Finite Group Databasebeta

← C43×#27069 #24947086

Subgroups — C43×#27069 #24947086

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2513C211yesmaximal, characteristic
2C43×#2365C211yesmaximal, characteristic, complemented
3C43×#2097C211yesmaximal, characteristic, complemented
4C43×#2055C211yesmaximal, characteristic
5C43×#2043C211yesmaximal, characteristic, complemented
6C43×#2013C211yesmaximal, characteristic
7C43×#1968C211yesmaximal, characteristic
8C43×#1928C211yesmaximal, characteristic, complemented
9C43×#1925C211yesmaximal, characteristic
10C43×#1920C211yesmaximal, characteristic, complemented
11C43×#1916C211yesmaximal, characteristic, complemented
12C43×#1880C211yesmaximal, characteristic
13C43×#1880C211yesmaximal, characteristic
14C43×#1805C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C2×C4⋊Q8×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C2×C4×Q8×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C43×#397—21no—
34C43×#397—21no—
35C43×#391C2211yescharacteristic
36C43×#391C2211yescharacteristic
37C43×#390C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#390C2211yescharacteristic
40C43×#389—21no—
41C43×#389C2211yescharacteristic
42C43×#388—21no—
43C43×#388—21no—
44C43×#387—21no—
45C43×#387—21no—
46C43×#382C2211yescharacteristic
47C4×C4⋊C4×C43—21no—
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×C43C2311yescharacteristic
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C2×SD16×C43—22no—
63C2×SD16×C43—22no—
64C2×SD16×C43—22no—
65C2×SD16×C43—41no—
66C2×SD16×C43—41no—
67C2×SD16×C43—41no—
68C22×C8×C43C2311yescharacteristic
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C4⋊Q8×C43—22no—
73C4⋊Q8×C43—22no—
74C4×Q8×C43—22no—
75C4×Q8×C43—22no—
76C4×Q8×C43—41no—
77C4×Q8×C43—41no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C42×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—41no—
104#106×C43—22no—
105C4⋊C8×C43—41no—
106#103×C43—22no—
107#103×C43—22no—
108#103×C43—22no—
109#103×C43—41no—
110#103×C43—41no—
111#103×C43—41no—
112#102×C43—22no—
113#102×C43—41no—
114C4×C8×C43—41no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43#4112yes—
138C2×Q8×C43#4112yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159SD16×C43—44no—
160SD16×C43—44no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43#4112yes—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43#4112yes—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—81no—
193C22⋊C4×C43—81no—
194C22⋊C4×C43—81no—
195C22⋊C4×C43—81no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—42no—
203C42×C43—42no—
204C42×C43—42no—
205C42×C43—81no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
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#13512yes—
264C2×C4×C43#13712yes—
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C8×C43—22no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275#27069C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43#52511yescharacteristic
284C22×C43#54611yescharacteristic
285C22×C43#55011yescharacteristic
286C22×C43C2×#13511yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57711yescharacteristic
290C4×C43—22no—
291C4×C43—22no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43#52911yescharacteristic
304C4×C43#53811yescharacteristic
305C4×C43#55111yescharacteristic
306C4×C43#55311yescharacteristic
307#2513C2×C4311yescharacteristic
308#2365C2×C4311yescharacteristic, complemented
309#2097C2×C4311yescharacteristic, complemented
310#2055C2×C4311yescharacteristic
311#2043C2×C4311yescharacteristic, complemented
312#2013C2×C4311yescharacteristic
313#1968C2×C4311yescharacteristic
314#1928C2×C4311yescharacteristic, complemented
315#1925C2×C4311yescharacteristic
316#1920C2×C4311yescharacteristic, complemented
317#1916C2×C4311yescharacteristic, complemented
318#1880C2×C4311yescharacteristic
319#1880C2×C4311yescharacteristic
320#1805C2×C4311yescharacteristic, complemented
321C4×#103C2×C4311yescharacteristic, complemented
322C2×C43—161no—
323C2×C43#246711yescharacteristic
324C2×C43#310811yescharacteristic
325C2×C43#312611yescharacteristic
326C2×C43#330311yescharacteristic
327C2×C43#332011yescharacteristic
328C2×C43#339411yescharacteristic
329C2×C43#340011yescharacteristic
330C22×SD16C22×C4311yescharacteristic
331C22×SD16C22×C4311yescharacteristic
332C2×C4⋊Q8C22×C4311yescharacteristic
333C2×C4×Q8C22×C4311yescharacteristic
334C2×C4×Q8C22×C4311yescharacteristic
335C2×#107C22×C4311yescharacteristic
336C2×#106C22×C4311yescharacteristic
337C2×C4⋊C8C22×C4311yescharacteristic
338C2×#103C22×C4311yescharacteristic
339C2×#103C22×C4311yescharacteristic
