Finite Group Databasebeta

← C41×#12705 #23788906

Subgroups — C41×#12705 #23788906

Order 10496.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3484C211yesmaximal, characteristic
2C41×#2121C214yesmaximal, complemented
3C41×#1783C211yesmaximal, characteristic, complemented
4C41×#1781C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C41C411yescharacteristic, complemented
6C23×D4×C41C2211yescharacteristic
7C41×#546—24no—
8D42×C41—24no—
9C41×#535—21no—
10C41×#534—21no—
11C41×#534C2212yes—
12C41×#525—21no—
13C2×#120×C41—21no—
14C2×#120×C41C412yescomplemented
15C41×#518C411yescharacteristic, complemented
16C2×#100×C41—21no—
17C2×#100×C41C2212yescomplemented
18C2×#99×C41—21no—
19C2×#99×C41C2212yescomplemented
20C41×#407—21no—
21C41×#379—21no—
22C41×#352—24no—
23C41×AΣL(1,𝔽16)—24no—
24C25×C41C2×C411yescharacteristic
25C25×C41D411yescharacteristic
26H(5,𝔽2)×C41—42no—
27H(5,𝔽2)×C41—42no—
28C2×#41×C41—21no—
29C2×#41×C41—22no—
30C22×D4×C41—21no—
31C22×D4×C41—22no—
32C22×D4×C41—22no—
33C22×D4×C41—22no—
34C22×D4×C41—24no—
35C22×D4×C41—42no—
36C22×D4×C41—42no—
37C22×D4×C41C2×C411yescharacteristic
38C22×D4×C41C2×C412yes—
39C22×D4×C41D411yescharacteristic
40C22×D4×C41D411yescharacteristic
41C22×D4×C41C2311yescharacteristic
42C23×C4×C41D411yescharacteristic
43C2×M16×C41—22no—
44#127×C41—22no—
45#124×C41—22no—
46#123×C41—22no—
47#123×C41—22no—
48#123×C41D414yes—
49C22⋊Q8×C41—22no—
50#121×C41—22no—
51#121×C41—24no—
52#121×C41—24no—
53#121×C41—24no—
54#120×C41—24no—
55#120×C41—22no—
56#120×C41—22no—
57#120×C41—22no—
58#120×C41—22no—
59#120×C41—24no—
60#120×C41D414yes—
61C4×D4×C41—24no—
62C4×D4×C41—24no—
63#117×C41—21no—
64C2×C22⋊C4×C41—22no—
65C2×C22⋊C4×C41—21no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—22no—
68C2×C22⋊C4×C41—42no—
69C2×C22⋊C4×C41C2×C412yes—
70#100×C41—24no—
71#100×C41—42no—
72#99×C41—24no—
73#99×C41—42no—
74C22⋊C8×C41—42no—
75C24×C41—21no—
76C24×C41—22no—
77C24×C41—22no—
78C24×C41—22no—
79C24×C41—41no—
80C24×C41—41no—
81C24×C41—41no—
82C24×C41—82no—
83C24×C41—82no—
84C24×C41C22⋊C411yescharacteristic
85C24×C41C22⋊C411yescharacteristic
86C24×C41C22⋊C411yescharacteristic
87C24×C41C22⋊C412yescomplemented
88C24×C41C22×C411yescharacteristic
89C24×C41C2×D411yescharacteristic
90#41×C41—42no—
91#41×C41—48no—
92#41×C41—42no—
93C2×Q8×C41—21no—
94C2×D4×C41—22no—
95C2×D4×C41—22no—
96C2×D4×C41—24no—
97C2×D4×C41—22no—
98C2×D4×C41—21no—
99C2×D4×C41—22no—
100C2×D4×C41—22no—
101C2×D4×C41—22no—
102C2×D4×C41—22no—
103C2×D4×C41—24no—
104C2×D4×C41—24no—
105C2×D4×C41—22no—
106C2×D4×C41—22no—
107C2×D4×C41—22no—
108C2×D4×C41—41no—
109C2×D4×C41—41no—
110C2×D4×C41—41no—
111C2×D4×C41—41no—
112C2×D4×C41—416no—
113C2×D4×C41—48no—
114C2×D4×C41—42no—
115C2×D4×C41—42no—
116C2×D4×C41—42no—
117C2×D4×C41—42no—
118C2×D4×C41—84no—
119C2×D4×C41—84no—
120C2×D4×C41C2×D414yes—
121C22×C4×C41—21no—
122C22×C4×C41—22no—
123C22×C4×C41—22no—
124C22×C4×C41—22no—
