Finite Group Databasebeta

← C41×#19369 #23795570

Subgroups — C41×#19369 #23795570

Order 10496.

644 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3253C211yesmaximal, characteristic
2C41×#3235C211yesmaximal, characteristic, complemented
3C41×#3182C211yesmaximal, characteristic, complemented
4C41×#2935C211yesmaximal, characteristic, complemented
5C41×#1703C211yesmaximal, characteristic, complemented
6C41×#1697C211yesmaximal, characteristic, complemented
7C41×#1695C211yesmaximal, characteristic, complemented
8C41×#1685C211yesmaximal, characteristic, complemented
9C41×#1683C211yesmaximal, characteristic, complemented
10C41×#1677C211yesmaximal, characteristic, complemented
11C41×#1675C211yesmaximal, characteristic, complemented
12C41×#1665C211yesmaximal, characteristic, complemented
13C41×#1569C211yesmaximal, characteristic, complemented
14C41×#1551C211yesmaximal, characteristic, complemented
15C41×#1550C211yesmaximal, characteristic, complemented
16C2×#131×C41—21no—
17C41×#533C2211yescharacteristic
18C41×#532C2211yescharacteristic
19C41×#532C2211yescharacteristic
20C41×#501—21no—
21C41×#500C2211yescharacteristic
22C41×#492C2211yescharacteristic
23C41×#490—21no—
24C41×#487C2211yescharacteristic
25C41×#486C2211yescharacteristic
26C41×#482—21no—
27C41×#482—21no—
28C41×#476—21no—
29C41×#476C2211yescharacteristic
30C41×#476C2211yescharacteristic
31C41×#476C2211yescharacteristic
32C41×#476C2211yescharacteristic
33C41×#474C2211yescharacteristic
34C41×#474C2211yescharacteristic
35C41×#469—21no—
36C41×#469—21no—
37C41×#468—21no—
38C41×#468—21no—
39C41×#459—21no—
40C41×#459C2211yescharacteristic
41C41×#459C2211yescharacteristic
42C41×#440—21no—
43C41×#440—21no—
44C41×#436C2211yescharacteristic
45C41×#436C2211yescharacteristic
46C41×#435—21no—
47C41×#435—21no—
48C8×D4×C41C2211yescharacteristic
49C8×D4×C41C2211yescharacteristic
50C41×#432C2211yescharacteristic
51C41×#423C2211yescharacteristic
52C2×C4⋊C8×C41C2211yescharacteristic
53C41×#408—21no—
54C4×M16×C41C2211yescharacteristic
55C41×#335C2211yescharacteristic
56C41×#335C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#334C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#333C2211yescharacteristic
61C41×#333C2211yescharacteristic
62C41×#333C2211yescharacteristic
63C41×#332C2211yescharacteristic
64C41×#332C2211yescharacteristic
65C41×#331C2211yescharacteristic
66C41×#331C2211yescharacteristic
67C2×#41×C41—21no—
68C2×#41×C41—21no—
69C2×SD16×C41—21no—
70C2×SD16×C41—21no—
71C2×D8×C41—21no—
72C2×D8×C41—21no—
73#131×C41—44no—
74C2×M16×C41—21no—
75C2×M16×C41—21no—
76C2×M16×C41—21no—
77C2×M16×C41D411yescharacteristic
78C2×M16×C41D411yescharacteristic
79C22×C8×C41—21no—
80C22×C8×C41—21no—
81C22×C8×C41—21no—
82C4⋊Q8×C41D411yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86#127×C41D411yescharacteristic
87#127×C41C2311yescharacteristic
88#125×C41—21no—
89#124×C41—21no—
90#124×C41—21no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—21no—
93#121×C41—21no—
94#121×C41—21no—
95#121×C41—21no—
96#121×C41D411yescharacteristic
97#121×C41D411yescharacteristic
98C4×Q8×C41—21no—
99C4×Q8×C41—21no—
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41C2311yescharacteristic
104C4×D4×C41C2311yescharacteristic
105#117×C41—21no—
106C2×C42×C41C2311yescharacteristic
107#107×C41—21no—
108#107×C41—21no—
109#107×C41—21no—
110#107×C41—21no—
111#106×C41—21no—
112#106×C41—21no—
113#106×C41—21no—
114#106×C41—21no—
115C4⋊C8×C41—21no—
116C4⋊C8×C41—21no—
117C4⋊C8×C41C2311yescharacteristic
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120C4⋊C8×C41C2311yescharacteristic
121C4⋊C8×C41C2311yescharacteristic
122C4⋊C8×C41C2311yescharacteristic
123#103×C41—21no—
124#103×C41—21no—
125#102×C41—21no—
126#102×C41—21no—
127#102×C41—21no—
128#102×C41—21no—
129#102×C41—21no—
130#102×C41—21no—
131#102×C41—21no—
132#102×C41—21no—
133#102×C41—21no—
134#102×C41—21no—
135C22⋊C8×C41—21no—
136C22⋊C8×C41—21no—
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140#97×C41—21no—
141#97×C41D411yescharacteristic
142#97×C41D411yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C4×C8×C41C2311yescharacteristic
145#41×C41—42no—
146#41×C41—42no—
147#41×C41—82no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
151C2×Q8×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—41no—
