Finite Group Databasebeta

← C41×#19316 #23795517

Subgroups — C41×#19316 #23795517

Order 10496.

682 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3138C211yesmaximal, characteristic, complemented
2C41×#3116C211yesmaximal, characteristic, complemented
3C41×#3038C211yesmaximal, characteristic
4C41×#2970C211yesmaximal, characteristic, complemented
5C41×#1702C212yesmaximal, complemented
6C41×#1698C212yesmaximal, complemented
7C41×#1681C212yesmaximal, complemented
8C41×#1677C212yesmaximal, complemented
9C41×#1569C211yesmaximal, characteristic, complemented
10C41×#1559C211yesmaximal, characteristic, complemented
11C41×#1555C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C41—21no—
13C41×#533C2211yescharacteristic
14C2×#127×C41C2211yescharacteristic
15C4×#41×C41C2211yescharacteristic
16C41×#490—21no—
17C41×#490—21no—
18C41×#486C2212yes—
19C41×#486C2212yes—
20C41×#485—21no—
21C41×#477C2211yescharacteristic, complemented
22C41×#476C2211yescharacteristic, complemented
23C41×#462C2211yescharacteristic, complemented
24C41×#461C2211yescharacteristic, complemented
25C41×#460—21no—
26C41×#460C2212yes—
27C41×#459—21no—
28C41×#459C2212yes—
29C41×#452—21no—
30C41×#446C2212yescomplemented
31C41×#441—21no—
32C41×#440—21no—
33C41×#435—22no—
34C8×D4×C41C2212yescomplemented
35C41×#432—21no—
36C41×#432C2211yescharacteristic
37C41×#432C2211yescharacteristic
38C41×#423C2211yescharacteristic
39C41×#418—22no—
40C41×#418—21no—
41C4×M16×C41C2211yescharacteristic
42C2×#97×C41—21no—
43C41×#335C2212yescomplemented
44C41×#334C2212yescomplemented
45C41×#333C2212yescomplemented
46C41×#332C2212yescomplemented
47C41×#331C2212yes—
48C41×#331C2212yes—
49C2×#41×C41D411yescharacteristic
50C22×D4×C41—21no—
51C22×D4×C41—21no—
52C22×D4×C41—21no—
53AGL(1,ℤ/8)×C41—44no—
54C2×Q16×C41—21no—
55C2×SD16×C41—22no—
56C2×SD16×C41—21no—
57C2×D8×C41—22no—
58C2×M16×C41—21no—
59C2×M16×C41D412yes—
60C22×C8×C41—22no—
61C4⋊Q8×C41C2311yescharacteristic
62C4⋊Q8×C41C2311yescharacteristic
63#127×C41—21no—
64#127×C41—21no—
65#127×C41—21no—
66#127×C41C2312yes—
67#125×C41—21no—
68C22⋊Q8×C41—21no—
69C22⋊Q8×C41—21no—
70C4×Q8×C41—21no—
71C4×Q8×C41—21no—
72C4×Q8×C41D411yescharacteristic
73C4×Q8×C41C2311yescharacteristic
74C4×D4×C41—21no—
75C4×D4×C41—21no—
76C4×D4×C41D411yescharacteristic
77C4×D4×C41C2311yescharacteristic
78#117×C41—21no—
79#117×C41—21no—
80#117×C41D411yescharacteristic
81C2×C42×C41—21no—
82C2×C42×C41C2311yescharacteristic
83#107×C41—21no—
84#106×C41—21no—
85C4⋊C8×C41—22no—
86C4⋊C8×C41—21no—
87C4⋊C8×C41C2312yes—
88C4⋊C8×C41C2311yescharacteristic
89C4⋊C8×C41C2311yescharacteristic
90C4⋊C8×C41C2312yes—
91#103×C41—21no—
92#103×C41—21no—
93#103×C41—21no—
94#102×C41—21no—
95#102×C41—22no—
96#102×C41—22no—
97#102×C41—22no—
98#102×C41—22no—
99#102×C41—22no—
100#102×C41—22no—
101C22⋊C8×C41—21no—
102C22⋊C8×C41—21no—
103C22⋊C8×C41—22no—
104#97×C41—22no—
105#97×C41—21no—
106#97×C41—21no—
