Finite Group Databasebeta

← C41×#33546 #23809747

Subgroups — C41×#33546 #23809747

Order 10496.

1236 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3481C211yesmaximal, characteristic, complemented
2C41×#3025C212yesmaximal, complemented
3C41×#3018C211yesmaximal, characteristic, complemented
4C41×#2198C212yesmaximal, complemented
5C41×#2197C214yesmaximal, complemented
6C41×#2196C212yesmaximal, complemented
7C41×#2126C211yesmaximal, characteristic, complemented
8C41×#2120C212yesmaximal, complemented
9C41×#585C2211yescharacteristic, complemented
10C41×#575—21no—
11C41×#559C2211yescharacteristic, complemented
12C41×#554—21no—
13C41×#553—22no—
14C41×#551—21no—
15C41×#551C2212yescomplemented
16C41×#546—22no—
17D42×C41C2211yescharacteristic, complemented
18C41×#532C2211yescharacteristic
19C41×#529—22no—
20C41×#525—21no—
21C41×#525—22no—
22C41×#525C2212yes—
23C4×#41×C41—21no—
24C2×C4×D4×C41—22no—
25C41×#458—22no—
26C41×#458C2214yescomplemented
27C41×B(4,𝔽2)—22no—
28C41×B(4,𝔽2)C2214yes—
29C41×#456—21no—
30C41×#455C2212yescomplemented
31C41×#454—21no—
32C41×#453C2212yes—
33C2×#104×C41—21no—
34C41×#413C2211yescharacteristic, complemented
35C41×#410—22no—
36C41×#410C2212yescomplemented
37C41×#354C2212yescomplemented
38C41×#353C2212yescomplemented
39C41×#352C2214yescomplemented
40C41×AΣL(1,𝔽16)C2214yescomplemented
412−1+4×C41—21no—
422−1+4×C41—41no—
43H(5,𝔽2)×C41—22no—
44H(5,𝔽2)×C41—41no—
45H(5,𝔽2)×C41C2312yes—
46C2×#41×C41—21no—
47C2×#41×C41—22no—
48C2×#41×C41—21no—
49C2×#41×C41—42no—
50C2×#41×C41D411yescharacteristic, complemented
51C2×#41×C41C2311yescharacteristic
52C22×D4×C41—22no—
53C23×C4×C41—21no—
54C23×C4×C41D412yescomplemented
55#137×C41—22no—
56#137×C41—41no—
57AGL(1,ℤ/8)×C41—22no—
58AGL(1,ℤ/8)×C41—41no—
59#135×C41—42no—
60C2×M16×C41—21no—
61C4⋊Q8×C41D411yescharacteristic, complemented
62#127×C41C2311yescharacteristic
63#126×C41—22no—
64#126×C41—22no—
65#125×C41—22no—
66#124×C41—22no—
67#124×C41D411yescharacteristic, complemented
68#124×C41C2311yescharacteristic
69#123×C41—21no—
70#123×C41—22no—
71#123×C41—21no—
72#123×C41—22no—
73#123×C41—24no—
74#123×C41D412yescomplemented
75#123×C41C2312yes—
76C22⋊Q8×C41—22no—
77C22⋊Q8×C41—22no—
78C22⋊Q8×C41—22no—
79C22⋊Q8×C41—42no—
80#121×C41—22no—
81#121×C41—22no—
82#121×C41—22no—
83#121×C41—22no—
84#121×C41—42no—
85#120×C41—21no—
86#120×C41—21no—
87#120×C41—24no—
88#120×C41D412yescomplemented
89#120×C41C2312yes—
90C4×Q8×C41—21no—
91C4×Q8×C41—21no—
92C4×D4×C41—21no—
93C4×D4×C41—22no—
94C4×D4×C41—22no—
95C4×D4×C41—22no—
96C4×D4×C41—22no—
97C4×D4×C41—22no—
98C4×D4×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41—21no—
103C4×D4×C41—44no—
104#117×C41—21no—
105#117×C41—21no—
106#117×C41—22no—
107#117×C41—22no—
108#117×C41D412yescomplemented
109C2×C4⋊C4×C41—22no—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C42×C41—22no—
113C2×C42×C41D411yescharacteristic, complemented
114#104×C41—22no—
115#104×C41—22no—
116#101×C41—21no—
117#100×C41C2312yes—
118#99×C41—22no—
119#99×C41—24no—
120#99×C41—24no—
121#99×C41C2314yes—
122C24×C41—21no—
123C24×C41C2×D412yes—
124#41×C41—22no—
125#41×C41—22no—
126#41×C41—41no—
127#41×C41—41no—
128#41×C41—42no—
129#41×C41—42no—
130#41×C41—42no—
131#41×C41—41no—
132#41×C41—44no—
133#41×C41—41no—
134#41×C41—41no—
135#41×C41—44no—
136#41×C41—42no—
137#41×C41—42no—
138#41×C41—41no—
139C2×Q8×C41—21no—
140C2×Q8×C41—22no—
