Finite Group Databasebeta

← C43×#60317 #24980334

Subgroups — C43×#60317 #24980334

Order 11008.

1892 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3481C211yesmaximal, characteristic
2C43×#2993C214yesmaximal, complemented
3C43×#2991C212yesmaximal, complemented
4C43×#2979C211yesmaximal, characteristic, complemented
5C43×#2978C214yesmaximal, complemented
6C43×#2975C214yesmaximal, complemented
7C43×#2969C214yesmaximal, complemented
8C43×#2965C212yesmaximal, complemented
9D4×M16×C43C214yesmaximal, complemented
10C43×#2931C211yesmaximal, characteristic, complemented
11C43×#2930C214yesmaximal, complemented
12C2×#131×C43C2212yescomplemented
13C22×M16×C43C2214yescomplemented
14C43×#559C411yescharacteristic
15C43×#554C412yes—
16C43×#553C414yes—
17C43×#551C414yes—
18C43×#546C414yes—
19D42×C43C411yescharacteristic
20C43×#532C2211yescharacteristic
21C43×#529C2214yes—
22C43×#525C2214yes—
23C4×#41×C43C2212yes—
24C2×C4×D4×C43C2214yes—
25C43×#446C2212yescomplemented
26C43×#446C2212yescomplemented
27C8×Q8×C43C2214yescomplemented
28C43×#436C2212yes—
29C43×#436C2214yes—
30C43×#436C2212yes—
31C43×#436C2218yescomplemented
32C43×#436C2218yescomplemented
33C43×#436C2214yescomplemented
34C43×#436C2218yescomplemented
35C43×#436C2214yescomplemented
36C43×#435C2214yescomplemented
37C43×#435C2218yescomplemented
38C43×#435C2218yescomplemented
39C43×#435C2214yescomplemented
40C8×D4×C43C2214yescomplemented
41C8×D4×C43C2214yescomplemented
42C43×#433C2218yescomplemented
43C43×#431C2214yescomplemented
44C43×#431C2212yescomplemented
45C43×#431C2214yescomplemented
46C43×#424C2214yescomplemented
47C43×#423C2211yescharacteristic, complemented
48C43×#423C2214yescomplemented
49C43×#408C2214yescomplemented
50C43×#408C2212yescomplemented
51C43×#407C2214yescomplemented
52C43×#407C2218yescomplemented
53C43×#405C2214yescomplemented
54C4×M16×C43C2214yescomplemented
55C2×C4×C8×C43C2211yescharacteristic, complemented
56C2×#41×C43C2×C412yes—
57C2×#41×C43C2312yes—
58C22×D4×C43C2×C414yes—
59C23×C4×C43C2314yes—
60#131×C43—44no—
61C2×M16×C43—48no—
62C2×M16×C43C2314yes—
63C2×M16×C43C2318yes—
64C2×M16×C43C2314yes—
65C2×M16×C43C2312yes—
66C2×M16×C43C2314yes—
67C2×M16×C43C2314yes—
68C22×C8×C43C2314yes—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2314yes—
71C22×C8×C43C2311yescharacteristic
72C4⋊Q8×C43C2×C411yescharacteristic
73#127×C43C2×C411yescharacteristic
74#126×C43C2×C418yes—
75#125×C43C2×C414yes—
76#124×C43C2×C414yes—
77#124×C43C2×C412yes—
78#123×C43C2×C414yes—
79#123×C43C2×C414yes—
80#123×C43C2×C418yes—
81C22⋊Q8×C43C2×C418yes—
82C22⋊Q8×C43C2×C414yes—
83#121×C43C2×C418yes—
84#121×C43C2×C414yes—
85#121×C43C2×C414yes—
86#120×C43C2×C414yes—
87#120×C43C2×C414yes—
88C4×Q8×C43C2×C412yes—
89C4×Q8×C43C2312yes—
90C4×D4×C43C2×C414yes—
91C4×D4×C43C2×C418yes—
92C4×D4×C43C2×C414yes—
93C4×D4×C43C2×C412yes—
94C4×D4×C43C2×C414yes—
95C4×D4×C43C2312yes—
96C4×D4×C43C2318yes—
97C4×D4×C43C2314yes—
