Finite Group Databasebeta

← C43×#61823 #24981840

Subgroups — C43×#61823 #24981840

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3522C211yesmaximal, characteristic, complemented
2Q8×#41×C43C211yesmaximal, characteristic, complemented
3Q8×Q16×C43C211yesmaximal, characteristic, complemented
4C43×#3381C213yesmaximal, complemented
5C43×#3380C213yesmaximal, complemented
6Q8×SD16×C43C211yesmaximal, characteristic, complemented
7C43×#3365C213yesmaximal, complemented
8C43×#3362C211yesmaximal, characteristic, complemented
9C43×#3361C213yesmaximal, complemented
10C43×#3358C211yesmaximal, characteristic, complemented
11C43×#3233C213yesmaximal, complemented
12C43×#3228C213yesmaximal, complemented
13C43×#3106C213yesmaximal, complemented
14C43×#3102C213yesmaximal, complemented
15C43×#2982C211yesmaximal, characteristic, complemented
16C43×#559C2213yes—
17Q82×C43C2211yescharacteristic
18Q82×C43C2211yescharacteristic
19C43×#557C2213yes—
20C43×#554—23no—
21C43×#554C2213yes—
22C43×#554C2213yes—
23C43×#550C2211yescharacteristic
24D4×Q8×C43—21no—
25D4×Q8×C43C2211yescharacteristic
26C43×#548—21no—
27C43×#547—23no—
28C43×#542—23no—
29C43×#533—23no—
30C43×#533C2213yes—
31C43×#532C2213yes—
32C43×#529C2213yes—
33C43×#520—21no—
34C4×#41×C43C2213yes—
35C2×C4×Q8×C43—21no—
36C2×C4×Q8×C43C2211yescharacteristic
37C43×#500C2213yes—
38C43×#499C2216yes—
39C43×#498C2213yes—
40C43×#488C2216yes—
41C43×#486C2213yes—
42C43×#486C2213yes—
43C43×#485C2213yes—
44C43×#482C2213yes—
45C43×#482C2216yes—
46C43×#479C2213yes—
47C43×#478C2213yes—
48C43×#478C2216yes—
49C43×#478C2216yes—
50C43×#477C2213yes—
51C43×#477C2213yes—
52C43×#476C2213yes—
53C43×#476C2213yes—
54C43×#475C2213yes—
55C43×#474C2213yes—
56C43×#464C2213yes—
57C43×#463C2213yes—
58C43×#460C2213yes—
59C43×#459C2213yes—
60C43×#452C2211yescharacteristic
61C43×#449C2213yes—
62C8×Q8×C43C2211yescharacteristic
63C8×Q8×C43C2213yes—
64C8×Q8×C43C2211yescharacteristic
65C8×Q8×C43C2213yes—
66C4×Q16×C43C2213yes—
67C4×SD16×C43C2213yes—
68C4×SD16×C43C2213yes—
69C4×SD16×C43C2216yes—
70C4×D8×C43C2213yes—
71C4×D8×C43C2216yes—
72C43×#431C2213yes—
73C43×#431C2213yes—
74C2×#41×C43—21no—
75C2×#41×C43—23no—
76C2×#41×C43C2311yescharacteristic
77C22×Q8×C43—21no—
78C22×Q8×C43D411yescharacteristic
79C2×Q16×C43C2311yescharacteristic
80C2×SD16×C43C2313yes—
81C2×SD16×C43C2311yescharacteristic
82C2×D8×C43C2313yes—
83C4⋊Q8×C43—23no—
84C4⋊Q8×C43—23no—
85C4⋊Q8×C43—23no—
86C4⋊Q8×C43C2313yes—
87C4⋊Q8×C43C2313yes—
88C4⋊Q8×C43C2313yes—
89#127×C43C2313yes—
90#126×C43—23no—
91#125×C43—26no—
92#125×C43C2313yes—
93#125×C43C2316yes—
94#124×C43—23no—
95#124×C43—23no—
96#124×C43C2313yes—
97#123×C43—23no—
98#123×C43—26no—
99C22⋊Q8×C43—23no—
100C22⋊Q8×C43—23no—
101C22⋊Q8×C43—23no—
102C22⋊Q8×C43—23no—
103C22⋊Q8×C43—23no—
104C22⋊Q8×C43—26no—
105C22⋊Q8×C43—26no—
106C22⋊Q8×C43C2311yescharacteristic
