Finite Group Databasebeta

← C43×#60238 #24980255

Subgroups — C43×#60238 #24980255

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3449C211yesmaximal, characteristic
2C43×#2978C214yesmaximal, complemented
3C43×#2977C214yesmaximal, complemented
4C43×#2976C218yesmaximal, complemented
5C43×#2935C214yesmaximal, complemented
6C43×#2932C212yesmaximal, complemented
7C43×#2931C212yesmaximal, complemented
8C43×#2921C211yesmaximal, characteristic, complemented
9C2×C43×#433C211yesmaximal, characteristic, complemented
10C43×#2880C214yesmaximal, complemented
11C22×#41×C43C2212yes—
12C2×#131×C43C2214yescomplemented
13C2×#131×C43C2214yescomplemented
14C43×#537C414yes—
15C43×#536C414yes—
16C43×#535C414yes—
17C43×#534C414yes—
18C43×#532C2212yes—
19C43×#532C2212yes—
20C43×#525C2214yes—
21C43×#525C2214yes—
22C2×#117×C43C2211yescharacteristic
23C43×#436C2214yescomplemented
24C43×#436C2214yescomplemented
25C43×#436C2218yescomplemented
26C43×#435C2218yescomplemented
27C43×#435C2218yescomplemented
28C43×#435C2218yescomplemented
29C43×#435C2218yescomplemented
30C8×D4×C43C2214yescomplemented
31C8×D4×C43C2214yescomplemented
32C8×D4×C43C2218yescomplemented
33C43×#433C2214yescomplemented
34C43×#433C2212yescomplemented
35C43×#433C2212yescomplemented
36C43×#433C2214yescomplemented
37C43×#433C2214yescomplemented
38C43×#423C2212yescomplemented
39C2×C4⋊C8×C43C2212yescomplemented
40C43×#408C2218yes—
41C43×#408C2218yes—
42C43×#408C2214yescomplemented
43C43×#408C2214yescomplemented
44C43×#407C2212yes—
45C43×#407C2218yescomplemented
46C2×C22⋊C8×C43C2212yes—
47C2×C22⋊C8×C43C2218yescomplemented
48C4×M16×C43C2212yescomplemented
49C2×#97×C43C2211yescharacteristic, complemented
50C2×C4×C8×C43C2211yescharacteristic, complemented
51C2×#41×C43—48no—
52C2×#41×C43C2×C414yes—
53C2×#41×C43C2×C414yes—
54C2×#41×C43C2314yes—
55C2×#41×C43C2314yes—
56C22×Q8×C43C2×C412yes—
57C22×D4×C43C2×C414yes—
58C22×D4×C43C2×C412yes—
59C23×C4×C43C2311yescharacteristic
60C23×C4×C43C2314yes—
61#131×C43—48no—
62#131×C43—48no—
63C2×M16×C43C2314yes—
64C2×M16×C43C2318yes—
65C2×M16×C43C2318yes—
66C22×C8×C43C2312yes—
67C22×C8×C43C2312yes—
68C22×C8×C43C2318yes—
69C22×C8×C43C2318yes—
70C4⋊Q8×C43C2×C412yes—
71C4⋊Q8×C43C2×C412yes—
72#127×C43C2×C412yes—
73#127×C43C2×C412yes—
74#124×C43C2×C414yes—
75#124×C43C2×C414yes—
76#123×C43C2×C418yes—
77#123×C43C2×C418yes—
78C22⋊Q8×C43C2×C418yes—
79C22⋊Q8×C43C2×C418yes—
80#121×C43C2×C418yes—
81#121×C43C2×C418yes—
82#121×C43C2×C414yes—
83#121×C43C2×C414yes—
84#121×C43C2×C418yes—
85#120×C43C2×C418yes—
86#120×C43C2×C418yes—
87C4×D4×C43C2314yes—
88C4×D4×C43C2318yes—
89C4×D4×C43C2314yes—
90#117×C43C2×C414yes—
91#117×C43C2312yes—
92#117×C43C2312yes—
93C2×C4⋊C4×C43C2×C412yes—
