Finite Group Databasebeta

← C41×#33678 #23809879

Subgroups — C41×#33678 #23809879

Order 10496.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3175C211yesmaximal, characteristic, complemented
2C41×#2948C211yesmaximal, characteristic, complemented
3C41×#2237C211yesmaximal, characteristic, complemented
4C41×#2234C211yesmaximal, characteristic, complemented
5C41×#2226C211yesmaximal, characteristic, complemented
6C41×#2224C211yesmaximal, characteristic, complemented
7C41×#2210C211yesmaximal, characteristic, complemented
8C41×#2210C211yesmaximal, characteristic, complemented
9C41×#2187C211yesmaximal, characteristic, complemented
10C41×#2184C211yesmaximal, characteristic
11C41×#2177C211yesmaximal, characteristic, complemented
12C41×#2175C211yesmaximal, characteristic, complemented
13C4×SD32×C41C211yesmaximal, characteristic, complemented
14C4×D16×C41C211yesmaximal, characteristic, complemented
15C41×#2164C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C41×#542—21no—
18C41×#518—21no—
19C2×SD32×C41C2211yescharacteristic
20C2×SD32×C41C2211yescharacteristic
21C2×D16×C41C2211yescharacteristic
22C2×D16×C41C2211yescharacteristic
23C41×#500C2211yescharacteristic, complemented
24C41×#495C2211yescharacteristic, complemented
25C41×#489—21no—
26C41×#468—21no—
27C41×#467C2211yescharacteristic
28C41×#466C2211yescharacteristic
29C41×#442—21no—
30C41×#442—21no—
31C41×#440—21no—
32C4×Q16×C41C2211yescharacteristic, complemented
33C4×D8×C41C2211yescharacteristic
34C4×D8×C41C2211yescharacteristic
35C4×D8×C41C2211yescharacteristic
36C4×D8×C41C2211yescharacteristic
37C4×D8×C41C2211yescharacteristic, complemented
38C41×#427C2211yescharacteristic
39C41×#418—21no—
40C41×#405C2211yescharacteristic
41C41×#367C2211yescharacteristic, complemented
42C41×#367C2211yescharacteristic, complemented
43C41×#366C2211yescharacteristic, complemented
44C41×#366C2211yescharacteristic, complemented
45C41×C4⋊C16C2211yescharacteristic, complemented
46C41×C4⋊C16C2211yescharacteristic, complemented
47C41×#358C2211yescharacteristic, complemented
48C41×#358C2211yescharacteristic, complemented
49C41×#357C2211yescharacteristic
50C41×#357C2211yescharacteristic
51C41×#357C2211yescharacteristic
52C41×#357C2211yescharacteristic
53C41×#357C2211yescharacteristic, complemented
54C41×#357C2211yescharacteristic, complemented
55C41×C22⋊C16C2211yescharacteristic
56C41×C22⋊C16C2211yescharacteristic
57C41×#346C2211yescharacteristic, complemented
58C4×C16×C41C2211yescharacteristic, complemented
59C22×D4×C41—21no—
60C2×Q16×C41C2311yescharacteristic
61C2×SD16×C41—21no—
62C2×D8×C41—22no—
63C2×D8×C41—22no—
64C2×D8×C41—21no—
65C2×D8×C41C2311yescharacteristic
66C2×D8×C41C2311yescharacteristic
67C2×D8×C41C2311yescharacteristic
68C2×M16×C41D411yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C4⋊Q8×C41—21no—
71#126×C41—41no—
72#124×C41—21no—
73#124×C41—41no—
74#123×C41—41no—
75C22⋊Q8×C41—21no—
76C22⋊Q8×C41—41no—
77#121×C41—21no—
78C4×Q8×C41—21no—
79C4×D4×C41—21no—
80C4×D4×C41—21no—
81C4×D4×C41—21no—
82C4×D4×C41—21no—
83C4×D4×C41—21no—
84C4×D4×C41—41no—
85C4×D4×C41—41no—
86#117×C41—21no—
87#117×C41D411yescharacteristic
88C2×C22⋊C4×C41—41no—
89C2×C22⋊C4×C41—41no—
90SD32×C41—22no—
91SD32×C41—22no—
92D16×C41—22no—
93D16×C41—22no—
94C2×C16×C41C2311yescharacteristic
95C2×C16×C41C2311yescharacteristic
96C2×C16×C41C2311yescharacteristic
97C2×C16×C41C2311yescharacteristic
98#107×C41—21no—
99#107×C41C2311yescharacteristic
100#107×C41C2311yescharacteristic
101#107×C41C2311yescharacteristic
102#107×C41C2311yescharacteristic
103#106×C41—21no—
