Finite Group Databasebeta

← C41×#10322 #23786523

Subgroups — C41×#10322 #23786523

Order 10496.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3187C211yesmaximal, characteristic, complemented
2C41×#2848C211yesmaximal, characteristic, complemented
3C41×#2847C211yesmaximal, characteristic
4C41×#1779C211yesmaximal, characteristic, complemented
5C41×#1520C211yesmaximal, characteristic, complemented
6C41×#1519C211yesmaximal, characteristic, complemented
7C41×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C41C2211yescharacteristic
9C2×C22⋊Q8×C41—21no—
10C2×C22⋊Q8×C41C2211yescharacteristic
11C2×#121×C41—21no—
12C2×#121×C41C2211yescharacteristic
13C2×#120×C41—21no—
14C41×#483—21no—
15C41×#481—21no—
16C41×#465—22no—
17C41×#450—21no—
18C41×#448—21no—
19C2×C22⋊C8×C41—22no—
20C2×C22⋊C8×C41C2211yescharacteristic
21C2×C22⋊C8×C41C2211yescharacteristic
22C41×#386—21no—
23C41×#386—22no—
24C41×#385—21no—
25C41×#385—22no—
26C41×#380—21no—
27C41×#380—21no—
28C41×#380C2211yescharacteristic
29C41×#380C2211yescharacteristic
30C41×#379—21no—
31C41×#328—22no—
32C41×#327—22no—
33C25×C41D411yescharacteristic
34C22×Q8×C41D411yescharacteristic, complemented
35C22×D4×C41—22no—
36C22×D4×C41—21no—
37C22×D4×C41D411yescharacteristic
38C23×C4×C41—21no—
39C23×C4×C41—21no—
40C23×C4×C41—21no—
41C23×C4×C41—21no—
42C23×C4×C41—21no—
43C23×C4×C41—21no—
44C23×C4×C41—44no—
45C23×C4×C41D411yescharacteristic
46C23×C4×C41C2311yescharacteristic
47C2×SD16×C41—22no—
48C22×C8×C41—21no—
49C22×C8×C41D412yescomplemented
50C22⋊Q8×C41—21no—
51C22⋊Q8×C41—21no—
52C22⋊Q8×C41—21no—
53C22⋊Q8×C41—21no—
54C22⋊Q8×C41—44no—
55#121×C41—21no—
56#121×C41—21no—
57#121×C41—21no—
58#121×C41—21no—
59#121×C41—44no—
60#120×C41—42no—
61#120×C41—42no—
62C2×C4⋊C4×C41—22no—
63C2×C4⋊C4×C41—21no—
64C2×C4⋊C4×C41—21no—
65C2×C4⋊C4×C41—21no—
66C2×C4⋊C4×C41D411yescharacteristic
67C2×C4⋊C4×C41D411yescharacteristic, complemented
68C2×C22⋊C4×C41—22no—
69C2×C22⋊C4×C41—22no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—22no—
72C2×C22⋊C4×C41—21no—
73C2×C22⋊C4×C41—21no—
74C2×C22⋊C4×C41—21no—
75C2×C22⋊C4×C41—21no—
76#106×C41—22no—
77#103×C41—22no—
78#102×C41—22no—
79C22⋊C8×C41—21no—
80C22⋊C8×C41—21no—
81C22⋊C8×C41—21no—
82C22⋊C8×C41—21no—
83C22⋊C8×C41—44no—
84#95×C41—22no—
85#95×C41—22no—
86#95×C41D412yes—
87#95×C41D412yescomplemented
88C24×C41—21no—
89C24×C41—21no—
90C24×C41—21no—
91C24×C41—21no—
92C24×C41—21no—
93C24×C41—21no—
94C24×C41—21no—
95C24×C41—42no—
96C24×C41—42no—
97C24×C41SD1612yescomplemented
98C24×C41C2×D411yescharacteristic
99C2×Q8×C41—21no—
100C2×Q8×C41—21no—
101C2×Q8×C41—42no—
102C2×D4×C41—21no—
103C2×D4×C41—21no—
104C2×D4×C41—42no—
105C2×D4×C41—44no—
106C2×D4×C41—44no—
107C2×D4×C41—44no—
108C2×D4×C41—41no—
109C2×D4×C41—41no—
110C2×D4×C41—41no—
111C2×D4×C41—41no—
112C2×D4×C41—41no—
113C2×D4×C41—41no—
114C22×C4×C41—24no—
115C22×C4×C41—24no—
116C22×C4×C41—24no—
117C22×C4×C41—21no—
118C22×C4×C41—21no—
119C22×C4×C41—21no—
120C22×C4×C41—21no—
121C22×C4×C41—21no—
122C22×C4×C41—22no—
123C22×C4×C41—22no—
124C22×C4×C41—21no—
125C22×C4×C41—42no—
126C22×C4×C41—42no—
127C22×C4×C41—42no—
128C22×C4×C41—42no—
129C22×C4×C41—42no—
130C22×C4×C41—42no—
131C22×C4×C41—42no—
132C22×C4×C41—42no—
133C22×C4×C41—42no—
134C22×C4×C41—42no—
135C22×C4×C41—42no—
136C22×C4×C41—41no—
137C22×C4×C41—41no—
138C22×C4×C41—41no—
139C22×C4×C41—41no—
140C22×C4×C41C2×D411yescharacteristic
141C22×C4×C41C2×D411yescharacteristic
142C22×C4×C41C2×D411yescharacteristic