107#97×C41D411yescharacteristic
108#97×C41D411yescharacteristic
109C4×C8×C41C2312yes—
110C24×C41—41no—
111#41×C41—22no—
112#41×C41—41no—
113C2×Q8×C41—21no—
114C2×Q8×C41—21no—
115C2×Q8×C41C2×D411yescharacteristic
116C2×D4×C41—21no—
117C2×D4×C41—22no—
118C2×D4×C41—22no—
119C2×D4×C41—22no—
120C2×D4×C41—42no—
121C2×D4×C41—44no—
122C2×D4×C41—42no—
123C2×D4×C41—41no—
124C2×D4×C41—41no—
125C2×D4×C41—41no—
126C2×D4×C41—82no—
127C2×D4×C41C2×D411yescharacteristic
128C22×C4×C41—21no—
129C22×C4×C41—21no—
130C22×C4×C41—21no—
131C22×C4×C41C2×D411yescharacteristic
132C22×C4×C41C2×D411yescharacteristic
133C22×C4×C41#4111yescharacteristic
134Q16×C41—42no—
135SD16×C41—44no—
136SD16×C41—42no—
137D8×C41—44no—
138M16×C41—42no—
139M16×C41—42no—
140C2×C8×C41—22no—
141C2×C8×C41—21no—
142C2×C8×C41—21no—
143C2×C8×C41—22no—
144C2×C8×C41—44no—
145C2×C8×C41C2×D412yes—
146C2×C8×C41C2×D412yes—
147C4⋊C4×C41—21no—
148C4⋊C4×C41—21no—
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×C41C2×D411yescharacteristic
156C4⋊C4×C41C2×D411yescharacteristic
157C22⋊C4×C41—21no—
158C22⋊C4×C41—21no—
159C22⋊C4×C41—21no—
160C22⋊C4×C41—41no—
161C42×C41—21no—
162C42×C41—21no—
163C42×C41—21no—
164C42×C41—41no—
165C42×C41C2×D411yescharacteristic
166C42×C41C2×D411yescharacteristic
167C42×C41#4111yescharacteristic
168C42×C41C2411yescharacteristic
169C23×C41—21no—
170C23×C41—42no—
171C23×C41—82no—
172C23×C41—82no—
173C23×C41—82no—
174C23×C41#12111yescharacteristic
175Q8×C41—21no—
176Q8×C41—21no—
177Q8×C41—41no—
178Q8×C41—41no—
179Q8×C41—81no—
180D4×C41—21no—
181D4×C41—42no—
182D4×C41—42no—
183D4×C41—44no—
184D4×C41—42no—
185D4×C41—82no—
186D4×C41—82no—
187D4×C41—82no—
188D4×C41—82no—
189D4×C41AGL(1,ℤ/8)12yes—
190C2×C4×C41—21no—
191C2×C4×C41—22no—
192C2×C4×C41—21no—
193C2×C4×C41—21no—
194C2×C4×C41—21no—
195C2×C4×C41—21no—
196C2×C4×C41—41no—
197C2×C4×C41—42no—
198C2×C4×C41—42no—
199C2×C4×C41—41no—
200C2×C4×C41—41no—
201C2×C4×C41—81no—
202C2×C4×C41#12111yescharacteristic
203C2×C4×C41#12111yescharacteristic
204C2×C4×C41#12111yescharacteristic
205C2×C4×C41C22×D411yescharacteristic
206C2×C4×C41C22×D411yescharacteristic
207C2×C4×C41C2×#4111yescharacteristic
208C8×C41—22no—
209C8×C41—22no—
210C8×C41—42no—
211C8×C41—41no—
212C8×C41—42no—
213C8×C41—41no—
214#19316C4111yesmaximal, characteristic, direct product factor, Sylow
215C22×C41—21no—
216C22×C41—21no—
217C22×C41—22no—
218C22×C41—21no—
219C22×C41—41no—
220C22×C41—41no—
221C22×C41—82no—
222C22×C41—82no—
223C22×C41—82no—
224C22×C41—164no—
225C22×C41C2×#12111yescharacteristic
226C4×C41—21no—
227C4×C41—21no—
228C4×C41—21no—
229C4×C41—21no—
230C4×C41—41no—
231C4×C41—41no—
232C4×C41—41no—
233C4×C41—81no—
234C4×C41—81no—
235C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C41#57512yes—
237C4×C41#57511yescharacteristic
238#3138C2×C4111yescharacteristic, complemented
239#3116C2×C4111yescharacteristic, complemented
240#3038C2×C4111yescharacteristic
