Finite Group Databasebeta

← C43×#26327 #24946344

Subgroups — C43×#26327 #24946344

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2592C211yesmaximal, characteristic
2C43×#2355C211yesmaximal, characteristic, complemented
3C43×#2097C211yesmaximal, characteristic, complemented
4C43×#2094C211yesmaximal, characteristic
5C43×#2073C211yesmaximal, characteristic
6C43×#2072C211yesmaximal, characteristic, complemented
7C43×#1984C211yesmaximal, characteristic, complemented
8C43×#1983C211yesmaximal, characteristic
9C43×#1958C211yesmaximal, characteristic
10C43×#1949C211yesmaximal, characteristic, complemented
11C43×#1927C211yesmaximal, characteristic, complemented
12C43×#1927C211yesmaximal, characteristic, complemented
13C43×#1926C211yesmaximal, characteristic
14C43×#1925C211yesmaximal, characteristic
15C4×#106×C43C211yesmaximal, characteristic, complemented
16C2×#124×C43C2211yescharacteristic
17C2×C4×Q8×C43C2211yescharacteristic
18C2×#107×C43C2211yescharacteristic
19C2×#106×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×#103×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×#397—21no—
33C43×#393—21no—
34C43×#391—21no—
35C43×#391C2211yescharacteristic
36C43×#391C2211yescharacteristic
37C43×#390C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C43×#387—21no—
42C43×#387—21no—
43C43×#384C2211yescharacteristic
44C43×#382C2211yescharacteristic
45C43×#382C2211yescharacteristic
46C4×C4⋊C4×C43—21no—
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C4×C4⋊C4×C43C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43D411yescharacteristic
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66#124×C43—22no—
67#124×C43—22no—
68C4×Q8×C43—22no—
69C4×Q8×C43—22no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C4⋊C4×C43C2311yescharacteristic
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43C2311yescharacteristic
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2311yescharacteristic
94#107×C43—41no—
95#106×C43—22no—
96#106×C43—22no—
97#106×C43—41no—
98C4⋊C8×C43—22no—
99#103×C43—22no—
100#103×C43—22no—
101#103×C43—41no—
102#103×C43—41no—
103#102×C43—22no—
104#102×C43—22no—
105#102×C43—41no—
106#102×C43—41no—
107C4×C8×C43—22no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120C24×C43—21no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—41no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43#4112yes—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43#4112yes—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—42no—
190C42×C43—81no—
191C42×C43—81no—
192C42×C43—81no—
193C42×C43#4112yes—
194C42×C43#4112yes—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—44no—
204Q8×C43—41no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—41no—
208D4×C43—41no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43#12312yes—
249C2×C4×C43#12312yes—
250C2×C4×C43#13512yes—
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C8×C43—22no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261#26327C4311yesmaximal, characteristic, direct product factor, Sylow
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12311yescharacteristic
270C22×C43#54811yescharacteristic
271C22×C43#55011yescharacteristic
272C22×C43C2×#13511yescharacteristic
273C22×C43#57511yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57711yescharacteristic
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#52911yescharacteristic
290C4×C43#54211yescharacteristic
291C4×C43#55611yescharacteristic
292C4×C43#55911yescharacteristic
293#2592C2×C4311yescharacteristic
294#2355C2×C4311yescharacteristic, complemented
295#2097C2×C4311yescharacteristic, complemented
296#2094C2×C4311yescharacteristic
297#2073C2×C4311yescharacteristic
298#2072C2×C4311yescharacteristic, complemented
299#1984C2×C4311yescharacteristic, complemented
300#1983C2×C4311yescharacteristic
301#1958C2×C4311yescharacteristic
302#1949C2×C4311yescharacteristic, complemented
303#1927C2×C4311yescharacteristic, complemented
304#1927C2×C4311yescharacteristic, complemented
305#1926C2×C4311yescharacteristic
306#1925C2×C4311yescharacteristic
307C4×#106C2×C4311yescharacteristic, complemented
308C2×C43—161no—
309C2×C43#244811yescharacteristic
310C2×C43#309111yescharacteristic
311C2×C43#309911yescharacteristic
312C2×C43#336011yescharacteristic
313C2×C43#337111yescharacteristic
314C2×C43#339411yescharacteristic
315C2×C43#340111yescharacteristic
316C2×#124C22×C4311yescharacteristic
317C2×C4×Q8C22×C4311yescharacteristic
