Finite Group Databasebeta

← C43×#19552 #24939569

Subgroups — C43×#19552 #24939569

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3254C211yesmaximal, characteristic, complemented
2C43×#3208C211yesmaximal, characteristic, complemented
3C43×#3205C211yesmaximal, characteristic
4C43×#2979C211yesmaximal, characteristic, complemented
5C43×#1701C212yesmaximal, complemented
6C43×#1685C212yesmaximal, complemented
7C43×#1681C212yesmaximal, complemented
8C43×#1665C212yesmaximal, complemented
9C43×#1574C211yesmaximal, characteristic, complemented
10C43×#1545C211yesmaximal, characteristic, complemented
11C43×#1544C211yesmaximal, characteristic, complemented
12C43×#533C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C2×#127×C43C2211yescharacteristic
15C43×#493—21no—
16C43×#492C2212yes—
17C43×#486—21no—
18C43×#486C2212yes—
19C43×#477—21no—
20C43×#474C2212yescomplemented
21C43×#468—22no—
22C43×#461C2212yescomplemented
23C43×#460—21no—
24C43×#460—21no—
25C43×#460—21no—
26C43×#459C2212yes—
27C43×#459C2212yes—
28C43×#450—22no—
29C43×#447—22no—
30C43×#436—21no—
31C43×#436C2212yescomplemented
32C8×D4×C43—21no—
33C8×D4×C43C2212yescomplemented
34C43×#431C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#431C2211yescharacteristic
37C43×#423C2211yescharacteristic
38C43×#408—22no—
39C43×#335C2212yescomplemented
40C43×#334C2212yescomplemented
41C43×#332C2211yescharacteristic, complemented
42C43×#332C2211yescharacteristic, complemented
43C43×#332C2211yescharacteristic, complemented
44C43×#332C2211yescharacteristic, complemented
45C43×#331C2212yes—
46C43×#331C2212yes—
47C2×#41×C43—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C2×SD16×C43—22no—
52C2×SD16×C43—22no—
53C2×SD16×C43—22no—
54C2×D8×C43—22no—
55C2×D8×C43—22no—
56C2×M16×C43—21no—
57C2×M16×C43—22no—
58C22×C8×C43—22no—
59C4⋊Q8×C43D411yescharacteristic
60C4⋊Q8×C43C2311yescharacteristic
61C4⋊Q8×C43C2311yescharacteristic
62#127×C43—21no—
63#127×C43—21no—
64#127×C43—21no—
65#127×C43D411yescharacteristic
66#127×C43C2312yes—
67#125×C43—21no—
68#124×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71#121×C43—21no—
72#121×C43D412yes—
73C4×Q8×C43—21no—
74C4×Q8×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43C2312yes—
77#117×C43—21no—
78C2×C42×C43C2311yescharacteristic
79#107×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C4⋊C8×C43C2311yescharacteristic
84C4⋊C8×C43C2311yescharacteristic
85C4⋊C8×C43C2312yes—
86C4⋊C8×C43C2311yescharacteristic
87C4⋊C8×C43C2311yescharacteristic
88#103×C43—22no—
89#102×C43—22no—
90#102×C43—22no—
91#102×C43—22no—
92#102×C43—22no—
93#102×C43—22no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96C22⋊C8×C43—22no—
97C22⋊C8×C43—22no—
98C22⋊C8×C43D412yes—
99C4×C8×C43—21no—
100C4×C8×C43—21no—
101C4×C8×C43C2312yes—
102C24×C43—41no—
103#41×C43—81no—
104#41×C43—81no—
105C2×Q8×C43—21no—
106C2×Q8×C43—21no—
107C2×Q8×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—81no—
118C2×D4×C43—81no—
119C2×D4×C43—81no—
120C2×D4×C43—81no—
121C2×D4×C43—82no—
122C2×D4×C43C2×D412yes—
123C22×C4×C43—22no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127SD16×C43—82no—
128SD16×C43—82no—
129SD16×C43—82no—
130D8×C43—82no—
131D8×C43—82no—
132M16×C43—82no—
133M16×C43—81no—
134C2×C8×C43—21no—
135C2×C8×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43—22no—
139C2×C8×C43—82no—
140C2×C8×C43C2×D412yes—
141C2×C8×C43C2×D412yes—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43C2×D412yes—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—41no—
153C42×C43—41no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43#4111yescharacteristic