94C2×C22⋊C4×C43C2×C412yes—
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97C4⋊C8×C43C2314yes—
98C4⋊C8×C43C2314yes—
99C4⋊C8×C43C2314yes—
100C4⋊C8×C43C2314yes—
101C22⋊C8×C43C2314yes—
102C22⋊C8×C43C2314yes—
103C22⋊C8×C43C2318yes—
104C22⋊C8×C43C2318yes—
105C22⋊C8×C43C2318yes—
106C22⋊C8×C43C2318yes—
107C22⋊C8×C43C2318yes—
108#97×C43C2312yes—
109#97×C43C2312yes—
110#97×C43C2314yes—
111C4×C8×C43C2311yescharacteristic
112C4×C8×C43C2312yes—
113C4×C8×C43C2311yescharacteristic
114C4×C8×C43C2314yes—
115C24×C43C22×C411yescharacteristic
116C24×C43C22×C414yes—
117#41×C43—28no—
118#41×C43—28no—
119#41×C43—48no—
120#41×C43—48no—
121#41×C43—48no—
122C2×Q8×C43—44no—
123C2×Q8×C43C22×C414yes—
124C2×Q8×C43C22×C414yes—
125C2×D4×C43—48no—
126C2×D4×C43—44no—
127C2×D4×C43C22×C418yes—
128C2×D4×C43C22×C414yes—
129C2×D4×C43C22×C414yes—
130C2×D4×C43C22×C418yes—
131C2×D4×C43C22×C414yes—
132C2×D4×C43C22×C418yes—
133C2×D4×C43C22×C414yes—
134C22×C4×C43—24no—
135C22×C4×C43—48no—
136C22×C4×C43C22×C411yescharacteristic
137C22×C4×C43C22×C412yes—
138C22×C4×C43C22×C412yes—
139C22×C4×C43C22×C412yes—
140C22×C4×C43C22×C418yes—
141C22×C4×C43C22×C414yes—
142C22×C4×C43C2412yes—
143C22×C4×C43C2418yes—
144C22×C4×C43C2411yescharacteristic
145M16×C43—28no—
146M16×C43—48no—
147M16×C43—48no—
148C2×C8×C43—24no—
149C2×C8×C43—24no—
150C2×C8×C43—48no—
151C2×C8×C43—48no—
152C2×C8×C43C2412yes—
153C2×C8×C43C2412yes—
154C2×C8×C43C2418yes—
155C2×C8×C43C2414yes—
156C4⋊C4×C43C22×C414yes—
157C4⋊C4×C43C22×C414yes—
158C4⋊C4×C43C22×C414yes—
159C4⋊C4×C43C22×C418yes—
160C4⋊C4×C43C22×C414yes—
161C22⋊C4×C43C22×C414yes—
162C22⋊C4×C43C22×C414yes—
163C22⋊C4×C43C22×C418yes—
164C22⋊C4×C43C22×C418yes—
165C22⋊C4×C43C22×C418yes—
166C22⋊C4×C43C22×C418yes—
167C42×C43C22×C412yes—
168C42×C43C22×C412yes—
169C42×C43C2411yescharacteristic
170C42×C43C2411yescharacteristic
171C42×C43C2412yes—
172C23×C43—22no—
173C23×C43—44no—
174C23×C43—42no—
175C23×C43—48no—
176C23×C43C23×C412yes—
177C23×C43C23×C418yes—
178C23×C43C23×C411yescharacteristic
179Q8×C43—28no—
180Q8×C43—44no—
181D4×C43—216no—
182D4×C43—28no—
183D4×C43—44no—
184D4×C43—48no—
185D4×C43—44no—
186D4×C43—48no—
187D4×C43—44no—
188C2×C4×C43—22no—
189C2×C4×C43—24no—
190C2×C4×C43—28no—
191C2×C4×C43—28no—
192C2×C4×C43—24no—
193C2×C4×C43—44no—
194C2×C4×C43—48no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43C23×C412yes—
198C2×C4×C43C23×C412yes—
199C2×C4×C43C23×C414yes—
200C2×C4×C43C23×C418yes—
201C2×C4×C43C23×C412yes—
202C2×C4×C43C23×C411yescharacteristic
203C2×C4×C43H(5,𝔽2)14yes—
204C2×C4×C43C2511yescharacteristic
205C8×C43—22no—
206C8×C43—24no—
207C8×C43—22no—
208C8×C43—28no—
209#60238C4311yesmaximal, characteristic, direct product factor, Sylow
210C22×C43—22no—
211C22×C43—22no—
