Finite Group Databasebeta

← C41×#9520 #23785721

Subgroups — C41×#9520 #23785721

Order 10496.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3003C211yesmaximal, characteristic
2C41×#2976C211yesmaximal, characteristic, complemented
3C41×#1786C211yesmaximal, characteristic, complemented
4C41×#1783C211yesmaximal, characteristic, complemented
5C41×#1513C211yesmaximal, characteristic, complemented
6C41×#1305C211yesmaximal, characteristic, complemented
7C41×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C41C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C41—21no—
10C41×#525C2211yescharacteristic
11C41×#450—21no—
12C41×#450C412yescomplemented
13C41×#447—21no—
14C41×#447C412yescomplemented
15C41×#436—21no—
16C41×#435—21no—
17C41×#435—21no—
18C8×D4×C41—21no—
19C41×#433—21no—
20C41×#418—21no—
21C2×#102×C41—21no—
22C2×#102×C41—21no—
23C2×#100×C41—21no—
24C2×#100×C41—21no—
25C41×#408—21no—
26C41×#407C2211yescharacteristic
27C41×#407C2211yescharacteristic
28C41×#407C2211yescharacteristic
29C2×C22⋊C8×C41C2211yescharacteristic
30C41×#380C2211yescharacteristic
31C41×#328—21no—
32C41×#327—21no—
33C25×C41—21no—
34C2×#41×C41D411yescharacteristic
35C22×D4×C41—21no—
36C22×D4×C41—21no—
37C22×D4×C41—21no—
38C22×D4×C41—21no—
39C22×D4×C41—21no—
40C22×D4×C41—42no—
41C22×D4×C41—42no—
42C22×D4×C41C2×C412yes—
43C23×C4×C41C2311yescharacteristic
44AGL(1,ℤ/8)×C41—42no—
45AGL(1,ℤ/8)×C41—42no—
46C2×SD16×C41—22no—
47C2×D8×C41—22no—
48C2×M16×C41—21no—
49C2×M16×C41—21no—
50C2×M16×C41—21no—
51C2×M16×C41D411yescharacteristic
52C2×M16×C41D411yescharacteristic
53C22×C8×C41—21no—
54C22×C8×C41D411yescharacteristic
55C22×C8×C41D411yescharacteristic
56#123×C41—21no—
57C22⋊Q8×C41C2×C411yescharacteristic
58C22⋊Q8×C41D411yescharacteristic
59#121×C41C2×C411yescharacteristic
60#121×C41D411yescharacteristic
61#120×C41—21no—
62C4×D4×C41—21no—
63C4×D4×C41—21no—
64#117×C41D411yescharacteristic
65C2×C4⋊C4×C41—21no—
66C2×C22⋊C4×C41—21no—
67C4⋊C8×C41—21no—
68C4⋊C8×C41—21no—
69#102×C41—22no—
70#102×C41—22no—
71#102×C41—42no—
72#102×C41—42no—
73#100×C41—42no—
74#100×C41—42no—
75C22⋊C8×C41—21no—
76C22⋊C8×C41—21no—
77C22⋊C8×C41—21no—
78C22⋊C8×C41—21no—
79C22⋊C8×C41—21no—
80C22⋊C8×C41—21no—
81C22⋊C8×C41—21no—
82C22⋊C8×C41—21no—
83C22⋊C8×C41—21no—
84C22⋊C8×C41C2×C412yes—
85#97×C41—21no—
86C4×C8×C41—21no—
87#95×C41—21no—
88C24×C41—22no—
89C24×C41—44no—
90C24×C41—41no—
91C24×C41—41no—
92C24×C41—81no—
93C24×C41—81no—
94C24×C41—82no—
95C24×C41#4111yescharacteristic
96#41×C41—41no—
97#41×C41—41no—
98C2×Q8×C41C22⋊C411yescharacteristic
99C2×D4×C41—22no—
100C2×D4×C41—22no—
101C2×D4×C41—22no—
102C2×D4×C41—22no—
103C2×D4×C41—22no—
104C2×D4×C41—22no—
105C2×D4×C41—21no—
106C2×D4×C41—21no—
107C2×D4×C41—21no—
108C2×D4×C41—22no—
109C2×D4×C41—22no—
110C2×D4×C41—41no—
111C2×D4×C41—41no—
112C2×D4×C41—41no—
113C2×D4×C41—41no—
114C2×D4×C41—41no—
115C2×D4×C41—41no—
116C2×D4×C41—44no—
117C2×D4×C41—44no—
118C2×D4×C41—44no—
119C2×D4×C41—41no—
120C2×D4×C41—41no—
121C2×D4×C41C22⋊C411yescharacteristic
122C22×C4×C41—21no—
123C22×C4×C41—41no—
124C22×C4×C41—41no—
125C22×C4×C41—41no—
126C22×C4×C41C22×C411yescharacteristic
127C22×C4×C41C2×D411yescharacteristic
128C22×C4×C41C2×D411yescharacteristic
