Finite Group Databasebeta

← C41×#33020 #23809221

Subgroups — C41×#33020 #23809221

Order 10496.

1824 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#518C211yesmaximal, characteristic, complemented
2C41×#2405C212yesmaximal, complemented
3C41×#2403C211yesmaximal, characteristic
4C41×#1889C214yesmaximal, complemented
5C41×#1867C214yesmaximal, complemented
6C41×#1819C212yesmaximal, complemented
7C41×#1781C211yesmaximal, characteristic, complemented
8C23×D4×C41C2211yescharacteristic
9C23×D4×C41C2211yescharacteristic
10C2×#123×C41—22no—
11C2×#120×C41—21no—
12C2×#120×C41C2212yes—
13C41×#518—22no—
14C41×#518—24no—
15C41×#518C2214yes—
16C2×C4×D4×C41—22no—
17C2×C4×D4×C41—22no—
18C2×#117×C41—21no—
19C22×C22⋊C4×C41—21no—
20C22×C22⋊C4×C41C2212yes—
21C2×#99×C41C2214yes—
22C41×#394—24no—
23C41×#392—22no—
24C41×#386—21no—
25C41×#386—22no—
26C41×#386C2212yes—
27C41×#385C2214yescomplemented
28C41×#379C2212yes—
29C41×#379C2211yescharacteristic
30C41×#379C2214yescomplemented
31C41×#342C2218yescomplemented
32C25×C41D411yescharacteristic
33C25×C41C2311yescharacteristic
34C25×C41C2311yescharacteristic
35C22×D4×C41—22no—
36C22×D4×C41—22no—
37C22×D4×C41—28no—
38C22×D4×C41—21no—
39C22×D4×C41—22no—
40C22×D4×C41—21no—
41C22×D4×C41—22no—
42C22×D4×C41—22no—
43C22×D4×C41—44no—
44C22×D4×C41D412yes—
45C22×D4×C41C2312yes—
46C23×C4×C41—21no—
47C23×C4×C41—21no—
48C23×C4×C41D411yescharacteristic
49C23×C4×C41D412yescomplemented
50C23×C4×C41D412yescomplemented
51C23×C4×C41C2311yescharacteristic
52#123×C41—48no—
53#120×C41—28no—
54#120×C41—44no—
55C4×D4×C41—28no—
56C4×D4×C41—28no—
57C4×D4×C41—28no—
58C4×D4×C41—28no—
59#117×C41—24no—
60#117×C41—24no—
61C2×C4⋊C4×C41—21no—
62C2×C4⋊C4×C41—21no—
63C2×C4⋊C4×C41—24no—
64C2×C22⋊C4×C41—22no—
65C2×C22⋊C4×C41—24no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—24no—
68C2×C22⋊C4×C41—22no—
69C2×C22⋊C4×C41—22no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—21no—
72C2×C22⋊C4×C41—22no—
73C2×C22⋊C4×C41—22no—
74C2×C22⋊C4×C41—22no—
75C2×C22⋊C4×C41—24no—
76C2×C22⋊C4×C41—21no—
77C2×C22⋊C4×C41—22no—
78C2×C22⋊C4×C41—24no—
79C2×C22⋊C4×C41D414yescomplemented
80C2×C22⋊C4×C41C2312yes—
81C2×C22⋊C4×C41C2314yes—
82C2×C22⋊C4×C41C2314yes—
83C2×C42×C41—22no—
84#99×C41—28no—
85#95×C41—24no—
86#95×C41—22no—
87C24×C41—21no—
88C24×C41—21no—
89C24×C41—24no—
90C24×C41—24no—
91C24×C41—22no—
92C24×C41—21no—
93C24×C41—24no—
94C24×C41—42no—
95C24×C41—42no—
96C24×C41—42no—
97C24×C41—81no—
98C24×C41—81no—
99C24×C41—81no—
100C24×C41C2×D411yescharacteristic
101C24×C41C2×D412yes—
102C24×C41C2×D411yescharacteristic
103C24×C41C2×D412yes—
104C24×C41C2×D412yes—
105C24×C41C2411yescharacteristic
106C2×D4×C41—216no—
107C2×D4×C41—216no—
108C2×D4×C41—24no—
109C2×D4×C41—24no—
110C2×D4×C41—24no—
111C2×D4×C41—24no—
112C2×D4×C41—24no—
113C2×D4×C41—28no—
114C2×D4×C41—24no—
