Finite Group Databasebeta

← C41×#11192 #23787393

Subgroups — C41×#11192 #23787393

Order 10496.

866 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#417C211yesmaximal, characteristic
2C2×C41×#417C211yesmaximal, characteristic
3C2×C41×#408C211yesmaximal, characteristic
4C2×C41×#343C211yesmaximal, characteristic, complemented
5C2×C41×#343C211yesmaximal, characteristic, complemented
6C2×C41×#341C211yesmaximal, characteristic, complemented
7C2×C41×#340C211yesmaximal, characteristic, complemented
8C22×#41×C41C2211yescharacteristic
9C22×M16×C41C2211yescharacteristic
10C22×M16×C41C2211yescharacteristic
11C22×M16×C41C2211yescharacteristic
12C23×C8×C41C2211yescharacteristic
13C22×C4⋊C4×C41C2211yescharacteristic
14C22×C4⋊C4×C41C2211yescharacteristic
15C41×#417—22no—
16C41×#417—22no—
17C41×#417—22no—
18C41×#417C414yescomplemented
19C2×#103×C41—21no—
20C2×#103×C41—21no—
21C2×#102×C41—21no—
22C2×#102×C41—21no—
23C41×#408—22no—
24C41×#408—22no—
25C2×C22⋊C8×C41—22no—
26C41×#343—22no—
27C41×#343—22no—
28C41×#341—22no—
29C41×#340—22no—
30C2×#41×C41—21no—
31C2×#41×C41—21no—
32C2×#41×C41—21no—
33C2×#41×C41—21no—
34C2×#41×C41—21no—
35C2×#41×C41—21no—
36C2×#41×C41—21no—
37C2×#41×C41—21no—
38C2×#41×C41—21no—
39C2×#41×C41—21no—
40C2×#41×C41C2×C412yes—
41C2×#41×C41D412yes—
42C22×Q8×C41D411yescharacteristic
43C22×D4×C41—21no—
44C22×D4×C41D411yescharacteristic
45C23×C4×C41—21no—
46C23×C4×C41—21no—
47C23×C4×C41—21no—
48C23×C4×C41C2311yescharacteristic
49C2×M16×C41—21no—
50C2×M16×C41—21no—
51C2×M16×C41—21no—
52C2×M16×C41—21no—
53C2×M16×C41—21no—
54C2×M16×C41—21no—
55C2×M16×C41—21no—
56C2×M16×C41—21no—
57C2×M16×C41—21no—
58C2×M16×C41—21no—
59C2×M16×C41—21no—
60C2×M16×C41—21no—
61C2×M16×C41—21no—
62C2×M16×C41—21no—
63C2×M16×C41—21no—
64C2×M16×C41C2×C412yes—
65C2×M16×C41D412yes—
66C2×M16×C41D412yes—
67C22×C8×C41—21no—
68C22×C8×C41—21no—
69C22×C8×C41—21no—
70C22×C8×C41—21no—
71C22×C8×C41—21no—
72C22×C8×C41—21no—
73C22×C8×C41—21no—
74C22×C8×C41—21no—
75C22×C8×C41—21no—
76C22×C8×C41D412yes—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41—21no—
81C2×C4⋊C4×C41—21no—
82C2×C4⋊C4×C41—21no—
83C2×C4⋊C4×C41—21no—
84C2×C4⋊C4×C41—21no—
85C2×C4⋊C4×C41—21no—
86C2×C4⋊C4×C41—21no—
87C2×C4⋊C4×C41C2×C412yes—
88C2×C4⋊C4×C41D412yes—
89#103×C41—24no—
90#103×C41—24no—
91#102×C41—24no—
92#102×C41—24no—
93C22⋊C8×C41—28no—
94C24×C41—21no—
95C24×C41#4111yescharacteristic
96#41×C41—22no—
97#41×C41—22no—
98#41×C41—22no—
99#41×C41—22no—
100#41×C41—22no—
101#41×C41—22no—
102#41×C41—22no—
103#41×C41—22no—
104#41×C41—41no—
105#41×C41—41no—
106#41×C41—41no—
107#41×C41—41no—
108#41×C41—41no—
109#41×C41—41no—
110#41×C41—41no—
111#41×C41—41no—
112C2×Q8×C41—21no—
113C2×Q8×C41—21no—
114C2×Q8×C41—21no—
115C2×Q8×C41—21no—
116C2×Q8×C41—21no—
117C2×Q8×C41C22⋊C412yes—
118C2×D4×C41—22no—
119C2×D4×C41—22no—
120C2×D4×C41—21no—
121C2×D4×C41—21no—
122C2×D4×C41—21no—
123C2×D4×C41—21no—
124C2×D4×C41—21no—
125C2×D4×C41—41no—
126C2×D4×C41—41no—
127C2×D4×C41—41no—
128C2×D4×C41—41no—
129C2×D4×C41C22⋊C412yes—
130C22×C4×C41—21no—
131C22×C4×C41—22no—
132C22×C4×C41—22no—
133C22×C4×C41—22no—
134C22×C4×C41—22no—
135C22×C4×C41—41no—
136C22×C4×C41—41no—
137C22×C4×C41—41no—
138C22×C4×C41—41no—
139C22×C4×C41—41no—
140C22×C4×C41—41no—
141C22×C4×C41—41no—
142C22×C4×C41—41no—
143C22×C4×C41—81no—
144C22×C4×C41—81no—
