Finite Group Databasebeta

← C41×#33561 #23809762

Subgroups — C41×#33561 #23809762

Order 10496.

1096 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3550C211yesmaximal, characteristic, complemented
2C41×#3028C212yesmaximal, complemented
3C41×#3018C211yesmaximal, characteristic
4C41×#2201C214yesmaximal, complemented
5C41×#2198C214yesmaximal, complemented
6C41×#2126C211yesmaximal, characteristic, complemented
7C41×#2123C212yesmaximal, complemented
8C41×#585C2211yescharacteristic
9C41×#575—21no—
10C41×#563—21no—
11C41×#563C2212yescomplemented
12C41×#559C2212yescomplemented
13Q82×C41—21no—
14C41×#556—22no—
15D4×Q8×C41—22no—
16C41×#542—24no—
17C41×#536—21no—
18C41×#536—22no—
19C41×#536C2212yes—
20C41×#533—21no—
21C41×#532C2211yescharacteristic
22C41×#458—24no—
23C41×#458C2218yes—
24C41×#456—21no—
25C41×#455C2212yes—
26C41×#454—21no—
27C41×#453C2212yes—
28C2×#104×C41—21no—
29C41×#413C2211yescharacteristic
30C41×#410—22no—
31C41×#410C2212yes—
32C41×#354C2212yescomplemented
33C41×#353C2212yescomplemented
34C41×#352C2218yescomplemented
352−1+4×C41—21no—
362−1+4×C41—41no—
37H(5,𝔽2)×C41—22no—
38H(5,𝔽2)×C41—41no—
39H(5,𝔽2)×C41C2312yes—
40C2×#41×C41—22no—
41C2×#41×C41—21no—
42C2×#41×C41—42no—
43C2×#41×C41D411yescharacteristic
44C2×#41×C41C2311yescharacteristic
45C22×Q8×C41—21no—
46C22×Q8×C41D412yes—
47#137×C41—22no—
48#137×C41—41no—
49AGL(1,ℤ/8)×C41—22no—
50AGL(1,ℤ/8)×C41—41no—
51#135×C41—42no—
52C2×M16×C41—21no—
53C4⋊Q8×C41—21no—
54C4⋊Q8×C41—21no—
55C4⋊Q8×C41—24no—
56C4⋊Q8×C41—22no—
57C4⋊Q8×C41—22no—
58C4⋊Q8×C41—42no—
59C4⋊Q8×C41D411yescharacteristic
60#127×C41C2311yescharacteristic
61#126×C41—24no—
62#126×C41—24no—
63#125×C41—22no—
64#124×C41—22no—
65#124×C41—22no—
66#124×C41—24no—
67#124×C41—42no—
68#124×C41D411yescharacteristic
69#124×C41C2311yescharacteristic
70#123×C41—22no—
71#123×C41—22no—
72#123×C41—28no—
73#123×C41D414yes—
74#123×C41C2314yes—
75C22⋊Q8×C41—22no—
76C22⋊Q8×C41—22no—
77C22⋊Q8×C41—24no—
78C22⋊Q8×C41—22no—
79C22⋊Q8×C41—22no—
80C22⋊Q8×C41—24no—
81C22⋊Q8×C41—44no—
82#121×C41—22no—
83C4×Q8×C41—22no—
84C4×Q8×C41—24no—
85C4×Q8×C41—22no—
86C4×D4×C41—22no—
87C4×D4×C41—24no—
88#117×C41—22no—
89#117×C41—21no—
90#117×C41—22no—
91#117×C41D412yes—
92C2×C42×C41D411yescharacteristic
93#104×C41—22no—
94#104×C41—22no—
95#101×C41—21no—
96#100×C41C2312yes—
97#99×C41—22no—
98#99×C41—28no—
99#99×C41C2314yes—
100#41×C41—22no—
101#41×C41—22no—
102#41×C41—41no—
103#41×C41—41no—
104#41×C41—42no—
105#41×C41—42no—
106#41×C41—42no—
107#41×C41—41no—
108#41×C41—44no—
109#41×C41—41no—
110#41×C41—41no—
111#41×C41—42no—
112#41×C41—42no—
113#41×C41—41no—
114C2×Q8×C41—22no—