104#103×C41—21no—
105#103×C41—21no—
106#102×C41—21no—
107#102×C41—21no—
108#102×C41—21no—
109#102×C41—21no—
110#102×C41—21no—
111#102×C41—21no—
112#97×C41D411yescharacteristic
113#97×C41D411yescharacteristic
114C4×C8×C41C2311yescharacteristic
115C4×C8×C41C2311yescharacteristic
116C24×C41—41no—
117C2×Q8×C41—21no—
118C2×Q8×C41—41no—
119C2×D4×C41—24no—
120C2×D4×C41—21no—
121C2×D4×C41—21no—
122C2×D4×C41—21no—
123C2×D4×C41—42no—
124C2×D4×C41—41no—
125C2×D4×C41—41no—
126C22×C4×C41—41no—
127C22×C4×C41—41no—
128C22×C4×C41—41no—
129C22×C4×C41—41no—
130C22×C4×C41—41no—
131C22×C4×C41C2×D411yescharacteristic
132Q16×C41—21no—
133Q16×C41—21no—
134SD16×C41—42no—
135D8×C41—24no—
136D8×C41—21no—
137D8×C41—21no—
138D8×C41—21no—
139D8×C41—21no—
140D8×C41#4112yes—
141D8×C41#4112yes—
142M16×C41—41no—
143C2×C8×C41—21no—
144C2×C8×C41—21no—
145C2×C8×C41C2×D411yescharacteristic
146C2×C8×C41C2×D411yescharacteristic
147C2×C8×C41C2×D411yescharacteristic
148C2×C8×C41C2411yescharacteristic
149C4⋊C4×C41—21no—
150C4⋊C4×C41—21no—
151C4⋊C4×C41—21no—
152C4⋊C4×C41—21no—
153C4⋊C4×C41—41no—
154C4⋊C4×C41—41no—
155C4⋊C4×C41—41no—
156C4⋊C4×C41D811yescharacteristic
157C4⋊C4×C41D811yescharacteristic
158C22⋊C4×C41—41no—
159C22⋊C4×C41—41no—
160C22⋊C4×C41—41no—
161C22⋊C4×C41—41no—
162C22⋊C4×C41—41no—
163C22⋊C4×C41—41no—
164C22⋊C4×C41—41no—
165C22⋊C4×C41—41no—
166C22⋊C4×C41—41no—
167C22⋊C4×C41—41no—
168C22⋊C4×C41D811yescharacteristic
169C22⋊C4×C41D811yescharacteristic
170C42×C41—41no—
171C42×C41—41no—
172C42×C41C2×D411yescharacteristic
173C42×C41C2×D411yescharacteristic
174C16×C41—21no—
175C16×C41—21no—
176C16×C41—21no—
177C16×C41—21no—
178C23×C41—44no—
179C23×C41—41no—
180C23×C41—41no—
181C23×C41—41no—
182C23×C41—161no—
183C23×C41—161no—
184C23×C41C2×D811yescharacteristic
185Q8×C41—41no—
186Q8×C41—41no—
187Q8×C41—161no—
188D4×C41—22no—
189D4×C41—22no—
190D4×C41—44no—
191D4×C41—41no—
192D4×C41—41no—
193D4×C41—41no—
194D4×C41—41no—
195D4×C41—161no—
196C2×C4×C41—21no—
197C2×C4×C41—21no—
198C2×C4×C41—41no—
199C2×C4×C41—41no—
200C2×C4×C41—41no—
201C2×C4×C41—41no—
202C2×C4×C41—41no—
203C2×C4×C41—161no—
204C2×C4×C41—161no—
205C2×C4×C41—161no—
206C2×C4×C41—161no—
207C2×C4×C41—161no—
208C2×C4×C41C2×D811yescharacteristic
209C2×C4×C41C2×D811yescharacteristic
210C2×C4×C41C2×D811yescharacteristic
211C2×C4×C41C2×D811yescharacteristic
212C2×C4×C41C2×D811yescharacteristic
213C2×C4×C41C22×D411yescharacteristic
214C8×C41—21no—
215C8×C41—21no—
216C8×C41—21no—
217C8×C41C2×#4111yescharacteristic
218C8×C41C2×#4111yescharacteristic
219#33678C4111yesmaximal, characteristic, direct product factor, Sylow
220C22×C41—21no—
221C22×C41—21no—
222C22×C41—21no—
223C22×C41—42no—
224C22×C41—42no—
225C22×C41—81no—
226C22×C41—81no—
227C22×C41—81no—
228C22×C41—81no—
229C22×C41—81no—
230C22×C41—81no—
231C22×C41—81no—
232C22×C41—164no—
233C22×C41C22×D811yescharacteristic
234C4×C41—21no—
235C4×C41—21no—
236C4×C41—21no—
237C4×C41—21no—
238C4×C41—21no—
239C4×C41—81no—
240C4×C41—81no—
241C4×C41—81no—
242C4×C41—81no—
243C4×C41—81no—
244C4×C41#52511yescharacteristic
245C4×C41#57511yescharacteristic
246#3175C2×C4111yescharacteristic, complemented
247#2948C2×C4111yescharacteristic, complemented
248#2237C2×C4111yescharacteristic, complemented
249#2234C2×C4111yescharacteristic, complemented
250#2226C2×C4111yescharacteristic, complemented
251#2224C2×C4111yescharacteristic, complemented
252#2210C2×C4111yescharacteristic, complemented
253#2210C2×C4111yescharacteristic, complemented
254#2187C2×C4111yescharacteristic, complemented
255#2184C2×C4111yescharacteristic
