Finite Group Databasebeta

← C41×#9914 #23786115

Subgroups — C41×#9914 #23786115

Order 10496.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#447C211yesmaximal, characteristic, complemented
2C41×#2617C211yesmaximal, characteristic, complemented
3C2×C41×#392C211yesmaximal, characteristic, complemented
4C41×#1786C211yesmaximal, characteristic, complemented
5C2×C41×#327C211yesmaximal, characteristic, complemented
6C2×C41×#323C211yesmaximal, characteristic, complemented
7C41×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C41—21no—
9C23×D4×C41C2211yescharacteristic
10C22×D8×C41—21no—
11C2×#121×C41C2211yescharacteristic
12C2×#120×C41—21no—
13C22×C22⋊C4×C41—21no—
14C22×C22⋊C4×C41C2211yescharacteristic
15C41×#447—22no—
16C41×#447—22no—
17C2×#102×C41—21no—
18C2×#102×C41—22no—
19C2×C22⋊C8×C41C2211yescharacteristic
20C2×C22⋊C8×C41C2211yescharacteristic
21C41×#397—21no—
22C41×#394—22no—
23C41×#392—21no—
24C41×#392—22no—
25C41×#392—22no—
26C41×#386—21no—
27C41×#380C2211yescharacteristic
28C2×#95×C41C2211yescharacteristic
29C41×#327—22no—
30C41×#323—22no—
31C25×C41—21no—
32C25×C41D411yescharacteristic
33C22×D4×C41—24no—
34C22×D4×C41—21no—
35C22×D4×C41—22no—
36C22×D4×C41—21no—
37C22×D4×C41—21no—
38C22×D4×C41—21no—
39C22×D4×C41—21no—
40C22×D4×C41—21no—
41C22×D4×C41—44no—
42C22×D4×C41—44no—
43C22×D4×C41—44no—
44C22×D4×C41—42no—
45C22×D4×C41—42no—
46C22×D4×C41D411yescharacteristic, complemented
47C22×D4×C41D412yescomplemented
48C23×C4×C41—21no—
49C23×C4×C41D411yescharacteristic
50C23×C4×C41C2311yescharacteristic
51C2×D8×C41—24no—
52C2×D8×C41—44no—
53C22×C8×C41—21no—
54C22×C8×C41—21no—
55#121×C41—21no—
56#121×C41—21no—
57#121×C41—21no—
58#121×C41—21no—
59#120×C41—42no—
60#120×C41—42no—
61C2×C4⋊C4×C41D411yescharacteristic, complemented
62C2×C4⋊C4×C41D412yescomplemented
63C2×C22⋊C4×C41—24no—
64C2×C22⋊C4×C41—22no—
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—21no—
71C2×C22⋊C4×C41—21no—
72C2×C22⋊C4×C41—21no—
73C2×C22⋊C4×C41—22no—
74C2×C22⋊C4×C41—44no—
75#102×C41—24no—
76#102×C41—44no—
77C22⋊C8×C41—21no—
78C22⋊C8×C41—21no—
79C22⋊C8×C41—21no—
80C22⋊C8×C41D412yescomplemented
81#95×C41—22no—
82#95×C41—21no—
83#95×C41—21no—
84#95×C41D412yescomplemented
85C24×C41—24no—
86C24×C41—21no—
87C24×C41—22no—
88C24×C41—21no—
89C24×C41—21no—
90C24×C41—21no—
91C24×C41—21no—
92C24×C41—21no—
93C24×C41—21no—
94C24×C41—42no—
95C24×C41—42no—
96C24×C41—42no—
97C24×C41—42no—
98C24×C41—42no—
99C24×C41—41no—
100C24×C41—41no—
101C24×C41—41no—
102C24×C41—41no—
103C24×C41—41no—
104C24×C41—41no—
105C24×C41D812yescomplemented
106C24×C41C2×D411yescharacteristic
107C2×D4×C41—24no—
108C2×D4×C41—24no—
109C2×D4×C41—22no—
110C2×D4×C41—21no—
111C2×D4×C41—22no—
112C2×D4×C41—21no—
113C2×D4×C41—42no—
114C2×D4×C41—42no—
115C2×D4×C41—48no—
116C2×D4×C41—42no—
117C2×D4×C41—44no—
118C2×D4×C41—44no—
119C2×D4×C41—44no—
120C2×D4×C41—44no—
121C2×D4×C41—48no—
122C2×D4×C41—48no—
123C2×D4×C41—416no—
124C2×D4×C41—416no—
125C2×D4×C41—44no—
126C2×D4×C41—41no—
127C2×D4×C41—41no—
128C2×D4×C41—41no—
129C2×D4×C41—41no—
130C2×D4×C41—41no—
131C2×D4×C41—41no—
132C2×D4×C41—41no—
133C2×D4×C41—41no—
134C2×D4×C41—82no—
135C2×D4×C41—82no—
136C22×C4×C41—24no—
137C22×C4×C41—22no—
138C22×C4×C41—21no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—22no—
142C22×C4×C41—21no—
143C22×C4×C41—42no—
144C22×C4×C41—42no—
145C22×C4×C41—41no—
146C22×C4×C41—41no—
147C22×C4×C41—42no—
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41#4111yescharacteristic
154D8×C41—48no—
155C2×C8×C41—22no—
156C2×C8×C41—42no—
157C2×C8×C41—42no—
158C2×C8×C41—41no—
159C4⋊C4×C41—21no—
160C4⋊C4×C41—21no—
161C4⋊C4×C41—42no—
162C22⋊C4×C41—48no—
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—
172C22⋊C4×C41—82no—