141C2×Q8×C41—21no—
142C2×Q8×C41—42no—
143C2×Q8×C41C2×D411yescharacteristic
144C2×Q8×C41C2×D411yescharacteristic
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—22no—
148C2×D4×C41—22no—
149C2×D4×C41—22no—
150C2×D4×C41—24no—
151C2×D4×C41—22no—
152C2×D4×C41—22no—
153C2×D4×C41—21no—
154C2×D4×C41—42no—
155C2×D4×C41—48no—
156C2×D4×C41—44no—
157C2×D4×C41—41no—
158C2×D4×C41—44no—
159C2×D4×C41C2×D412yes—
160C2×D4×C41C2×D411yescharacteristic
161C2×D4×C41C2411yescharacteristic
162C22×C4×C41—22no—
163C22×C4×C41—22no—
164C22×C4×C41—24no—
165C22×C4×C41—21no—
166C22×C4×C41—22no—
167C22×C4×C41—21no—
168C22×C4×C41—22no—
169C22×C4×C41—21no—
170C22×C4×C41—22no—
171C22×C4×C41—41no—
172C22×C4×C41—42no—
173C22×C4×C41—42no—
174C22×C4×C41—81no—
175C22×C4×C41—81no—
176C22×C4×C41C2×D412yes—
177C22×C4×C41C2×D411yescharacteristic
178C22×C4×C41C2×D412yes—
179Q16×C41—42no—
180SD16×C41—42no—
181SD16×C41—42no—
182D8×C41—42no—
183M16×C41—22no—
184M16×C41—41no—
185C2×C8×C41—41no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—22no—
190C4⋊C4×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—22no—
193C4⋊C4×C41—22no—
194C4⋊C4×C41—22no—
195C4⋊C4×C41—42no—
196C4⋊C4×C41—44no—
197C22⋊C4×C41—22no—
198C22⋊C4×C41—22no—
199C22⋊C4×C41—22no—
200C22⋊C4×C41—21no—
201C22⋊C4×C41—21no—
202C22⋊C4×C41—22no—
203C22⋊C4×C41—22no—
204C22⋊C4×C41—22no—
205C22⋊C4×C41—22no—
206C22⋊C4×C41—22no—
207C22⋊C4×C41—22no—
208C22⋊C4×C41—24no—
209C22⋊C4×C41—44no—
210C22⋊C4×C41—44no—
211C22⋊C4×C41C2×D412yes—
212C22⋊C4×C41C2×D412yes—
213C42×C41—22no—
214C42×C41—22no—
215C42×C41—21no—
216C42×C41—22no—
217C42×C41—42no—
218C42×C41C2×D411yescharacteristic
219C42×C41C2×D411yescharacteristic
220C23×C41—22no—
221C23×C41—24no—
222C23×C41—21no—
223C23×C41—42no—
224C23×C41—44no—
225C23×C41—44no—
226C23×C41—41no—
227C23×C41—81no—
228C23×C41#12011yescharacteristic
229C23×C41C22×D412yes—
230Q8×C41—22no—
231Q8×C41—41no—
232Q8×C41—41no—
233Q8×C41—42no—
234Q8×C41—42no—
235Q8×C41—41no—
236D4×C41—24no—
237D4×C41—22no—
238D4×C41—42no—
239D4×C41—41no—
240D4×C41—41no—
241D4×C41—44no—
242D4×C41—42no—
243D4×C41—44no—
244D4×C41—44no—
245D4×C41—44no—
246D4×C41—44no—
247D4×C41—42no—
248D4×C41—42no—
249D4×C41—41no—
250D4×C41—81no—
251D4×C41—88no—
252C2×C4×C41—21no—
253C2×C4×C41—22no—
254C2×C4×C41—21no—
255C2×C4×C41—22no—
256C2×C4×C41—21no—
257C2×C4×C41—24no—
258C2×C4×C41—21no—
259C2×C4×C41—22no—
260C2×C4×C41—22no—
261C2×C4×C41—22no—
262C2×C4×C41—21no—
263C2×C4×C41—44no—
264C2×C4×C41—44no—
265C2×C4×C41—42no—
266C2×C4×C41—42no—
267C2×C4×C41—44no—
268C2×C4×C41—41no—
269C2×C4×C41—42no—
270C2×C4×C41—41no—
271C2×C4×C41—42no—
272C2×C4×C41—42no—
273C2×C4×C41—41no—
274C2×C4×C41—42no—
275C2×C4×C41—44no—
276C2×C4×C41—82no—
277C2×C4×C41—81no—
278C2×C4×C41—82no—
279C2×C4×C41#12012yes—
280C2×C4×C41#12011yescharacteristic
281C2×C4×C41C22×D411yescharacteristic
282C8×C41—42no—
283#33546C4111yesmaximal, characteristic, direct product factor, Sylow
284C22×C41—24no—
285C22×C41—22no—
286C22×C41—21no—
287C22×C41—41no—
288C22×C41—42no—
289C22×C41—42no—
290C22×C41—42no—
291C22×C41—44no—
292C22×C41—42no—
293C22×C41—42no—
294C22×C41—41no—
295C22×C41—82no—
296C22×C41—84no—
297C22×C41—84no—
298C22×C41—161no—
299C22×C41C2×#12011yescharacteristic
300C4×C41—22no—
301C4×C41—21no—
302C4×C41—22no—
303C4×C41—41no—
304C4×C41—42no—
305C4×C41—42no—
306C4×C41—42no—
307C4×C41—42no—
308C4×C41—41no—
309C4×C41—84no—
