Finite Group Databasebeta

← C43×#28781 #24948798

Subgroups — C43×#28781 #24948798

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2441C211yesmaximal, characteristic
2C43×#2440C211yesmaximal, characteristic
3C43×#2084C211yesmaximal, characteristic, complemented
4C43×#2083C211yesmaximal, characteristic, complemented
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2057C211yesmaximal, characteristic, complemented
7C43×#1992C211yesmaximal, characteristic, complemented
8C43×#1990C211yesmaximal, characteristic, complemented
9C43×#1943C211yesmaximal, characteristic, complemented
10C43×#1942C211yesmaximal, characteristic, complemented
11C43×#1854C211yesmaximal, characteristic
12C43×#1852C211yesmaximal, characteristic
13C43×#1809C211yesmaximal, characteristic
14C43×#1753C211yesmaximal, characteristic
15C43×#1736C211yesmaximal, characteristic
16C22×M16×C43C2211yescharacteristic
17C2×C4⋊Q8×C43C2211yescharacteristic
18C2×#125×C43C2211yescharacteristic
19C2×C22⋊Q8×C43—21no—
20C2×#117×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#399—21no—
32C43×#398—21no—
33C43×#396—21no—
34C43×#395—21no—
35C43×#389—21no—
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#387—21no—
41C43×#385—21no—
42C43×#384C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C4×C22⋊C4×C43C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C2×M16×C43—41no—
63C2×M16×C43—41no—
64C2×M16×C43Q814yescomplemented
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C4⋊Q8×C43—22no—
70C4⋊Q8×C43—41no—
71#125×C43—22no—
72#125×C43—41no—
73C22⋊Q8×C43—44no—
74#117×C43—22no—
75#117×C43—41no—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43—21no—
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×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—41no—
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43D411yescharacteristic
103C2×C42×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C2×C42×C43C2311yescharacteristic
106#107×C43—22no—
107#107×C43—22no—
108#107×C43—41no—
109#107×C43—41no—
110#106×C43—41no—
111#106×C43—41no—
112C22⋊C8×C43Q814yescomplemented
113#97×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×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123C24×C43C2×D411yescharacteristic
124C2×Q8×C43—42no—
125C2×Q8×C43—42no—
126C2×Q8×C43—81no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43—81no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×Q812yes—
148C22×C4×C43C2×Q812yes—
149C22×C4×C43C2411yescharacteristic
150M16×C43—44no—
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×C43C2×Q812yes—
160C2×C8×C43C2×Q812yes—
161C2×C8×C43C2×Q812yes—
162C2×C8×C43C2×Q812yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
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—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—81no—
187C4⋊C4×C43—81no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43#4112yes—
190C4⋊C4×C43#4112yes—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—42no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43C4⋊Q812yes—
208C23×C43C22×D411yescharacteristic
209Q8×C43—84no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
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—41no—
249C2×C4×C43—41no—
250C2×C4×C43—84no—
251C2×C4×C43C4⋊Q812yes—
252C2×C4×C43AGL(1,ℤ/8)12yes—
253C2×C4×C43#13712yes—
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C8×C43—22no—
261C8×C43—22no—
262C8×C43—22no—
263C8×C43—22no—
264#28781C4311yesmaximal, characteristic, direct product factor, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×C4⋊Q811yescharacteristic
273C22×C43#54611yescharacteristic
274C22×C43#54611yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57611yescharacteristic
278C22×C43#57811yescharacteristic
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#53311yescharacteristic
293C4×C43#54311yescharacteristic
294C4×C43#55411yescharacteristic
295C4×C43#55411yescharacteristic
296#2441C2×C4311yescharacteristic
297#2440C2×C4311yescharacteristic
298#2084C2×C4311yescharacteristic, complemented
299#2083C2×C4311yescharacteristic, complemented
300#2059C2×C4311yescharacteristic, complemented
301#2057C2×C4311yescharacteristic, complemented
302#1992C2×C4311yescharacteristic, complemented
303#1990C2×C4311yescharacteristic, complemented
304#1943C2×C4311yescharacteristic, complemented
305#1942C2×C4311yescharacteristic, complemented
306#1854C2×C4311yescharacteristic
307#1852C2×C4311yescharacteristic
308#1809C2×C4311yescharacteristic
309#1753C2×C4311yescharacteristic
310#1736C2×C4311yescharacteristic
311C2×C43—42no—
312C2×C43#254911yescharacteristic
313C2×C43#316411yescharacteristic
314C2×C43#316511yescharacteristic
315C2×C43#331211yescharacteristic
316C2×C43#331811yescharacteristic
317C2×C43#333011yescharacteristic
318C2×C43#333311yescharacteristic
319C22×M16C22×C4311yescharacteristic
320C2×C4⋊Q8C22×C4311yescharacteristic
321C2×#125C22×C4311yescharacteristic
322C2×C22⋊Q8—21no—
323C2×#117C22×C4311yescharacteristic
324C22×C4⋊C4C22×C4311yescharacteristic