160C2×D4×C41C2×D411yescharacteristic
161C2×D4×C41C2×D411yescharacteristic
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—41no—
165C22×C4×C41C2×D411yescharacteristic
166C22×C4×C41C2×D411yescharacteristic
167C22×C4×C41#4111yescharacteristic
168SD16×C41—42no—
169SD16×C41—42no—
170D8×C41—81no—
171D8×C41—81no—
172M16×C41—22no—
173M16×C41—41no—
174M16×C41—42no—
175M16×C41—42no—
176M16×C41—81no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—42no—
184C2×C8×C41—42no—
185C2×C8×C41—42no—
186C2×C8×C41C2×D411yescharacteristic
187C2×C8×C41C2×D411yescharacteristic
188C2×C8×C41C2×D411yescharacteristic
189C2×C8×C41C2×D411yescharacteristic
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—41no—
198C4⋊C4×C41—41no—
199C4⋊C4×C41C2×D411yescharacteristic
200C4⋊C4×C41C2×D411yescharacteristic
201C22⋊C4×C41—21no—
202C22⋊C4×C41—21no—
203C22⋊C4×C41—21no—
204C22⋊C4×C41—21no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C22⋊C4×C41—41no—
208C42×C41—41no—
209C42×C41C2×D411yescharacteristic
210C42×C41C2×D411yescharacteristic
211C42×C41#4111yescharacteristic
212C42×C41C2411yescharacteristic
213C23×C41—21no—
214C23×C41—21no—
215C23×C41—41no—
216C23×C41#12111yescharacteristic
217Q8×C41—42no—
218Q8×C41—41no—
219Q8×C41—41no—
220Q8×C41—81no—
221Q8×C41—81no—
222D4×C41—21no—
223D4×C41—21no—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—42no—
227D4×C41—42no—
228D4×C41—42no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—41no—
233D4×C41—81no—
234D4×C41—81no—
235D4×C41—82no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—82no—
251C2×C4×C41#12111yescharacteristic
252C2×C4×C41#12111yescharacteristic
253C2×C4×C41#12111yescharacteristic
254C2×C4×C41C22×D411yescharacteristic
255C2×C4×C41C22×D411yescharacteristic
256C2×C4×C41C2×#4111yescharacteristic
257C8×C41—21no—
258C8×C41—21no—
259C8×C41—21no—
260C8×C41—41no—
261C8×C41—41no—
262C8×C41—41no—
263C8×C41—41no—
264C8×C41—41no—
265C8×C41—41no—
266C8×C41AGL(1,ℤ/8)12yes—
267#19369C4111yesmaximal, characteristic, direct product factor, Sylow
268C22×C41—21no—
269C22×C41—21no—
270C22×C41—21no—
271C22×C41—41no—
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—41no—
276C22×C41—41no—
277C22×C41—81no—
278C22×C41—81no—
279C22×C41—81no—
280C22×C41C2×#12111yescharacteristic
281C4×C41—21no—
282C4×C41—21no—
283C4×C41—21no—
284C4×C41—21no—
285C4×C41—41no—
286C4×C41—41no—
287C4×C41—81no—
288C4×C41—81no—
289C4×C41—81no—
290C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C41#57511yescharacteristic
292C4×C41#57711yescharacteristic
293C4×C41#57811yescharacteristic
294#3253C2×C4111yescharacteristic
295#3235C2×C4111yescharacteristic, complemented
296#3182C2×C4111yescharacteristic, complemented
297#2935C2×C4111yescharacteristic, complemented
298#1703C2×C4111yescharacteristic, complemented
299#1697C2×C4111yescharacteristic, complemented
300#1695C2×C4111yescharacteristic, complemented
301#1685C2×C4111yescharacteristic, complemented
302#1683C2×C4111yescharacteristic, complemented
303#1677C2×C4111yescharacteristic, complemented
304#1675C2×C4111yescharacteristic, complemented
305#1665C2×C4111yescharacteristic, complemented
306#1569C2×C4111yescharacteristic, complemented
307#1551C2×C4111yescharacteristic, complemented
308#1550C2×C4111yescharacteristic, complemented
309C2×C41—41no—
310C2×C41—81no—
311C2×C41—81no—
312C2×C41—161no—
313C2×C41#303611yescharacteristic
314C2×C41#306311yescharacteristic
315C2×C41#306811yescharacteristic
316C2×#131—21no—
317#533C22×C4111yescharacteristic
318#532C22×C4111yescharacteristic
319#532C22×C4111yescharacteristic
320#501—21no—
321#500C22×C4111yescharacteristic
322#492C22×C4111yescharacteristic
323#490—21no—
324#487C22×C4111yescharacteristic
325#486C22×C4111yescharacteristic
326#482—21no—
327#482—21no—
328#476—21no—
329#476C22×C4111yescharacteristic
330#476C22×C4111yescharacteristic
331#476C22×C4111yescharacteristic
332#476C22×C4111yescharacteristic
333#474C22×C4111yescharacteristic
334#474C22×C4111yescharacteristic
335#469—21no—
336#469—21no—
337#468—21no—
338#468—21no—
339#459—21no—
340#459C22×C4111yescharacteristic
341#459C22×C4111yescharacteristic
342#440—21no—
343#440—21no—
344#436C22×C4111yescharacteristic
345#436C22×C4111yescharacteristic
346#435—21no—
347#435—21no—