145C22×C4×C41—81no—
146C22×C4×C41—81no—
147C22×C4×C41C22×C411yescharacteristic
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41C2×D411yescharacteristic
154C22×C4×C41#4111yescharacteristic
155C22×C4×C41#4111yescharacteristic
156C22×C4×C41#4111yescharacteristic
157C22×C4×C41#4111yescharacteristic
158C22×C4×C41#4111yescharacteristic
159C22×C4×C41#4111yescharacteristic
160C22×C4×C41#4111yescharacteristic
161M16×C41—22no—
162M16×C41—22no—
163M16×C41—22no—
164M16×C41—22no—
165M16×C41—22no—
166M16×C41—22no—
167M16×C41—41no—
168M16×C41—41no—
169M16×C41—41no—
170M16×C41—41no—
171M16×C41—41no—
172M16×C41—41no—
173C2×C8×C41—22no—
174C2×C8×C41—22no—
175C2×C8×C41—22no—
176C2×C8×C41—22no—
177C2×C8×C41—22no—
178C2×C8×C41—22no—
179C2×C8×C41—41no—
180C2×C8×C41—41no—
181C2×C8×C41—41no—
182C2×C8×C41—41no—
183C2×C8×C41—41no—
184C2×C8×C41—41no—
185C2×C8×C41—41no—
186C2×C8×C41—41no—
187C2×C8×C41—41no—
188C2×C8×C41—41no—
189C4⋊C4×C41—22no—
190C4⋊C4×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—22no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41—41no—
197C23×C41—21no—
198C23×C41—21no—
199C23×C41—21no—
200C23×C41—21no—
201C23×C41—22no—
202C23×C41—41no—
203C23×C41—41no—
204C23×C41—41no—
205C23×C41—41no—
206C23×C41—41no—
207C23×C41—41no—
208C23×C41C4×D411yescharacteristic
209C23×C41#12111yescharacteristic
210C23×C41#12311yescharacteristic
211C23×C41#12311yescharacteristic
212C23×C41#12411yescharacteristic
213C23×C41#12611yescharacteristic
214C23×C41#12611yescharacteristic
215Q8×C41—22no—
216Q8×C41—22no—
217Q8×C41—41no—
218Q8×C41—41no—
219D4×C41—22no—
220D4×C41—22no—
221D4×C41—42no—
222D4×C41—42no—
223D4×C41—42no—
224D4×C41—42no—
225D4×C41—41no—
226D4×C41—41no—
227C2×C4×C41—22no—
228C2×C4×C41—41no—
229C2×C4×C41—41no—
230C2×C4×C41—42no—
231C2×C4×C41—42no—
232C2×C4×C41—42no—
233C2×C4×C41—42no—
234C2×C4×C41—42no—
235C2×C4×C41—42no—
236C2×C4×C41—82no—
237C2×C4×C41—82no—
238C2×C4×C41—81no—
239C2×C4×C41—81no—
240C2×C4×C41—81no—
241C2×C4×C41—81no—
242C2×C4×C41—82no—
243C2×C4×C41—82no—
244C2×C4×C41C2×C22⋊C411yescharacteristic
245C2×C4×C41#11711yescharacteristic
246C2×C4×C41#11711yescharacteristic
247C2×C4×C41C4×D411yescharacteristic
248C2×C4×C41C4×D411yescharacteristic
249C2×C4×C41C4×D411yescharacteristic
250C2×C4×C41#12011yescharacteristic
251C2×C4×C41#12011yescharacteristic
252C2×C4×C41#12111yescharacteristic
253C2×C4×C41#12111yescharacteristic
254C2×C4×C41#12111yescharacteristic
255C2×C4×C41#12111yescharacteristic
256C2×C4×C41#12111yescharacteristic
257C2×C4×C41#12111yescharacteristic
258C2×C4×C41#12111yescharacteristic
259C2×C4×C41#12311yescharacteristic
260C2×C4×C41#12311yescharacteristic
261C2×C4×C41#12311yescharacteristic
262C2×C4×C41#12311yescharacteristic
263C2×C4×C41#12311yescharacteristic
264C2×C4×C41#12311yescharacteristic
265C2×C4×C41#12311yescharacteristic
266C2×C4×C41#12311yescharacteristic
267C2×C4×C41#12411yescharacteristic
268C2×C4×C41#12411yescharacteristic
269C2×C4×C41#12411yescharacteristic
270C2×C4×C41#12611yescharacteristic
271C2×C4×C41#12611yescharacteristic
272C8×C41—42no—
273C8×C41—42no—
274C8×C41—42no—
275C8×C41—42no—
276#11192C4111yesmaximal, characteristic, direct product factor, Sylow
277C22×C41—21no—
278C22×C41—21no—
279C22×C41—21no—
280C22×C41—21no—
281C22×C41—21no—
282C22×C41—21no—
283C22×C41—21no—
284C22×C41—21no—
285C22×C41—21no—