115C2×Q8×C41—22no—
116C2×Q8×C41—22no—
117C2×Q8×C41—22no—
118C2×Q8×C41—22no—
119C2×Q8×C41—21no—
120C2×Q8×C41—42no—
121C2×Q8×C41—42no—
122C2×Q8×C41—42no—
123C2×Q8×C41—81no—
124C2×Q8×C41—81no—
125C2×Q8×C41C2×D411yescharacteristic
126C2×Q8×C41C2×D411yescharacteristic
127C2×D4×C41—21no—
128C2×D4×C41—22no—
129C2×D4×C41—24no—
130C2×D4×C41—22no—
131C2×D4×C41—21no—
132C2×D4×C41—42no—
133C2×D4×C41—44no—
134C2×D4×C41—41no—
135C2×D4×C41C2×D412yes—
136C2×D4×C41C2×D411yescharacteristic
137C2×D4×C41C2411yescharacteristic
138C22×C4×C41—24no—
139C22×C4×C41—21no—
140C22×C4×C41—22no—
141C22×C4×C41—21no—
142C22×C4×C41—41no—
143C22×C4×C41C2×D412yes—
144C22×C4×C41C2×D411yescharacteristic
145C22×C4×C41C2×D414yes—
146Q16×C41—42no—
147SD16×C41—42no—
148SD16×C41—42no—
149D8×C41—42no—
150M16×C41—22no—
151M16×C41—41no—
152C2×C8×C41—41no—
153C4⋊C4×C41—22no—
154C4⋊C4×C41—22no—
155C4⋊C4×C41—22no—
156C4⋊C4×C41—24no—
157C4⋊C4×C41—24no—
158C4⋊C4×C41—22no—
159C4⋊C4×C41—24no—
160C4⋊C4×C41—22no—
161C4⋊C4×C41—24no—
162C4⋊C4×C41—42no—
163C4⋊C4×C41—48no—
164C22⋊C4×C41—22no—
165C22⋊C4×C41—24no—
166C22⋊C4×C41—24no—
167C22⋊C4×C41—22no—
168C22⋊C4×C41—24no—
169C22⋊C4×C41—22no—
170C22⋊C4×C41—24no—
171C22⋊C4×C41—48no—
172C22⋊C4×C41C2×D414yes—
173C42×C41—24no—
174C42×C41—22no—
175C42×C41—22no—
176C42×C41—21no—
177C42×C41—42no—
178C42×C41C2×D411yescharacteristic
179C42×C41C2×D411yescharacteristic
180C23×C41—24no—
181C23×C41—21no—
182C23×C41—41no—
183C23×C41#12011yescharacteristic
184C23×C41C22×D412yes—
185Q8×C41—22no—
186Q8×C41—41no—
187Q8×C41—41no—
188Q8×C41—44no—
189Q8×C41—42no—
190Q8×C41—41no—
191Q8×C41—42no—
192Q8×C41—42no—
193Q8×C41—82no—
194Q8×C41—82no—
195D4×C41—22no—
196D4×C41—42no—
197D4×C41—41no—
198D4×C41—41no—
199D4×C41—44no—
200D4×C41—42no—
201D4×C41—44no—
202D4×C41—42no—
203D4×C41—42no—
204D4×C41—41no—
205D4×C41—81no—
206C2×C4×C41—21no—
207C2×C4×C41—22no—
208C2×C4×C41—22no—
209C2×C4×C41—21no—
210C2×C4×C41—21no—
211C2×C4×C41—24no—
212C2×C4×C41—24no—
213C2×C4×C41—21no—
214C2×C4×C41—21no—
215C2×C4×C41—24no—
216C2×C4×C41—42no—
217C2×C4×C41—44no—
218C2×C4×C41—42no—
219C2×C4×C41—41no—
220C2×C4×C41—42no—
221C2×C4×C41—41no—
222C2×C4×C41—41no—
223C2×C4×C41—44no—
224C2×C4×C41—44no—
225C2×C4×C41—82no—
226C2×C4×C41#12012yes—
227C2×C4×C41#12011yescharacteristic
228C2×C4×C41C22×D411yescharacteristic
229C8×C41—42no—
230#33561C4111yesmaximal, characteristic, direct product factor, Sylow
231C22×C41—22no—
232C22×C41—21no—
233C22×C41—41no—
234C22×C41—42no—
235C22×C41—42no—
236C22×C41—42no—
237C22×C41—41no—
238C22×C41—84no—
239C22×C41—161no—
240C22×C41C2×#12011yescharacteristic
241C4×C41—22no—