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×C43D411yescharacteristic
116C4×Q8×C43D413yes—
117C4×Q8×C43C2313yes—
118C4×Q8×C43C2313yes—
119C4×Q8×C43C2313yes—
120C4×Q8×C43C2311yescharacteristic
121C4×Q8×C43C2313yes—
122C4×D4×C43—23no—
123C4×D4×C43—23no—
124C4×D4×C43—23no—
125C4×D4×C43—23no—
126C4×D4×C43—23no—
127C4×D4×C43C2313yes—
128C4×D4×C43C2313yes—
129C4×D4×C43C2313yes—
130C4×D4×C43C2316yes—
131#117×C43—23no—
132#117×C43—23no—
133#117×C43C2313yes—
134C2×C4⋊C4×C43—23no—
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×C43C2311yescharacteristic
150#103×C43C2313yes—
151#103×C43C2313yes—
152#103×C43C2313yes—
153#102×C43C2311yescharacteristic
154#102×C43C2313yes—
155#102×C43C2316yes—
156#102×C43C2313yes—
157#102×C43C2316yes—
158#102×C43C2313yes—
159C22⋊C8×C43C2313yes—
160C22⋊C8×C43C2311yescharacteristic
161C4×C8×C43C2313yes—
162C4×C8×C43C2316yes—
163C4×C8×C43C2313yes—
164#41×C43—22no—
165#41×C43—22no—
166#41×C43—44no—
167#41×C43—86no—
168C2×Q8×C43—24no—
169C2×Q8×C43—23no—
170C2×Q8×C43—23no—
171C2×Q8×C43—23no—
172C2×Q8×C43—44no—
173C2×Q8×C43C2×D413yes—
174C2×Q8×C43C2×D411yescharacteristic
175C2×Q8×C43C2411yescharacteristic
176C2×Q8×C43C2411yescharacteristic
177C2×D4×C43—23no—
178C2×D4×C43—23no—
179C2×D4×C43—21no—
180C2×D4×C43—23no—
181C2×D4×C43C2413yes—
182C2×D4×C43C2411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—23no—
185C22×C4×C43—23no—
186C22×C4×C43—23no—
187C22×C4×C43—26no—
188C22×C4×C43C2×D413yes—
189C22×C4×C43C2×D413yes—
190C22×C4×C43C2411yescharacteristic
191Q16×C43—22no—
192SD16×C43—26no—
193SD16×C43—22no—
194D8×C43—26no—
195C2×C8×C43C2411yescharacteristic
196C2×C8×C43C2411yescharacteristic
197C2×C8×C43C2413yes—
198C2×C8×C43C2413yes—
199C4⋊C4×C43—23no—
200C4⋊C4×C43—23no—
201C4⋊C4×C43—26no—
202C4⋊C4×C43—23no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—23no—
205C4⋊C4×C43—23no—
206C4⋊C4×C43—23no—
207C4⋊C4×C43—23no—
208C4⋊C4×C43—26no—
209C4⋊C4×C43—23no—
210C4⋊C4×C43C2×D413yes—
211C4⋊C4×C43C2×D413yes—
212C4⋊C4×C43C2×D416yes—
213C4⋊C4×C43C2413yes—
214C4⋊C4×C43C2413yes—
215C4⋊C4×C43C2411yescharacteristic
216C4⋊C4×C43C2413yes—
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—26no—
224C22⋊C4×C43—23no—
225C22⋊C4×C43—21no—
226C42×C43—23no—
227C42×C43—23no—
228C42×C43—23no—
229C42×C43—23no—
230C42×C43C2×D413yes—
231C42×C43C2×D413yes—
232C42×C43C2413yes—
233C42×C43C2413yes—
234C23×C43—21no—
235C23×C43—23no—
236C23×C43C22×D411yescharacteristic
237Q8×C43—26no—
238Q8×C43—21no—
239Q8×C43—21no—
240Q8×C43—21no—
241Q8×C43—46no—
242Q8×C43—83no—
243Q8×C43—83no—
244Q8×C43#13514yes—
245Q8×C432−1+412yes—
246D4×C43—24no—
247D4×C43—21no—
248D4×C43—23no—
249D4×C43—23no—
250D4×C43—46no—
251D4×C43—46no—
252D4×C43—83no—
253D4×C432−1+412yes—
254C2×C4×C43—24no—
255C2×C4×C43—21no—
256C2×C4×C43—26no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—23no—
261C2×C4×C43—23no—