212C22×C43—28no—
213C22×C43—24no—
214C22×C43—28no—
215C22×C43—28no—
216C22×C43—82no—
217C22×C43—88no—
218C22×C43#51812yes—
219C22×C43C24×C411yescharacteristic
220C4×C43—22no—
221C4×C43—28no—
222C4×C43—22no—
223C4×C43—22no—
224C4×C43—24no—
225C4×C43#51812yes—
226C4×C43C2×H(5,𝔽2)12yes—
227#3449C2×C4311yescharacteristic
228#2978C2×C4314yescomplemented
229#2977C2×C4314yescomplemented
230#2976C2×C4318yescomplemented
231#2935C2×C4314yescomplemented
232#2932C2×C4312yescomplemented
233#2931C2×C4312yescomplemented
234#2921C2×C4311yescharacteristic, complemented
235C2×#433C2×C4311yescharacteristic, complemented
236#2880C2×C4314yescomplemented
237C2×C43—22no—
238C2×C43—48no—
239C2×C43—42no—
240C2×C43C2×#51811yescharacteristic
241C2×C43#357312yes—
242C22×#41C22×C4312yes—
243C2×#131C22×C4314yescomplemented
244C2×#131C22×C4314yescomplemented
245#537C4×C4314yes—
246#536C4×C4314yes—
247#535C4×C4314yes—
248#534C4×C4314yes—
249#532C22×C4312yes—
250#532C22×C4312yes—
251#525C22×C4314yes—
252#525C22×C4314yes—
253C2×#117C22×C4311yescharacteristic
254#436C22×C4314yescomplemented
255#436C22×C4314yescomplemented
256#436C22×C4318yescomplemented
257#435C22×C4318yescomplemented
258#435C22×C4318yescomplemented
259#435C22×C4318yescomplemented
260#435C22×C4318yescomplemented
261C8×D4C22×C4314yescomplemented
262C8×D4C22×C4314yescomplemented
263C8×D4C22×C4318yescomplemented
264#433C22×C4314yescomplemented
265#433C22×C4312yescomplemented
266#433C22×C4312yescomplemented
267#433C22×C4314yescomplemented
268#433C22×C4314yescomplemented
269#423C22×C4312yescomplemented
270C2×C4⋊C8C22×C4312yescomplemented
271#408C22×C4318yes—
272#408C22×C4318yes—
273#408C22×C4314yescomplemented
274#408C22×C4314yescomplemented
275#407C22×C4312yes—
276#407C22×C4318yescomplemented
277C2×C22⋊C8C22×C4312yes—
278C2×C22⋊C8C22×C4318yescomplemented
279C4×M16C22×C4312yescomplemented
280C2×#97C22×C4311yescharacteristic, complemented
281C2×C4×C8C22×C4311yescharacteristic, complemented
282C43#6023811yescharacteristic, direct product factor, Sylow
283C2×#41—48no—
284C2×#41C2×C4×C4314yes—
285C2×#41C2×C4×C4314yes—
286C2×#41C23×C4314yes—
287C2×#41C23×C4314yes—
288C22×Q8C2×C4×C4312yes—
289C22×D4C2×C4×C4314yes—
290C22×D4C2×C4×C4312yes—
291C23×C4C23×C4311yescharacteristic
292C23×C4C23×C4314yes—
293#131—48no—
294#131—48no—
295C2×M16C23×C4314yes—
296C2×M16C23×C4318yes—
297C2×M16C23×C4318yes—
298C22×C8C23×C4312yes—
299C22×C8C23×C4312yes—
300C22×C8C23×C4318yes—
301C22×C8C23×C4318yes—
302C4⋊Q8C2×C4×C4312yes—
303C4⋊Q8C2×C4×C4312yes—
304#127C2×C4×C4312yes—
305#127C2×C4×C4312yes—
306#124C2×C4×C4314yes—
307#124C2×C4×C4314yes—
308#123C2×C4×C4318yes—
309#123C2×C4×C4318yes—
310C22⋊Q8C2×C4×C4318yes—
311C22⋊Q8C2×C4×C4318yes—
