—
444C2×C42—23no—
445C2×C42C23×C4313yes—
446#107C23×C4313yes—
447#107C23×C4316yes—
448#107C23×C4313yes—
449#106C23×C4313yes—
450#106C23×C4316yes—
451#106C23×C4313yes—
452C4⋊C8C23×C4313yes—
453C4⋊C8C23×C4313yes—
454C4⋊C8C23×C4313yes—
455C4⋊C8C23×C4311yescharacteristic
456#103C23×C4316yes—
457#103C23×C4316yes—
458#103C23×C4313yes—
459#103C23×C4313yes—
460#103C23×C4311yescharacteristic
461#103C23×C4313yes—
462#102C23×C4313yes—
463#102C23×C4313yes—
464#102C23×C4313yes—
465#102C23×C4311yescharacteristic
466C22⋊C8C23×C4313yes—
467C22⋊C8C23×C4313yes—
468C4×C8C23×C4313yes—
469C4×C8C23×C4313yes—
470#41—24no—
471#41—26no—
472#41—43no—
473C2×Q8—23no—
474C2×Q8—23no—
475C2×Q8—23no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8C2×D4×C4311yescharacteristic
479C2×Q8C24×C4313yes—
480C2×Q8C24×C4311yescharacteristic
481C2×D4—23no—
482C2×D4—23no—
483C2×D4C2×D4×C4313yes—
484C2×D4C24×C4311yescharacteristic
485C2×D4C24×C4311yescharacteristic
486C22×C4—21no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4C2×D4×C4313yes—
491C22×C4C2×D4×C4313yes—
492C22×C4C24×C4313yes—
493Q16—43no—
494SD16—22no—
495SD16—43no—
496D8—22no—
497C2×C8—46no—
498C2×C8C24×C4311yescharacteristic
499C2×C8C24×C4311yescharacteristic
500C2×C8C24×C4313yes—
501C2×C8C24×C4313yes—
502C4⋊C4—23no—
503C4⋊C4—26no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4C2×D4×C4313yes—
515C4⋊C4C2×D4×C4313yes—
516C4⋊C4C24×C4313yes—
517C4⋊C4C24×C4313yes—
518C4⋊C4C24×C4311yescharacteristic
519C4⋊C4C24×C4313yes—
520C22⋊C4—26no—
521C22⋊C4—23no—
522C22⋊C4—26no—
523C22⋊C4—23no—
524C22⋊C4—21no—
525C22⋊C4—23no—
526C22⋊C4—21no—
527C22⋊C4—23no—
528C22⋊C4—21no—
529C22⋊C4—23no—
530C22⋊C4C2×D4×C4316yes—
531C42—23no—
532C42—23no—
533C42—23no—
534C42—26no—
535C42—23no—
536C42C2×D4×C4313yes—
537C42C2×D4×C4313yes—
538C42C24×C4313yes—
539C42C24×C4311yescharacteristic
540C23—21no—
541C23—21no—
542C23C22×D4×C4313yes—
543Q8—21no—
544Q8—23no—
545Q8—23no—
546Q8—21no—
547Q8—46no—
548Q8—46no—
549Q8—83no—
550Q8#135×C4314yes—
551D4—26no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—46no—
556D4—83no—
557D42−1+4×C4312yes—
558C2×C4—26no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—43no—
568C2×C4—46no—
569C2×C4—42no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4C22×D4×C4311yescharacteristic
573C2×C4C22×D4×C4313yes—
574C2×C4C22×D4×C4311yescharacteristic
575C2×C4C22×D4×C4313yes—
576C2×C4C22×D4×C4313yes—
577C2×C4C25×C4311yescharacteristic
578C8—21no—
579C8—21no—
580C8—23no—
581C8—23no—
582C22—23no—
583C22—22no—
584C22—23no—
585C22—23no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C23×D4×C4311yescharacteristic
592C4—23no—
593C4—21no—
594C4—21no—
595C4—23no—
596C4—43no—
597C4—41no—
598C4—43no—
599C4—43no—
600C4—41no—
601C4—43no—
602C4C2×#135×C4316yes—
603C4C2×2−1+4×C4311yescharacteristic
604C4C43×#58511yescharacteristic
605C2—43no—
606C2—42no—
607C2—81no—
608C2C43×#348911yescharacteristic
609C2C22×#135×C4311yescharacteristic
610C2C43×#358611yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
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×#3518C2semidirect
2. C43×#3482C2semidirect
3. Q8×SD16×C43C2semidirect
4. Q8×D8×C43C2semidirect
5. C43×#3363C2semidirect
6. C43×#3359C2semidirect
7. C43×#3342C2semidirect
8. C43×#3340C2semidirect
9. C43×#3303C2semidirect
10. C43×#3302C2semidirect
11. C43×#3248C2semidirect
12. C43×#3231C2semidirect
13. C43×#3102C2semidirect
14. C43×#3076C2semidirect
15. C43×#2988C2semidirect
276. #62105C43direct (N × H)
300. #3518C2×C43semidirect
301. #3482C2×C43semidirect
302. Q8×SD16C2×C43semidirect
303. Q8×D8C2×C43semidirect
304. #3363C2×C43semidirect
305. #3359C2×C43semidirect
306. #3342C2×C43semidirect
307. #3340C2×C43semidirect
308. #3303C2×C43semidirect
309. #3302C2×C43semidirect
310. #3248C2×C43semidirect
311. #3231C2×C43semidirect
312. #3102C2×C43semidirect
313. #3076C2×C43semidirect
314. #2988C2×C43semidirect
379. C43#62105direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35182
C43×#34822
Q8×SD16×C432
Q8×D8×C432
C43×#33632
C43×#33592
C43×#33422
C43×#33402
C43×#33032
C43×#33022
C43×#32482
C43×#32312
C43×#31022
C43×#30762
C43×#29882
#6210543