Finite Group Databasebeta

← C41×#9113 #23785314

Subgroups — C41×#9113 #23785314

Order 10496.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C41C211yesmaximal, characteristic, complemented
2C41×#2847C211yesmaximal, characteristic
3C2×C41×#327C212yesmaximal, complemented
4C41×C22⋊#95C211yesmaximal, characteristic, complemented
5C41×#1294C212yesmaximal, complemented
6C24×C4×C41C2211yescharacteristic
7C23×C8×C41—21no—
8C2×#121×C41C411yescharacteristic, complemented
9C2×#121×C41C411yescharacteristic, complemented
10C2×#121×C41C2211yescharacteristic
11C2×#120×C41—21no—
12C22×C22⋊C4×C41—21no—
13C2×C22⋊C8×C41—21no—
14C2×C22⋊C8×C41—24no—
15C2×C22⋊C8×C41C2212yes—
16C41×#386—21no—
17C41×#386—21no—
18C41×#386—21no—
19C41×#380C411yescharacteristic, complemented
20C41×#380C411yescharacteristic, complemented
21C41×#380C2211yescharacteristic
22C2×#95×C41—21no—
23C2×#95×C41C2212yes—
24C41×#327—24no—
25C25×C41D411yescharacteristic
26C22×D4×C41—21no—
27C22×D4×C41—21no—
28C22×D4×C41—21no—
29C22×D4×C41C2×C411yescharacteristic
30C23×C4×C41—22no—
31C23×C4×C41—22no—
32C23×C4×C41—22no—
33C23×C4×C41—42no—
34C23×C4×C41—42no—
35C23×C4×C41C2×C411yescharacteristic
36C23×C4×C41C2×C411yescharacteristic
37C23×C4×C41D411yescharacteristic
38C23×C4×C41D411yescharacteristic
39C23×C4×C41D411yescharacteristic
40C23×C4×C41C2311yescharacteristic
41C22×C8×C41—24no—
42C22×C8×C41—22no—
43C22×C8×C41—42no—
44C22×C8×C41—42no—
45#121×C41—22no—
46#121×C41—22no—
47#121×C41—42no—
48#121×C41—42no—
49#120×C41—42no—
50#120×C41—42no—
51C2×C4⋊C4×C41C2×C411yescharacteristic
52C2×C4⋊C4×C41C2×C411yescharacteristic
53C2×C4⋊C4×C41C2×C411yescharacteristic
54C2×C22⋊C4×C41—24no—
55C2×C22⋊C4×C41—21no—
56C2×C22⋊C4×C41—21no—
57C2×C22⋊C4×C41—21no—
58C2×C22⋊C4×C41—21no—
59C2×C22⋊C4×C41—21no—
60C2×C22⋊C4×C41—21no—
61C2×C22⋊C4×C41—42no—
62C2×C22⋊C4×C41—42no—
63C22⋊C8×C41—24no—
64C22⋊C8×C41—22no—
65C22⋊C8×C41D414yescomplemented
66#95×C41—21no—
67#95×C41—21no—
68#95×C41—21no—
69#95×C41—22no—
70#95×C41—22no—
71#95×C41—42no—
72C24×C41—22no—
73C24×C41—22no—
74C24×C41—22no—
75C24×C41—22no—
76C24×C41—21no—
77C24×C41—41no—
78C24×C41—41no—
79C24×C41C22⋊C411yescharacteristic
80C24×C41C22⋊C411yescharacteristic
81C24×C41D812yes—
82C24×C41SD1612yes—
83C24×C41C2×D411yescharacteristic
84C2×D4×C41—22no—
85C2×D4×C41—41no—
86C2×D4×C41—41no—
87C2×D4×C41—42no—
88C2×D4×C41—42no—
89C2×D4×C41—42no—
90C2×D4×C41—42no—
91C2×D4×C41—42no—
92C2×D4×C41—42no—
93C2×D4×C41—42no—
94C2×D4×C41—41no—
95C2×D4×C41—41no—
96C2×D4×C41—42no—
97C22×C4×C41—22no—
98C22×C4×C41—22no—
99C22×C4×C41—21no—
100C22×C4×C41—21no—
101C22×C4×C41—22no—
102C22×C4×C41—22no—
103C22×C4×C41—22no—
104C22×C4×C41—22no—
105C22×C4×C41—22no—
106C22×C4×C41—22no—
107C22×C4×C41—21no—
108C22×C4×C41—21no—
109C22×C4×C41—24no—
110C22×C4×C41—21no—
111C22×C4×C41—21no—
112C22×C4×C41—21no—
113C22×C4×C41—41no—
114C22×C4×C41—41no—
115C22×C4×C41—41no—
116C22×C4×C41—41no—
117C22×C4×C41—41no—
118C22×C4×C41—41no—
119C22×C4×C41—41no—
120C22×C4×C41—48no—
121C22×C4×C41—48no—
122C22×C4×C41—42no—
123C22×C4×C41—42no—
124C22×C4×C41—42no—
125C22×C4×C41—42no—
126C22×C4×C41—42no—
127C22×C4×C41—42no—
128C22×C4×C41C22⋊C411yescharacteristic
129C22×C4×C41C22⋊C411yescharacteristic
130C22×C4×C41C22×C411yescharacteristic
131C22×C4×C41C2×D411yescharacteristic
132C22×C4×C41C2×D412yes—
133C22×C4×C41#4112yes—
134C2×C8×C41—24no—
135C2×C8×C41—48no—
136C2×C8×C41—42no—
137C2×C8×C41—42no—
138C4⋊C4×C41—22no—
139C4⋊C4×C41—41no—
140C4⋊C4×C41—41no—
141C22⋊C4×C41—42no—
142C22⋊C4×C41—48no—
143C22⋊C4×C41—42no—
