Finite Group Databasebeta

← C43×#25833 #24945850

Subgroups — C43×#25833 #24945850

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3504C211yesmaximal, characteristic
2C43×#3165C211yesmaximal, characteristic, complemented
3C43×#3079C211yesmaximal, characteristic
4C43×#2660C211yesmaximal, characteristic, complemented
5C43×#2061C212yesmaximal, complemented
6C43×#2060C212yesmaximal, complemented
7C43×#1998C211yesmaximal, characteristic, complemented
8C43×#1995C211yesmaximal, characteristic, complemented
9C43×#1860C212yesmaximal
10C43×#1859C212yesmaximal
11C43×#1759C211yesmaximal, characteristic
12C43×#557—21no—
13C43×#557—21no—
14C43×#554—21no—
15C43×#554—21no—
16C43×#554—22no—
17C43×#554—22no—
18C43×#544—21no—
19C43×#544—21no—
20C43×#544C2211yescharacteristic
21C43×#544C2211yescharacteristic
22C43×#533—21no—
23C43×#533C2211yescharacteristic
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×#125×C43—21no—
26C2×#125×C43C2211yescharacteristic
27C43×#520C2211yescharacteristic
28C43×#520C2211yescharacteristic
29C4×#41×C43C2211yescharacteristic
30C43×#501—21no—
31C43×#501—21no—
32C43×#500—21no—
33C43×#498—21no—
34C43×#477—21no—
35C43×#476—21no—
36C43×#475—21no—
37C43×#474—21no—
38C43×#428C2212yes—
39C43×#428C2212yes—
40C43×#428C2212yes—
41C43×#423C2211yescharacteristic
42C2×#104×C43C2212yes—
43C43×#417C2212yes—
44C4×M16×C43C2211yescharacteristic
45C43×#398—22no—
46C43×#395—22no—
47C43×#384C2212yes—
48C43×#382C2212yes—
49C43×#376C2211yescharacteristic
50C43×#343C2212yes—
51C43×#343C2212yes—
52C43×#339C2212yes—
53C43×#339C2212yes—
54C43×#339C2212yes—
55C2×#41×C43C2311yescharacteristic
56C22×Q8×C43—21no—
57C2×M16×C43C2312yes—
58C2×M16×C43C2312yes—
59C4⋊Q8×C43—22no—
60C4⋊Q8×C43—22no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43D411yescharacteristic
70C4⋊Q8×C43D411yescharacteristic
71#125×C43—22no—
72#125×C43—22no—
73#125×C43—22no—
74#125×C43—22no—
75#125×C43—21no—
76#125×C43—21no—
77#125×C43—21no—
78#125×C43—21no—
79#125×C43—21no—
80#125×C43—21no—
81#125×C43—21no—
82#125×C43—21no—
83#125×C43D411yescharacteristic
84#125×C43D411yescharacteristic
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C22⋊Q8×C43—22no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43D411yescharacteristic
102C4×Q8×C43D411yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43D411yescharacteristic
110C4×D4×C43D411yescharacteristic
111#117×C43—21no—
112#117×C43—21no—
113#117×C43—21no—
114#117×C43C2311yescharacteristic
115#117×C43C2311yescharacteristic
116#117×C43C2311yescharacteristic
117C2×C4⋊C4×C43—22no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—24no—
123C2×C4⋊C4×C43D412yes—
124C2×C4⋊C4×C43D412yes—
125C2×C4⋊C4×C43C2312yes—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2312yes—
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#107×C43—22no—
133#107×C43—22no—
134#106×C43—22no—
135#106×C43—22no—
136#106×C43—22no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43—21no—
139#104×C43Q818yescomplemented
140#103×C43—22no—
141#102×C43—22no—
142#97×C43—21no—
143C4×C8×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—24no—
147#41×C43—22no—
148#41×C43C2×Q814yes—
149C2×Q8×C43—22no—
150C2×Q8×C43—22no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—41no—
154C2×Q8×C43—41no—
155C2×Q8×C43—82no—
156C2×Q8×C43C2×D411yescharacteristic
157C2×D4×C43—21no—
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D412yes—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171M16×C43—22no—
172M16×C43—24no—
173M16×C43C2×Q814yes—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—84no—