143C22×C4×C41C2×D411yescharacteristic
144C22×C4×C41C2×D411yescharacteristic
145C22×C4×C41#4111yescharacteristic
146SD16×C41—82no—
147C2×C8×C41—22no—
148C2×C8×C41—42no—
149C2×C8×C41—42no—
150C2×C8×C41—41no—
151C4⋊C4×C41—21no—
152C4⋊C4×C41—21no—
153C4⋊C4×C41—21no—
154C4⋊C4×C41—21no—
155C4⋊C4×C41—42no—
156C4⋊C4×C41—42no—
157C4⋊C4×C41—44no—
158C4⋊C4×C41—41no—
159C4⋊C4×C41—41no—
160C22⋊C4×C41—44no—
161C22⋊C4×C41—44no—
162C22⋊C4×C41—44no—
163C22⋊C4×C41—44no—
164C22⋊C4×C41—41no—
165C22⋊C4×C41—41no—
166C22⋊C4×C41—41no—
167C22⋊C4×C41—41no—
168C22⋊C4×C41—41no—
169C22⋊C4×C41—41no—
170C22⋊C4×C41—41no—
171C22⋊C4×C41—41no—
172C23×C41—22no—
173C23×C41—22no—
174C23×C41—22no—
175C23×C41—22no—
176C23×C41—22no—
177C23×C41—22no—
178C23×C41—22no—
179C23×C41—22no—
180C23×C41—22no—
181C23×C41—41no—
182C23×C41—44no—
183C23×C41—41no—
184C23×C41—41no—
185C23×C41—41no—
186C23×C41—41no—
187C23×C41—41no—
188C23×C41—41no—
189C23×C41—41no—
190C23×C41—44no—
191C23×C41—44no—
192C23×C41—44no—
193C23×C41—42no—
194C23×C41—42no—
195C23×C41—41no—
196C23×C41—41no—
197C23×C41—41no—
198C23×C41—41no—
199C23×C41—41no—
200C23×C41—41no—
201C23×C41—41no—
202C23×C41#12011yescharacteristic
203C23×C41#12011yescharacteristic
204C23×C41#12111yescharacteristic
205C23×C41C2×SD1611yescharacteristic
206C23×C41#13511yescharacteristic
207C23×C41AGL(1,ℤ/8)11yescharacteristic
208C23×C41#13711yescharacteristic
209Q8×C41—42no—
210Q8×C41—81no—
211D4×C41—42no—
212D4×C41—81no—
213D4×C41—88no—
214D4×C41—81no—
215D4×C41—81no—
216D4×C41—81no—
217D4×C41—81no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—22no—
223C2×C4×C41—22no—
224C2×C4×C41—41no—
225C2×C4×C41—41no—
226C2×C4×C41—41no—
227C2×C4×C41—44no—
228C2×C4×C41—44no—
229C2×C4×C41—44no—
230C2×C4×C41—41no—
231C2×C4×C41—41no—
232C2×C4×C41—41no—
233C2×C4×C41—41no—
234C2×C4×C41—44no—
235C2×C4×C41—42no—
236C2×C4×C41—42no—
237C2×C4×C41—42no—
238C2×C4×C41—42no—
239C2×C4×C41—42no—
240C2×C4×C41—42no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—42no—
245C2×C4×C41—42no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41#12011yescharacteristic
249C2×C4×C41#12111yescharacteristic
250C2×C4×C41#12111yescharacteristic
251C2×C4×C41#12711yescharacteristic
252C8×C41—42no—
253C8×C41—81no—
254#10322C4111yesmaximal, characteristic, direct product factor, Sylow
255C22×C41—21no—
256C22×C41—21no—
257C22×C41—21no—
258C22×C41—21no—
259C22×C41—21no—
260C22×C41—21no—
261C22×C41—24no—
262C22×C41—24no—
263C22×C41—24no—
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—41no—
267C22×C41—41no—
268C22×C41—42no—
269C22×C41—42no—
270C22×C41—42no—
271C22×C41—42no—
272C22×C41—42no—
273C22×C41—42no—
274C22×C41—42no—
275C22×C41—42no—
276C22×C41—42no—
277C22×C41—42no—
278C22×C41—42no—
279C22×C41—42no—
280C22×C41—82no—
281C22×C41—82no—
282C22×C41—81no—
283C22×C41—81no—
284C22×C41—81no—
285C22×C41#39211yescharacteristic
286C22×C41#44811yescharacteristic
287C22×C41#44911yescharacteristic
288C22×C41#45011yescharacteristic
289C22×C41#45211yescharacteristic
290C22×C41#46511yescharacteristic
291C22×C41#46811yescharacteristic
292C4×C41—21no—
293C4×C41—21no—
294C4×C41—21no—
295C4×C41—42no—
296C4×C41—82no—
297C4×C41—82no—
298C4×C41—81no—
299C4×C41—81no—
300C4×C41—81no—
301C4×C41B(4,𝔽2)12yes—
302#3187C2×C4111yescharacteristic, complemented
303#2848C2×C4111yescharacteristic, complemented
304#2847C2×C4111yescharacteristic
305#1779C2×C4111yescharacteristic, complemented
306#1520C2×C4111yescharacteristic, complemented