173C23×C41—22no—
174C23×C41—22no—
175C23×C41—24no—
176C23×C41—22no—
177C23×C41—22no—
178C23×C41—22no—
179C23×C41—44no—
180C23×C41—42no—
181C23×C41—44no—
182C23×C41—44no—
183C23×C41—44no—
184C23×C41—42no—
185C23×C41—42no—
186C23×C41—42no—
187C23×C41—42no—
188C23×C41—44no—
189C23×C41—44no—
190C23×C41—44no—
191C23×C41—41no—
192C23×C41—42no—
193C23×C41—42no—
194C23×C41—41no—
195C23×C41—41no—
196C23×C41—42no—
197C23×C41—42no—
198C23×C41—44no—
199C23×C41—42no—
200C23×C41—41no—
201C23×C41—41no—
202C23×C41—41no—
203C23×C41—41no—
204C23×C41—42no—
205C23×C41—42no—
206C23×C41—82no—
207C23×C41—82no—
208C23×C41—81no—
209C23×C41—81no—
210C23×C41—82no—
211C23×C41—82no—
212C23×C41—82no—
213C23×C41—82no—
214C23×C41—82no—
215C23×C41—81no—
216C23×C41—81no—
217C23×C41—82no—
218C23×C41—81no—
219C23×C41—81no—
220C23×C41#12011yescharacteristic
221C23×C41#12011yescharacteristic
222C23×C41#12111yescharacteristic
223C23×C41C2×D811yescharacteristic
224C23×C41#13511yescharacteristic
225C23×C41AGL(1,ℤ/8)11yescharacteristic
226C23×C41AGL(1,ℤ/8)11yescharacteristic
227D4×C41—24no—
228D4×C41—24no—
229D4×C41—42no—
230D4×C41—44no—
231D4×C41—42no—
232D4×C41—44no—
233D4×C41—42no—
234D4×C41—432no—
235D4×C41—81no—
236D4×C41—88no—
237D4×C41—81no—
238D4×C41—81no—
239D4×C41—81no—
240D4×C41—81no—
241C2×C4×C41—22no—
242C2×C4×C41—22no—
243C2×C4×C41—24no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—44no—
249C2×C4×C41—44no—
250C2×C4×C41—42no—
251C2×C4×C41—42no—
252C2×C4×C41—42no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—42no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—42no—
259C2×C4×C41—42no—
260C2×C4×C41—42no—
261C2×C4×C41—81no—
262C2×C4×C41#12011yescharacteristic
263C2×C4×C41#12111yescharacteristic
264C2×C4×C41#12111yescharacteristic
265C2×C4×C41#12711yescharacteristic
266C8×C41—42no—
267C8×C41—81no—
268#9914C4111yesmaximal, characteristic, direct product factor, Sylow
269C22×C41—22no—
270C22×C41—22no—
271C22×C41—22no—
272C22×C41—22no—
273C22×C41—21no—
274C22×C41—21no—
275C22×C41—21no—
276C22×C41—21no—
277C22×C41—44no—
278C22×C41—44no—
279C22×C41—44no—
280C22×C41—44no—
281C22×C41—42no—
282C22×C41—44no—
283C22×C41—82no—
284C22×C41—82no—
285C22×C41—82no—
286C22×C41—82no—
287C22×C41—84no—
288C22×C41—82no—
289C22×C41—84no—
290C22×C41—84no—
291C22×C41—82no—
292C22×C41—84no—
293C22×C41—82no—
294C22×C41—81no—
295C22×C41—82no—
296C22×C41—81no—
297C22×C41—82no—
298C22×C41—82no—
299C22×C41—81no—
300C22×C41—81no—
301C22×C41—81no—
302C22×C41#39211yescharacteristic
303C22×C41#44711yescharacteristic
304C22×C41#44711yescharacteristic
305C22×C41#44911yescharacteristic
306C22×C41#44911yescharacteristic
307C22×C41#45312yes—
308C22×C41B(4,𝔽2)12yes—
309C22×C41#46611yescharacteristic
310C22×C41#46911yescharacteristic
311C4×C41—21no—
312C4×C41—21no—
313C4×C41—21no—
314C4×C41—21no—
315C4×C41—44no—
316C4×C41—82no—
317C4×C41—81no—
318C4×C41—81no—
319C2×#447C2×C4111yescharacteristic, complemented
320#2617C2×C4111yescharacteristic, complemented
321C2×#392C2×C4111yescharacteristic, complemented
322#1786C2×C4111yescharacteristic, complemented
323C2×#327C2×C4111yescharacteristic, complemented
324C2×#323C2×C4111yescharacteristic, complemented
325#1294C2×C4111yescharacteristic, complemented
326C2×C41—21no—
327C2×C41—21no—
328C2×C41—21no—
329C2×C41—21no—
330C2×C41—82no—
331C2×C41—84no—
332C2×C41—161no—
333C2×C41#159512yes—
334C2×C41#160012yes—
335C2×C41#199911yescharacteristic
336C2×C41#200211yescharacteristic
337C2×C41#202111yescharacteristic
338C23×D4—21no—
339C23×D4C22×C4111yescharacteristic
340C22×D8—21no—
341C2×#121C22×C4111yescharacteristic
342C2×#120—21no—
343C22×C22⋊C4—21no—
344C22×C22⋊C4C22×C4111yescharacteristic
345#447—22no—
346#447—22no—
347C2×#102—21no—
348C2×#102—22no—