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C4⋊C4×C43C2×D411yescharacteristic
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—21no—
215C22⋊C4×C43—21no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—21no—
218C42×C43—22no—
219C42×C43—22no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—21no—
225C42×C43—22no—
226C42×C43C2×D411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C42×C43C2×D411yescharacteristic
230C42×C43C2×Q814yes—
231C23×C43—21no—
232C23×C43C22×D411yescharacteristic
233Q8×C43—21no—
234Q8×C43—81no—
235Q8×C43—81no—
236Q8×C43—82no—
237Q8×C43—82no—
238Q8×C43—82no—
239Q8×C43—82no—
240Q8×C43C4⋊Q812yes—
241D4×C43—24no—
242D4×C43—21no—
243D4×C43C4⋊Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—24no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—24no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—44no—
262C2×C4×C43—42no—
263C2×C4×C43—81no—
264C2×C4×C43—81no—
265C2×C4×C43—82no—
266C2×C4×C43—82no—
267C2×C4×C43#12011yescharacteristic
268C2×C4×C43#12011yescharacteristic
269C2×C4×C43#12011yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×Q812yes—
274C2×C4×C432−1+412yes—
275C8×C43—24no—
276C8×C43—42no—
277#25833C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—22no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43C2×#12011yescharacteristic
284C22×C43D4×Q812yes—
285C4×C43—22no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—44no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—42no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—82no—
300C4×C43C2×C4⋊Q811yescharacteristic
301C4×C43#53611yescharacteristic
302C4×C43D4×Q812yes—
303#3504C2×C4311yescharacteristic
304#3165C2×C4311yescharacteristic, complemented
305#3079C2×C4311yescharacteristic
306#2660C2×C4311yescharacteristic, complemented
307#2061C2×C4312yescomplemented
308#2060C2×C4312yescomplemented
309#1998C2×C4311yescharacteristic, complemented
310#1995C2×C4311yescharacteristic, complemented
311#1860C2×C4312yes—
312#1859C2×C4312yes—
313#1759C2×C4311yescharacteristic
314C2×C43—22no—
315C2×C43—42no—
316C2×C43#243411yescharacteristic
317C2×C43#302111yescharacteristic
318C2×C43#302211yescharacteristic
319#557—21no—
320#557—21no—
321#554—21no—
322#554—21no—
323#554—22no—
324#554—22no—
325#544—21no—
326#544—21no—
327#544C22×C4311yescharacteristic
328#544C22×C4311yescharacteristic
329#533—21no—
330#533C22×C4311yescharacteristic
331C2×C4⋊Q8C22×C4311yescharacteristic
332C2×#125—21no—
333C2×#125C22×C4311yescharacteristic
334#520C22×C4311yescharacteristic
335#520C22×C4311yescharacteristic
336C4×#41C22×C4311yescharacteristic
337#501—21no—
338#501—21no—
339#500—21no—
340#498—21no—
341#477—21no—
342#476—21no—
343#475—21no—
344#474—21no—
345#428C22×C4312yes—
346#428C22×C4312yes—
347#428C22×C4312yes—
348#423C22×C4311yescharacteristic
349C2×#104C22×C4312yes—
350#417C22×C4312yes—
351C4×M16C22×C4311yescharacteristic
352#398—22no—
353#395—22no—
354#384C22×C4312yes—
355#382C22×C4312yes—
356#376C22×C4311yescharacteristic
357#343C22×C4312yes—
358#343C22×C4312yes—
359#339C22×C4312yes—
360#339C22×C4312yes—
361#339C22×C4312yes—
362C43#2583311yescharacteristic, direct product factor, Sylow
363C2×#41C23×C4311yescharacteristic
364C22×Q8—21no—
365C2×M16C23×C4312yes—
366C2×M16C23×C4312yes—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8D4×C4311yescharacteristic
378C4⋊Q8D4×C4311yescharacteristic
379#125—22no—
380#125—22no—
381#125—22no—
382#125—22no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125—21no—
