Finite Group Databasebeta

← C43×#25692 #24945709

Subgroups — C43×#25692 #24945709

Order 11008.

976 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3510C211yesmaximal, characteristic
2C43×#3165C211yesmaximal, characteristic, complemented
3C43×#3079C211yesmaximal, characteristic, complemented
4C43×#2640C211yesmaximal, characteristic, complemented
5C43×#2038C212yesmaximal, complemented
6C43×#2037C212yesmaximal
7C43×#1995C211yesmaximal, characteristic, complemented
8C43×#1967C211yesmaximal, characteristic, complemented
9C43×#1857C212yesmaximal, complemented
10C43×#1856C212yesmaximal, complemented
11C43×#1759C211yesmaximal, characteristic, complemented
12C43×#559—21no—
13C43×#559—21no—
14C43×#556—21no—
15C43×#556—21no—
16C43×#551—22no—
17C43×#551—22no—
18C43×#542—21no—
19C43×#542—21no—
20C43×#536C2211yescharacteristic
21C43×#535C2211yescharacteristic
22C43×#533C2211yescharacteristic
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#529—21no—
25C43×#529—21no—
26C2×#124×C43C2211yescharacteristic
27C43×#519C2211yescharacteristic
28C43×#518C2211yescharacteristic
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—
44C2×#101×C43C2212yes—
45C2×#100×C43C2212yes—
46C4×M16×C43C2211yescharacteristic
47C43×#397—22no—
48C43×#393—22no—
49C43×#391C2212yes—
50C43×#390C2212yes—
51C43×#376C2211yescharacteristic
52C43×#339C2212yes—
53C43×#339C2212yes—
54C43×#339C2212yes—
55C2×#41×C43C2311yescharacteristic
56C22×Q8×C43—21no—
57C22×Q8×C43C2311yescharacteristic
58C22×D4×C43C2311yescharacteristic
59C2×M16×C43C2312yes—
60C2×M16×C43C2312yes—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43D411yescharacteristic
67C4⋊Q8×C43D411yescharacteristic
68#127×C43—21no—
69#126×C43—22no—
70#126×C43—22no—
71#126×C43—22no—
72#126×C43—22no—
73#125×C43D411yescharacteristic
74#125×C43D411yescharacteristic
75#124×C43—22no—
76#124×C43—22no—
77#124×C43—21no—
78#124×C43—21no—
79#124×C43—21no—
80#124×C43—21no—
81#124×C43—21no—
82#124×C43—21no—
83#123×C43—22no—
84#123×C43—22no—
85#123×C43—22no—
86#123×C43—22no—
87#123×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#120×C43—22no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43D411yescharacteristic
104C4×Q8×C43D411yescharacteristic
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43—21no—
112C4×D4×C43—21no—
113C4×D4×C43D411yescharacteristic
114C4×D4×C43D411yescharacteristic
115#117×C43—22no—
116#117×C43—22no—
117#117×C43—22no—
118#117×C43—21no—
119#117×C43C2311yescharacteristic
120#117×C43C2311yescharacteristic
121#117×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2312yes—
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—24no—
126C2×C22⋊C4×C43D412yes—
127C2×C22⋊C4×C43D412yes—
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×C43—24no—
140#103×C43—22no—
141#102×C43—22no—
142#101×C43—24no—
143#100×C43—24no—
144#97×C43—21no—
145C4×C8×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—24no—
149C24×C43C2×D412yes—
150#41×C43—22no—
151#41×C43—22no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—22no—
157C2×Q8×C43—22no—
158C2×Q8×C43—41no—
159C2×Q8×C43—41no—
160C2×Q8×C43—82no—
161C2×Q8×C43C2×D411yescharacteristic
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—21no—
169C2×D4×C43C2×D411yescharacteristic
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43C2×D412yes—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181M16×C43—22no—
182M16×C43—22no—
183M16×C43—22no—
184M16×C43#4114yes—
185C2×C8×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
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—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D411yescharacteristic
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—21no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—21no—
224C22⋊C4×C43—84no—
225C42×C43—22no—
