Finite Group Databasebeta

← C43×#18996 #24939013

Subgroups — C43×#18996 #24939013

Order 11008.

948 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3529C211yesmaximal, characteristic
2C43×#3239C212yesmaximal, complemented
3C43×#3152C211yesmaximal, characteristic, complemented
4C43×#1661C214yesmaximal, complemented
5C43×#1660C212yesmaximal, complemented
6C43×#1659C212yesmaximal, complemented
7C43×#1536C211yesmaximal, characteristic, complemented
8C43×#1529C212yesmaximal, complemented
9C2×#137×C43—21no—
10C2×#137×C43—21no—
11C43×#563—21no—
12C43×#563C2211yescharacteristic
13C43×#562—22no—
14C43×#562C2212yes—
15C43×H(3,𝔽4)C2211yescharacteristic
16C43×#560—21no—
17C43×#560—22no—
18C43×#532—21no—
19C43×#532C2211yescharacteristic
20C2×C4⋊Q8×C43C2211yescharacteristic, complemented
21C43×#529—22no—
22C43×#529C2212yes—
23C43×#525—21no—
24C43×#525—22no—
25C43×#501C2214yescomplemented
26C43×#497C2212yes—
27C43×#497C2212yescomplemented
28C43×#494—21no—
29C43×#492—21no—
30C43×#489C2214yes—
31C43×#484—22no—
32C43×#481—22no—
33C43×#475—22no—
34C43×#474—22no—
35C43×#432C2212yescomplemented
36C4×M16×C43C2211yescharacteristic, complemented
37C43×#330C2214yescomplemented
38C43×#329C2212yes—
39C43×#329C2214yes—
40C43×#329C2212yescomplemented
41C2×#41×C43—21no—
42C2×#41×C43D411yescharacteristic
43C2×#41×C43D411yescharacteristic
44C22×Q8×C43—21no—
45C23×C4×C43—21no—
46#137×C43—44no—
47#137×C43—44no—
48C2×Q16×C43—22no—
49C2×Q16×C43—22no—
50C2×SD16×C43—22no—
51C2×SD16×C43—22no—
52C2×M16×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43C2312yes—
58#127×C43—21no—
59#127×C43D411yescharacteristic
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—22no—
63#125×C43—22no—
64#125×C43C2312yes—
65#124×C43—21no—
66#124×C43—22no—
67#124×C43—21no—
68#124×C43C2311yescharacteristic
69#124×C43C2311yescharacteristic
70#124×C43C2312yes—
71#123×C43—22no—
72#123×C43—21no—
73#123×C43—22no—
74#123×C43—21no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—22no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43D412yes—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—22no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43D412yes—
91#120×C43—21no—
92#120×C43—22no—
93#120×C43—21no—
94#120×C43—22no—
95C4×Q8×C43D412yes—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43D412yes—
101#117×C43—21no—
102#117×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#107×C43—24no—
107#106×C43—24no—
108C4⋊C8×C43—22no—
109#103×C43—24no—
110#102×C43—24no—
111C22⋊C8×C43—22no—
112#97×C43C2312yes—
113#97×C43C2314yes—
114C4×C8×C43—21no—
115C24×C43—21no—
116#41×C43—42no—
117#41×C43—42no—
118#41×C43—82no—
119C2×Q8×C43—21no—
120C2×Q8×C43—22no—
121C2×Q8×C43—42no—
122C2×Q8×C43—42no—
123C2×Q8×C43—41no—
124C2×Q8×C43C2×D412yes—
125C2×Q8×C43C2×D411yescharacteristic
126C2×Q8×C43C2×D411yescharacteristic
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—21no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C2×D412yes—
136C2×D4×C43C2×D411yescharacteristic
137C2×D4×C43C2×D411yescharacteristic
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—41no—
145C22×C4×C43—82no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D412yes—
148Q16×C43—44no—
149Q16×C43—44no—
150SD16×C43—44no—
151SD16×C43—44no—
152M16×C43—24no—
153C2×C8×C43—22no—
154C2×C8×C43—24no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C2×D412yes—