125C22×C4×C41—22no—
126C22×C4×C41—22no—
127C22×C4×C41—41no—
128C22×C4×C41—42no—
129C22×C4×C41C22⋊C411yescharacteristic
130C22×C4×C41C22⋊C412yescomplemented
131C22×C4×C41C2×D411yescharacteristic
132M16×C41—42no—
133M16×C41—42no—
134C2×C8×C41—42no—
135C4⋊C4×C41—22no—
136C4⋊C4×C41—24no—
137C22⋊C4×C41—24no—
138C22⋊C4×C41—22no—
139C22⋊C4×C41—24no—
140C22⋊C4×C41—22no—
141C22⋊C4×C41—24no—
142C22⋊C4×C41—24no—
143C22⋊C4×C41—42no—
144C22⋊C4×C41—42no—
145C22⋊C4×C41—84no—
146C22⋊C4×C41C22⋊C414yescomplemented
147C42×C41—22no—
148C23×C41—21no—
149C23×C41—21no—
150C23×C41—21no—
151C23×C41—21no—
152C23×C41—21no—
153C23×C41—21no—
154C23×C41—21no—
155C23×C41—21no—
156C23×C41—21no—
157C23×C41—21no—
158C23×C41—22no—
159C23×C41—21no—
160C23×C41—21no—
161C23×C41—42no—
162C23×C41—44no—
163C23×C41—44no—
164C23×C41—44no—
165C23×C41—44no—
166C23×C41—44no—
167C23×C41—42no—
168C23×C41—42no—
169C23×C41—82no—
170C23×C41—82no—
171C23×C41—82no—
172C23×C41—81no—
173C23×C41—81no—
174C23×C41—81no—
175C23×C41—81no—
176C23×C41—82no—
177C23×C41—82no—
178C23×C41—82no—
179C23×C41—82no—
180C23×C41—82no—
181C23×C41—82no—
182C23×C41—82no—
183C23×C41—82no—
184C23×C41#9912yes—
185C23×C41C2×C22⋊C412yes—
186C23×C41C2×C22⋊C411yescharacteristic
187C23×C41#12012yes—
188Q8×C41—42no—
189D4×C41—28no—
190D4×C41—44no—
191D4×C41—44no—
192D4×C41—44no—
193D4×C41—42no—
194D4×C41—44no—
195D4×C41—44no—
196D4×C41—48no—
197D4×C41—42no—
198D4×C41—42no—
199D4×C41—84no—
200D4×C41—84no—
201C2×C4×C41—21no—
202C2×C4×C41—21no—
203C2×C4×C41—21no—
204C2×C4×C41—21no—
205C2×C4×C41—24no—
206C2×C4×C41—22no—
207C2×C4×C41—44no—
208C2×C4×C41—44no—
209C2×C4×C41—42no—
210C2×C4×C41—42no—
211C2×C4×C41—82no—
212C2×C4×C41—82no—
213C2×C4×C41—82no—
214C2×C4×C41—84no—
215C2×C4×C41#9912yes—
216C2×C4×C41#12012yes—
217C8×C41—82no—
218#12705C4111yesmaximal, characteristic, direct product factor, Sylow
219C22×C41—22no—
220C22×C41—22no—
221C22×C41—22no—
222C22×C41—22no—
223C22×C41—22no—
224C22×C41—22no—
225C22×C41—41no—
226C22×C41—42no—
227C22×C41—42no—
228C22×C41—42no—
229C22×C41—42no—
230C22×C41—42no—
231C22×C41—41no—
232C22×C41—41no—
233C22×C41—41no—
234C22×C41—44no—
235C22×C41—42no—
236C22×C41—41no—
237C22×C41—42no—
238C22×C41—41no—
239C22×C41—81no—
240C22×C41—81no—
241C22×C41—81no—
242C22×C41—81no—
243C22×C41—81no—
244C22×C41—81no—
245C22×C41—88no—
246C22×C41—88no—
247C22×C41—162no—
248C22×C41—162no—
249C22×C41#37911yescharacteristic
250C22×C41C2×#9911yescharacteristic
251C22×C41C2×#9911yescharacteristic
252C4×C41—22no—
253C4×C41—22no—
254C4×C41—44no—
255C4×C41—42no—
256C4×C41—162no—
257#3484C2×C4111yescharacteristic
258#2121C2×C4114yescomplemented
259#1783C2×C4111yescharacteristic, complemented
260#1781C2×C4111yescharacteristic, complemented
261C2×C41—21no—
262C2×C41—21no—
263C2×C41—21no—
264C2×C41—42no—
265C2×C41—42no—
266C2×C41—42no—
267C2×C41—42no—
268C2×C41—81no—
269C2×C41—82no—
270C2×C41#178111yescharacteristic
