Finite Group Databasebeta

← C41×#9922 #23786123

Subgroups — C41×#9922 #23786123

Order 10496.

1278 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#450C211yesmaximal, characteristic, complemented
2C41×#2626C211yesmaximal, characteristic, complemented
3C2×C41×#392C211yesmaximal, characteristic
4C41×#1786C211yesmaximal, characteristic, complemented
5C2×C41×#328C211yesmaximal, characteristic, complemented
6C2×C41×#323C211yesmaximal, characteristic, complemented
7C41×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C41—21no—
9C23×D4×C41C2211yescharacteristic
10C22×SD16×C41—21no—
11C2×C22⋊Q8×C41C2211yescharacteristic
12C22×C22⋊C4×C41—21no—
13C22×C22⋊C4×C41C2211yescharacteristic
14C41×#450—22no—
15C41×#450—22no—
16C2×#102×C41—21no—
17C2×#102×C41—22no—
18C2×C22⋊C8×C41C2211yescharacteristic
19C2×C22⋊C8×C41C2211yescharacteristic
20C41×#399—21no—
21C41×#396—22no—
22C41×#393—21no—
23C41×#392—22no—
24C41×#392—22no—
25C41×#385—21no—
26C41×#380C2211yescharacteristic
27C41×#379—21no—
28C2×#95×C41C2211yescharacteristic
29C41×#328—22no—
30C41×#323—22no—
31C25×C41—21no—
32C25×C41D411yescharacteristic
33C22×Q8×C41D411yescharacteristic, complemented
34C22×D4×C41—24no—
35C22×D4×C41—21no—
36C22×D4×C41—21no—
37C22×D4×C41—21no—
38C22×D4×C41—21no—
39C22×D4×C41—21no—
40C22×D4×C41—44no—
41C22×D4×C41—44no—
42C22×D4×C41—44no—
43C22×D4×C41—42no—
44C22×D4×C41—42no—
45C22×D4×C41D412yes—
46C23×C4×C41—21no—
47C23×C4×C41D411yescharacteristic
48C23×C4×C41C2311yescharacteristic
49C2×SD16×C41—24no—
50C2×SD16×C41—44no—
51C22×C8×C41—21no—
52C22×C8×C41—21no—
53C22⋊Q8×C41—21no—
54C22⋊Q8×C41—21no—
55C22⋊Q8×C41—21no—
56C22⋊Q8×C41—21no—
57C2×C4⋊C4×C41—21no—
58C2×C4⋊C4×C41—22no—
59C2×C4⋊C4×C41D411yescharacteristic, complemented
60C2×C4⋊C4×C41D412yescomplemented
61C2×C22⋊C4×C41—24no—
62C2×C22⋊C4×C41—21no—
63C2×C22⋊C4×C41—21no—
64C2×C22⋊C4×C41—21no—
65C2×C22⋊C4×C41—21no—
66C2×C22⋊C4×C41—21no—
67C2×C22⋊C4×C41—21no—
68C2×C22⋊C4×C41—21no—
69C2×C22⋊C4×C41—21no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—22no—
72C2×C22⋊C4×C41—44no—
73#102×C41—24no—
74#102×C41—44no—
75C22⋊C8×C41—21no—
76C22⋊C8×C41—21no—
77C22⋊C8×C41—21no—
78C22⋊C8×C41D412yescomplemented
79#95×C41—22no—
80#95×C41—21no—
81#95×C41—21no—
82#95×C41D412yes—
83C24×C41—24no—
84C24×C41—21no—
85C24×C41—22no—
86C24×C41—21no—
87C24×C41—21no—
88C24×C41—21no—
89C24×C41—21no—
90C24×C41—21no—
91C24×C41—42no—
92C24×C41—42no—
93C24×C41—42no—
94C24×C41—42no—
95C24×C41—42no—
96C24×C41—41no—
97C24×C41—41no—
98C24×C41—41no—
99C24×C41—41no—
100C24×C41—41no—
101C24×C41—41no—
102C24×C41SD1612yescomplemented
103C24×C41C2×D411yescharacteristic
104C2×Q8×C41—21no—
105C2×Q8×C41—21no—
106C2×Q8×C41—42no—
107C2×D4×C41—24no—
108C2×D4×C41—24no—
109C2×D4×C41—22no—
110C2×D4×C41—22no—
111C2×D4×C41—42no—
112C2×D4×C41—42no—
113C2×D4×C41—48no—
114C2×D4×C41—44no—
115C2×D4×C41—44no—
116C2×D4×C41—44no—
117C2×D4×C41—44no—
118C2×D4×C41—48no—
119C2×D4×C41—48no—
120C2×D4×C41—416no—
121C2×D4×C41—416no—
122C2×D4×C41—41no—
123C2×D4×C41—41no—