312#121C2×C4×C4318yes—
313#121C2×C4×C4318yes—
314#121C2×C4×C4314yes—
315#121C2×C4×C4314yes—
316#121C2×C4×C4318yes—
317#120C2×C4×C4318yes—
318#120C2×C4×C4318yes—
319C4×D4C23×C4314yes—
320C4×D4C23×C4318yes—
321C4×D4C23×C4314yes—
322#117C2×C4×C4314yes—
323#117C23×C4312yes—
324#117C23×C4312yes—
325C2×C4⋊C4C2×C4×C4312yes—
326C2×C22⋊C4C2×C4×C4312yes—
327C2×C42C23×C4311yescharacteristic
328C2×C42C23×C4311yescharacteristic
329C4⋊C8C23×C4314yes—
330C4⋊C8C23×C4314yes—
331C4⋊C8C23×C4314yes—
332C4⋊C8C23×C4314yes—
333C22⋊C8C23×C4314yes—
334C22⋊C8C23×C4314yes—
335C22⋊C8C23×C4318yes—
336C22⋊C8C23×C4318yes—
337C22⋊C8C23×C4318yes—
338C22⋊C8C23×C4318yes—
339C22⋊C8C23×C4318yes—
340#97C23×C4312yes—
341#97C23×C4312yes—
342#97C23×C4314yes—
343C4×C8C23×C4311yescharacteristic
344C4×C8C23×C4312yes—
345C4×C8C23×C4311yescharacteristic
346C4×C8C23×C4314yes—
347C24C22×C4×C4311yescharacteristic
348C24C22×C4×C4314yes—
349#41—28no—
350#41—28no—
351#41—48no—
352#41—48no—
353#41—48no—
354C2×Q8—44no—
355C2×Q8C22×C4×C4314yes—
356C2×Q8C22×C4×C4314yes—
357C2×D4—44no—
358C2×D4—48no—
359C2×D4C22×C4×C4318yes—
360C2×D4C22×C4×C4314yes—
361C2×D4C22×C4×C4314yes—
362C2×D4C22×C4×C4318yes—
363C2×D4C22×C4×C4314yes—
364C2×D4C22×C4×C4318yes—
365C2×D4C22×C4×C4314yes—
366C22×C4—24no—
367C22×C4—48no—
368C22×C4C22×C4×C4311yescharacteristic
369C22×C4C22×C4×C4312yes—
370C22×C4C22×C4×C4312yes—
371C22×C4C22×C4×C4312yes—
372C22×C4C22×C4×C4318yes—
373C22×C4C22×C4×C4314yes—
374C22×C4C24×C4312yes—
375C22×C4C24×C4318yes—
376C22×C4C24×C4311yescharacteristic
377M16—28no—
378M16—48no—
379M16—48no—
380C2×C8—24no—
381C2×C8—24no—
382C2×C8—48no—
383C2×C8—48no—
384C2×C8C24×C4312yes—
385C2×C8C24×C4312yes—
386C2×C8C24×C4318yes—
387C2×C8C24×C4314yes—
388C4⋊C4C22×C4×C4314yes—
389C4⋊C4C22×C4×C4314yes—
390C4⋊C4C22×C4×C4314yes—
391C4⋊C4C22×C4×C4318yes—
392C4⋊C4C22×C4×C4314yes—
393C22⋊C4C22×C4×C4314yes—
394C22⋊C4C22×C4×C4314yes—
395C22⋊C4C22×C4×C4318yes—
396C22⋊C4C22×C4×C4318yes—
397C22⋊C4C22×C4×C4318yes—
398C22⋊C4C22×C4×C4318yes—
399C42C22×C4×C4312yes—
400C42C22×C4×C4312yes—
401C42C24×C4311yescharacteristic
402C42C24×C4311yescharacteristic
403C42C24×C4312yes—
404C23—22no—
405C23—44no—
406C23—42no—
407C23—48no—
408C23C23×C4×C4312yes—
409C23C23×C4×C4318yes—
410C23C23×C4×C4311yescharacteristic
411Q8—28no—
412Q8—44no—
413D4—216no—
414D4—28no—
415D4—44no—
416D4—48no—
417D4—44no—
418D4—48no—
419D4—44no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—28no—
424C2×C4—24no—
425C2×C4—44no—
426C2×C4—48no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4C23×C4×C4312yes—
430C2×C4C23×C4×C4312yes—
431C2×C4C23×C4×C4314yes—
432C2×C4C23×C4×C4318yes—
433C2×C4C23×C4×C4312yes—
434C2×C4C23×C4×C4311yescharacteristic
435C2×C4H(5,𝔽2)×C4314yes—