242C4×C41—21no—
243C4×C41—22no—
244C4×C41—41no—
245C4×C41—44no—
246C4×C41—42no—
247C4×C41—41no—
248C4×C41—44no—
249C4×C41—84no—
250C4×C41B(4,𝔽2)11yescharacteristic
251C4×C41B(4,𝔽2)11yescharacteristic
252#3550C2×C4111yescharacteristic, complemented
253#3028C2×C4112yescomplemented
254#3018C2×C4111yescharacteristic
255#2201C2×C4114yescomplemented
256#2198C2×C4114yescomplemented
257#2126C2×C4111yescharacteristic, complemented
258#2123C2×C4112yescomplemented
259C2×C41—21no—
260C2×C41—42no—
261C2×C41—41no—
262C2×C41—81no—
263C2×C41—82no—
264C2×C41C2×B(4,𝔽2)11yescharacteristic
265#585C22×C4111yescharacteristic
266#575—21no—
267#563—21no—
268#563C22×C4112yescomplemented
269#559C22×C4112yescomplemented
270Q82—21no—
271#556—22no—
272D4×Q8—22no—
273#542—24no—
274#536—21no—
275#536—22no—
276#536C22×C4112yes—
277#533—21no—
278#532C22×C4111yescharacteristic
279#458—24no—
280#458C22×C4118yes—
281#456—21no—
282#455C22×C4112yes—
283#454—21no—
284#453C22×C4112yes—
285C2×#104—21no—
286#413C22×C4111yescharacteristic
287#410—22no—
288#410C22×C4112yes—
289#354C22×C4112yescomplemented
290#353C22×C4112yescomplemented
291#352C22×C4118yescomplemented
292C41#3356111yescharacteristic, direct product factor, Sylow
2932−1+4—21no—
2942−1+4—41no—
295H(5,𝔽2)—22no—
296H(5,𝔽2)—41no—
297H(5,𝔽2)C23×C4112yes—
298C2×#41—22no—
299C2×#41—21no—
300C2×#41—42no—
301C2×#41D4×C4111yescharacteristic
302C2×#41C23×C4111yescharacteristic
303C22×Q8—21no—
304C22×Q8D4×C4112yes—
305#137—22no—
306#137—41no—
307AGL(1,ℤ/8)—22no—
308AGL(1,ℤ/8)—41no—
309#135—42no—
310C2×M16—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—42no—
317C4⋊Q8D4×C4111yescharacteristic
318#127C23×C4111yescharacteristic
319#126—24no—
320#126—24no—
321#125—22no—
322#124—22no—
323#124—22no—
324#124—24no—
325#124—42no—
326#124D4×C4111yescharacteristic
327#124C23×C4111yescharacteristic
328#123—22no—
329#123—22no—
330#123—28no—
331#123D4×C4114yes—
332#123C23×C4114yes—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—44no—
340#121—22no—
341C4×Q8—22no—
342C4×Q8—24no—
343C4×Q8—22no—
344C4×D4—22no—
345C4×D4—24no—
346#117—22no—
347#117—21no—
348#117—22no—
349#117D4×C4112yes—
350C2×C42D4×C4111yescharacteristic
351#104—22no—
352#104—22no—
353#101—21no—
354#100C23×C4112yes—
355#99—22no—
356#99—28no—
357#99C23×C4114yes—
358#41—22no—
359#41—22no—
360#41—41no—
361#41—41no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—41no—
366#41—44no—
367#41—41no—
368#41—41no—
369#41—42no—
370#41—41no—
371#41—42no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—42no—
381C2×Q8—81no—
382C2×Q8—81no—
383C2×Q8C2×D4×C4111yescharacteristic