307#1519C2×C4111yescharacteristic, complemented
308#1289C2×C4111yescharacteristic, complemented
309C2×C41—21no—
310C2×C41—21no—
311C2×C41—21no—
312C2×C41—21no—
313C2×C41—21no—
314C2×C41—21no—
315C2×C41—44no—
316C2×C41—161no—
317C2×C41#200011yescharacteristic
318C2×C41#201011yescharacteristic
319C2×C41#202111yescharacteristic
320C24×C4C22×C4111yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8C22×C4111yescharacteristic
323C2×#121—21no—
324C2×#121C22×C4111yescharacteristic
325C2×#120—21no—
326#483—21no—
327#481—21no—
328#465—22no—
329#450—21no—
330#448—21no—
331C2×C22⋊C8—22no—
332C2×C22⋊C8C22×C4111yescharacteristic
333C2×C22⋊C8C22×C4111yescharacteristic
334#386—21no—
335#386—22no—
336#385—21no—
337#385—22no—
338#380—21no—
339#380—21no—
340#380C22×C4111yescharacteristic
341#380C22×C4111yescharacteristic
342#379—21no—
343#328—22no—
344#327—22no—
345C41#1032211yescharacteristic, direct product factor, Sylow
346C25D4×C4111yescharacteristic
347C22×Q8D4×C4111yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C4111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C4111yescharacteristic
359C23×C4C23×C4111yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C4112yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C4111yescharacteristic
380C2×C4⋊C4D4×C4111yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C4112yes—
400#95D4×C4112yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C4112yescomplemented
411C24C2×D4×C4111yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C4111yescharacteristic
454C22×C4C2×D4×C4111yescharacteristic
455C22×C4C2×D4×C4111yescharacteristic
456C22×C4C2×D4×C4111yescharacteristic
457C22×C4C2×D4×C4111yescharacteristic
458C22×C4#41×C4111yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C4111yescharacteristic
516C23#120×C4111yescharacteristic
517C23#121×C4111yescharacteristic
518C23C2×SD16×C4111yescharacteristic
519C23#135×C4111yescharacteristic
520C23AGL(1,ℤ/8)×C4111yescharacteristic
521C23#137×C4111yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C4111yescharacteristic
562C2×C4#121×C4111yescharacteristic
563C2×C4#121×C4111yescharacteristic
564C2×C4#127×C4111yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C41×#39211yescharacteristic
598C22C41×#44811yescharacteristic
599C22C41×#44911yescharacteristic
600C22C41×#45011yescharacteristic
601C22C41×#45211yescharacteristic
602C22C41×#46511yescharacteristic
603C22C41×#46811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C41×B(4,𝔽2)12yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C41×#200011yescharacteristic
623C2C41×#201011yescharacteristic
624C2C41×#202111yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC41×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3187C2semidirect
2. C41×#2848C2semidirect
4. C41×#1779C2semidirect
5. C41×#1520C2semidirect
6. C41×#1519C2semidirect
7. C41×#1289C2semidirect
34. C22×Q8×C41D4semidirect
49. C22×C8×C41D4semidirect
67. C2×C4⋊C4×C41D4semidirect
87. #95×C41D4semidirect
97. C24×C41SD16semidirect
254. #10322C41direct (N × H)
302. #3187C2×C41semidirect
303. #2848C2×C41semidirect
305. #1779C2×C41semidirect
306. #1520C2×C41semidirect
307. #1519C2×C41semidirect
308. #1289C2×C41semidirect
345. C41#10322direct (N × H)
347. C22×Q8D4×C41semidirect
362. C22×C8D4×C41semidirect
380. C2×C4⋊C4D4×C41semidirect
400. #95D4×C41semidirect
410. C24SD16×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31872
C41×#28482
C41×#28472
C41×#17792
C41×#15202
C41×#15192
C41×#12892
#1032241