349C2×C22⋊C8C22×C4111yescharacteristic
350C2×C22⋊C8C22×C4111yescharacteristic
351#397—21no—
352#394—22no—
353#392—21no—
354#392—22no—
355#392—22no—
356#386—21no—
357#380C22×C4111yescharacteristic
358C2×#95C22×C4111yescharacteristic
359#327—22no—
360#323—22no—
361C41#991411yescharacteristic, direct product factor, Sylow
362C25—21no—
363C25D4×C4111yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C4111yescharacteristic, complemented
378C22×D4D4×C4112yescomplemented
379C23×C4—21no—
380C23×C4D4×C4111yescharacteristic
381C23×C4C23×C4111yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C4111yescharacteristic, complemented
393C2×C4⋊C4D4×C4112yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C4112yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C4112yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C4112yescomplemented
437C24C2×D4×C4111yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C4111yescharacteristic
480C22×C4C2×D4×C4111yescharacteristic
481C22×C4C2×D4×C4111yescharacteristic
482C22×C4C2×D4×C4111yescharacteristic
483C22×C4C2×D4×C4111yescharacteristic
484C22×C4#41×C4111yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23—42no—
519C23—42no—
520C23—44no—
521C23—44no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—44no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—82no—
538C23—81no—
539C23—82no—
540C23—81no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C4111yescharacteristic
552C23#120×C4111yescharacteristic
553C23#121×C4111yescharacteristic
554C23C2×D8×C4111yescharacteristic
555C23#135×C4111yescharacteristic
556C23AGL(1,ℤ/8)×C4111yescharacteristic
557C23AGL(1,ℤ/8)×C4111yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4#120×C4111yescharacteristic
594C2×C4#121×C4111yescharacteristic
595C2×C4#121×C4111yescharacteristic
596C2×C4#127×C4111yescharacteristic
597C8—42no—
598C8—81no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—42no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—81no—
621C22—84no—
622C22—82no—
623C22—84no—
624C22—82no—
625C22—81no—
626C22—82no—
627C22—81no—
628C22—82no—
629C22—82no—
630C22—81no—
631C22—81no—
632C22C41×#39211yescharacteristic
633C22C41×#44711yescharacteristic
634C22C41×#44711yescharacteristic
635C22C41×#44911yescharacteristic
636C22C41×#44911yescharacteristic
637C22C41×#45312yes—
638C22C41×B(4,𝔽2)12yes—
639C22C41×#46611yescharacteristic
640C22C41×#46911yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—82no—
647C4—81no—
648C4—81no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2C41×#159512yes—
657C2C41×#160012yes—
658C2C41×#199911yescharacteristic
659C2C41×#200211yescharacteristic
660C2C41×#202111yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC23×C4C23×C41
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×#447C2semidirect
2. C41×#2617C2semidirect
3. C2×C41×#392C2semidirect
4. C41×#1786C2semidirect
5. C2×C41×#327C2semidirect
6. C2×C41×#323C2semidirect
7. C41×#1294C2semidirect
46. C22×D4×C41D4semidirect
47. C22×D4×C41D4semidirect
61. C2×C4⋊C4×C41D4semidirect
62. C2×C4⋊C4×C41D4semidirect
80. C22⋊C8×C41D4semidirect
84. #95×C41D4semidirect
105. C24×C41D8semidirect
268. #9914C41direct (N × H)
319. C2×#447C2×C41semidirect
320. #2617C2×C41semidirect
321. C2×#392C2×C41semidirect
322. #1786C2×C41semidirect
323. C2×#327C2×C41semidirect
324. C2×#323C2×C41semidirect
325. #1294C2×C41semidirect
361. C41#9914direct (N × H)
377. C22×D4D4×C41semidirect
378. C22×D4D4×C41semidirect
392. C2×C4⋊C4D4×C41semidirect
393. C2×C4⋊C4D4×C41semidirect
411. C22⋊C8D4×C41semidirect
415. #95D4×C41semidirect
436. C24D8×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4472
C41×#26172
C2×C41×#3922
C41×#17862
C2×C41×#3272
C2×C41×#3232
C41×#12942
#991441