98C4×D4×C43C2314yes—
99#117×C43C2×C414yes—
100#117×C43C2×C412yes—
101#117×C43C2314yes—
102C2×C4⋊C4×C43C2×C414yes—
103C2×C22⋊C4×C43C2×C418yes—
104C2×C42×C43C2314yes—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43C2312yes—
107C4⋊C8×C43C2314yes—
108C4⋊C8×C43C2318yes—
109C4⋊C8×C43C2314yes—
110C4⋊C8×C43C2312yes—
111C4⋊C8×C43C2314yes—
112C22⋊C8×C43C2314yes—
113C22⋊C8×C43C2314yes—
114C22⋊C8×C43C2318yes—
115C22⋊C8×C43C2318yes—
116C22⋊C8×C43C2318yes—
117C22⋊C8×C43C2314yes—
118#97×C43C2314yes—
119#97×C43C2314yes—
120C4×C8×C43C2312yes—
121C4×C8×C43C2312yes—
122C4×C8×C43C2314yes—
123C4×C8×C43C2318yes—
124C24×C43C22×C414yes—
125#41×C43—42no—
126#41×C43—42no—
127#41×C43—44no—
128C2×Q8×C43C22×C412yes—
129C2×Q8×C43C22×C412yes—
130C2×D4×C43—48no—
131C2×D4×C43C22×C412yes—
132C2×D4×C43C22×C414yes—
133C2×D4×C43C22×C414yes—
134C2×D4×C43C22×C418yes—
135C2×D4×C43C22×C412yes—
136C2×D4×C43C22×C414yes—
137C22×C4×C43—44no—
138C22×C4×C43—44no—
139C22×C4×C43C22×C414yes—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C22×C414yes—
142C22×C4×C43C22×C418yes—
143C22×C4×C43C22×C414yes—
144C22×C4×C43C2411yescharacteristic
145C22×C4×C43C2414yes—
146C22×C4×C43C2414yes—
147M16×C43—28no—
148M16×C43—48no—
149M16×C43—44no—
150M16×C43—44no—
151M16×C43—44no—
152M16×C43—42no—
153C2×C8×C43—28no—
154C2×C8×C43—22no—
155C2×C8×C43—41no—
156C2×C8×C43—44no—
157C2×C8×C43C2414yes—
158C2×C8×C43C2412yes—
159C2×C8×C43C2411yescharacteristic
160C2×C8×C43C2414yes—
161C2×C8×C43C2414yes—
162C2×C8×C43C2411yescharacteristic
163C4⋊C4×C43C22×C412yes—
164C4⋊C4×C43C22×C414yes—
165C4⋊C4×C43C22×C418yes—
166C4⋊C4×C43C22×C412yes—
167C4⋊C4×C43C22×C414yes—
168C4⋊C4×C43C22×C414yes—
169C4⋊C4×C43C22×C418yes—
170C22⋊C4×C43C22×C414yes—
171C22⋊C4×C43C22×C418yes—
172C22⋊C4×C43C22×C418yes—
173C22⋊C4×C43C22×C418yes—
174C22⋊C4×C43C22×C414yes—
175C22⋊C4×C43C22×C414yes—
176C22⋊C4×C43C22×C414yes—
177C22⋊C4×C43C22×C414yes—
178C42×C43C22×C411yescharacteristic
179C42×C43C22×C414yes—
180C42×C43C22×C414yes—
181C42×C43C22×C411yescharacteristic
182C42×C43C2412yes—
183C42×C43C2414yes—
184C23×C43—44no—
185C23×C43—48no—
186C23×C43C23×C414yes—
187C23×C43C23×C414yes—
188C23×C43C23×C411yescharacteristic
189Q8×C43—24no—
190Q8×C43—42no—
191D4×C43—24no—
192D4×C43—28no—
193D4×C43—48no—
194D4×C43—44no—
195D4×C43—42no—
196D4×C43—44no—
197C2×C4×C43—28no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—21no—
201C2×C4×C43—24no—
202C2×C4×C43—21no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—44no—
206C2×C4×C43—48no—
207C2×C4×C43—44no—
208C2×C4×C43C23×C412yes—
209C2×C4×C43C23×C414yes—
210C2×C4×C43C23×C411yescharacteristic
211C2×C4×C43C23×C414yes—
212C2×C4×C43C23×C414yes—
213C2×C4×C43C23×C414yes—
214C2×C4×C43C23×C412yes—
215C2×C4×C43C2511yescharacteristic
216C8×C43—24no—
217C8×C43—21no—
218C8×C43—24no—
219C8×C43—22no—
220C8×C43—24no—
221C8×C43H(5,𝔽2)12yes—
222#60317C4311yesmaximal, characteristic, direct product factor, Sylow
223C22×C43—24no—