436C2×C4C25×C4311yescharacteristic
437C8—22no—
438C8—24no—
439C8—22no—
440C8—28no—
441C22—22no—
442C22—22no—
443C22—28no—
444C22—28no—
445C22—28no—
446C22—24no—
447C22—82no—
448C22—88no—
449C22C43×#51812yes—
450C22C24×C4×C4311yescharacteristic
451C4—22no—
452C4—28no—
453C4—22no—
454C4—22no—
455C4—24no—
456C4C43×#51812yes—
457C4C2×H(5,𝔽2)×C4312yes—
458C2—22no—
459C2—42no—
460C2—48no—
461C2C2×C43×#51811yescharacteristic
462C2C43×#357312yes—
subgroupG/H
centerC2×C4×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC43×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2978C2semidirect
3. C43×#2977C2semidirect
4. C43×#2976C2semidirect
5. C43×#2935C2semidirect
6. C43×#2932C2semidirect
7. C43×#2931C2semidirect
8. C43×#2921C2semidirect
9. C2×C43×#433C2semidirect
10. C43×#2880C2semidirect
12. C2×#131×C43C22semidirect
13. C2×#131×C43C22semidirect
23. C43×#436C22semidirect
24. C43×#436C22semidirect
25. C43×#436C22semidirect
26. C43×#435C22semidirect
27. C43×#435C22semidirect
28. C43×#435C22semidirect
29. C43×#435C22semidirect
30. C8×D4×C43C22semidirect
31. C8×D4×C43C22semidirect
32. C8×D4×C43C22semidirect
33. C43×#433C22semidirect
34. C43×#433C22semidirect
35. C43×#433C22semidirect
36. C43×#433C22semidirect
37. C43×#433C22semidirect
38. C43×#423C22semidirect
39. C2×C4⋊C8×C43C22semidirect
42. C43×#408C22semidirect
43. C43×#408C22semidirect
45. C43×#407C22semidirect
47. C2×C22⋊C8×C43C22semidirect
48. C4×M16×C43C22semidirect
49. C2×#97×C43C22semidirect
50. C2×C4×C8×C43C22semidirect
209. #60238C43direct (N × H)
228. #2978C2×C43semidirect
229. #2977C2×C43semidirect
230. #2976C2×C43semidirect
231. #2935C2×C43semidirect
232. #2932C2×C43semidirect
233. #2931C2×C43semidirect
234. #2921C2×C43semidirect
235. C2×#433C2×C43semidirect
236. #2880C2×C43semidirect
243. C2×#131C22×C43semidirect
244. C2×#131C22×C43semidirect
254. #436C22×C43semidirect
255. #436C22×C43semidirect
256. #436C22×C43semidirect
257. #435C22×C43semidirect
258. #435C22×C43semidirect
259. #435C22×C43semidirect
260. #435C22×C43semidirect
261. C8×D4C22×C43semidirect
262. C8×D4C22×C43semidirect
263. C8×D4C22×C43semidirect
264. #433C22×C43semidirect
265. #433C22×C43semidirect
266. #433C22×C43semidirect
267. #433C22×C43semidirect
268. #433C22×C43semidirect
269. #423C22×C43semidirect
270. C2×C4⋊C8C22×C43semidirect
273. #408C22×C43semidirect
274. #408C22×C43semidirect
276. #407C22×C43semidirect
278. C2×C22⋊C8C22×C43semidirect
279. C4×M16C22×C43semidirect
280. C2×#97C22×C43semidirect
281. C2×C4×C8C22×C43semidirect
282. C43#60238direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34492
C43×#29782
C43×#29772
C43×#29762
C43×#29352
C43×#29322
C43×#29312
C43×#29212
C2×C43×#4332
C43×#28802
#6023843