241#2970C2×C4111yescharacteristic, complemented
242#1702C2×C4112yescomplemented
243#1698C2×C4112yescomplemented
244#1681C2×C4112yescomplemented
245#1677C2×C4112yescomplemented
246#1569C2×C4111yescharacteristic, complemented
247#1559C2×C4111yescharacteristic, complemented
248#1555C2×C4111yescharacteristic, complemented
249C2×C41—41no—
250C2×C41—42no—
251C2×C41—162no—
252C2×C41#304011yescharacteristic
253C2×C41#305511yescharacteristic
254C2×C41#306811yescharacteristic
255C2×AGL(1,ℤ/8)—21no—
256#533C22×C4111yescharacteristic
257C2×#127C22×C4111yescharacteristic
258C4×#41C22×C4111yescharacteristic
259#490—21no—
260#490—21no—
261#486C22×C4112yes—
262#486C22×C4112yes—
263#485—21no—
264#477C22×C4111yescharacteristic, complemented
265#476C22×C4111yescharacteristic, complemented
266#462C22×C4111yescharacteristic, complemented
267#461C22×C4111yescharacteristic, complemented
268#460—21no—
269#460C22×C4112yes—
270#459—21no—
271#459C22×C4112yes—
272#452—21no—
273#446C22×C4112yescomplemented
274#441—21no—
275#440—21no—
276#435—22no—
277C8×D4C22×C4112yescomplemented
278#432—21no—
279#432C22×C4111yescharacteristic
280#432C22×C4111yescharacteristic
281#423C22×C4111yescharacteristic
282#418—22no—
283#418—21no—
284C4×M16C22×C4111yescharacteristic
285C2×#97—21no—
286#335C22×C4112yescomplemented
287#334C22×C4112yescomplemented
288#333C22×C4112yescomplemented
289#332C22×C4112yescomplemented
290#331C22×C4112yes—
291#331C22×C4112yes—
292C41#1931611yescharacteristic, direct product factor, Sylow
293C2×#41D4×C4111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297AGL(1,ℤ/8)—44no—
298C2×Q16—21no—
299C2×SD16—22no—
300C2×SD16—21no—
301C2×D8—22no—
302C2×M16—21no—
303C2×M16D4×C4112yes—
304C22×C8—22no—
305C4⋊Q8C23×C4111yescharacteristic
306C4⋊Q8C23×C4111yescharacteristic
307#127—21no—
308#127—21no—
309#127—21no—
310#127C23×C4112yes—
311#125—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C4111yescharacteristic
317C4×Q8C23×C4111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C4111yescharacteristic
321C4×D4C23×C4111yescharacteristic
322#117—21no—
323#117—21no—
324#117D4×C4111yescharacteristic
325C2×C42—21no—
326C2×C42C23×C4111yescharacteristic
327#107—21no—
328#106—21no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8C23×C4112yes—
332C4⋊C8C23×C4111yescharacteristic
333C4⋊C8C23×C4111yescharacteristic
334C4⋊C8C23×C4112yes—
335#103—21no—
336#103—21no—
337#103—21no—
338#102—21no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348#97—22no—
349#97—21no—
350#97—21no—
351#97D4×C4111yescharacteristic
352#97D4×C4111yescharacteristic
353C4×C8C23×C4112yes—
354C24—41no—
355#41—22no—
356#41—41no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8C2×D4×C4111yescharacteristic
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—44no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4C2×D4×C4111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C2×D4×C4111yescharacteristic