340C2×#103C22×C4311yescharacteristic
341C2×#103C22×C4311yescharacteristic
342C2×#103C22×C4311yescharacteristic
343C2×#103C22×C4311yescharacteristic
344C2×#102C22×C4311yescharacteristic
345C2×#102C22×C4311yescharacteristic
346C2×C4×C8C22×C4311yescharacteristic
347#397—21no—
348#397—21no—
349#391C22×C4311yescharacteristic
350#391C22×C4311yescharacteristic
351#390C22×C4311yescharacteristic
352#390C22×C4311yescharacteristic
353#390C22×C4311yescharacteristic
354#389—21no—
355#389C22×C4311yescharacteristic
356#388—21no—
357#388—21no—
358#387—21no—
359#387—21no—
360#382C22×C4311yescharacteristic
361C4×C4⋊C4—21no—
362C4×C4⋊C4C22×C4311yescharacteristic
363C4×C4⋊C4C22×C4311yescharacteristic
364C4×C4⋊C4C22×C4311yescharacteristic
365#340C22×C4311yescharacteristic
366#340C22×C4311yescharacteristic
367#340C22×C4311yescharacteristic
368#340C22×C4311yescharacteristic
369#336C22×C4311yescharacteristic
370#336C22×C4311yescharacteristic
371#336C22×C4311yescharacteristic
372#336C22×C4311yescharacteristic
373C43#2706911yescharacteristic, direct product factor, Sylow
374C22×Q8C23×C4311yescharacteristic
375C22×Q8C23×C4311yescharacteristic
376C22×D4C23×C4311yescharacteristic
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—41no—
381C2×SD16—41no—
382C2×SD16—41no—
383C22×C8C23×C4311yescharacteristic
384C22×C8C23×C4311yescharacteristic
385C22×C8C23×C4311yescharacteristic
386C22×C8C23×C4311yescharacteristic
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—41no—
392C4×Q8—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C4311yescharacteristic
399C2×C4⋊C4D4×C4311yescharacteristic
400C2×C4⋊C4C23×C4311yescharacteristic
401C2×C4⋊C4C23×C4311yescharacteristic
402C2×C4⋊C4C23×C4311yescharacteristic
403C2×C4⋊C4C23×C4311yescharacteristic
404C2×C4⋊C4C23×C4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C4311yescharacteristic
416C2×C42C23×C4311yescharacteristic
417C2×C42C23×C4311yescharacteristic
418#107—41no—
419#106—22no—
420C4⋊C8—41no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—41no—
425#103—41no—
426#103—41no—
427#102—22no—
428#102—41no—
429C4×C8—41no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95D4×C4311yescharacteristic
440#95D4×C4311yescharacteristic
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8#41×C4312yes—
453C2×Q8#41×C4312yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4C2×D4×C4311yescharacteristic
468C22×C4C2×D4×C4311yescharacteristic
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4C2×D4×C4311yescharacteristic
471C22×C4C2×D4×C4311yescharacteristic
472C22×C4C2×D4×C4311yescharacteristic
473C22×C4C24×C4311yescharacteristic
474SD16—44no—
475SD16—44no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8#41×C4312yes—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4#41×C4312yes—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—42no—
520C42—81no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4#135×C4312yes—
579C2×C4#137×C4312yes—
580C2×C4C2×#41×C4311yescharacteristic
581C2×C4C2×#41×C4311yescharacteristic
582C2×C4C2×#41×C4311yescharacteristic
583C2×C4C2×#41×C4311yescharacteristic
584C2×C4H(5,𝔽2)×C4311yescharacteristic
585C2×C4H(5,𝔽2)×C4311yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C43×#52511yescharacteristic
598C22C43×#54611yescharacteristic
599C22C43×#55011yescharacteristic
600C22C2×#135×C4311yescharacteristic
601C22C2×#137×C4311yescharacteristic
602C22C43×#57711yescharacteristic
603C22C43×#57711yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4C43×#52911yescharacteristic
618C4C43×#53811yescharacteristic
619C4C43×#55111yescharacteristic
620C4C43×#55311yescharacteristic
621C2—161no—
622C2C43×#246711yescharacteristic
623C2C43×#310811yescharacteristic
624C2C43×#312611yescharacteristic
625C2C43×#330311yescharacteristic
626C2C43×#332011yescharacteristic
627C2C43×#339411yescharacteristic
628C2C43×#340011yescharacteristic
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
2. C43×#2365C2semidirect
3. C43×#2097C2semidirect
5. C43×#2043C2semidirect
8. C43×#1928C2semidirect
10. C43×#1920C2semidirect
11. C43×#1916C2semidirect
14. C43×#1805C2semidirect
15. C4×#103×C43C2semidirect
275. #27069C43direct (N × H)
308. #2365C2×C43semidirect
309. #2097C2×C43semidirect
311. #2043C2×C43semidirect
314. #1928C2×C43semidirect
316. #1920C2×C43semidirect
317. #1916C2×C43semidirect
320. #1805C2×C43semidirect
321. C4×#103C2×C43semidirect
373. C43#27069direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25132
C43×#23652
C43×#20972
C43×#20552
C43×#20432
C43×#20132
C43×#19682
C43×#19282
C43×#19252
C43×#19202
C43×#19162
C43×#18802
C43×#18052
C4×#103×C432
#2706943