262C2×C4×C43—23no—
263C2×C4×C43—21no—
264C2×C4×C43—43no—
265C2×C4×C43—46no—
266C2×C4×C43—46no—
267C2×C4×C43—83no—
268C2×C4×C43—86no—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×D413yes—
271C2×C4×C43C22×D413yes—
272C2×C4×C43C22×D413yes—
273C2×C4×C43C22×D413yes—
274C2×C4×C43C2511yescharacteristic
275C8×C43—23no—
276C8×C43—23no—
277C8×C43—21no—
278C8×C43—21no—
279#61823C4311yesmaximal, characteristic, direct product factor, Sylow
280C22×C43—21no—
281C22×C43—22no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—43no—
287C22×C43—43no—
288C22×C43—43no—
289C22×C43C23×D411yescharacteristic
290C4×C43—23no—
291C4×C43—23no—
292C4×C43—21no—
293C4×C43—22no—
294C4×C43—23no—
295C4×C43—43no—
296C4×C43—43no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—43no—
300C4×C43C2×#13516yes—
301C4×C43C2×2−1+411yescharacteristic
302C4×C43C2×2−1+411yescharacteristic
303#3522C2×C4311yescharacteristic, complemented
304Q8×#41C2×C4311yescharacteristic, complemented
305Q8×Q16C2×C4311yescharacteristic, complemented
306#3381C2×C4313yescomplemented
307#3380C2×C4313yescomplemented
308Q8×SD16C2×C4311yescharacteristic, complemented
309#3365C2×C4313yescomplemented
310#3362C2×C4311yescharacteristic, complemented
311#3361C2×C4313yescomplemented
312#3358C2×C4311yescharacteristic, complemented
313#3233C2×C4313yescomplemented
314#3228C2×C4313yescomplemented
315#3106C2×C4313yescomplemented
316#3102C2×C4313yescomplemented
317#2982C2×C4311yescharacteristic, complemented
318C2×C43—41no—
319C2×C43—42no—
320C2×C43—83no—
321C2×C43#348611yescharacteristic
322C2×C43C22×#13511yescharacteristic
323C2×C43#358511yescharacteristic
324#559C22×C4313yes—
325Q82C22×C4311yescharacteristic
326Q82C22×C4311yescharacteristic
327#557C22×C4313yes—
328#554—23no—
329#554C22×C4313yes—
330#554C22×C4313yes—
331#550C22×C4311yescharacteristic
332D4×Q8—21no—
333D4×Q8C22×C4311yescharacteristic
334#548—21no—
335#547—23no—
336#542—23no—
337#533—23no—
338#533C22×C4313yes—
339#532C22×C4313yes—
340#529C22×C4313yes—
341#520—21no—
342C4×#41C22×C4313yes—
343C2×C4×Q8—21no—
344C2×C4×Q8C22×C4311yescharacteristic
345#500C22×C4313yes—
346#499C22×C4316yes—
347#498C22×C4313yes—
348#488C22×C4316yes—
349#486C22×C4313yes—
350#486C22×C4313yes—
351#485C22×C4313yes—
352#482C22×C4313yes—
353#482C22×C4316yes—
354#479C22×C4313yes—
355#478C22×C4313yes—
356#478C22×C4316yes—
357#478C22×C4316yes—
358#477C22×C4313yes—
359#477C22×C4313yes—
360#476C22×C4313yes—
361#476C22×C4313yes—
362#475C22×C4313yes—
363#474C22×C4313yes—
364#464C22×C4313yes—
365#463C22×C4313yes—
366#460C22×C4313yes—
367#459C22×C4313yes—
368#452C22×C4311yescharacteristic
369#449C22×C4313yes—
370C8×Q8C22×C4311yescharacteristic
371C8×Q8C22×C4313yes—
372C8×Q8C22×C4311yescharacteristic
373C8×Q8C22×C4313yes—
374C4×Q16C22×C4313yes—
375C4×SD16C22×C4313yes—
376C4×SD16C22×C4313yes—
377C4×SD16C22×C4316yes—