286C22×C41—21no—
287C22×C41—21no—
288C22×C41—21no—
289C22×C41—42no—
290C22×C41—42no—
291C22×C41—42no—
292C22×C41—81no—
293C22×C41—81no—
294C22×C41—81no—
295C22×C41—81no—
296C22×C41#38611yescharacteristic
297C22×C41#38811yescharacteristic
298C22×C41#38811yescharacteristic
299C22×C41#39411yescharacteristic
300C22×C41#39711yescharacteristic
301C22×C41#39711yescharacteristic
302C22×C41#39711yescharacteristic
303C22×C41#47111yescharacteristic
304C22×C41#47111yescharacteristic
305C22×C41#47211yescharacteristic
306C22×C41#47311yescharacteristic
307C4×C41—42no—
308C4×C41—82no—
309C4×C41—82no—
310C4×C41#38111yescharacteristic
311C4×C41#38611yescharacteristic
312C4×C41#38811yescharacteristic
313C4×C41#38811yescharacteristic
314C4×C41#39411yescharacteristic
315C4×C41#39411yescharacteristic
316C4×C41#39411yescharacteristic
317C4×C41#39711yescharacteristic
318C2×#417C2×C4111yescharacteristic
319C2×#417C2×C4111yescharacteristic
320C2×#408C2×C4111yescharacteristic
321C2×#343C2×C4111yescharacteristic, complemented
322C2×#343C2×C4111yescharacteristic, complemented
323C2×#341C2×C4111yescharacteristic, complemented
324C2×#340C2×C4111yescharacteristic, complemented
325C2×C41—21no—
326C2×C41—21no—
327C2×C41—21no—
328C2×C41—21no—
329C2×C41—82no—
330C2×C41#144011yescharacteristic
331C2×C41#190711yescharacteristic
332C2×C41#190811yescharacteristic
333C2×C41#205111yescharacteristic
334C2×C41#205211yescharacteristic
335C2×C41#207811yescharacteristic
336C2×C41#207911yescharacteristic
337C22×#41C22×C4111yescharacteristic
338C22×M16C22×C4111yescharacteristic
339C22×M16C22×C4111yescharacteristic
340C22×M16C22×C4111yescharacteristic
341C23×C8C22×C4111yescharacteristic
342C22×C4⋊C4C22×C4111yescharacteristic
343C22×C4⋊C4C22×C4111yescharacteristic
344#417—22no—
345#417—22no—
346#417—22no—
347#417C4×C4114yescomplemented
348C2×#103—21no—
349C2×#103—21no—
350C2×#102—21no—
351C2×#102—21no—
352#408—22no—
353#408—22no—
354C2×C22⋊C8—22no—
355#343—22no—
356#343—22no—
357#341—22no—
358#340—22no—
359C41#1119211yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41C2×C4×C4112yes—
371C2×#41D4×C4112yes—
372C22×Q8D4×C4111yescharacteristic
373C22×D4—21no—
374C22×D4D4×C4111yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C23×C4C23×C4111yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16C2×C4×C4112yes—
395C2×M16D4×C4112yes—
396C2×M16D4×C4112yes—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—21no—
406C22×C8D4×C4112yes—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4C2×C4×C4112yes—
418C2×C4⋊C4D4×C4112yes—
419#103—24no—
420#103—24no—
421#102—24no—
422#102—24no—
423C22⋊C8—28no—
424C24—21no—
425C24#41×C4111yescharacteristic
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C22⋊C4×C4112yes—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C22⋊C4×C4112yes—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4C22×C4×C4111yescharacteristic
478C22×C4C2×D4×C4111yescharacteristic
479C22×C4C2×D4×C4111yescharacteristic
480C22×C4C2×D4×C4111yescharacteristic
481C22×C4C2×D4×C4111yescharacteristic
482C22×C4C2×D4×C4111yescharacteristic
483C22×C4C2×D4×C4111yescharacteristic
484C22×C4#41×C4111yescharacteristic
485C22×C4#41×C4111yescharacteristic
486C22×C4#41×C4111yescharacteristic
487C22×C4#41×C4111yescharacteristic
488C22×C4#41×C4111yescharacteristic
489C22×C4#41×C4111yescharacteristic
