Finite Group Databasebeta

← C43×#25289 #24945306

Subgroups — C43×#25289 #24945306

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#491C211yesmaximal, characteristic, complemented
2C2×C43×#478C211yesmaximal, characteristic
3C43×#2547C211yesmaximal, characteristic
4C43×#2370C211yesmaximal, characteristic, complemented
5C43×#2068C211yesmaximal, characteristic, complemented
6C43×#2066C211yesmaximal, characteristic, complemented
7C43×#2042C211yesmaximal, characteristic
8C43×#2042C211yesmaximal, characteristic
9C43×#1983C211yesmaximal, characteristic
10C43×#1983C211yesmaximal, characteristic
11C43×#1981C211yesmaximal, characteristic, complemented
12C43×#1940C211yesmaximal, characteristic, complemented
13C43×#1928C211yesmaximal, characteristic, complemented
14C43×#1927C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×#124×C43C2211yescharacteristic
19C2×#124×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C43×#491—24no—
22C43×#478—24no—
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×#103×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C43×#397—21no—
42C43×#397—21no—
43C43×#391C2211yescharacteristic
44C43×#391C2211yescharacteristic
45C43×#389—21no—
46C43×#389C2211yescharacteristic
47C43×#389C2211yescharacteristic
48C43×#387—21no—
49C43×#387—21no—
50C43×#380—21no—
51C43×#380—21no—
52C4×C4⋊C4×C43—21no—
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×Q8×C43C2311yescharacteristic
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43—21no—
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C4⋊Q8×C43—22no—
70C4⋊Q8×C43—22no—
71#125×C43—22no—
72#125×C43D414yes—
73#124×C43—22no—
74#124×C43—22no—
75#124×C43—41no—
76#124×C43—41no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101C2×C42×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104#106×C43—22no—
105C4⋊C8×C43—22no—
106C4⋊C8×C43—41no—
107C4⋊C8×C43—41no—
108#103×C43—22no—
109#103×C43—22no—
110#103×C43—22no—
111#103×C43—22no—
112#103×C43—22no—
113#103×C43—22no—
114#103×C43—41no—
115#103×C43—41no—
116#102×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#97×C43—22no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43—42no—
194C4⋊C4×C43—81no—
195C4⋊C4×C43C2×D412yes—
196C4⋊C4×C43C2×D412yes—
197C4⋊C4×C43#4112yes—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43—42no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—42no—
208C42×C43—81no—
209C42×C43—81no—
210C42×C43C2×D412yes—
211C42×C43#4112yes—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—84no—
270C2×C4×C43#12112yes—
271C2×C4×C43#12112yes—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C8×C43—41no—
279C8×C43—41no—
280C8×C43—41no—
281C8×C43—41no—
282#25289C4311yesmaximal, characteristic, direct product factor, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×#12111yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54811yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57711yescharacteristic
296C22×C43#57811yescharacteristic
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43—42no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#52911yescharacteristic
311C4×C43#54211yescharacteristic
312C4×C43#54811yescharacteristic
313C4×C43#55011yescharacteristic
314C2×#491C2×C4311yescharacteristic, complemented
315C2×#478C2×C4311yescharacteristic
316#2547C2×C4311yescharacteristic
317#2370C2×C4311yescharacteristic, complemented
318#2068C2×C4311yescharacteristic, complemented
319#2066C2×C4311yescharacteristic, complemented
320#2042C2×C4311yescharacteristic
321#2042C2×C4311yescharacteristic
322#1983C2×C4311yescharacteristic
323#1983C2×C4311yescharacteristic
324#1981C2×C4311yescharacteristic, complemented
325#1940C2×C4311yescharacteristic, complemented
326#1928C2×C4311yescharacteristic, complemented
327#1927C2×C4311yescharacteristic, complemented
328#1762C2×C4311yescharacteristic
329C2×C43—82no—
330C2×C43#242611yescharacteristic
331C2×C43#304011yescharacteristic
332C2×C43#304611yescharacteristic
333C2×C43#330711yescharacteristic
334C2×C43#331511yescharacteristic
335C2×C43#337611yescharacteristic
336C2×C43#337711yescharacteristic
337C2×C4⋊Q8C22×C4311yescharacteristic
338C2×#125C22×C4311yescharacteristic
339C2×#124C22×C4311yescharacteristic
340C2×#124C22×C4311yescharacteristic
341C2×C4×D4C22×C4311yescharacteristic
342#491—24no—
343#478—24no—
344C2×#107C22×C4311yescharacteristic
345C2×#106C22×C4311yescharacteristic
346C2×C4⋊C8C22×C4311yescharacteristic
347C2×C4⋊C8C22×C4311yescharacteristic
348C2×C4⋊C8C22×C4311yescharacteristic
349C2×#103C22×C4311yescharacteristic
350C2×#103C22×C4311yescharacteristic
351C2×#103C22×C4311yescharacteristic
352C2×#103C22×C4311yescharacteristic
353C2×#103C22×C4311yescharacteristic
354C2×#103C22×C4311yescharacteristic