115C2×D4×C41—42no—
116C2×D4×C41—44no—
117C2×D4×C41—44no—
118C2×D4×C41—42no—
119C2×D4×C41—44no—
120C2×D4×C41—42no—
121C2×D4×C41—41no—
122C2×D4×C41—42no—
123C2×D4×C41—41no—
124C2×D4×C41—44no—
125C2×D4×C41—44no—
126C2×D4×C41—82no—
127C2×D4×C41#4118yes—
128C22×C4×C41—21no—
129C22×C4×C41—21no—
130C22×C4×C41—24no—
131C22×C4×C41—22no—
132C22×C4×C41—22no—
133C22×C4×C41—21no—
134C22×C4×C41—22no—
135C22×C4×C41—24no—
136C22×C4×C41—24no—
137C22×C4×C41—22no—
138C22×C4×C41—22no—
139C22×C4×C41—24no—
140C22×C4×C41—22no—
141C22×C4×C41—42no—
142C22×C4×C41—44no—
143C22×C4×C41—82no—
144C22×C4×C41—82no—
145C22×C4×C41—82no—
146C22×C4×C41C2×D412yes—
147C22×C4×C41C2×D414yes—
148C22×C4×C41C2×D414yes—
149C4⋊C4×C41—24no—
150C4⋊C4×C41—24no—
151C4⋊C4×C41—48no—
152C22⋊C4×C41—28no—
153C22⋊C4×C41—24no—
154C22⋊C4×C41—24no—
155C22⋊C4×C41—24no—
156C22⋊C4×C41—24no—
157C22⋊C4×C41—28no—
158C22⋊C4×C41—24no—
159C22⋊C4×C41—44no—
160C22⋊C4×C41—42no—
161C22⋊C4×C41—48no—
162C22⋊C4×C41—44no—
163C22⋊C4×C41—44no—
164C22⋊C4×C41—84no—
165C22⋊C4×C41—82no—
166C22⋊C4×C41—81no—
167C42×C41—28no—
168C23×C41—24no—
169C23×C41—24no—
170C23×C41—22no—
171C23×C41—22no—
172C23×C41—24no—
173C23×C41—24no—
174C23×C41—22no—
175C23×C41—22no—
176C23×C41—22no—
177C23×C41—24no—
178C23×C41—24no—
179C23×C41—22no—
180C23×C41—41no—
181C23×C41—42no—
182C23×C41—41no—
183C23×C41—41no—
184C23×C41—42no—
185C23×C41—41no—
186C23×C41—42no—
187C23×C41—41no—
188C23×C41—42no—
189C23×C41—42no—
190C23×C41—42no—
191C23×C41—44no—
192C23×C41—42no—
193C23×C41—41no—
194C23×C41—42no—
195C23×C41—42no—
196C23×C41—41no—
197C23×C41—42no—
198C23×C41—44no—
199C23×C41—81no—
200C23×C41—81no—
201C23×C41—88no—
202C23×C41—88no—
203C23×C41—88no—
204C23×C41#12011yescharacteristic
205C23×C41#12012yes—
206C23×C41#12011yescharacteristic
207C23×C41#12314yescomplemented
208C23×C41C22×D411yescharacteristic
209C23×C41C22×D412yes—
210C23×C41C2×#4114yes—
211D4×C41—216no—
212D4×C41—216no—
213D4×C41—48no—
214D4×C41—44no—
215D4×C41—44no—
216D4×C41—88no—
217C2×C4×C41—24no—
218C2×C4×C41—24no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—24no—
223C2×C4×C41—24no—
224C2×C4×C41—24no—
225C2×C4×C41—42no—
226C2×C4×C41—41no—
227C2×C4×C41—44no—
228C2×C4×C41—41no—
229C2×C4×C41—44no—
230C2×C4×C41—44no—
231C2×C4×C41—44no—
232C2×C4×C41—44no—
233C2×C4×C41—42no—
234C2×C4×C41—44no—
235C2×C4×C41—42no—
236C2×C4×C41—42no—
237C2×C4×C41—44no—
238C2×C4×C41—82no—
239C2×C4×C41—82no—
240C2×C4×C41—84no—
241C2×C4×C41—84no—
242C2×C4×C41#12314yescomplemented
243#33020C4111yesmaximal, characteristic, direct product factor, Sylow
244C22×C41—21no—
245C22×C41—22no—
246C22×C41—21no—
247C22×C41—21no—
248C22×C41—22no—
249C22×C41—21no—
250C22×C41—21no—
251C22×C41—22no—
252C22×C41—24no—
253C22×C41—22no—
254C22×C41—21no—
255C22×C41—22no—
256C22×C41—21no—
257C22×C41—44no—
258C22×C41—48no—