376C22×C4C2×D4×C4111yescharacteristic
377C22×C4#41×C4111yescharacteristic
378Q16—42no—
379SD16—44no—
380SD16—42no—
381D8—44no—
382M16—42no—
383M16—42no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—44no—
389C2×C8C2×D4×C4112yes—
390C2×C8C2×D4×C4112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C4111yescharacteristic
400C4⋊C4C2×D4×C4111yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—41no—
409C42C2×D4×C4111yescharacteristic
410C42C2×D4×C4111yescharacteristic
411C42#41×C4111yescharacteristic
412C42C24×C4111yescharacteristic
413C23—21no—
414C23—42no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23#121×C4111yescharacteristic
419Q8—21no—
420Q8—21no—
421Q8—41no—
422Q8—41no—
423Q8—81no—
424D4—21no—
425D4—42no—
426D4—42no—
427D4—44no—
428D4—42no—
429D4—82no—
430D4—82no—
431D4—82no—
432D4—82no—
433D4AGL(1,ℤ/8)×C4112yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4#121×C4111yescharacteristic
447C2×C4#121×C4111yescharacteristic
448C2×C4#121×C4111yescharacteristic
449C2×C4C22×D4×C4111yescharacteristic
450C2×C4C22×D4×C4111yescharacteristic
451C2×C4C2×#41×C4111yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—42no—
457C8—41no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C2×#121×C4111yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—81no—
478C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
479C4C41×#57512yes—
480C4C41×#57511yescharacteristic
481C2—41no—
482C2—42no—
483C2—162no—
484C2C41×#304011yescharacteristic
485C2C41×#305511yescharacteristic
486C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3038C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3138C2semidirect
2. C41×#3116C2semidirect
4. C41×#2970C2semidirect
5. C41×#1702C2semidirect
6. C41×#1698C2semidirect
7. C41×#1681C2semidirect
8. C41×#1677C2semidirect
9. C41×#1569C2semidirect
10. C41×#1559C2semidirect
11. C41×#1555C2semidirect
21. C41×#477C22semidirect
22. C41×#476C22semidirect
23. C41×#462C22semidirect
24. C41×#461C22semidirect
30. C41×#446C22semidirect
34. C8×D4×C41C22semidirect
43. C41×#335C22semidirect
44. C41×#334C22semidirect
45. C41×#333C22semidirect
46. C41×#332C22semidirect
214. #19316C41direct (N × H)
238. #3138C2×C41semidirect
239. #3116C2×C41semidirect
241. #2970C2×C41semidirect
242. #1702C2×C41semidirect
243. #1698C2×C41semidirect
244. #1681C2×C41semidirect
245. #1677C2×C41semidirect
246. #1569C2×C41semidirect
247. #1559C2×C41semidirect
248. #1555C2×C41semidirect
264. #477C22×C41semidirect
265. #476C22×C41semidirect
266. #462C22×C41semidirect
267. #461C22×C41semidirect
273. #446C22×C41semidirect
277. C8×D4C22×C41semidirect
286. #335C22×C41semidirect
287. #334C22×C41semidirect
288. #333C22×C41semidirect
289. #332C22×C41semidirect
292. C41#19316direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31382
C41×#31162
C41×#30382
C41×#29702
C41×#17022
C41×#16982
C41×#16812
C41×#16772
C41×#15692
C41×#15592
C41×#15552
#1931641