318C2×#107C22×C4311yescharacteristic
319C2×#106C22×C4311yescharacteristic
320C2×#106C22×C4311yescharacteristic
321C2×#106C22×C4311yescharacteristic
322C2×C4⋊C8C22×C4311yescharacteristic
323C2×#103C22×C4311yescharacteristic
324C2×#103C22×C4311yescharacteristic
325C2×#103C22×C4311yescharacteristic
326C2×#103C22×C4311yescharacteristic
327C2×#102C22×C4311yescharacteristic
328C2×#102C22×C4311yescharacteristic
329C2×#102C22×C4311yescharacteristic
330C2×#102C22×C4311yescharacteristic
331C2×C4×C8C22×C4311yescharacteristic
332#397—21no—
333#393—21no—
334#391—21no—
335#391C22×C4311yescharacteristic
336#391C22×C4311yescharacteristic
337#390C22×C4311yescharacteristic
338#390C22×C4311yescharacteristic
339#388—21no—
340#388—21no—
341#387—21no—
342#387—21no—
343#384C22×C4311yescharacteristic
344#382C22×C4311yescharacteristic
345#382C22×C4311yescharacteristic
346C4×C4⋊C4—21no—
347C4×C4⋊C4C22×C4311yescharacteristic
348C4×C4⋊C4C22×C4311yescharacteristic
349C4×C4⋊C4C22×C4311yescharacteristic
350C4×C4⋊C4C22×C4311yescharacteristic
351#340C22×C4311yescharacteristic
352#340C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#336C22×C4311yescharacteristic
356#336C22×C4311yescharacteristic
357#336C22×C4311yescharacteristic
358#336C22×C4311yescharacteristic
359C43#2632711yescharacteristic, direct product factor, Sylow
360C22×Q8D4×C4311yescharacteristic
361C22×Q8C23×C4311yescharacteristic
362C22×D4C23×C4311yescharacteristic
363C22×C8C23×C4311yescharacteristic
364C22×C8C23×C4311yescharacteristic
365C22×C8C23×C4311yescharacteristic
366C22×C8C23×C4311yescharacteristic
367#124—22no—
368#124—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C4311yescharacteristic
374C2×C4⋊C4D4×C4311yescharacteristic
375C2×C4⋊C4D4×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C4⋊C4C23×C4311yescharacteristic
379C2×C4⋊C4C23×C4311yescharacteristic
380C2×C4⋊C4C23×C4311yescharacteristic
381C2×C4⋊C4C23×C4311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C4311yescharacteristic
393C2×C42C23×C4311yescharacteristic
394C2×C42C23×C4311yescharacteristic
395#107—41no—
396#106—22no—
397#106—22no—
398#106—41no—
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—41no—
403#103—41no—
404#102—22no—
405#102—22no—
406#102—41no—
407#102—41no—
408C4×C8—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C24—21no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4C24×C4311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8#41×C4312yes—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4#41×C4312yes—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C42—81no—
494C42#41×C4312yes—
495C42#41×C4312yes—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×D4×C4311yescharacteristic
504Q8—44no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4#123×C4312yes—
550C2×C4#123×C4312yes—
551C2×C4#135×C4312yes—
552C2×C4C2×#41×C4311yescharacteristic
553C2×C4C2×#41×C4311yescharacteristic
554C2×C4C2×#41×C4311yescharacteristic
555C2×C4C2×#41×C4311yescharacteristic
556C2×C4H(5,𝔽2)×C4311yescharacteristic
557C2×C42−1+4×C4311yescharacteristic
558C8—22no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×#123×C4311yescharacteristic
570C22C43×#54811yescharacteristic
571C22C43×#55011yescharacteristic
572C22C2×#135×C4311yescharacteristic
573C22C43×#57511yescharacteristic
574C22C43×#57711yescharacteristic
575C22C43×#57711yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C43×#52911yescharacteristic
590C4C43×#54211yescharacteristic
591C4C43×#55611yescharacteristic
592C4C43×#55911yescharacteristic
593C2—161no—
594C2C43×#244811yescharacteristic
595C2C43×#309111yescharacteristic
596C2C43×#309911yescharacteristic
597C2C43×#336011yescharacteristic
598C2C43×#337111yescharacteristic
599C2C43×#339411yescharacteristic
600C2C43×#340111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2355C2semidirect
3. C43×#2097C2semidirect
6. C43×#2072C2semidirect
7. C43×#1984C2semidirect
10. C43×#1949C2semidirect
11. C43×#1927C2semidirect
12. C43×#1927C2semidirect
15. C4×#106×C43C2semidirect
261. #26327C43direct (N × H)
294. #2355C2×C43semidirect
295. #2097C2×C43semidirect
298. #2072C2×C43semidirect
299. #1984C2×C43semidirect
302. #1949C2×C43semidirect
303. #1927C2×C43semidirect
304. #1927C2×C43semidirect
307. C4×#106C2×C43semidirect
359. C43#26327direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25922
C43×#23552
C43×#20972
C43×#20942
C43×#20732
C43×#20722
C43×#19842
C43×#19832
C43×#19582
C43×#19492
C43×#19272
C43×#19262
C43×#19252
C4×#106×C432
#2632743