226C42×C43—22no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—22no—
233C42×C43—22no—
234C42×C43C2×D411yescharacteristic
235C42×C43C2×D411yescharacteristic
236C42×C43C2×D411yescharacteristic
237C42×C43C2×D411yescharacteristic
238C23×C43—22no—
239C23×C43—21no—
240C23×C43—24no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43C22×D411yescharacteristic
244Q8×C43—21no—
245Q8×C43—21no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—42no—
249Q8×C43—81no—
250Q8×C43—81no—
251Q8×C43—82no—
252Q8×C43—82no—
253D4×C43—21no—
254D4×C43—21no—
255D4×C43—42no—
256D4×C43—41no—
257D4×C43—41no—
258D4×C43—42no—
259D4×C43—82no—
260D4×C43—82no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—24no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—44no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—81no—
279C2×C4×C43—81no—
280C2×C4×C43—82no—
281C2×C4×C43—82no—
282C2×C4×C43#12011yescharacteristic
283C2×C4×C43#12011yescharacteristic
284C2×C4×C43#12011yescharacteristic
285C2×C4×C43#12011yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4112yes—
289C2×C4×C432−1+412yes—
290C8×C43—24no—
291C8×C43—42no—
292#25692C4311yesmaximal, characteristic, direct product factor, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—42no—
296C22×C43—41no—
297C22×C43—42no—
298C22×C43—41no—
299C22×C43—42no—
300C22×C43—41no—
301C22×C43—84no—
302C22×C43C2×#12011yescharacteristic
303C22×C43#54712yes—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—82no—
317C4×C43—82no—
318C4×C43#53211yescharacteristic
319C4×C43#53611yescharacteristic
320C4×C43#54812yes—
321#3510C2×C4311yescharacteristic
322#3165C2×C4311yescharacteristic, complemented
323#3079C2×C4311yescharacteristic, complemented
324#2640C2×C4311yescharacteristic, complemented
325#2038C2×C4312yescomplemented
326#2037C2×C4312yes—
327#1995C2×C4311yescharacteristic, complemented
328#1967C2×C4311yescharacteristic, complemented
329#1857C2×C4312yescomplemented
330#1856C2×C4312yescomplemented
331#1759C2×C4311yescharacteristic, complemented
332C2×C43—22no—
333C2×C43—81no—
334C2×C43—82no—
335C2×C43#243211yescharacteristic
336C2×C43#302111yescharacteristic
337C2×C43#302211yescharacteristic
338#559—21no—
339#559—21no—
340#556—21no—
341#556—21no—
342#551—22no—
343#551—22no—
344#542—21no—
345#542—21no—
346#536C22×C4311yescharacteristic
347#535C22×C4311yescharacteristic
348#533C22×C4311yescharacteristic
349C2×C4⋊Q8C22×C4311yescharacteristic
350#529—21no—
351#529—21no—
352C2×#124C22×C4311yescharacteristic
353#519C22×C4311yescharacteristic
354#518C22×C4311yescharacteristic
355C4×#41C22×C4311yescharacteristic
356#501—21no—
357#501—21no—
358#500—21no—
359#498—21no—
360#477—21no—
361#476—21no—
362#475—21no—
363#474—21no—
364#428C22×C4312yes—
365#428C22×C4312yes—
366#428C22×C4312yes—
367#423C22×C4311yescharacteristic
368C2×#104C22×C4312yes—
369#417C22×C4312yes—
370C2×#101C22×C4312yes—
371C2×#100C22×C4312yes—
372C4×M16C22×C4311yescharacteristic
373#397—22no—
374#393—22no—
375#391C22×C4312yes—
376#390C22×C4312yes—
377#376C22×C4311yescharacteristic
378#339C22×C4312yes—
379#339C22×C4312yes—
380#339C22×C4312yes—
381C43#2569211yescharacteristic, direct product factor, Sylow
382C2×#41C23×C4311yescharacteristic
383C22×Q8—21no—
384C22×Q8C23×C4311yescharacteristic
385C22×D4C23×C4311yescharacteristic
386C2×M16C23×C4312yes—
387C2×M16C23×C4312yes—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8D4×C4311yescharacteristic
394C4⋊Q8D4×C4311yescharacteristic
395#127—21no—
396#126—22no—
397#126—22no—
398#126—22no—
399#126—22no—
400#125D4×C4311yescharacteristic
401#125D4×C4311yescharacteristic
402#124—22no—
403#124—22no—
404#124—21no—
405#124—21no—
406#124—21no—
407#124—21no—
408#124—21no—
409#124—21no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421#121—21no—
422#121—21no—