256#2177C2×C4111yescharacteristic, complemented
257#2175C2×C4111yescharacteristic, complemented
258C4×SD32C2×C4111yescharacteristic, complemented
259C4×D16C2×C4111yescharacteristic, complemented
260#2164C2×C4111yescharacteristic, complemented
261C2×C41—41no—
262C2×C41—82no—
263C2×C41—82no—
264C2×C41—161no—
265C2×C41#310011yescharacteristic
266C2×C41#341511yescharacteristic
267C2×C41#341611yescharacteristic
268C22×D8C22×C4111yescharacteristic
269#542—21no—
270#518—21no—
271C2×SD32C22×C4111yescharacteristic
272C2×SD32C22×C4111yescharacteristic
273C2×D16C22×C4111yescharacteristic
274C2×D16C22×C4111yescharacteristic
275#500C22×C4111yescharacteristic, complemented
276#495C22×C4111yescharacteristic, complemented
277#489—21no—
278#468—21no—
279#467C22×C4111yescharacteristic
280#466C22×C4111yescharacteristic
281#442—21no—
282#442—21no—
283#440—21no—
284C4×Q16C22×C4111yescharacteristic, complemented
285C4×D8C22×C4111yescharacteristic
286C4×D8C22×C4111yescharacteristic
287C4×D8C22×C4111yescharacteristic
288C4×D8C22×C4111yescharacteristic
289C4×D8C22×C4111yescharacteristic, complemented
290#427C22×C4111yescharacteristic
291#418—21no—
292#405C22×C4111yescharacteristic
293#367C22×C4111yescharacteristic, complemented
294#367C22×C4111yescharacteristic, complemented
295#366C22×C4111yescharacteristic, complemented
296#366C22×C4111yescharacteristic, complemented
297C4⋊C16C22×C4111yescharacteristic, complemented
298C4⋊C16C22×C4111yescharacteristic, complemented
299#358C22×C4111yescharacteristic, complemented
300#358C22×C4111yescharacteristic, complemented
301#357C22×C4111yescharacteristic
302#357C22×C4111yescharacteristic
303#357C22×C4111yescharacteristic
304#357C22×C4111yescharacteristic
305#357C22×C4111yescharacteristic, complemented
306#357C22×C4111yescharacteristic, complemented
307C22⋊C16C22×C4111yescharacteristic
308C22⋊C16C22×C4111yescharacteristic
309#346C22×C4111yescharacteristic, complemented
310C4×C16C22×C4111yescharacteristic, complemented
311C41#3367811yescharacteristic, direct product factor, Sylow
312C22×D4—21no—
313C2×Q16C23×C4111yescharacteristic
314C2×SD16—21no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8C23×C4111yescharacteristic
319C2×D8C23×C4111yescharacteristic
320C2×D8C23×C4111yescharacteristic
321C2×M16D4×C4111yescharacteristic
322C22×C8C23×C4111yescharacteristic
323C4⋊Q8—21no—
324#126—41no—
325#124—21no—
326#124—41no—
327#123—41no—
328C22⋊Q8—21no—
329C22⋊Q8—41no—
330#121—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—41no—
338C4×D4—41no—
339#117—21no—
340#117D4×C4111yescharacteristic
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343SD32—22no—
344SD32—22no—
345D16—22no—
346D16—22no—
347C2×C16C23×C4111yescharacteristic
348C2×C16C23×C4111yescharacteristic
349C2×C16C23×C4111yescharacteristic
350C2×C16C23×C4111yescharacteristic
351#107—21no—
352#107C23×C4111yescharacteristic
353#107C23×C4111yescharacteristic
354#107C23×C4111yescharacteristic
355#107C23×C4111yescharacteristic
356#106—21no—
357#103—21no—
358#103—21no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#102—21no—
364#102—21no—
365#97D4×C4111yescharacteristic
366#97D4×C4111yescharacteristic
367C4×C8C23×C4111yescharacteristic
368C4×C8C23×C4111yescharacteristic
369C24—41no—
370C2×Q8—21no—
371C2×Q8—41no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4C2×D4×C4111yescharacteristic
385Q16—21no—
386Q16—21no—
387SD16—42no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8#41×C4112yes—
394D8#41×C4112yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×D4×C4111yescharacteristic