378C4×D8C22×C4313yes—
379C4×D8C22×C4316yes—
380#431C22×C4313yes—
381#431C22×C4313yes—
382C43#6182311yescharacteristic, direct product factor, Sylow
383C2×#41—21no—
384C2×#41—23no—
385C2×#41C23×C4311yescharacteristic
386C22×Q8—21no—
387C22×Q8D4×C4311yescharacteristic
388C2×Q16C23×C4311yescharacteristic
389C2×SD16C23×C4313yes—
390C2×SD16C23×C4311yescharacteristic
391C2×D8C23×C4313yes—
392C4⋊Q8—23no—
393C4⋊Q8—23no—
394C4⋊Q8—23no—
395C4⋊Q8C23×C4313yes—
396C4⋊Q8C23×C4313yes—
397C4⋊Q8C23×C4313yes—
398#127C23×C4313yes—
399#126—23no—
400#125—26no—
401#125C23×C4313yes—
402#125C23×C4316yes—
403#124—23no—
404#124—23no—
405#124C23×C4313yes—
406#123—23no—
407#123—26no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8—23no—
412C22⋊Q8—23no—
413C22⋊Q8—26no—
414C22⋊Q8—26no—
415C22⋊Q8C23×C4311yescharacteristic
416#121—23no—
417#121—23no—
418#121C23×C4313yes—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—23no—
422C4×Q8—23no—
423C4×Q8—23no—
424C4×Q8D4×C4311yescharacteristic
425C4×Q8D4×C4313yes—
426C4×Q8C23×C4313yes—
427C4×Q8C23×C4313yes—
428C4×Q8C23×C4313yes—
429C4×Q8C23×C4311yescharacteristic
430C4×Q8C23×C4313yes—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4C23×C4313yes—
437C4×D4C23×C4313yes—
438C4×D4C23×C4313yes—
439C4×D4C23×C4316yes—
440#117—23no—
441#117—23no—
442#117C23×C4313yes—
443C2×C4⋊C4—23no—
444C2×C4⋊C4—23no—
445C2×C4⋊C4D4×C4313yes—
446C2×C42—23no—
447C2×C42C23×C4313yes—
448#107C23×C4313yes—
449#107C23×C4316yes—
450#107C23×C4313yes—
451#106C23×C4316yes—
452#106C23×C4313yes—
453#106C23×C4313yes—
454C4⋊C8C23×C4313yes—
455C4⋊C8C23×C4313yes—
456C4⋊C8C23×C4313yes—
457C4⋊C8C23×C4313yes—
458#103C23×C4311yescharacteristic
459#103C23×C4313yes—
460#103C23×C4313yes—
461#103C23×C4313yes—
462#102C23×C4311yescharacteristic
463#102C23×C4313yes—
464#102C23×C4316yes—
465#102C23×C4313yes—
466#102C23×C4316yes—
467#102C23×C4313yes—
468C22⋊C8C23×C4313yes—
469C22⋊C8C23×C4311yescharacteristic
470C4×C8C23×C4316yes—
471C4×C8C23×C4313yes—
472C4×C8C23×C4313yes—
473#41—22no—
474#41—22no—
475#41—44no—
476#41—86no—
477C2×Q8—24no—
478C2×Q8—23no—
479C2×Q8—23no—
480C2×Q8—23no—
481C2×Q8—44no—
482C2×Q8C2×D4×C4313yes—
483C2×Q8C2×D4×C4311yescharacteristic
484C2×Q8C24×C4311yescharacteristic
485C2×Q8C24×C4311yescharacteristic
486C2×D4—21no—
487C2×D4—23no—
488C2×D4—23no—
489C2×D4—23no—
490C2×D4C24×C4313yes—
491C2×D4C24×C4311yescharacteristic
492C22×C4—21no—
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—26no—
497C22×C4C2×D4×C4313yes—
498C22×C4C2×D4×C4313yes—
499C22×C4C24×C4311yescharacteristic
500Q16—22no—
501SD16—26no—
502SD16—22no—
503D8—26no—
504C2×C8C24×C4311yescharacteristic
505C2×C8C24×C4313yes—
506C2×C8C24×C4311yescharacteristic
507C2×C8C24×C4313yes—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—26no—
511C4⋊C4—23no—
512C4⋊C4—21no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—26no—