157C42×C43C2411yescharacteristic
158C23×C43—22no—
159C23×C43—42no—
160C23×C43—82no—
161C23×C43—82no—
162C23×C43—82no—
163C23×C43#12111yescharacteristic
164Q8×C43—41no—
165Q8×C43—41no—
166Q8×C43—41no—
167Q8×C43—41no—
168Q8×C43—81no—
169D4×C43—22no—
170D4×C43—22no—
171D4×C43—42no—
172D4×C43—42no—
173D4×C43—42no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—81no—
177D4×C43—82no—
178D4×C43—82no—
179D4×C43—82no—
180D4×C43—82no—
181D4×C43—82no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C2×#4111yescharacteristic
198C8×C43—22no—
199C8×C43—22no—
200C8×C43—41no—
201C8×C43—41no—
202C8×C43—42no—
203C8×C43—41no—
204C8×C43—41no—
205#19552C4311yesmaximal, characteristic, direct product factor, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—42no—
210C22×C43—42no—
211C22×C43—42no—
212C22×C43—82no—
213C22×C43—82no—
214C22×C43—82no—
215C22×C43—164no—
216C22×C43C2×#12111yescharacteristic
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—42no—
221C4×C43—81no—
222C4×C43—81no—
223C4×C43#47112yes—
224C4×C43#57611yescharacteristic
225C4×C43#57611yescharacteristic
226C4×C43#57611yescharacteristic
227C4×C43#57711yescharacteristic
228#3254C2×C4311yescharacteristic, complemented
229#3208C2×C4311yescharacteristic, complemented
230#3205C2×C4311yescharacteristic
231#2979C2×C4311yescharacteristic, complemented
232#1701C2×C4312yescomplemented
233#1685C2×C4312yescomplemented
234#1681C2×C4312yescomplemented
235#1665C2×C4312yescomplemented
236#1574C2×C4311yescharacteristic, complemented
237#1545C2×C4311yescharacteristic, complemented
238#1544C2×C4311yescharacteristic, complemented
239C2×C43—41no—
240C2×C43—82no—
241C2×C43—162no—
242C2×C43#304111yescharacteristic
243C2×C43#306211yescharacteristic
244C2×C43C2×#47111yescharacteristic
245#533C22×C4311yescharacteristic
246#532C22×C4311yescharacteristic
247C2×#127C22×C4311yescharacteristic
248#493—21no—
249#492C22×C4312yes—
250#486—21no—
251#486C22×C4312yes—
252#477—21no—
253#474C22×C4312yescomplemented
254#468—22no—
255#461C22×C4312yescomplemented
256#460—21no—
257#460—21no—
258#460—21no—
259#459C22×C4312yes—
260#459C22×C4312yes—
261#450—22no—
262#447—22no—
263#436—21no—
264#436C22×C4312yescomplemented
265C8×D4—21no—
266C8×D4C22×C4312yescomplemented
267#431C22×C4311yescharacteristic
268#431C22×C4311yescharacteristic
269#431C22×C4311yescharacteristic
270#423C22×C4311yescharacteristic
271#408—22no—
272#335C22×C4312yescomplemented
273#334C22×C4312yescomplemented
274#332C22×C4311yescharacteristic, complemented
275#332C22×C4311yescharacteristic, complemented
276#332C22×C4311yescharacteristic, complemented
277#332C22×C4311yescharacteristic, complemented
278#331C22×C4312yes—
279#331C22×C4312yes—
280C43#1955211yescharacteristic, direct product factor, Sylow
281C2×#41—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16—22no—
288C2×D8—22no—
289C2×D8—22no—
290C2×M16—21no—
291C2×M16—22no—
292C22×C8—22no—
293C4⋊Q8D4×C4311yescharacteristic
294C4⋊Q8C23×C4311yescharacteristic
295C4⋊Q8C23×C4311yescharacteristic
296#127—21no—
297#127—21no—
298#127—21no—
299#127D4×C4311yescharacteristic
300#127C23×C4312yes—
301#125—21no—
302#124—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305#121—21no—
306#121D4×C4312yes—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×D4—21no—
310C4×D4C23×C4312yes—
311#117—21no—
312C2×C42C23×C4311yescharacteristic
313#107—22no—
314C4⋊C8—21no—
315C4⋊C8D4×C4311yescharacteristic
316C4⋊C8D4×C4311yescharacteristic
317C4⋊C8C23×C4311yescharacteristic
318C4⋊C8C23×C4311yescharacteristic
319C4⋊C8C23×C4312yes—