423#120—22no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8D4×C4311yescharacteristic
431C4×Q8D4×C4311yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4D4×C4311yescharacteristic
441C4×D4D4×C4311yescharacteristic
442#117—22no—
443#117—22no—
444#117—22no—
445#117—21no—
446#117C23×C4311yescharacteristic
447#117C23×C4311yescharacteristic
448#117C23×C4311yescharacteristic
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C4312yes—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4D4×C4312yes—
454C2×C22⋊C4D4×C4312yes—
455C2×C42—21no—
456C2×C42C23×C4312yes—
457C2×C42C23×C4311yescharacteristic
458#107—22no—
459#107—22no—
460#107—22no—
461#106—22no—
462#106—22no—
463#106—22no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466#104—24no—
467#103—22no—
468#102—22no—
469#101—24no—
470#100—24no—
471#97—21no—
472C4×C8—21no—
473#95—21no—
474#95—21no—
475#95—24no—
476C24C2×D4×C4312yes—
477#41—22no—
478#41—22no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—82no—
488C2×Q8C2×D4×C4311yescharacteristic
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4C2×D4×C4311yescharacteristic
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4C2×D4×C4312yes—
505C22×C4C2×D4×C4311yescharacteristic
506C22×C4C2×D4×C4311yescharacteristic
507C22×C4C24×C4311yescharacteristic
508M16—22no—
509M16—22no—
510M16—22no—
511M16#41×C4314yes—
512C2×C8—22no—
513C2×C8—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C4311yescharacteristic
531C4⋊C4C2×D4×C4311yescharacteristic
532C4⋊C4C2×D4×C4311yescharacteristic
533C4⋊C4C2×D4×C4311yescharacteristic
534C4⋊C4C2×D4×C4311yescharacteristic
535C4⋊C4C2×D4×C4311yescharacteristic
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—84no—
552C42—22no—
553C42—22no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—22no—
560C42—22no—
561C42C2×D4×C4311yescharacteristic
562C42C2×D4×C4311yescharacteristic
563C42C2×D4×C4311yescharacteristic
564C42C2×D4×C4311yescharacteristic
565C23—22no—
566C23—21no—
567C23—24no—
568C23—42no—
569C23—42no—
570C23C22×D4×C4311yescharacteristic
571Q8—21no—
572Q8—21no—
573Q8—41no—
574Q8—41no—
575Q8—42no—
576Q8—81no—
577Q8—81no—
578Q8—82no—
579Q8—82no—
580D4—21no—
581D4—21no—
582D4—42no—
583D4—41no—
584D4—41no—
585D4—42no—
586D4—82no—
587D4—82no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—24no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4#120×C4311yescharacteristic
610C2×C4#120×C4311yescharacteristic
611C2×C4#120×C4311yescharacteristic
612C2×C4#120×C4311yescharacteristic
613C2×C4C22×D4×C4311yescharacteristic
614C2×C4C22×D4×C4311yescharacteristic
615C2×C4C2×#41×C4312yes—
616C2×C42−1+4×C4312yes—
617C8—24no—
618C8—42no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—84no—
628C22C2×#120×C4311yescharacteristic
629C22C43×#54712yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—82no—
643C4—82no—
644C4C43×#53211yescharacteristic
645C4C43×#53611yescharacteristic
646C4C43×#54812yes—
647C2—22no—
648C2—82no—
649C2—81no—
650C2C43×#243211yescharacteristic
651C2C43×#302111yescharacteristic
652C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#535C22
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
3. C43×#3079C2semidirect
4. C43×#2640C2semidirect
5. C43×#2038C2semidirect
7. C43×#1995C2semidirect
8. C43×#1967C2semidirect
9. C43×#1857C2semidirect
10. C43×#1856C2semidirect
11. C43×#1759C2semidirect
292. #25692C43direct (N × H)
322. #3165C2×C43semidirect
323. #3079C2×C43semidirect
324. #2640C2×C43semidirect
325. #2038C2×C43semidirect
327. #1995C2×C43semidirect
328. #1967C2×C43semidirect
329. #1857C2×C43semidirect
330. #1856C2×C43semidirect
331. #1759C2×C43semidirect
381. C43#25692direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35102
C43×#31652
C43×#30792
C43×#26402
C43×#20382
C43×#20372
C43×#19952
C43×#19672
C43×#18572
C43×#18562
C43×#17592
#2569243