518C4⋊C4—23no—
519C4⋊C4C2×D4×C4313yes—
520C4⋊C4C2×D4×C4313yes—
521C4⋊C4C2×D4×C4316yes—
522C4⋊C4C24×C4313yes—
523C4⋊C4C24×C4313yes—
524C4⋊C4C24×C4311yescharacteristic
525C4⋊C4C24×C4313yes—
526C22⋊C4—23no—
527C22⋊C4—21no—
528C22⋊C4—23no—
529C22⋊C4—23no—
530C22⋊C4—23no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—26no—
535C42—23no—
536C42—23no—
537C42—23no—
538C42—23no—
539C42C2×D4×C4313yes—
540C42C2×D4×C4313yes—
541C42C24×C4313yes—
542C42C24×C4313yes—
543C23—21no—
544C23—23no—
545C23C22×D4×C4311yescharacteristic
546Q8—26no—
547Q8—21no—
548Q8—21no—
549Q8—21no—
550Q8—46no—
551Q8—83no—
552Q8—83no—
553Q8#135×C4314yes—
554Q82−1+4×C4312yes—
555D4—24no—
556D4—21no—
557D4—23no—
558D4—23no—
559D4—46no—
560D4—46no—
561D4—83no—
562D42−1+4×C4312yes—
563C2×C4—24no—
564C2×C4—21no—
565C2×C4—26no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—21no—
573C2×C4—43no—
574C2×C4—46no—
575C2×C4—46no—
576C2×C4—86no—
577C2×C4—83no—
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4C22×D4×C4313yes—
580C2×C4C22×D4×C4313yes—
581C2×C4C22×D4×C4313yes—
582C2×C4C22×D4×C4313yes—
583C2×C4C25×C4311yescharacteristic
584C8—23no—
585C8—23no—
586C8—21no—
587C8—21no—
588C22—21no—
589C22—22no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—43no—
595C22—43no—
596C22—43no—
597C22C23×D4×C4311yescharacteristic
598C4—21no—
599C4—22no—
600C4—23no—
601C4—23no—
602C4—23no—
603C4—41no—
604C4—41no—
605C4—43no—
606C4—43no—
607C4—43no—
608C4C2×#135×C4316yes—
609C4C2×2−1+4×C4311yescharacteristic
610C4C2×2−1+4×C4311yescharacteristic
611C2—41no—
612C2—42no—
613C2—83no—
614C2C43×#348611yescharacteristic
615C2C22×#135×C4311yescharacteristic
616C2C43×#358511yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
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×#3522C2semidirect
2. Q8×#41×C43C2semidirect
3. Q8×Q16×C43C2semidirect
4. C43×#3381C2semidirect
5. C43×#3380C2semidirect
6. Q8×SD16×C43C2semidirect
7. C43×#3365C2semidirect
8. C43×#3362C2semidirect
9. C43×#3361C2semidirect
10. C43×#3358C2semidirect
11. C43×#3233C2semidirect
12. C43×#3228C2semidirect
13. C43×#3106C2semidirect
14. C43×#3102C2semidirect
15. C43×#2982C2semidirect
279. #61823C43direct (N × H)
303. #3522C2×C43semidirect
304. Q8×#41C2×C43semidirect
305. Q8×Q16C2×C43semidirect
306. #3381C2×C43semidirect
307. #3380C2×C43semidirect
308. Q8×SD16C2×C43semidirect
309. #3365C2×C43semidirect
310. #3362C2×C43semidirect
311. #3361C2×C43semidirect
312. #3358C2×C43semidirect
313. #3233C2×C43semidirect
314. #3228C2×C43semidirect
315. #3106C2×C43semidirect
316. #3102C2×C43semidirect
317. #2982C2×C43semidirect
382. C43#61823direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35222
Q8×#41×C432
Q8×Q16×C432
C43×#33812
C43×#33802
Q8×SD16×C432
C43×#33652
C43×#33622
C43×#33612
C43×#33582
C43×#32332
C43×#32282
C43×#31062
C43×#31022
C43×#29822
#6182343