Finite Group Databasebeta

← C43×#29101 #24949118

Subgroups — C43×#29101 #24949118

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2512C211yesmaximal, characteristic
2C43×#2451C211yesmaximal, characteristic, complemented
3C43×#2088C211yesmaximal, characteristic, complemented
4C43×#2072C211yesmaximal, characteristic, complemented
5C43×#2055C211yesmaximal, characteristic
6C43×#2023C211yesmaximal, characteristic
7C43×#1990C211yesmaximal, characteristic, complemented
8C43×#1968C211yesmaximal, characteristic
9C43×#1936C211yesmaximal, characteristic
10C43×#1936C211yesmaximal, characteristic
11C43×#1935C211yesmaximal, characteristic, complemented
12C43×#1919C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic
14C43×#1771C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C2×C4⋊Q8×C43C2211yescharacteristic
18C2×#126×C43—21no—
19C2×C4×Q8×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×#103×C43C2211yescharacteristic
23C2×#103×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#398—21no—
32C43×#397—21no—
33C43×#396—21no—
34C43×#395—21no—
35C43×#391—21no—
36C43×#391C2211yescharacteristic
37C43×#391C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#390C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#389C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#388—21no—
45C43×#387—21no—
46C43×#384C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C2×SD16×C43—22no—
63C2×SD16×C43—22no—
64C2×SD16×C43—41no—
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C4⋊Q8×C43—22no—
70C4⋊Q8×C43—41no—
71#126×C43—44no—
72C4×Q8×C43—22no—
73C4×Q8×C43—41no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43D411yescharacteristic
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C22⋊C4×C43—21no—
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×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2311yescharacteristic
99C2×C42×C43C2311yescharacteristic
100#106×C43—22no—
101C4⋊C8×C43—22no—
102#103×C43—22no—
103#103×C43—22no—
104#103×C43—22no—
105#102×C43—22no—
106#102×C43—22no—
107#102×C43—41no—
108#97×C43—22no—
109#97×C43—41no—
110C4×C8×C43—41no—
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×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C24×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—42no—
128C2×Q8×C43—42no—
129C2×Q8×C43—81no—
130C2×Q8×C43#4112yes—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×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×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151SD16×C43—44no—
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—21no—
162C2×C8×C43#4112yes—
163C2×C8×C43#4112yes—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
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—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43#4112yes—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—42no—
189C22⋊C4×C43—81no—
190C22⋊C4×C43—81no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—42no—
198C42×C43—42no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—84no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43AGL(1,ℤ/8)12yes—
254C2×C4×C43#13712yes—
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C8×C43—22no—
262C8×C43—22no—
263C8×C43—41no—
264C8×C43—41no—
265#29101C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43#53211yescharacteristic
274C22×C43#54611yescharacteristic
275C22×C43#54811yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57711yescharacteristic
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#52911yescharacteristic
294C4×C43#53911yescharacteristic
295C4×C43#55111yescharacteristic
296C4×C43#55611yescharacteristic
297#2512C2×C4311yescharacteristic
298#2451C2×C4311yescharacteristic, complemented
299#2088C2×C4311yescharacteristic, complemented
300#2072C2×C4311yescharacteristic, complemented
301#2055C2×C4311yescharacteristic
302#2023C2×C4311yescharacteristic
303#1990C2×C4311yescharacteristic, complemented
304#1968C2×C4311yescharacteristic
305#1936C2×C4311yescharacteristic
306#1936C2×C4311yescharacteristic
307#1935C2×C4311yescharacteristic, complemented
308#1919C2×C4311yescharacteristic, complemented
309#1880C2×C4311yescharacteristic
310#1771C2×C4311yescharacteristic, complemented
311#1763C2×C4311yescharacteristic, complemented
312C2×C43—161no—
313C2×C43#256011yescharacteristic
314C2×C43#317311yescharacteristic
315C2×C43#318211yescharacteristic
316C2×C43#330611yescharacteristic
317C2×C43#332011yescharacteristic
318C2×C43#336811yescharacteristic
319C2×C43#336911yescharacteristic
320C22×SD16C22×C4311yescharacteristic
321C2×C4⋊Q8C22×C4311yescharacteristic
322C2×#126—21no—
323C2×C4×Q8C22×C4311yescharacteristic
324C2×#106C22×C4311yescharacteristic