224C22×C43—24no—
225C22×C43—21no—
226C22×C43—24no—
227C22×C43—24no—
228C22×C43—28no—
229C22×C43—22no—
230C22×C43—88no—
231C22×C43C24×C411yescharacteristic
232C4×C43—24no—
233C4×C43—24no—
234C4×C43—21no—
235C4×C43—22no—
236C4×C43—24no—
237C4×C43—24no—
238C4×C43#56814yes—
239C4×C43C2×H(5,𝔽2)11yescharacteristic
240C4×C43#58511yescharacteristic
241#3481C2×C4311yescharacteristic
242#2993C2×C4314yescomplemented
243#2991C2×C4312yescomplemented
244#2979C2×C4311yescharacteristic, complemented
245#2978C2×C4314yescomplemented
246#2975C2×C4314yescomplemented
247#2969C2×C4314yescomplemented
248#2965C2×C4312yescomplemented
249D4×M16C2×C4314yescomplemented
250#2931C2×C4311yescharacteristic, complemented
251#2930C2×C4314yescomplemented
252C2×C43—41no—
253C2×C43—44no—
254C2×C43—44no—
255C2×C43C4×H(5,𝔽2)11yescharacteristic
256C2×C43C2×#56812yes—
257C2×#131C22×C4312yescomplemented
258C22×M16C22×C4314yescomplemented
259#559C4×C4311yescharacteristic
260#554C4×C4312yes—
261#553C4×C4314yes—
262#551C4×C4314yes—
263#546C4×C4314yes—
264D42C4×C4311yescharacteristic
265#532C22×C4311yescharacteristic
266#529C22×C4314yes—
267#525C22×C4314yes—
268C4×#41C22×C4312yes—
269C2×C4×D4C22×C4314yes—
270#446C22×C4312yescomplemented
271#446C22×C4312yescomplemented
272C8×Q8C22×C4314yescomplemented
273#436C22×C4312yes—
274#436C22×C4314yes—
275#436C22×C4312yes—
276#436C22×C4318yescomplemented
277#436C22×C4318yescomplemented
278#436C22×C4314yescomplemented
279#436C22×C4318yescomplemented
280#436C22×C4314yescomplemented
281#435C22×C4314yescomplemented
282#435C22×C4318yescomplemented
283#435C22×C4318yescomplemented
284#435C22×C4314yescomplemented
285C8×D4C22×C4314yescomplemented
286C8×D4C22×C4314yescomplemented
287#433C22×C4318yescomplemented
288#431C22×C4314yescomplemented
289#431C22×C4312yescomplemented
290#431C22×C4314yescomplemented
291#424C22×C4314yescomplemented
292#423C22×C4311yescharacteristic, complemented
293#423C22×C4314yescomplemented
294#408C22×C4314yescomplemented
295#408C22×C4312yescomplemented
296#407C22×C4314yescomplemented
297#407C22×C4318yescomplemented
298#405C22×C4314yescomplemented
299C4×M16C22×C4314yescomplemented
300C2×C4×C8C22×C4311yescharacteristic, complemented
301C43#6031711yescharacteristic, direct product factor, Sylow
302C2×#41C2×C4×C4312yes—
303C2×#41C23×C4312yes—
304C22×D4C2×C4×C4314yes—
305C23×C4C23×C4314yes—
306#131—44no—
307C2×M16—48no—
308C2×M16C23×C4314yes—
309C2×M16C23×C4318yes—
310C2×M16C23×C4314yes—
311C2×M16C23×C4312yes—
312C2×M16C23×C4314yes—
313C2×M16C23×C4314yes—
314C22×C8C23×C4314yes—
315C22×C8C23×C4311yescharacteristic
316C22×C8C23×C4314yes—
317C22×C8C23×C4311yescharacteristic
318C4⋊Q8C2×C4×C4311yescharacteristic
319#127C2×C4×C4311yescharacteristic
320#126C2×C4×C4318yes—
321#125C2×C4×C4314yes—
322#124C2×C4×C4314yes—
323#124C2×C4×C4312yes—
324#123C2×C4×C4314yes—
325#123C2×C4×C4314yes—
326#123C2×C4×C4318yes—
327C22⋊Q8C2×C4×C4318yes—
328C22⋊Q8C2×C4×C4314yes—