144C22⋊C4×C41—42no—
145C22⋊C4×C41—41no—
146C22⋊C4×C41—41no—
147C22⋊C4×C41—42no—
148C22⋊C4×C41—41no—
149C22⋊C4×C41—41no—
150C23×C41—21no—
151C23×C41—21no—
152C23×C41—21no—
153C23×C41—21no—
154C23×C41—21no—
155C23×C41—21no—
156C23×C41—21no—
157C23×C41—21no—
158C23×C41—24no—
159C23×C41—24no—
160C23×C41—21no—
161C23×C41—21no—
162C23×C41—21no—
163C23×C41—21no—
164C23×C41—21no—
165C23×C41—21no—
166C23×C41—24no—
167C23×C41—24no—
168C23×C41—42no—
169C23×C41—42no—
170C23×C41—44no—
171C23×C41—44no—
172C23×C41—44no—
173C23×C41—44no—
174C23×C41—41no—
175C23×C41—41no—
176C23×C41—41no—
177C23×C41—41no—
178C23×C41—41no—
179C23×C41—41no—
180C23×C41—41no—
181C23×C41#9912yes—
182C23×C41#10212yes—
183C23×C41#10212yes—
184C23×C41#10412yes—
185C23×C41C2×C22⋊C411yescharacteristic
186C23×C41#12112yes—
187C23×C41C2×D811yescharacteristic
188C23×C41C2×SD1611yescharacteristic
189C23×C41#13512yes—
190D4×C41—82no—
191D4×C41—84no—
192D4×C41—84no—
193D4×C41—82no—
194D4×C41—82no—
195C2×C4×C41—24no—
196C2×C4×C41—24no—
197C2×C4×C41—21no—
198C2×C4×C41—21no—
199C2×C4×C41—21no—
200C2×C4×C41—21no—
201C2×C4×C41—21no—
202C2×C4×C41—21no—
203C2×C4×C41—21no—
204C2×C4×C41—21no—
205C2×C4×C41—21no—
206C2×C4×C41—42no—
207C2×C4×C41—42no—
208C2×C4×C41—44no—
209C2×C4×C41—44no—
210C2×C4×C41—44no—
211C2×C4×C41—42no—
212C2×C4×C41—42no—
213C2×C4×C41—44no—
214C2×C4×C41—44no—
215C2×C4×C41—44no—
216C2×C4×C41—41no—
217C2×C4×C41—41no—
218C2×C4×C41—41no—
219C2×C4×C41—41no—
220C2×C4×C41—41no—
221C2×C4×C41—41no—
222C2×C4×C41—41no—
223C2×C4×C41—41no—
224C2×C4×C41—41no—
225C2×C4×C41—82no—
226C2×C4×C41—82no—
227C2×C4×C41—82no—
228C2×C4×C41—82no—
229C2×C4×C41#9912yes—
230C2×C4×C41C4×D412yes—
231C2×C4×C41#12011yescharacteristic
232C2×C4×C41#12311yescharacteristic
233C8×C41—44no—
234#9113C4111yesmaximal, characteristic, direct product factor, Sylow
235C22×C41—22no—
236C22×C41—22no—
237C22×C41—22no—
238C22×C41—22no—
239C22×C41—22no—
240C22×C41—21no—
241C22×C41—21no—
242C22×C41—22no—
243C22×C41—22no—
244C22×C41—22no—
245C22×C41—22no—
246C22×C41—21no—
247C22×C41—22no—
248C22×C41—21no—
249C22×C41—22no—
250C22×C41—22no—
251C22×C41—22no—
252C22×C41—48no—
253C22×C41—48no—
254C22×C41—41no—
255C22×C41—41no—
256C22×C41—41no—
257C22×C41—41no—
258C22×C41—81no—
259C22×C41—81no—
260C22×C41—81no—
261C22×C41—81no—
262C22×C41—81no—
263C22×C41—81no—
264C22×C41—81no—
265C22×C41#32714yescomplemented
266C22×C41#38611yescharacteristic
267C22×C41C2×#9911yescharacteristic
268C22×C41C2×#9911yescharacteristic
269C22×C41C2×#10211yescharacteristic
270C22×C41#41611yescharacteristic
271C22×C41C2×#10411yescharacteristic
272C22×C41#42111yescharacteristic
273C22×C41#46512yes—
274C22×C41#46612yes—
275C4×C41—21no—
276C4×C41—22no—
277C4×C41—21no—
278C4×C41—22no—
279C4×C41—41no—
280C4×C41—84no—
281C4×C41—81no—
282C4×C41—81no—
283C4×C41—81no—
284C22×C22⋊C8C2×C4111yescharacteristic, complemented
285#2847C2×C4111yescharacteristic
286C2×#327C2×C4112yescomplemented
287C22⋊#95C2×C4111yescharacteristic, complemented
288#1294C2×C4112yescomplemented
289C2×C41—22no—
290C2×C41—24no—
291C2×C41—22no—
292C2×C41—42no—
293C2×C41—161no—
294C2×C41C2×#32711yescharacteristic
295C2×C41#150111yescharacteristic
296C2×C41#151611yescharacteristic
297C2×C41#151911yescharacteristic
298C2×C41#187111yescharacteristic
299C2×C41#189311yescharacteristic
300C2×C41#189811yescharacteristic
301C24×C4C22×C4111yescharacteristic
302C23×C8—21no—
303C2×#121C4×C4111yescharacteristic, complemented
304C2×#121C4×C4111yescharacteristic, complemented