124C22×C4×C41—24no—
125C22×C4×C41—22no—
126C22×C4×C41—21no—
127C22×C4×C41—22no—
128C22×C4×C41—21no—
129C22×C4×C41—21no—
130C22×C4×C41—21no—
131C22×C4×C41—21no—
132C22×C4×C41—42no—
133C22×C4×C41—42no—
134C22×C4×C41—41no—
135C22×C4×C41—41no—
136C22×C4×C41—42no—
137C22×C4×C41C2×D411yescharacteristic
138C22×C4×C41C2×D411yescharacteristic
139C22×C4×C41C2×D411yescharacteristic
140C22×C4×C41C2×D411yescharacteristic
141C22×C4×C41C2×D411yescharacteristic
142C22×C4×C41#4111yescharacteristic
143SD16×C41—48no—
144C2×C8×C41—22no—
145C2×C8×C41—42no—
146C2×C8×C41—42no—
147C2×C8×C41—41no—
148C4⋊C4×C41—21no—
149C4⋊C4×C41—21no—
150C4⋊C4×C41—42no—
151C4⋊C4×C41—41no—
152C4⋊C4×C41—41no—
153C4⋊C4×C41—82no—
154C22⋊C4×C41—48no—
155C22⋊C4×C41—41no—
156C22⋊C4×C41—41no—
157C22⋊C4×C41—41no—
158C22⋊C4×C41—41no—
159C22⋊C4×C41—41no—
160C22⋊C4×C41—41no—
161C22⋊C4×C41—41no—
162C22⋊C4×C41—41no—
163C22⋊C4×C41—82no—
164C22⋊C4×C41—82no—
165C23×C41—22no—
166C23×C41—22no—
167C23×C41—24no—
168C23×C41—22no—
169C23×C41—22no—
170C23×C41—22no—
171C23×C41—44no—
172C23×C41—42no—
173C23×C41—44no—
174C23×C41—44no—
175C23×C41—44no—
176C23×C41—42no—
177C23×C41—42no—
178C23×C41—42no—
179C23×C41—42no—
180C23×C41—44no—
181C23×C41—44no—
182C23×C41—44no—
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—41no—
193C23×C41—82no—
194C23×C41—82no—
195C23×C41—81no—
196C23×C41—81no—
197C23×C41—82no—
198C23×C41—82no—
199C23×C41—82no—
200C23×C41—82no—
201C23×C41—82no—
202C23×C41—81no—
203C23×C41—81no—
204C23×C41—82no—
205C23×C41—81no—
206C23×C41—81no—
207C23×C41#12011yescharacteristic
208C23×C41#12011yescharacteristic
209C23×C41#12111yescharacteristic
210C23×C41C2×SD1611yescharacteristic
211C23×C41#13511yescharacteristic
212C23×C41AGL(1,ℤ/8)11yescharacteristic
213C23×C41#13711yescharacteristic
214Q8×C41—42no—
215Q8×C41—81no—
216D4×C41—24no—
217D4×C41—24no—
218D4×C41—42no—
219D4×C41—44no—
220D4×C41—42no—
221D4×C41—44no—
222D4×C41—432no—
223C2×C4×C41—22no—
224C2×C4×C41—22no—
225C2×C4×C41—24no—
226C2×C4×C41—41no—
227C2×C4×C41—41no—
228C2×C4×C41—41no—
229C2×C4×C41—41no—
230C2×C4×C41—44no—
231C2×C4×C41—44no—
232C2×C4×C41—42no—
233C2×C4×C41—42no—
234C2×C4×C41—42no—
235C2×C4×C41—41no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—42no—
239C2×C4×C41—42no—
240C2×C4×C41—42no—
241C2×C4×C41—42no—
242C2×C4×C41—42no—
243C2×C4×C41—42no—
244C2×C4×C41—81no—
245C2×C4×C41#12011yescharacteristic
246C2×C4×C41#12111yescharacteristic
247C2×C4×C41#12111yescharacteristic
248C2×C4×C41#12711yescharacteristic
249C8×C41—42no—
250C8×C41—81no—
251#9922C4111yesmaximal, characteristic, direct product factor, Sylow
252C22×C41—22no—
253C22×C41—22no—
254C22×C41—22no—
255C22×C41—22no—
256C22×C41—21no—
257C22×C41—21no—
258C22×C41—21no—
259C22×C41—21no—
260C22×C41—44no—
261C22×C41—44no—
262C22×C41—44no—
263C22×C41—44no—
264C22×C41—42no—
265C22×C41—44no—
266C22×C41—82no—
267C22×C41—82no—
268C22×C41—82no—
269C22×C41—82no—
270C22×C41—84no—
271C22×C41—82no—
272C22×C41—84no—
273C22×C41—84no—
274C22×C41—82no—
275C22×C41—84no—