166C4⋊C4×C43C2×D412yes—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—22no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D412yes—
185C42×C43C2411yescharacteristic
186C23×C43—21no—
187C23×C43—22no—
188C23×C43—21no—
189C23×C43—81no—
190C23×C43—82no—
191C23×C43#12011yescharacteristic
192Q8×C43—41no—
193Q8×C43—41no—
194Q8×C43—42no—
195Q8×C43—42no—
196Q8×C43—42no—
197Q8×C43—81no—
198Q8×C43—82no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—42no—
202D4×C43—82no—
203D4×C43—82no—
204D4×C43—81no—
205D4×C43—81no—
206D4×C43—82no—
207D4×C43—82no—
208D4×C43—82no—
209D4×C43—81no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—44no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—82no—
222C2×C4×C43—82no—
223C2×C4×C43—81no—
224C2×C4×C43—82no—
225C2×C4×C43#12012yes—
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43C22×D412yes—
228C2×C4×C43C22×D411yescharacteristic
229C8×C43—24no—
230C8×C43—44no—
231#18996C4311yesmaximal, characteristic, direct product factor, Sylow
232C22×C43—21no—
233C22×C43—22no—
234C22×C43—41no—
235C22×C43—42no—
236C22×C43—41no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—84no—
242C22×C43C2×#12011yescharacteristic
243C4×C43—21no—
244C4×C43—22no—
245C4×C43—22no—
246C4×C43—41no—
247C4×C43—42no—
248C4×C43—41no—
249C4×C43—42no—
250C4×C43—42no—
251C4×C43—82no—
252C4×C43#45312yes—
253#3529C2×C4311yescharacteristic
254#3239C2×C4312yescomplemented
255#3152C2×C4311yescharacteristic, complemented
256#1661C2×C4314yescomplemented
257#1660C2×C4312yescomplemented
258#1659C2×C4312yescomplemented
259#1536C2×C4311yescharacteristic, complemented
260#1529C2×C4312yescomplemented
261C2×C43—41no—
262C2×C43—81no—
263C2×C43—81no—
264C2×C43—82no—
265C2×C43C2×#45311yescharacteristic
266C2×C43#302212yes—
267C2×#137—21no—
268C2×#137—21no—
269#563—21no—
270#563C22×C4311yescharacteristic
271#562—22no—
272#562C22×C4312yes—
273H(3,𝔽4)C22×C4311yescharacteristic
274#560—21no—
275#560—22no—
276#532—21no—
277#532C22×C4311yescharacteristic
278C2×C4⋊Q8C22×C4311yescharacteristic, complemented
279#529—22no—
280#529C22×C4312yes—
281#525—21no—
282#525—22no—
283#501C22×C4314yescomplemented
284#497C22×C4312yes—
285#497C22×C4312yescomplemented
286#494—21no—
287#492—21no—
288#489C22×C4314yes—
289#484—22no—
290#481—22no—
291#475—22no—
292#474—22no—
293#432C22×C4312yescomplemented
294C4×M16C22×C4311yescharacteristic, complemented
295#330C22×C4314yescomplemented
296#329C22×C4312yes—
297#329C22×C4314yes—
298#329C22×C4312yescomplemented
299C43#1899611yescharacteristic, direct product factor, Sylow
300C2×#41—21no—
301C2×#41D4×C4311yescharacteristic
302C2×#41D4×C4311yescharacteristic
303C22×Q8—21no—
304C23×C4—21no—
305#137—44no—
306#137—44no—
307C2×Q16—22no—
308C2×Q16—22no—
309C2×SD16—22no—
310C2×SD16—22no—
311C2×M16—21no—
312C4⋊Q8—21no—
313C4⋊Q8—22no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C4311yescharacteristic
316C4⋊Q8C23×C4312yes—
317#127—21no—
318#127D4×C4311yescharacteristic
319#126—22no—
320#126—22no—
321#126—22no—
322#125—22no—
323#125C23×C4312yes—
324#124—21no—
325#124—22no—
326#124—21no—
327#124C23×C4312yes—
328#124C23×C4311yescharacteristic
329#124C23×C4311yescharacteristic
330#123—22no—
331#123—21no—
332#123—22no—
333#123—21no—
334#123—22no—
335#123—22no—
336#123—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8D4×C4312yes—