129C22×C4×C41C2×D411yescharacteristic
130C22×C4×C41C2×D411yescharacteristic
131C22×C4×C41#4111yescharacteristic
132SD16×C41—44no—
133D8×C41—44no—
134M16×C41—41no—
135M16×C41—41no—
136M16×C41—41no—
137M16×C41—41no—
138M16×C41—41no—
139M16×C41—41no—
140M16×C41—81no—
141C2×C8×C41—22no—
142C2×C8×C41—21no—
143C2×C8×C41—21no—
144C2×C8×C41—21no—
145C2×C8×C41—21no—
146C2×C8×C41—41no—
147C2×C8×C41—41no—
148C2×C8×C41—41no—
149C2×C8×C41—81no—
150C4⋊C4×C41—21no—
151C4⋊C4×C41—21no—
152C4⋊C4×C41—41no—
153C4⋊C4×C41—41no—
154C4⋊C4×C41C22⋊C411yescharacteristic
155C4⋊C4×C41C22⋊C411yescharacteristic
156C22⋊C4×C41—21no—
157C22⋊C4×C41—21no—
158C22⋊C4×C41—21no—
159C22⋊C4×C41—21no—
160C22⋊C4×C41—21no—
161C22⋊C4×C41—81no—
162C42×C41—21no—
163C23×C41—21no—
164C23×C41—21no—
165C23×C41—24no—
166C23×C41—21no—
167C23×C41—41no—
168C23×C41—41no—
169C23×C41—42no—
170C23×C41—42no—
171C23×C41—42no—
172C23×C41—42no—
173C23×C41—42no—
174C23×C41—42no—
175C23×C41—82no—
176C23×C41—82no—
177C23×C41—82no—
178C23×C41—81no—
179C23×C41—81no—
180C23×C41—82no—
181C23×C41—88no—
182C23×C41—88no—
183C23×C41—81no—
184C23×C41—81no—
185C23×C41C4×D411yescharacteristic
186C23×C41#12111yescharacteristic
187C23×C41#12311yescharacteristic
188Q8×C41—41no—
189D4×C41—24no—
190D4×C41—24no—
191D4×C41—41no—
192D4×C41—42no—
193D4×C41—42no—
194D4×C41—42no—
195D4×C41—42no—
196D4×C41—41no—
197D4×C41—41no—
198D4×C41—42no—
199D4×C41—42no—
200D4×C41—81no—
201D4×C41—81no—
202C2×C4×C41—21no—
203C2×C4×C41—21no—
204C2×C4×C41—21no—
205C2×C4×C41—21no—
206C2×C4×C41—21no—
207C2×C4×C41—21no—
208C2×C4×C41—21no—
209C2×C4×C41—21no—
210C2×C4×C41—21no—
211C2×C4×C41—41no—
212C2×C4×C41—41no—
213C2×C4×C41—41no—
214C2×C4×C41—41no—
215C2×C4×C41—41no—
216C2×C4×C41—81no—
217C2×C4×C41—81no—
218C2×C4×C41—81no—
219C2×C4×C41C2×C22⋊C411yescharacteristic
220C2×C4×C41C4×D411yescharacteristic
221C2×C4×C41#12011yescharacteristic
222C2×C4×C41#12111yescharacteristic
223C8×C41—42no—
224C8×C41—41no—
225C8×C41—41no—
226C8×C41—41no—
227C8×C41—41no—
228C8×C41—81no—
229#9520C4111yesmaximal, characteristic, direct product factor, Sylow
230C22×C41—21no—
231C22×C41—21no—
232C22×C41—21no—
233C22×C41—21no—
234C22×C41—21no—
235C22×C41—21no—
236C22×C41—21no—
237C22×C41—21no—
238C22×C41—42no—
239C22×C41—42no—
240C22×C41—41no—
241C22×C41—44no—
242C22×C41—41no—
243C22×C41—41no—
244C22×C41—82no—
245C22×C41—82no—
246C22×C41—82no—
247C22×C41—82no—
248C22×C41—84no—
249C22×C41—84no—
250C22×C41—84no—
251C22×C41—84no—
252C22×C41—82no—
253C22×C41—82no—
254C22×C41#38611yescharacteristic
255C22×C41#47111yescharacteristic
256C22×C41#47211yescharacteristic
257C4×C41—21no—
258C4×C41—21no—
259C4×C41—21no—
260C4×C41—41no—
261C4×C41—41no—
262C4×C41—41no—
263C4×C41—161no—
264C4×C41B(4,𝔽2)11yescharacteristic
265C4×C41B(4,𝔽2)11yescharacteristic
266#3003C2×C4111yescharacteristic
267#2976C2×C4111yescharacteristic, complemented
268#1786C2×C4111yescharacteristic, complemented
269#1783C2×C4111yescharacteristic, complemented
270#1513C2×C4111yescharacteristic, complemented
271#1305C2×C4111yescharacteristic, complemented
272#1293C2×C4111yescharacteristic, complemented
273C2×C41—21no—
274C2×C41—21no—
275C2×C41—41no—
276C2×C41—41no—