391#125D4×C4311yescharacteristic
392#125D4×C4311yescharacteristic
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8D4×C4311yescharacteristic
410C4×Q8D4×C4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4D4×C4311yescharacteristic
418C4×D4D4×C4311yescharacteristic
419#117—21no—
420#117—21no—
421#117—21no—
422#117C23×C4311yescharacteristic
423#117C23×C4311yescharacteristic
424#117C23×C4311yescharacteristic
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4D4×C4312yes—
432C2×C4⋊C4D4×C4312yes—
433C2×C4⋊C4C23×C4312yes—
434C2×C4⋊C4C23×C4311yescharacteristic
435C2×C4⋊C4C23×C4311yescharacteristic
436C2×C42—21no—
437C2×C42C23×C4312yes—
438C2×C42C23×C4311yescharacteristic
439#107—22no—
440#107—22no—
441#107—22no—
442#106—22no—
443#106—22no—
444#106—22no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447#104Q8×C4318yescomplemented
448#103—22no—
449#102—22no—
450#97—21no—
451C4×C8—21no—
452#95—21no—
453#95—21no—
454#95—24no—
455#41—22no—
456#41C2×Q8×C4314yes—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—82no—
464C2×Q8C2×D4×C4311yescharacteristic
465C2×D4—21no—
466C2×D4C2×D4×C4311yescharacteristic
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4C2×D4×C4312yes—
475C22×C4C2×D4×C4312yes—
476C22×C4C2×D4×C4311yescharacteristic
477C22×C4C2×D4×C4311yescharacteristic
478C22×C4C24×C4311yescharacteristic
479M16—22no—
480M16—24no—
481M16C2×Q8×C4314yes—
482C2×C8—22no—
483C2×C8—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—84no—
513C4⋊C4C2×D4×C4311yescharacteristic
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C42—22no—
527C42—22no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—22no—
534C42C2×D4×C4311yescharacteristic
535C42C2×D4×C4311yescharacteristic
536C42C2×D4×C4311yescharacteristic
537C42C2×D4×C4311yescharacteristic
538C42C2×Q8×C4314yes—
539C23—21no—
540C23C22×D4×C4311yescharacteristic
541Q8—21no—
542Q8—81no—
543Q8—81no—
544Q8—82no—
545Q8—82no—
546Q8—82no—
547Q8—82no—
548Q8C4⋊Q8×C4312yes—
549D4—24no—
550D4—21no—
551D4C4⋊Q8×C4312yes—
552C2×C4—21no—
553C2×C4—24no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4#120×C4311yescharacteristic
576C2×C4#120×C4311yescharacteristic
577C2×C4#120×C4311yescharacteristic
578C2×C4#120×C4311yescharacteristic
579C2×C4C22×D4×C4311yescharacteristic
580C2×C4C22×D4×C4311yescharacteristic
581C2×C4C22×Q8×C4312yes—
582C2×C42−1+4×C4312yes—
583C8—24no—
584C8—42no—
585C22—21no—
586C22—21no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22C2×#120×C4311yescharacteristic
591C22D4×Q8×C4312yes—
592C4—22no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—44no—
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—82no—
607C4C2×C4⋊Q8×C4311yescharacteristic
608C4C43×#53611yescharacteristic
609C4D4×Q8×C4312yes—
610C2—22no—
611C2—42no—
612C2C43×#243411yescharacteristic
613C2C43×#302111yescharacteristic
614C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#41×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3165C2semidirect
4. C43×#2660C2semidirect
5. C43×#2061C2semidirect
6. C43×#2060C2semidirect
7. C43×#1998C2semidirect
8. C43×#1995C2semidirect
139. #104×C43Q8semidirect
277. #25833C43direct (N × H)
304. #3165C2×C43semidirect
306. #2660C2×C43semidirect
307. #2061C2×C43semidirect
308. #2060C2×C43semidirect
309. #1998C2×C43semidirect
310. #1995C2×C43semidirect
362. C43#25833direct (N × H)
447. #104Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35042
C43×#31652
C43×#30792
C43×#26602
C43×#20612
C43×#20602
C43×#19982
C43×#19952
C43×#18602
C43×#18592
C43×#17592
#2583343