342#121—22no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348#121—22no—
349#121D4×C4312yes—
350#120—21no—
351#120—22no—
352#120—21no—
353#120—22no—
354C4×Q8D4×C4312yes—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4D4×C4312yes—
360#117—21no—
361#117—22no—
362C2×C4⋊C4—22no—
363C2×C42—21no—
364C2×C42C23×C4311yescharacteristic
365#107—24no—
366#106—24no—
367C4⋊C8—22no—
368#103—24no—
369#102—24no—
370C22⋊C8—22no—
371#97C23×C4314yes—
372#97C23×C4312yes—
373C4×C8—21no—
374C24—21no—
375#41—42no—
376#41—42no—
377#41—82no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×Q8—41no—
383C2×Q8C2×D4×C4312yes—
384C2×Q8C2×D4×C4311yescharacteristic
385C2×Q8C2×D4×C4311yescharacteristic
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4C2×D4×C4312yes—
395C2×D4C2×D4×C4311yescharacteristic
396C2×D4C2×D4×C4311yescharacteristic
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—82no—
405C22×C4C2×D4×C4311yescharacteristic
406C22×C4C2×D4×C4312yes—
407Q16—44no—
408Q16—44no—
409SD16—44no—
410SD16—44no—
411M16—24no—
412C2×C8—22no—
413C2×C8—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—42no—
424C4⋊C4C2×D4×C4312yes—
425C4⋊C4C2×D4×C4312yes—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C42—21no—
440C42—21no—
441C42—22no—
442C42C2×D4×C4311yescharacteristic
443C42C2×D4×C4312yes—
444C42C24×C4311yescharacteristic
445C23—21no—
446C23—22no—
447C23—21no—
448C23—81no—
449C23—82no—
450C23#120×C4311yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—81no—
457Q8—82no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—82no—
462D4—81no—
463D4—81no—
464D4—82no—
465D4—82no—
466D4—81no—
467D4—82no—
468D4—82no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—81no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4#120×C4312yes—
485C2×C4#120×C4311yescharacteristic
486C2×C4C22×D4×C4312yes—
487C2×C4C22×D4×C4311yescharacteristic
488C8—24no—
489C8—44no—
490C22—21no—
491C22—22no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22C2×#120×C4311yescharacteristic
501C4—21no—
502C4—22no—
503C4—22no—
504C4—41no—
505C4—42no—
506C4—41no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4C43×#45312yes—
511C2—41no—
512C2—81no—
513C2—82no—
514C2—81no—
515C2C2×C43×#45311yescharacteristic
516C2C43×#302212yes—
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3529C2
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
2. C43×#3239C2semidirect
3. C43×#3152C2semidirect
4. C43×#1661C2semidirect
5. C43×#1660C2semidirect
6. C43×#1659C2semidirect
7. C43×#1536C2semidirect
8. C43×#1529C2semidirect
20. C2×C4⋊Q8×C43C22semidirect
25. C43×#501C22semidirect
27. C43×#497C22semidirect
35. C43×#432C22semidirect
36. C4×M16×C43C22semidirect
37. C43×#330C22semidirect
40. C43×#329C22semidirect
231. #18996C43direct (N × H)
254. #3239C2×C43semidirect
255. #3152C2×C43semidirect
256. #1661C2×C43semidirect
257. #1660C2×C43semidirect
258. #1659C2×C43semidirect
259. #1536C2×C43semidirect
260. #1529C2×C43semidirect
278. C2×C4⋊Q8C22×C43semidirect
283. #501C22×C43semidirect
285. #497C22×C43semidirect
293. #432C22×C43semidirect
294. C4×M16C22×C43semidirect
295. #330C22×C43semidirect
298. #329C22×C43semidirect
299. C43#18996direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35292
C43×#32392
C43×#31522
C43×#16612
C43×#16602
C43×#16592
C43×#15362
C43×#15292
#1899643