310C4×C41B(4,𝔽2)11yescharacteristic
311C4×C41B(4,𝔽2)11yescharacteristic
312#3481C2×C4111yescharacteristic, complemented
313#3025C2×C4112yescomplemented
314#3018C2×C4111yescharacteristic, complemented
315#2198C2×C4112yescomplemented
316#2197C2×C4114yescomplemented
317#2196C2×C4112yescomplemented
318#2126C2×C4111yescharacteristic, complemented
319#2120C2×C4112yescomplemented
320C2×C41—21no—
321C2×C41—42no—
322C2×C41—44no—
323C2×C41—41no—
324C2×C41—81no—
325C2×C41—82no—
326C2×C41C2×B(4,𝔽2)11yescharacteristic
327#585C22×C4111yescharacteristic, complemented
328#575—21no—
329#559C22×C4111yescharacteristic, complemented
330#554—21no—
331#553—22no—
332#551—21no—
333#551C22×C4112yescomplemented
334#546—22no—
335D42C22×C4111yescharacteristic, complemented
336#532C22×C4111yescharacteristic
337#529—22no—
338#525—21no—
339#525—22no—
340#525C22×C4112yes—
341C4×#41—21no—
342C2×C4×D4—22no—
343#458—22no—
344#458C22×C4114yescomplemented
345B(4,𝔽2)—22no—
346B(4,𝔽2)C22×C4114yes—
347#456—21no—
348#455C22×C4112yescomplemented
349#454—21no—
350#453C22×C4112yes—
351C2×#104—21no—
352#413C22×C4111yescharacteristic, complemented
353#410—22no—
354#410C22×C4112yescomplemented
355#354C22×C4112yescomplemented
356#353C22×C4112yescomplemented
357#352C22×C4114yescomplemented
358AΣL(1,𝔽16)C22×C4114yescomplemented
359C41#3354611yescharacteristic, direct product factor, Sylow
3602−1+4—21no—
3612−1+4—41no—
362H(5,𝔽2)—22no—
363H(5,𝔽2)—41no—
364H(5,𝔽2)C23×C4112yes—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—21no—
368C2×#41—42no—
369C2×#41D4×C4111yescharacteristic, complemented
370C2×#41C23×C4111yescharacteristic
371C22×D4—22no—
372C23×C4—21no—
373C23×C4D4×C4112yescomplemented
374#137—22no—
375#137—41no—
376AGL(1,ℤ/8)—22no—
377AGL(1,ℤ/8)—41no—
378#135—42no—
379C2×M16—21no—
380C4⋊Q8D4×C4111yescharacteristic, complemented
381#127C23×C4111yescharacteristic
382#126—22no—
383#126—22no—
384#125—22no—
385#124—22no—
386#124D4×C4111yescharacteristic, complemented
387#124C23×C4111yescharacteristic
388#123—21no—
389#123—22no—
390#123—21no—
391#123—22no—
392#123—24no—
393#123D4×C4112yescomplemented
394#123C23×C4112yes—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—42no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—42no—
404#120—21no—
405#120—21no—
406#120—24no—
407#120D4×C4112yescomplemented
408#120C23×C4112yes—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—44no—
423#117—21no—
424#117—21no—
425#117—22no—
426#117—22no—
427#117D4×C4112yescomplemented
428C2×C4⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C42—22no—
432C2×C42D4×C4111yescharacteristic, complemented
433#104—22no—
434#104—22no—
435#101—21no—
436#100C23×C4112yes—
437#99—22no—
438#99—24no—
439#99—24no—
440#99C23×C4114yes—
441C24—21no—
442C24C2×D4×C4112yes—
443#41—22no—
444#41—22no—
445#41—41no—
446#41—41no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—41no—
451#41—44no—
452#41—41no—
453#41—41no—
454#41—44no—
455#41—42no—
456#41—41no—
457#41—42no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—42no—
462C2×Q8C2×D4×C4111yescharacteristic
463C2×Q8C2×D4×C4111yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—41no—
477C2×D4—44no—
478C2×D4C2×D4×C4112yes—
479C2×D4C2×D4×C4111yescharacteristic
480C2×D4C24×C4111yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4C2×D4×C4112yes—
496C22×C4C2×D4×C4111yescharacteristic
497C22×C4C2×D4×C4112yes—
498Q16—42no—
499SD16—42no—