259C22×C41—44no—
260C22×C41—44no—
261C22×C41—48no—
262C22×C41—44no—
263C22×C41—48no—
264C22×C41—42no—
265C22×C41—42no—
266C22×C41—42no—
267C22×C41—82no—
268C22×C41—82no—
269C22×C41—84no—
270C22×C41—82no—
271C22×C41—84no—
272C22×C41—84no—
273C22×C41—81no—
274C22×C41—81no—
275C22×C41B(4,𝔽2)12yes—
276C22×C41C2×#12011yescharacteristic
277C22×C41C2×#12312yes—
278C22×C41#52514yes—
279C4×C41—24no—
280C4×C41—42no—
281C4×C41—44no—
282C4×C41—44no—
283C4×C41—84no—
284C4×C41—82no—
285C2×#518C2×C4111yescharacteristic, complemented
286#2405C2×C4112yescomplemented
287#2403C2×C4111yescharacteristic
288#1889C2×C4114yescomplemented
289#1867C2×C4114yescomplemented
290#1819C2×C4112yescomplemented
291#1781C2×C4111yescharacteristic, complemented
292C2×C41—22no—
293C2×C41—24no—
294C2×C41—22no—
295C2×C41—42no—
296C2×C41—41no—
297C2×C41—44no—
298C2×C41—82no—
299C2×C41#284911yescharacteristic
300C2×C41C2×B(4,𝔽2)11yescharacteristic
301C2×C41#302611yescharacteristic
302C23×D4C22×C4111yescharacteristic
303C23×D4C22×C4111yescharacteristic
304C2×#123—22no—
305C2×#120—21no—
306C2×#120C22×C4112yes—
307#518—22no—
308#518—24no—
309#518C22×C4114yes—
310C2×C4×D4—22no—
311C2×C4×D4—22no—
312C2×#117—21no—
313C22×C22⋊C4—21no—
314C22×C22⋊C4C22×C4112yes—
315C2×#99C22×C4114yes—
316#394—24no—
317#392—22no—
318#386—21no—
319#386—22no—
320#386C22×C4112yes—
321#385C22×C4114yescomplemented
322#379C22×C4111yescharacteristic
323#379C22×C4112yes—
324#379C22×C4114yescomplemented
325#342C22×C4118yescomplemented
326C41#3302011yescharacteristic, direct product factor, Sylow
327C25D4×C4111yescharacteristic
328C25C23×C4111yescharacteristic
329C25C23×C4111yescharacteristic
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—28no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—44no—
339C22×D4D4×C4112yes—
340C22×D4C23×C4112yes—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4D4×C4111yescharacteristic
344C23×C4D4×C4112yescomplemented
345C23×C4D4×C4112yescomplemented
346C23×C4C23×C4111yescharacteristic
347#123—48no—
348#120—28no—
349#120—44no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—28no—
353C4×D4—28no—
354#117—24no—
355#117—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4D4×C4114yescomplemented
375C2×C22⋊C4C23×C4112yes—
376C2×C22⋊C4C23×C4114yes—
377C2×C22⋊C4C23×C4114yes—
378C2×C42—22no—
379#99—28no—
380#95—24no—
381#95—22no—
382C24—21no—
383C24—21no—
384C24—24no—
385C24—24no—
386C24—22no—
387C24—21no—
388C24—24no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—81no—
393C24—81no—
394C24—81no—
395C24C2×D4×C4111yescharacteristic
396C24C2×D4×C4112yes—
397C24C2×D4×C4111yescharacteristic
398C24C2×D4×C4112yes—
399C24C2×D4×C4112yes—
400C24C24×C4111yescharacteristic
401C2×D4—216no—
402C2×D4—216no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—42no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—82no—