277C2×C41—81no—
278C2×C41—84no—
279C2×C41#188911yescharacteristic
280C2×C41#190311yescharacteristic
281C2×C41#190711yescharacteristic
282C23×D4C22×C4111yescharacteristic
283C2×AGL(1,ℤ/8)—21no—
284#525C22×C4111yescharacteristic
285#450—21no—
286#450C4×C4112yescomplemented
287#447—21no—
288#447C4×C4112yescomplemented
289#436—21no—
290#435—21no—
291#435—21no—
292C8×D4—21no—
293#433—21no—
294#418—21no—
295C2×#102—21no—
296C2×#102—21no—
297C2×#100—21no—
298C2×#100—21no—
299#408—21no—
300#407C22×C4111yescharacteristic
301#407C22×C4111yescharacteristic
302#407C22×C4111yescharacteristic
303C2×C22⋊C8C22×C4111yescharacteristic
304#380C22×C4111yescharacteristic
305#328—21no—
306#327—21no—
307C41#952011yescharacteristic, direct product factor, Sylow
308C25—21no—
309C2×#41D4×C4111yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C4112yes—
318C23×C4C23×C4111yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C4111yescharacteristic
327C2×M16D4×C4111yescharacteristic
328C22×C8—21no—
329C22×C8D4×C4111yescharacteristic
330C22×C8D4×C4111yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C4111yescharacteristic
333C22⋊Q8D4×C4111yescharacteristic
334#121C2×C4×C4111yescharacteristic
335#121D4×C4111yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C4111yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C4112yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C4111yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C4111yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C4111yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C4111yescharacteristic
402C22×C4C2×D4×C4111yescharacteristic
403C22×C4C2×D4×C4111yescharacteristic
404C22×C4C2×D4×C4111yescharacteristic
405C22×C4C2×D4×C4111yescharacteristic
406C22×C4#41×C4111yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C4111yescharacteristic
430C4⋊C4C22⋊C4×C4111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C4111yescharacteristic
461C23#121×C4111yescharacteristic
462C23#123×C4111yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C4111yescharacteristic
495C2×C4C4×D4×C4111yescharacteristic
496C2×C4#120×C4111yescharacteristic
497C2×C4#121×C4111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C41×#38611yescharacteristic
529C22C41×#47111yescharacteristic
530C22C41×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C41×B(4,𝔽2)11yescharacteristic
539C4C41×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C41×#188911yescharacteristic
547C2C41×#190311yescharacteristic
548C2C41×#190711yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC41×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2976C2semidirect
3. C41×#1786C2semidirect
4. C41×#1783C2semidirect
5. C41×#1513C2semidirect
6. C41×#1305C2semidirect
7. C41×#1293C2semidirect
12. C41×#450C4semidirect
14. C41×#447C4semidirect
229. #9520C41direct (N × H)
267. #2976C2×C41semidirect
268. #1786C2×C41semidirect
269. #1783C2×C41semidirect
270. #1513C2×C41semidirect
271. #1305C2×C41semidirect
272. #1293C2×C41semidirect
286. #450C4×C41semidirect
288. #447C4×C41semidirect
307. C41#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30032
C41×#29762
C41×#17862
C41×#17832
C41×#15132
C41×#13052
C41×#12932
#952041