276C22×C41—82no—
277C22×C41—81no—
278C22×C41—82no—
279C22×C41—81no—
280C22×C41#39211yescharacteristic
281C22×C41#44811yescharacteristic
282C22×C41#44911yescharacteristic
283C22×C41#45011yescharacteristic
284C22×C41#45211yescharacteristic
285C22×C41#45312yes—
286C22×C41B(4,𝔽2)12yes—
287C22×C41#46511yescharacteristic
288C22×C41#46811yescharacteristic
289C4×C41—21no—
290C4×C41—21no—
291C4×C41—21no—
292C4×C41—21no—
293C4×C41—44no—
294C4×C41—82no—
295C4×C41—81no—
296C4×C41—81no—
297C4×C41—81no—
298C2×#450C2×C4111yescharacteristic, complemented
299#2626C2×C4111yescharacteristic, complemented
300C2×#392C2×C4111yescharacteristic
301#1786C2×C4111yescharacteristic, complemented
302C2×#328C2×C4111yescharacteristic, complemented
303C2×#323C2×C4111yescharacteristic, complemented
304#1294C2×C4111yescharacteristic, complemented
305C2×C41—21no—
306C2×C41—21no—
307C2×C41—21no—
308C2×C41—21no—
309C2×C41—82no—
310C2×C41—84no—
311C2×C41#159612yes—
312C2×C41#160012yes—
313C2×C41#200011yescharacteristic
314C2×C41#200211yescharacteristic
315C2×C41#202111yescharacteristic
316C23×D4—21no—
317C23×D4C22×C4111yescharacteristic
318C22×SD16—21no—
319C2×C22⋊Q8C22×C4111yescharacteristic
320C22×C22⋊C4—21no—
321C22×C22⋊C4C22×C4111yescharacteristic
322#450—22no—
323#450—22no—
324C2×#102—21no—
325C2×#102—22no—
326C2×C22⋊C8C22×C4111yescharacteristic
327C2×C22⋊C8C22×C4111yescharacteristic
328#399—21no—
329#396—22no—
330#393—21no—
331#392—22no—
332#392—22no—
333#385—21no—
334#380C22×C4111yescharacteristic
335#379—21no—
336C2×#95C22×C4111yescharacteristic
337#328—22no—
338#323—22no—
339C41#992211yescharacteristic, direct product factor, Sylow
340C25—21no—
341C25D4×C4111yescharacteristic
342C22×Q8D4×C4111yescharacteristic, complemented
343C22×D4—24no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—44no—
350C22×D4—44no—
351C22×D4—44no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4D4×C4112yes—
355C23×C4—21no—
356C23×C4D4×C4111yescharacteristic
357C23×C4C23×C4111yescharacteristic
358C2×SD16—24no—
359C2×SD16—44no—
360C22×C8—21no—
361C22×C8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4D4×C4111yescharacteristic, complemented
369C2×C4⋊C4D4×C4112yescomplemented
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—44no—
382#102—24no—
383#102—44no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8D4×C4112yescomplemented
388#95—22no—
389#95—21no—
390#95—21no—
391#95D4×C4112yes—
392C24—24no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24SD16×C4112yescomplemented
412C24C2×D4×C4111yescharacteristic
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—42no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—416no—
430C2×D4—416no—
431C2×D4—41no—
432C2×D4—41no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—42no—
446C22×C4C2×D4×C4111yescharacteristic
447C22×C4C2×D4×C4111yescharacteristic
448C22×C4C2×D4×C4111yescharacteristic
449C22×C4C2×D4×C4111yescharacteristic
450C22×C4C2×D4×C4111yescharacteristic
451C22×C4#41×C4111yescharacteristic