422C2×D4#41×C4118yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—82no—
441C22×C4C2×D4×C4112yes—
442C22×C4C2×D4×C4114yes—
443C22×C4C2×D4×C4114yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—48no—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—42no—
456C22⋊C4—48no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—84no—
460C22⋊C4—82no—
461C22⋊C4—81no—
462C42—28no—
463C23—24no—
464C23—24no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—24no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—44no—
494C23—81no—
495C23—81no—
496C23—88no—
497C23—88no—
498C23—88no—
499C23#120×C4111yescharacteristic
500C23#120×C4112yes—
501C23#120×C4111yescharacteristic
502C23#123×C4114yescomplemented
503C23C22×D4×C4111yescharacteristic
504C23C22×D4×C4112yes—
505C23C2×#41×C4114yes—
506D4—216no—
507D4—216no—
508D4—48no—
509D4—44no—
510D4—44no—
511D4—88no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—44no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—84no—
537C2×C4#123×C4114yescomplemented
538C22—21no—
539C22—22no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—24no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—44no—
552C22—44no—
553C22—48no—
554C22—44no—
555C22—48no—
556C22—44no—
557C22—48no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—82no—
563C22—84no—
564C22—82no—
565C22—84no—
566C22—84no—
567C22—81no—
568C22—81no—
569C22C41×B(4,𝔽2)12yes—
570C22C2×#120×C4111yescharacteristic
571C22C2×#123×C4112yes—
572C22C41×#52514yes—
573C4—24no—
574C4—42no—
575C4—44no—
576C4—44no—
577C4—82no—
578C4—84no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—41no—
583C2—42no—
584C2—44no—
585C2—82no—
586C2C41×#284911yescharacteristic
587C2C2×C41×B(4,𝔽2)11yescharacteristic
588C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#2403C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#518C2semidirect
2. C41×#2405C2semidirect
4. C41×#1889C2semidirect
5. C41×#1867C2semidirect
6. C41×#1819C2semidirect
7. C41×#1781C2semidirect
27. C41×#385C22semidirect
30. C41×#379C22semidirect
31. C41×#342C22semidirect
49. C23×C4×C41D4semidirect
50. C23×C4×C41D4semidirect
79. C2×C22⋊C4×C41D4semidirect
207. C23×C41#123semidirect
242. C2×C4×C41#123semidirect
243. #33020C41direct (N × H)
285. C2×#518C2×C41semidirect
286. #2405C2×C41semidirect
288. #1889C2×C41semidirect
289. #1867C2×C41semidirect
290. #1819C2×C41semidirect
291. #1781C2×C41semidirect
321. #385C22×C41semidirect
324. #379C22×C41semidirect
325. #342C22×C41semidirect
326. C41#33020direct (N × H)
344. C23×C4D4×C41semidirect
345. C23×C4D4×C41semidirect
374. C2×C22⋊C4D4×C41semidirect
502. C23#123×C41semidirect
537. C2×C4#123×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5182
C41×#24052
C41×#24032
C41×#18892
C41×#18672
C41×#18192
C41×#17812
#3302041