329#121C2×C4×C4318yes—
330#121C2×C4×C4314yes—
331#121C2×C4×C4314yes—
332#120C2×C4×C4314yes—
333#120C2×C4×C4314yes—
334C4×Q8C2×C4×C4312yes—
335C4×Q8C23×C4312yes—
336C4×D4C2×C4×C4314yes—
337C4×D4C2×C4×C4318yes—
338C4×D4C2×C4×C4314yes—
339C4×D4C2×C4×C4312yes—
340C4×D4C2×C4×C4314yes—
341C4×D4C23×C4312yes—
342C4×D4C23×C4318yes—
343C4×D4C23×C4314yes—
344C4×D4C23×C4314yes—
345#117C2×C4×C4314yes—
346#117C2×C4×C4312yes—
347#117C23×C4314yes—
348C2×C4⋊C4C2×C4×C4314yes—
349C2×C22⋊C4C2×C4×C4318yes—
350C2×C42C23×C4314yes—
351C2×C42C23×C4311yescharacteristic
352C4⋊C8C23×C4312yes—
353C4⋊C8C23×C4314yes—
354C4⋊C8C23×C4318yes—
355C4⋊C8C23×C4314yes—
356C4⋊C8C23×C4312yes—
357C4⋊C8C23×C4314yes—
358C22⋊C8C23×C4314yes—
359C22⋊C8C23×C4314yes—
360C22⋊C8C23×C4318yes—
361C22⋊C8C23×C4318yes—
362C22⋊C8C23×C4318yes—
363C22⋊C8C23×C4314yes—
364#97C23×C4314yes—
365#97C23×C4314yes—
366C4×C8C23×C4312yes—
367C4×C8C23×C4312yes—
368C4×C8C23×C4314yes—
369C4×C8C23×C4318yes—
370C24C22×C4×C4314yes—
371#41—42no—
372#41—42no—
373#41—44no—
374C2×Q8C22×C4×C4312yes—
375C2×Q8C22×C4×C4312yes—
376C2×D4—48no—
377C2×D4C22×C4×C4312yes—
378C2×D4C22×C4×C4314yes—
379C2×D4C22×C4×C4314yes—
380C2×D4C22×C4×C4318yes—
381C2×D4C22×C4×C4312yes—
382C2×D4C22×C4×C4314yes—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4C22×C4×C4314yes—
386C22×C4C22×C4×C4312yes—
387C22×C4C22×C4×C4314yes—
388C22×C4C22×C4×C4318yes—
389C22×C4C22×C4×C4314yes—
390C22×C4C24×C4311yescharacteristic
391C22×C4C24×C4314yes—
392C22×C4C24×C4314yes—
393M16—28no—
394M16—48no—
395M16—44no—
396M16—42no—
397M16—44no—
398M16—44no—
399C2×C8—28no—
400C2×C8—22no—
401C2×C8—44no—
402C2×C8—41no—
403C2×C8C24×C4314yes—
404C2×C8C24×C4312yes—
405C2×C8C24×C4311yescharacteristic
406C2×C8C24×C4314yes—
407C2×C8C24×C4314yes—
408C2×C8C24×C4311yescharacteristic
409C4⋊C4C22×C4×C4312yes—
410C4⋊C4C22×C4×C4314yes—
411C4⋊C4C22×C4×C4318yes—
412C4⋊C4C22×C4×C4318yes—
413C4⋊C4C22×C4×C4314yes—
414C4⋊C4C22×C4×C4312yes—
415C4⋊C4C22×C4×C4314yes—
416C22⋊C4C22×C4×C4314yes—
417C22⋊C4C22×C4×C4318yes—
418C22⋊C4C22×C4×C4318yes—
419C22⋊C4C22×C4×C4318yes—
420C22⋊C4C22×C4×C4314yes—
421C22⋊C4C22×C4×C4314yes—
422C22⋊C4C22×C4×C4314yes—
423C22⋊C4C22×C4×C4314yes—
424C42C22×C4×C4311yescharacteristic
425C42C22×C4×C4314yes—
426C42C22×C4×C4314yes—
427C42C22×C4×C4311yescharacteristic
428C42C24×C4312yes—
429C42C24×C4314yes—
430C23—44no—
431C23—48no—
432C23C23×C4×C4314yes—
433C23C23×C4×C4314yes—
434C23C23×C4×C4311yescharacteristic
435Q8—24no—
436Q8—42no—
437D4—24no—
438D4—28no—
439D4—48no—
440D4—44no—
441D4—42no—
442D4—44no—
443C2×C4—28no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4C23×C4×C4312yes—
455C2×C4C23×C4×C4314yes—
456C2×C4C23×C4×C4311yescharacteristic
457C2×C4C23×C4×C4314yes—
458C2×C4C23×C4×C4314yes—
459C2×C4C23×C4×C4314yes—
460C2×C4C23×C4×C4312yes—
461C2×C4C25×C4311yescharacteristic
462C8—24no—
463C8—21no—
464C8—24no—
465C8—22no—
466C8—24no—
467C8H(5,𝔽2)×C4312yes—