271C2×H(5,𝔽2)C4×C4111yescharacteristic, complemented
272C23×D4C22×C4111yescharacteristic
273#546—24no—
274D42—24no—
275#535—21no—
276#534—21no—
277#534C22×C4112yes—
278#525—21no—
279C2×#120—21no—
280C2×#120C4×C4112yescomplemented
281#518C4×C4111yescharacteristic, complemented
282C2×#100—21no—
283C2×#100C22×C4112yescomplemented
284C2×#99—21no—
285C2×#99C22×C4112yescomplemented
286#407—21no—
287#379—21no—
288#352—24no—
289AΣL(1,𝔽16)—24no—
290C41#1270511yescharacteristic, direct product factor, Sylow
291C25C2×C4×C4111yescharacteristic
292C25D4×C4111yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C4111yescharacteristic
305C22×D4C2×C4×C4112yes—
306C22×D4D4×C4111yescharacteristic
307C22×D4D4×C4111yescharacteristic
308C22×D4C23×C4111yescharacteristic
309C23×C4D4×C4111yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C4114yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C4114yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C4112yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C4111yescharacteristic
352C24C22⋊C4×C4111yescharacteristic
353C24C22⋊C4×C4111yescharacteristic
354C24C22⋊C4×C4112yescomplemented
355C24C22×C4×C4111yescharacteristic
356C24C2×D4×C4111yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C4114yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C4111yescharacteristic
397C22×C4C22⋊C4×C4112yescomplemented
398C22×C4C2×D4×C4111yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C4114yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C4112yes—
452C23C2×C22⋊C4×C4112yes—
453C23C2×C22⋊C4×C4111yescharacteristic
454C23#120×C4112yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C4112yes—
483C2×C4#120×C4112yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22C41×#37911yescharacteristic
516C22C2×#99×C4111yescharacteristic
517C22C2×#99×C4111yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2C41×#178111yescharacteristic
subgroupG/H
center, socleC2×C41#1781
commutatorC24C22×C4×C41
Frattini, cosocleC22×D4C23×C41
prime radicalC41×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C23×C41 ◁ C23×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2121C2semidirect
3. C41×#1783C2semidirect
4. C41×#1781C2semidirect
5. C2×H(5,𝔽2)×C41C4semidirect
14. C2×#120×C41C4semidirect
15. C41×#518C4semidirect
17. C2×#100×C41C22semidirect
19. C2×#99×C41C22semidirect
87. C24×C41C22⋊C4semidirect
130. C22×C4×C41C22⋊C4semidirect
146. C22⋊C4×C41C22⋊C4semidirect
218. #12705C41direct (N × H)
258. #2121C2×C41semidirect
259. #1783C2×C41semidirect
260. #1781C2×C41semidirect
271. C2×H(5,𝔽2)C4×C41semidirect
280. C2×#120C4×C41semidirect
281. #518C4×C41semidirect
283. C2×#100C22×C41semidirect
285. C2×#99C22×C41semidirect
290. C41#12705direct (N × H)
354. C24C22⋊C4×C41semidirect
397. C22×C4C22⋊C4×C41semidirect
413. C22⋊C4C22⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34842
C41×#21212
C41×#17832
C41×#17812
#1270541