399C2×C8C2×D4×C4111yescharacteristic
400C2×C8C2×D4×C4111yescharacteristic
401C2×C8C24×C4111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4D8×C4111yescharacteristic
410C4⋊C4D8×C4111yescharacteristic
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4D8×C4111yescharacteristic
422C22⋊C4D8×C4111yescharacteristic
423C42—41no—
424C42—41no—
425C42C2×D4×C4111yescharacteristic
426C42C2×D4×C4111yescharacteristic
427C16—21no—
428C16—21no—
429C16—21no—
430C16—21no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—161no—
436C23—161no—
437C23C2×D8×C4111yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—161no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—161no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—161no—
457C2×C4—161no—
458C2×C4—161no—
459C2×C4—161no—
460C2×C4—161no—
461C2×C4C2×D8×C4111yescharacteristic
462C2×C4C2×D8×C4111yescharacteristic
463C2×C4C2×D8×C4111yescharacteristic
464C2×C4C2×D8×C4111yescharacteristic
465C2×C4C2×D8×C4111yescharacteristic
466C2×C4C22×D4×C4111yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#41×C4111yescharacteristic
471C8C2×#41×C4111yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—164no—
485C22C22×D8×C4111yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4C41×#52511yescharacteristic
497C4C41×#57511yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—161no—
502C2C41×#310011yescharacteristic
503C2C41×#341511yescharacteristic
504C2C41×#341611yescharacteristic
subgroupG/H
center, socleC22×C41C22×D8
commutator, Frattini, cosocleC2×C8C24×C41
prime radicalC41×#2184C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ #117×C41 ◁ C41×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3175C2semidirect
2. C41×#2948C2semidirect
3. C41×#2237C2semidirect
4. C41×#2234C2semidirect
5. C41×#2226C2semidirect
6. C41×#2224C2semidirect
7. C41×#2210C2semidirect
8. C41×#2210C2semidirect
9. C41×#2187C2semidirect
11. C41×#2177C2semidirect
12. C41×#2175C2semidirect
13. C4×SD32×C41C2semidirect
14. C4×D16×C41C2semidirect
15. C41×#2164C2semidirect
23. C41×#500C22semidirect
24. C41×#495C22semidirect
32. C4×Q16×C41C22semidirect
37. C4×D8×C41C22semidirect
41. C41×#367C22semidirect
42. C41×#367C22semidirect
43. C41×#366C22semidirect
44. C41×#366C22semidirect
45. C41×C4⋊C16C22semidirect
46. C41×C4⋊C16C22semidirect
47. C41×#358C22semidirect
48. C41×#358C22semidirect
53. C41×#357C22semidirect
54. C41×#357C22semidirect
57. C41×#346C22semidirect
58. C4×C16×C41C22semidirect
219. #33678C41direct (N × H)
246. #3175C2×C41semidirect
247. #2948C2×C41semidirect
248. #2237C2×C41semidirect
249. #2234C2×C41semidirect
250. #2226C2×C41semidirect
251. #2224C2×C41semidirect
252. #2210C2×C41semidirect
253. #2210C2×C41semidirect
254. #2187C2×C41semidirect
256. #2177C2×C41semidirect
257. #2175C2×C41semidirect
258. C4×SD32C2×C41semidirect
259. C4×D16C2×C41semidirect
260. #2164C2×C41semidirect
275. #500C22×C41semidirect
276. #495C22×C41semidirect
284. C4×Q16C22×C41semidirect
289. C4×D8C22×C41semidirect
293. #367C22×C41semidirect
294. #367C22×C41semidirect
295. #366C22×C41semidirect
296. #366C22×C41semidirect
297. C4⋊C16C22×C41semidirect
298. C4⋊C16C22×C41semidirect
299. #358C22×C41semidirect
300. #358C22×C41semidirect
305. #357C22×C41semidirect
306. #357C22×C41semidirect
309. #346C22×C41semidirect
310. C4×C16C22×C41semidirect
311. C41#33678direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31752
C41×#29482
C41×#22372
C41×#22342
C41×#22262
C41×#22242
C41×#22102
C41×#21872
C41×#21842
C41×#21772
C41×#21752
C4×SD32×C412
C4×D16×C412
C41×#21642
#3367841