490C22×C4#41×C4111yescharacteristic
491M16—22no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—22no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—41no—
502M16—41no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C4×D4×C4111yescharacteristic
539C23#121×C4111yescharacteristic
540C23#123×C4111yescharacteristic
541C23#123×C4111yescharacteristic
542C23#124×C4111yescharacteristic
543C23#126×C4111yescharacteristic
544C23#126×C4111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549D4—22no—
550D4—22no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—41no—
556D4—41no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C2×C22⋊C4×C4111yescharacteristic
575C2×C4#117×C4111yescharacteristic
576C2×C4#117×C4111yescharacteristic
577C2×C4C4×D4×C4111yescharacteristic
578C2×C4C4×D4×C4111yescharacteristic
579C2×C4C4×D4×C4111yescharacteristic
580C2×C4#120×C4111yescharacteristic
581C2×C4#120×C4111yescharacteristic
582C2×C4#121×C4111yescharacteristic
583C2×C4#121×C4111yescharacteristic
584C2×C4#121×C4111yescharacteristic
585C2×C4#121×C4111yescharacteristic
586C2×C4#121×C4111yescharacteristic
587C2×C4#121×C4111yescharacteristic
588C2×C4#121×C4111yescharacteristic
589C2×C4#123×C4111yescharacteristic
590C2×C4#123×C4111yescharacteristic
591C2×C4#123×C4111yescharacteristic
592C2×C4#123×C4111yescharacteristic
593C2×C4#123×C4111yescharacteristic
594C2×C4#123×C4111yescharacteristic
595C2×C4#123×C4111yescharacteristic
596C2×C4#123×C4111yescharacteristic
597C2×C4#124×C4111yescharacteristic
598C2×C4#124×C4111yescharacteristic
599C2×C4#124×C4111yescharacteristic
600C2×C4#126×C4111yescharacteristic
601C2×C4#126×C4111yescharacteristic
602C8—42no—
603C8—42no—
604C8—42no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C41×#38611yescharacteristic
626C22C41×#38811yescharacteristic
627C22C41×#38811yescharacteristic
628C22C41×#39411yescharacteristic
629C22C41×#39711yescharacteristic
630C22C41×#39711yescharacteristic
631C22C41×#39711yescharacteristic
632C22C41×#47111yescharacteristic
633C22C41×#47111yescharacteristic
634C22C41×#47211yescharacteristic
635C22C41×#47311yescharacteristic
636C4—42no—
637C4—82no—
638C4—82no—
639C4C41×#38111yescharacteristic
640C4C41×#38611yescharacteristic
641C4C41×#38811yescharacteristic
642C4C41×#38811yescharacteristic
643C4C41×#39411yescharacteristic
644C4C41×#39411yescharacteristic
645C4C41×#39411yescharacteristic
646C4C41×#39711yescharacteristic
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—82no—
652C2C41×#144011yescharacteristic
653C2C41×#190711yescharacteristic
654C2C41×#190811yescharacteristic
655C2C41×#205111yescharacteristic
656C2C41×#205211yescharacteristic
657C2C41×#207811yescharacteristic
658C2C41×#207911yescharacteristic
subgroupG/H
center, socleC23×C41#121
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC22×#41×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C41×#343C2semidirect
5. C2×C41×#343C2semidirect
6. C2×C41×#341C2semidirect
7. C2×C41×#340C2semidirect
18. C41×#417C4semidirect
276. #11192C41direct (N × H)
321. C2×#343C2×C41semidirect
322. C2×#343C2×C41semidirect
323. C2×#341C2×C41semidirect
324. C2×#340C2×C41semidirect
347. #417C4×C41semidirect
359. C41#11192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4172
C2×C41×#4082
C2×C41×#3432
C2×C41×#3412
C2×C41×#3402
#1119241