468C22—24no—
469C22—24no—
470C22—21no—
471C22—22no—
472C22—24no—
473C22—24no—
474C22—28no—
475C22—88no—
476C22C24×C4×C4311yescharacteristic
477C4—24no—
478C4—24no—
479C4—21no—
480C4—22no—
481C4—24no—
482C4—24no—
483C4C43×#56814yes—
484C4C2×H(5,𝔽2)×C4311yescharacteristic
485C4C43×#58511yescharacteristic
486C2—44no—
487C2—44no—
488C2—41no—
489C2C4×H(5,𝔽2)×C4311yescharacteristic
490C2C2×C43×#56812yes—
subgroupG/H
centerC2×C4×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC43×#3481C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2993C2semidirect
3. C43×#2991C2semidirect
4. C43×#2979C2semidirect
5. C43×#2978C2semidirect
6. C43×#2975C2semidirect
7. C43×#2969C2semidirect
8. C43×#2965C2semidirect
9. D4×M16×C43C2semidirect
10. C43×#2931C2semidirect
11. C43×#2930C2semidirect
12. C2×#131×C43C22semidirect
13. C22×M16×C43C22semidirect
25. C43×#446C22semidirect
26. C43×#446C22semidirect
27. C8×Q8×C43C22semidirect
31. C43×#436C22semidirect
32. C43×#436C22semidirect
33. C43×#436C22semidirect
34. C43×#436C22semidirect
35. C43×#436C22semidirect
36. C43×#435C22semidirect
37. C43×#435C22semidirect
38. C43×#435C22semidirect
39. C43×#435C22semidirect
40. C8×D4×C43C22semidirect
41. C8×D4×C43C22semidirect
42. C43×#433C22semidirect
43. C43×#431C22semidirect
44. C43×#431C22semidirect
45. C43×#431C22semidirect
46. C43×#424C22semidirect
47. C43×#423C22semidirect
48. C43×#423C22semidirect
49. C43×#408C22semidirect
50. C43×#408C22semidirect
51. C43×#407C22semidirect
52. C43×#407C22semidirect
53. C43×#405C22semidirect
54. C4×M16×C43C22semidirect
55. C2×C4×C8×C43C22semidirect
222. #60317C43direct (N × H)
242. #2993C2×C43semidirect
243. #2991C2×C43semidirect
244. #2979C2×C43semidirect
245. #2978C2×C43semidirect
246. #2975C2×C43semidirect
247. #2969C2×C43semidirect
248. #2965C2×C43semidirect
249. D4×M16C2×C43semidirect
250. #2931C2×C43semidirect
251. #2930C2×C43semidirect
257. C2×#131C22×C43semidirect
258. C22×M16C22×C43semidirect
270. #446C22×C43semidirect
271. #446C22×C43semidirect
272. C8×Q8C22×C43semidirect
276. #436C22×C43semidirect
277. #436C22×C43semidirect
278. #436C22×C43semidirect
279. #436C22×C43semidirect
280. #436C22×C43semidirect
281. #435C22×C43semidirect
282. #435C22×C43semidirect
283. #435C22×C43semidirect
284. #435C22×C43semidirect
285. C8×D4C22×C43semidirect
286. C8×D4C22×C43semidirect
287. #433C22×C43semidirect
288. #431C22×C43semidirect
289. #431C22×C43semidirect
290. #431C22×C43semidirect
291. #424C22×C43semidirect
292. #423C22×C43semidirect
293. #423C22×C43semidirect
294. #408C22×C43semidirect
295. #408C22×C43semidirect
296. #407C22×C43semidirect
297. #407C22×C43semidirect
298. #405C22×C43semidirect
299. C4×M16C22×C43semidirect
300. C2×C4×C8C22×C43semidirect
301. C43#60317direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34812
C43×#29932
C43×#29912
C43×#29792
C43×#29782
C43×#29752
C43×#29692
C43×#29652
D4×M16×C432
C43×#29312
C43×#29302
#6031743