355C2×#103C22×C4311yescharacteristic
356C2×#103C22×C4311yescharacteristic
357C2×#102C22×C4311yescharacteristic
358C2×#102C22×C4311yescharacteristic
359C2×#102C22×C4311yescharacteristic
360C2×#102C22×C4311yescharacteristic
361C2×#97C22×C4311yescharacteristic
362#397—21no—
363#397—21no—
364#391C22×C4311yescharacteristic
365#391C22×C4311yescharacteristic
366#389—21no—
367#389C22×C4311yescharacteristic
368#389C22×C4311yescharacteristic
369#387—21no—
370#387—21no—
371#380—21no—
372#380—21no—
373C4×C4⋊C4—21no—
374C4×C4⋊C4C22×C4311yescharacteristic
375C4×C4⋊C4C22×C4311yescharacteristic
376C4×C4⋊C4C22×C4311yescharacteristic
377C4×C4⋊C4C22×C4311yescharacteristic
378#340C22×C4311yescharacteristic
379#340C22×C4311yescharacteristic
380#336C22×C4311yescharacteristic
381#336C22×C4311yescharacteristic
382C43#2528911yescharacteristic, direct product factor, Sylow
383C22×Q8C23×C4311yescharacteristic
384C22×Q8C23×C4311yescharacteristic
385C22×D4C23×C4311yescharacteristic
386C23×C4—21no—
387C22×C8C23×C4311yescharacteristic
388C22×C8C23×C4311yescharacteristic
389C22×C8C23×C4311yescharacteristic
390C22×C8C23×C4311yescharacteristic
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393#125—22no—
394#125D4×C4314yes—
395#124—22no—
396#124—22no—
397#124—41no—
398#124—41no—
399C4×D4—22no—
400C4×D4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C4311yescharacteristic
408C2×C4⋊C4D4×C4311yescharacteristic
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C4⋊C4C23×C4311yescharacteristic
412C2×C4⋊C4C23×C4311yescharacteristic
413C2×C4⋊C4C23×C4311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C23×C4311yescharacteristic
423C2×C42C23×C4311yescharacteristic
424C2×C42C23×C4311yescharacteristic
425#107—22no—
426#106—22no—
427C4⋊C8—22no—
428C4⋊C8—41no—
429C4⋊C8—41no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—41no—
437#103—41no—
438#102—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442#97—22no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95D4×C4311yescharacteristic
453#95D4×C4311yescharacteristic
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4#41×C4312yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4C2×D4×C4311yescharacteristic
484C22×C4C2×D4×C4311yescharacteristic
485C22×C4C2×D4×C4311yescharacteristic
486C22×C4C2×D4×C4311yescharacteristic
487C22×C4C2×D4×C4311yescharacteristic
488C22×C4C2×D4×C4311yescharacteristic
489C22×C4C24×C4311yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—81no—
517C4⋊C4C2×D4×C4312yes—
518C4⋊C4C2×D4×C4312yes—
519C4⋊C4#41×C4312yes—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—81no—
531C42—81no—
532C42C2×D4×C4312yes—
533C42#41×C4312yes—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×D4×C4311yescharacteristic
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
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—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—84no—
592C2×C4#121×C4312yes—
593C2×C4#121×C4312yes—
594C2×C4C22×D4×C4311yescharacteristic
595C2×C4C2×#41×C4311yescharacteristic
596C2×C4C2×#41×C4311yescharacteristic
597C2×C4C2×#41×C4311yescharacteristic
598C2×C4H(5,𝔽2)×C4311yescharacteristic
599C2×C42−1+4×C4311yescharacteristic
600C8—41no—
601C8—41no—
602C8—41no—
603C8—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×#121×C4311yescharacteristic
612C22C43×#54611yescharacteristic
613C22C43×#54811yescharacteristic
614C22C43×#57511yescharacteristic
615C22C43×#57511yescharacteristic
616C22C43×#57711yescharacteristic
617C22C43×#57811yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—42no—
622C4—42no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4C43×#52911yescharacteristic
632C4C43×#54211yescharacteristic
633C4C43×#54811yescharacteristic
634C4C43×#55011yescharacteristic
635C2—82no—
636C2C43×#242611yescharacteristic
637C2C43×#304011yescharacteristic
638C2C43×#304611yescharacteristic
639C2C43×#330711yescharacteristic
640C2C43×#331511yescharacteristic
641C2C43×#337611yescharacteristic
642C2C43×#337711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#491C2semidirect
4. C43×#2370C2semidirect
5. C43×#2068C2semidirect
6. C43×#2066C2semidirect
11. C43×#1981C2semidirect
12. C43×#1940C2semidirect
13. C43×#1928C2semidirect
14. C43×#1927C2semidirect
282. #25289C43direct (N × H)
314. C2×#491C2×C43semidirect
317. #2370C2×C43semidirect
318. #2068C2×C43semidirect
319. #2066C2×C43semidirect
324. #1981C2×C43semidirect
325. #1940C2×C43semidirect
326. #1928C2×C43semidirect
327. #1927C2×C43semidirect
382. C43#25289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4912
C2×C43×#4782
C43×#25472
C43×#23702
C43×#20682
C43×#20662
C43×#20422
C43×#19832
C43×#19812
C43×#19402
C43×#19282
C43×#19272
C43×#17622
#2528943