325C2×#107C22×C4311yescharacteristic
326C2×#107C22×C4311yescharacteristic
327C2×#107C22×C4311yescharacteristic
328C2×#107C22×C4311yescharacteristic
329C2×#106C22×C4311yescharacteristic
330C2×#106C22×C4311yescharacteristic
331C2×C22⋊C8C22×C4311yescharacteristic
332C2×#97C22×C4311yescharacteristic
333C2×C4×C8C22×C4311yescharacteristic
334#399—21no—
335#398—21no—
336#396—21no—
337#395—21no—
338#389—21no—
339#389C22×C4311yescharacteristic
340#389C22×C4311yescharacteristic
341#389C22×C4311yescharacteristic
342#389C22×C4311yescharacteristic
343#387—21no—
344#385—21no—
345#384C22×C4311yescharacteristic
346#384C22×C4311yescharacteristic
347#380C22×C4311yescharacteristic
348#380C22×C4311yescharacteristic
349C4×C22⋊C4C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#340C22×C4311yescharacteristic
352#340C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#340C22×C4311yescharacteristic
356#340C22×C4311yescharacteristic
357#340C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#336C22×C4311yescharacteristic
361#336C22×C4311yescharacteristic
362C43#2878111yescharacteristic, direct product factor, Sylow
363C22×Q8—21no—
364C23×C4—21no—
365C23×C4C23×C4311yescharacteristic
366C2×M16—41no—
367C2×M16—41no—
368C2×M16Q8×C4314yescomplemented
369C22×C8C23×C4311yescharacteristic
370C22×C8C23×C4311yescharacteristic
371C22×C8C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C4⋊Q8—22no—
374C4⋊Q8—41no—
375#125—22no—
376#125—41no—
377C22⋊Q8—44no—
378#117—22no—
379#117—41no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4C23×C4311yescharacteristic
395C2×C4⋊C4C23×C4311yescharacteristic
396C2×C4⋊C4C23×C4311yescharacteristic
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C4⋊C4C23×C4311yescharacteristic
401C2×C4⋊C4C23×C4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4D4×C4311yescharacteristic
406C2×C22⋊C4D4×C4311yescharacteristic
407C2×C42—21no—
408C2×C42C23×C4311yescharacteristic
409C2×C42C23×C4311yescharacteristic
410#107—22no—
411#107—22no—
412#107—41no—
413#107—41no—
414#106—41no—
415#106—41no—
416C22⋊C8Q8×C4314yescomplemented
417#97—41no—
418C4×C8—41no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95D4×C4311yescharacteristic
426#95D4×C4311yescharacteristic
427C24C2×D4×C4311yescharacteristic
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—81no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—81no—
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4C2×D4×C4311yescharacteristic
451C22×C4C2×Q8×C4312yes—
452C22×C4C2×Q8×C4312yes—
453C22×C4C24×C4311yescharacteristic
454M16—44no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8C2×Q8×C4312yes—
464C2×C8C2×Q8×C4312yes—
465C2×C8C2×Q8×C4312yes—
466C2×C8C2×Q8×C4312yes—
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—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4#41×C4312yes—
494C4⋊C4#41×C4312yes—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4⋊Q8×C4312yes—
512C23C22×D4×C4311yescharacteristic
513Q8—84no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
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—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—84no—
555C2×C4C4⋊Q8×C4312yes—
556C2×C4AGL(1,ℤ/8)×C4312yes—
557C2×C4#137×C4312yes—
558C2×C4C22×Q8×C4311yescharacteristic
559C2×C4C22×Q8×C4311yescharacteristic
560C2×C4C2×#41×C4311yescharacteristic
561C2×C4C2×#41×C4311yescharacteristic
562C2×C4H(5,𝔽2)×C4311yescharacteristic
563C2×C4H(5,𝔽2)×C4311yescharacteristic
564C8—22no—
565C8—22no—
566C8—22no—
567C8—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×C4⋊Q8×C4311yescharacteristic
576C22C43×#54611yescharacteristic
577C22C43×#54611yescharacteristic
578C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
579C22C2×#137×C4311yescharacteristic
580C22C43×#57611yescharacteristic
581C22C43×#57811yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C43×#53311yescharacteristic
596C4C43×#54311yescharacteristic
597C4C43×#55411yescharacteristic
598C4C43×#55411yescharacteristic
599C2—42no—
600C2C43×#254911yescharacteristic
601C2C43×#316411yescharacteristic
602C2C43×#316511yescharacteristic
603C2C43×#331211yescharacteristic
604C2C43×#331811yescharacteristic
605C2C43×#333011yescharacteristic
606C2C43×#333311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2084C2semidirect
4. C43×#2083C2semidirect
5. C43×#2059C2semidirect
6. C43×#2057C2semidirect
7. C43×#1992C2semidirect
8. C43×#1990C2semidirect
9. C43×#1943C2semidirect
10. C43×#1942C2semidirect
64. C2×M16×C43Q8semidirect
112. C22⋊C8×C43Q8semidirect
264. #28781C43direct (N × H)
298. #2084C2×C43semidirect
299. #2083C2×C43semidirect
300. #2059C2×C43semidirect
301. #2057C2×C43semidirect
302. #1992C2×C43semidirect
303. #1990C2×C43semidirect
304. #1943C2×C43semidirect
305. #1942C2×C43semidirect
362. C43#28781direct (N × H)
368. C2×M16Q8×C43semidirect
416. C22⋊C8Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#24412
C43×#24402
C43×#20842
C43×#20832
C43×#20592
C43×#20572
C43×#19922
C43×#19902
C43×#19432
C43×#19422
C43×#18542
C43×#18522
C43×#18092
C43×#17532
C43×#17362
#2878143