320C4⋊C8C23×C4311yescharacteristic
321C4⋊C8C23×C4311yescharacteristic
322#103—22no—
323#102—22no—
324#102—22no—
325#102—22no—
326#102—22no—
327#102—22no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8D4×C4312yes—
333C4×C8—21no—
334C4×C8—21no—
335C4×C8C23×C4312yes—
336C24—41no—
337#41—81no—
338#41—81no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—81no—
352C2×D4—81no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4—82no—
356C2×D4C2×D4×C4312yes—
357C22×C4—22no—
358C22×C4C2×D4×C4311yescharacteristic
359C22×C4C2×D4×C4311yescharacteristic
360C22×C4#41×C4311yescharacteristic
361SD16—82no—
362SD16—82no—
363SD16—82no—
364D8—82no—
365D8—82no—
366M16—82no—
367M16—81no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—82no—
374C2×C8C2×D4×C4312yes—
375C2×C8C2×D4×C4312yes—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4C2×D4×C4312yes—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—41no—
387C42—41no—
388C42C2×D4×C4311yescharacteristic
389C42C2×D4×C4311yescharacteristic
390C42#41×C4311yescharacteristic
391C42C24×C4311yescharacteristic
392C23—22no—
393C23—42no—
394C23—82no—
395C23—82no—
396C23—82no—
397C23#121×C4311yescharacteristic
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—81no—
403D4—22no—
404D4—22no—
405D4—42no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—81no—
411D4—82no—
412D4—82no—
413D4—82no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4#121×C4311yescharacteristic
427C2×C4#121×C4311yescharacteristic
428C2×C4#121×C4311yescharacteristic
429C2×C4C22×D4×C4311yescharacteristic
430C2×C4C22×D4×C4311yescharacteristic
431C2×C4C2×#41×C4311yescharacteristic
432C8—22no—
433C8—22no—
434C8—41no—
435C8—41no—
436C8—42no—
437C8—41no—
438C8—41no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—82no—
446C22—82no—
447C22—82no—
448C22—164no—
449C22C2×#121×C4311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—42no—
454C4—81no—
455C4—81no—
456C4C43×#47112yes—
457C4C43×#57611yescharacteristic
458C4C43×#57611yescharacteristic
459C4C43×#57611yescharacteristic
460C4C43×#57711yescharacteristic
461C2—41no—
462C2—82no—
463C2—162no—
464C2C43×#304111yescharacteristic
465C2C43×#306211yescharacteristic
466C2C2×C43×#47111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3205C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3254C2semidirect
2. C43×#3208C2semidirect
4. C43×#2979C2semidirect
5. C43×#1701C2semidirect
6. C43×#1685C2semidirect
7. C43×#1681C2semidirect
8. C43×#1665C2semidirect
9. C43×#1574C2semidirect
10. C43×#1545C2semidirect
11. C43×#1544C2semidirect
20. C43×#474C22semidirect
22. C43×#461C22semidirect
31. C43×#436C22semidirect
33. C8×D4×C43C22semidirect
39. C43×#335C22semidirect
40. C43×#334C22semidirect
41. C43×#332C22semidirect
42. C43×#332C22semidirect
43. C43×#332C22semidirect
44. C43×#332C22semidirect
205. #19552C43direct (N × H)
228. #3254C2×C43semidirect
229. #3208C2×C43semidirect
231. #2979C2×C43semidirect
232. #1701C2×C43semidirect
233. #1685C2×C43semidirect
234. #1681C2×C43semidirect
235. #1665C2×C43semidirect
236. #1574C2×C43semidirect
237. #1545C2×C43semidirect
238. #1544C2×C43semidirect
253. #474C22×C43semidirect
255. #461C22×C43semidirect
264. #436C22×C43semidirect
266. C8×D4C22×C43semidirect
272. #335C22×C43semidirect
273. #334C22×C43semidirect
274. #332C22×C43semidirect
275. #332C22×C43semidirect
276. #332C22×C43semidirect
277. #332C22×C43semidirect
280. C43#19552direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32542
C43×#32082
C43×#32052
C43×#29792
C43×#17012
C43×#16852
C43×#16812
C43×#16652
C43×#15742
C43×#15452
C43×#15442
#1955243