500SD16—42no—
501D8—42no—
502M16—22no—
503M16—41no—
504C2×C8—41no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4—44no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—24no—
528C22⋊C4—44no—
529C22⋊C4—44no—
530C22⋊C4C2×D4×C4112yes—
531C22⋊C4C2×D4×C4112yes—
532C42—22no—
533C42—22no—
534C42—21no—
535C42—22no—
536C42—42no—
537C42C2×D4×C4111yescharacteristic
538C42C2×D4×C4111yescharacteristic
539C23—22no—
540C23—24no—
541C23—21no—
542C23—42no—
543C23—44no—
544C23—44no—
545C23—41no—
546C23—81no—
547C23#120×C4111yescharacteristic
548C23C22×D4×C4112yes—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—42no—
553Q8—42no—
554Q8—41no—
555D4—24no—
556D4—22no—
557D4—42no—
558D4—41no—
559D4—41no—
560D4—42no—
561D4—44no—
562D4—44no—
563D4—44no—
564D4—44no—
565D4—44no—
566D4—42no—
567D4—42no—
568D4—41no—
569D4—81no—
570D4—88no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—82no—
598C2×C4#120×C4112yes—
599C2×C4#120×C4111yescharacteristic
600C2×C4C22×D4×C4111yescharacteristic
601C8—42no—
602C22—24no—
603C22—22no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—82no—
614C22—84no—
615C22—84no—
616C22—161no—
617C22C2×#120×C4111yescharacteristic
618C4—22no—
619C4—21no—
620C4—22no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—41no—
627C4—84no—
628C4C41×B(4,𝔽2)11yescharacteristic
629C4C41×B(4,𝔽2)11yescharacteristic
630C2—21no—
631C2—42no—
632C2—44no—
633C2—41no—
634C2—81no—
635C2—82no—
636C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
centerC4×C41B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
socleC2×C41C2×B(4,𝔽2)
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C41 ◁ C2×C4×C41 ◁ C2×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3481C2semidirect
2. C41×#3025C2semidirect
3. C41×#3018C2semidirect
4. C41×#2198C2semidirect
5. C41×#2197C2semidirect
6. C41×#2196C2semidirect
7. C41×#2126C2semidirect
8. C41×#2120C2semidirect
9. C41×#585C22semidirect
11. C41×#559C22semidirect
15. C41×#551C22semidirect
17. D42×C41C22semidirect
26. C41×#458C22semidirect
30. C41×#455C22semidirect
34. C41×#413C22semidirect
36. C41×#410C22semidirect
37. C41×#354C22semidirect
38. C41×#353C22semidirect
39. C41×#352C22semidirect
40. C41×AΣL(1,𝔽16)C22semidirect
50. C2×#41×C41D4semidirect
54. C23×C4×C41D4semidirect
61. C4⋊Q8×C41D4semidirect
67. #124×C41D4semidirect
74. #123×C41D4semidirect
88. #120×C41D4semidirect
108. #117×C41D4semidirect
113. C2×C42×C41D4semidirect
283. #33546C41direct (N × H)
312. #3481C2×C41semidirect
313. #3025C2×C41semidirect
314. #3018C2×C41semidirect
315. #2198C2×C41semidirect
316. #2197C2×C41semidirect
317. #2196C2×C41semidirect
318. #2126C2×C41semidirect
319. #2120C2×C41semidirect
327. #585C22×C41semidirect
329. #559C22×C41semidirect
333. #551C22×C41semidirect
335. D42C22×C41semidirect
344. #458C22×C41semidirect
348. #455C22×C41semidirect
352. #413C22×C41semidirect
354. #410C22×C41semidirect
355. #354C22×C41semidirect
356. #353C22×C41semidirect
357. #352C22×C41semidirect
358. AΣL(1,𝔽16)C22×C41semidirect
359. C41#33546direct (N × H)
369. C2×#41D4×C41semidirect
373. C23×C4D4×C41semidirect
380. C4⋊Q8D4×C41semidirect
386. #124D4×C41semidirect
393. #123D4×C41semidirect
407. #120D4×C41semidirect
427. #117D4×C41semidirect
432. C2×C42D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34812
C41×#30252
C41×#30182
C41×#21982
C41×#21972
C41×#21962
C41×#21262
C41×#21202
#3354641