452SD16—48no—
453C2×C8—22no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8—41no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—82no—
463C22⋊C4—48no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—82no—
473C22⋊C4—82no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—44no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—44no—
485C23—44no—
486C23—44no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—44no—
501C23—41no—
502C23—82no—
503C23—81no—
504C23—82no—
505C23—81no—
506C23—82no—
507C23—82no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—81no—
512C23—81no—
513C23—82no—
514C23—81no—
515C23—81no—
516C23#120×C4111yescharacteristic
517C23#120×C4111yescharacteristic
518C23#121×C4111yescharacteristic
519C23C2×SD16×C4111yescharacteristic
520C23#135×C4111yescharacteristic
521C23AGL(1,ℤ/8)×C4111yescharacteristic
522C23#137×C4111yescharacteristic
523Q8—42no—
524Q8—81no—
525D4—24no—
526D4—24no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—44no—
531D4—432no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—81no—
554C2×C4#120×C4111yescharacteristic
555C2×C4#121×C4111yescharacteristic
556C2×C4#121×C4111yescharacteristic
557C2×C4#127×C4111yescharacteristic
558C8—42no—
559C8—81no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—21no—
567C22—21no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—44no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22—84no—
581C22—81no—
582C22—84no—
583C22—82no—
584C22—84no—
585C22—82no—
586C22—81no—
587C22—82no—
588C22C41×#39211yescharacteristic
589C22C41×#44811yescharacteristic
590C22C41×#44911yescharacteristic
591C22C41×#45011yescharacteristic
592C22C41×#45211yescharacteristic
593C22C41×#45312yes—
594C22C41×B(4,𝔽2)12yes—
595C22C41×#46511yescharacteristic
596C22C41×#46811yescharacteristic
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—44no—
602C4—81no—
603C4—82no—
604C4—81no—
605C4—81no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—84no—
612C2C41×#159612yes—
613C2C41×#160012yes—
614C2C41×#200011yescharacteristic
615C2C41×#200211yescharacteristic
616C2C41×#202111yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC2×C41×#392C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#450C2semidirect
2. C41×#2626C2semidirect
4. C41×#1786C2semidirect
5. C2×C41×#328C2semidirect
6. C2×C41×#323C2semidirect
7. C41×#1294C2semidirect
33. C22×Q8×C41D4semidirect
59. C2×C4⋊C4×C41D4semidirect
60. C2×C4⋊C4×C41D4semidirect
78. C22⋊C8×C41D4semidirect
102. C24×C41SD16semidirect
251. #9922C41direct (N × H)
298. C2×#450C2×C41semidirect
299. #2626C2×C41semidirect
301. #1786C2×C41semidirect
302. C2×#328C2×C41semidirect
303. C2×#323C2×C41semidirect
304. #1294C2×C41semidirect
339. C41#9922direct (N × H)
342. C22×Q8D4×C41semidirect
368. C2×C4⋊C4D4×C41semidirect
369. C2×C4⋊C4D4×C41semidirect
387. C22⋊C8D4×C41semidirect
411. C24SD16×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4502
C41×#26262
C2×C41×#3922
C41×#17862
C2×C41×#3282
C2×C41×#3232
C41×#12942
#992241