325C2×C4⋊C8C22×C4311yescharacteristic
326C2×#103C22×C4311yescharacteristic
327C2×#103C22×C4311yescharacteristic
328C2×#103C22×C4311yescharacteristic
329C2×#102C22×C4311yescharacteristic
330C2×#102C22×C4311yescharacteristic
331C2×#102C22×C4311yescharacteristic
332C2×#97C22×C4311yescharacteristic
333C2×#97C22×C4311yescharacteristic
334C2×C4×C8C22×C4311yescharacteristic
335#398—21no—
336#397—21no—
337#396—21no—
338#395—21no—
339#391—21no—
340#391C22×C4311yescharacteristic
341#391C22×C4311yescharacteristic
342#390C22×C4311yescharacteristic
343#390C22×C4311yescharacteristic
344#390C22×C4311yescharacteristic
345#389C22×C4311yescharacteristic
346#389C22×C4311yescharacteristic
347#389C22×C4311yescharacteristic
348#388—21no—
349#387—21no—
350#384C22×C4311yescharacteristic
351C4×C4⋊C4C22×C4311yescharacteristic
352C4×C4⋊C4C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#340C22×C4311yescharacteristic
356#340C22×C4311yescharacteristic
357#340C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#336C22×C4311yescharacteristic
362#336C22×C4311yescharacteristic
363C43#2910111yescharacteristic, direct product factor, Sylow
364C22×Q8—21no—
365C22×Q8C23×C4311yescharacteristic
366C22×D4C23×C4311yescharacteristic
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—41no—
370C22×C8C23×C4311yescharacteristic
371C22×C8C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C22×C8C23×C4311yescharacteristic
374C4⋊Q8—22no—
375C4⋊Q8—41no—
376#126—44no—
377C4×Q8—22no—
378C4×Q8—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C4311yescharacteristic
387C2×C4⋊C4D4×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C4⋊C4C23×C4311yescharacteristic
391C2×C4⋊C4C23×C4311yescharacteristic
392C2×C4⋊C4C23×C4311yescharacteristic
393C2×C4⋊C4C23×C4311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42C23×C4311yescharacteristic
403C2×C42C23×C4311yescharacteristic
404C2×C42C23×C4311yescharacteristic
405#106—22no—
406C4⋊C8—22no—
407#103—22no—
408#103—22no—
409#103—22no—
410#102—22no—
411#102—22no—
412#102—41no—
413#97—22no—
414#97—41no—
415C4×C8—41no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95D4×C4311yescharacteristic
425#95D4×C4311yescharacteristic
426C24—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8#41×C4312yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4C2×D4×C4311yescharacteristic
451C22×C4C2×D4×C4311yescharacteristic
452C22×C4C2×D4×C4311yescharacteristic
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4C24×C4311yescharacteristic
456SD16—44no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8#41×C4312yes—
468C2×C8#41×C4312yes—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4#41×C4312yes—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—81no—
495C22⋊C4—81no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C4311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516Q8—84no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4AGL(1,ℤ/8)×C4312yes—
559C2×C4#137×C4312yes—
560C2×C4C2×#41×C4311yescharacteristic
561C2×C4C2×#41×C4311yescharacteristic
562C2×C4C2×#41×C4311yescharacteristic
563C2×C4C2×#41×C4311yescharacteristic
564C2×C4H(5,𝔽2)×C4311yescharacteristic
565C2×C42−1+4×C4311yescharacteristic
566C8—22no—
567C8—22no—
568C8—41no—
569C8—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C43×#53211yescharacteristic
578C22C43×#54611yescharacteristic
579C22C43×#54811yescharacteristic
580C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
581C22C2×#137×C4311yescharacteristic
582C22C43×#57711yescharacteristic
583C22C43×#57711yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C43×#52911yescharacteristic
598C4C43×#53911yescharacteristic
599C4C43×#55111yescharacteristic
600C4C43×#55611yescharacteristic
601C2—161no—
602C2C43×#256011yescharacteristic
603C2C43×#317311yescharacteristic
604C2C43×#318211yescharacteristic
605C2C43×#330611yescharacteristic
606C2C43×#332011yescharacteristic
607C2C43×#336811yescharacteristic
608C2C43×#336911yescharacteristic
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×#2451C2semidirect
3. C43×#2088C2semidirect
4. C43×#2072C2semidirect
7. C43×#1990C2semidirect
11. C43×#1935C2semidirect
12. C43×#1919C2semidirect
14. C43×#1771C2semidirect
15. C43×#1763C2semidirect
265. #29101C43direct (N × H)
298. #2451C2×C43semidirect
299. #2088C2×C43semidirect
300. #2072C2×C43semidirect
303. #1990C2×C43semidirect
307. #1935C2×C43semidirect
308. #1919C2×C43semidirect
310. #1771C2×C43semidirect
311. #1763C2×C43semidirect
363. C43#29101direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25122
C43×#24512
C43×#20882
C43×#20722
C43×#20552
C43×#20232
C43×#19902
C43×#19682
C43×#19362
C43×#19352
C43×#19192
C43×#18802
C43×#17712
C43×#17632
#2910143