384C2×Q8C2×D4×C4111yescharacteristic
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—44no—
392C2×D4—41no—
393C2×D4C2×D4×C4112yes—
394C2×D4C2×D4×C4111yescharacteristic
395C2×D4C24×C4111yescharacteristic
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—41no—
401C22×C4C2×D4×C4112yes—
402C22×C4C2×D4×C4111yescharacteristic
403C22×C4C2×D4×C4114yes—
404Q16—42no—
405SD16—42no—
406SD16—42no—
407D8—42no—
408M16—22no—
409M16—41no—
410C2×C8—41no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—42no—
421C4⋊C4—48no—
422C22⋊C4—22no—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—48no—
430C22⋊C4C2×D4×C4114yes—
431C42—24no—
432C42—22no—
433C42—21no—
434C42—22no—
435C42—42no—
436C42C2×D4×C4111yescharacteristic
437C42C2×D4×C4111yescharacteristic
438C23—24no—
439C23—21no—
440C23—41no—
441C23#120×C4111yescharacteristic
442C23C22×D4×C4112yes—
443Q8—22no—
444Q8—41no—
445Q8—41no—
446Q8—42no—
447Q8—44no—
448Q8—41no—
449Q8—42no—
450Q8—42no—
451Q8—82no—
452Q8—82no—
453D4—22no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4—42no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—81no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—82no—
484C2×C4#120×C4112yes—
485C2×C4#120×C4111yescharacteristic
486C2×C4C22×D4×C4111yescharacteristic
487C8—42no—
488C22—22no—
489C22—21no—
490C22—41no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—41no—
495C22—84no—
496C22—161no—
497C22C2×#120×C4111yescharacteristic
498C4—22no—
499C4—21no—
500C4—22no—
501C4—41no—
502C4—44no—
503C4—42no—
504C4—41no—
505C4—44no—
506C4—84no—
507C4C41×B(4,𝔽2)11yescharacteristic
508C4C41×B(4,𝔽2)11yescharacteristic
509C2—21no—
510C2—42no—
511C2—41no—
512C2—81no—
513C2—82no—
514C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C41C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
prime radicalC41×#3018C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3550C2semidirect
2. C41×#3028C2semidirect
4. C41×#2201C2semidirect
5. C41×#2198C2semidirect
6. C41×#2126C2semidirect
7. C41×#2123C2semidirect
11. C41×#563C22semidirect
12. C41×#559C22semidirect
32. C41×#354C22semidirect
33. C41×#353C22semidirect
34. C41×#352C22semidirect
230. #33561C41direct (N × H)
252. #3550C2×C41semidirect
253. #3028C2×C41semidirect
255. #2201C2×C41semidirect
256. #2198C2×C41semidirect
257. #2126C2×C41semidirect
258. #2123C2×C41semidirect
268. #563C22×C41semidirect
269. #559C22×C41semidirect
289. #354C22×C41semidirect
290. #353C22×C41semidirect
291. #352C22×C41semidirect
292. C41#33561direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35502
C41×#30282
C41×#30182
C41×#22012
C41×#21982
C41×#21262
C41×#21232
#3356141