305C2×#121C22×C4111yescharacteristic
306C2×#120—21no—
307C22×C22⋊C4—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8—24no—
310C2×C22⋊C8C22×C4112yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#380C4×C4111yescharacteristic, complemented
315#380C4×C4111yescharacteristic, complemented
316#380C22×C4111yescharacteristic
317C2×#95—21no—
318C2×#95C22×C4112yes—
319#327—24no—
320C41#911311yescharacteristic, direct product factor, Sylow
321C25D4×C4111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C4111yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C4111yescharacteristic
332C23×C4C2×C4×C4111yescharacteristic
333C23×C4D4×C4111yescharacteristic
334C23×C4D4×C4111yescharacteristic
335C23×C4D4×C4111yescharacteristic
336C23×C4C23×C4111yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C4111yescharacteristic
348C2×C4⋊C4C2×C4×C4111yescharacteristic
349C2×C4⋊C4C2×C4×C4111yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C4114yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C4111yescharacteristic
376C24C22⋊C4×C4111yescharacteristic
377C24D8×C4112yes—
378C24SD16×C4112yes—
379C24C2×D4×C4111yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C4111yescharacteristic
425C22×C4C22⋊C4×C4111yescharacteristic
426C22×C4C22×C4×C4111yescharacteristic
427C22×C4C2×D4×C4111yescharacteristic
428C22×C4C2×D4×C4112yes—
429C22×C4#41×C4112yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C4112yes—
478C23#102×C4112yes—
479C23#102×C4112yes—
480C23#104×C4112yes—
481C23C2×C22⋊C4×C4111yescharacteristic
482C23#121×C4112yes—
483C23C2×D8×C4111yescharacteristic
484C23C2×SD16×C4111yescharacteristic
485C23#135×C4112yes—
486D4—82no—
487D4—84no—
488D4—84no—
489D4—82no—
490D4—82no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C4112yes—
526C2×C4C4×D4×C4112yes—
527C2×C4#120×C4111yescharacteristic
528C2×C4#123×C4111yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—21no—
535C22—22no—
536C22—21no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C41×#32714yescomplemented
561C22C41×#38611yescharacteristic
562C22C2×#99×C4111yescharacteristic
563C22C2×#99×C4111yescharacteristic
564C22C2×#102×C4111yescharacteristic
565C22C41×#41611yescharacteristic
566C22C2×#104×C4111yescharacteristic
567C22C41×#42111yescharacteristic
568C22C41×#46512yes—
569C22C41×#46612yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—42no—
583C2—161no—
584C2C2×C41×#32711yescharacteristic
585C2C41×#150111yescharacteristic
586C2C41×#151611yescharacteristic
587C2C41×#151911yescharacteristic
588C2C41×#187111yescharacteristic
589C2C41×#189311yescharacteristic
590C2C41×#189811yescharacteristic
subgroupG/H
center, socleC23×C41C2×C22⋊C4
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC41×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C24×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C41C2semidirect
3. C2×C41×#327C2semidirect
4. C41×C22⋊#95C2semidirect
5. C41×#1294C2semidirect
8. C2×#121×C41C4semidirect
9. C2×#121×C41C4semidirect
19. C41×#380C4semidirect
20. C41×#380C4semidirect
65. C22⋊C8×C41D4semidirect
234. #9113C41direct (N × H)
265. C22×C41#327semidirect
284. C22×C22⋊C8C2×C41semidirect
286. C2×#327C2×C41semidirect
287. C22⋊#95C2×C41semidirect
288. #1294C2×C41semidirect
303. C2×#121C4×C41semidirect
304. C2×#121C4×C41semidirect
314. #380C4×C41semidirect
315. #380C4×C41semidirect
320. C41#9113direct (N × H)
361. C22⋊C8D4×C41semidirect
560. C22C41×#327semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C412
C41×#28472
C2×C41×#3272
C41×C22⋊#952
C41×#12942
#911341