348C8×D4C22×C4111yescharacteristic
349C8×D4C22×C4111yescharacteristic
350#432C22×C4111yescharacteristic
351#423C22×C4111yescharacteristic
352C2×C4⋊C8C22×C4111yescharacteristic
353#408—21no—
354C4×M16C22×C4111yescharacteristic
355#335C22×C4111yescharacteristic
356#335C22×C4111yescharacteristic
357#334C22×C4111yescharacteristic
358#334C22×C4111yescharacteristic
359#333C22×C4111yescharacteristic
360#333C22×C4111yescharacteristic
361#333C22×C4111yescharacteristic
362#333C22×C4111yescharacteristic
363#332C22×C4111yescharacteristic
364#332C22×C4111yescharacteristic
365#331C22×C4111yescharacteristic
366#331C22×C4111yescharacteristic
367C41#1936911yescharacteristic, direct product factor, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×D8—21no—
373C2×D8—21no—
374#131—44no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16D4×C4111yescharacteristic
379C2×M16D4×C4111yescharacteristic
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8D4×C4111yescharacteristic
384C4⋊Q8C23×C4111yescharacteristic
385C4⋊Q8C23×C4111yescharacteristic
386C4⋊Q8C23×C4111yescharacteristic
387#127D4×C4111yescharacteristic
388#127C23×C4111yescharacteristic
389#125—21no—
390#124—21no—
391#124—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121D4×C4111yescharacteristic
398#121D4×C4111yescharacteristic
399C4×Q8—21no—
400C4×Q8—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C4111yescharacteristic
405C4×D4C23×C4111yescharacteristic
406#117—21no—
407C2×C42C23×C4111yescharacteristic
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C4111yescharacteristic
419C4⋊C8C23×C4111yescharacteristic
420C4⋊C8C23×C4111yescharacteristic
421C4⋊C8C23×C4111yescharacteristic
422C4⋊C8C23×C4111yescharacteristic
423C4⋊C8C23×C4111yescharacteristic
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442#97D4×C4111yescharacteristic
443#97D4×C4111yescharacteristic
444C4×C8C23×C4111yescharacteristic
445C4×C8C23×C4111yescharacteristic
446#41—42no—
447#41—42no—
448#41—82no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C4111yescharacteristic
462C2×D4C2×D4×C4111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C4111yescharacteristic
467C22×C4C2×D4×C4111yescharacteristic
468C22×C4#41×C4111yescharacteristic
469SD16—42no—
470SD16—42no—
471D8—81no—
472D8—81no—
473M16—22no—
474M16—41no—
475M16—42no—
476M16—42no—
477M16—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8C2×D4×C4111yescharacteristic
488C2×C8C2×D4×C4111yescharacteristic
489C2×C8C2×D4×C4111yescharacteristic
490C2×C8C2×D4×C4111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C4111yescharacteristic
501C4⋊C4C2×D4×C4111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—41no—
510C42C2×D4×C4111yescharacteristic
511C42C2×D4×C4111yescharacteristic
512C42#41×C4111yescharacteristic
513C42C24×C4111yescharacteristic
514C23—21no—
515C23—21no—
516C23—41no—
517C23#121×C4111yescharacteristic
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#121×C4111yescharacteristic
553C2×C4#121×C4111yescharacteristic
554C2×C4#121×C4111yescharacteristic
555C2×C4C22×D4×C4111yescharacteristic
556C2×C4C22×D4×C4111yescharacteristic
557C2×C4C2×#41×C4111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8AGL(1,ℤ/8)×C4112yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C4111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
591C4C41×#57511yescharacteristic
592C4C41×#57711yescharacteristic
593C4C41×#57811yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C41×#303611yescharacteristic
599C2C41×#306311yescharacteristic
600C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3253C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3235C2semidirect
3. C41×#3182C2semidirect
4. C41×#2935C2semidirect
5. C41×#1703C2semidirect
6. C41×#1697C2semidirect
7. C41×#1695C2semidirect
8. C41×#1685C2semidirect
9. C41×#1683C2semidirect
10. C41×#1677C2semidirect
11. C41×#1675C2semidirect
12. C41×#1665C2semidirect
13. C41×#1569C2semidirect
14. C41×#1551C2semidirect
15. C41×#1550C2semidirect
267. #19369C41direct (N × H)
295. #3235C2×C41semidirect
296. #3182C2×C41semidirect
297. #2935C2×C41semidirect
298. #1703C2×C41semidirect
299. #1697C2×C41semidirect
300. #1695C2×C41semidirect
301. #1685C2×C41semidirect
302. #1683C2×C41semidirect
303. #1677C2×C41semidirect
304. #1675C2×C41semidirect
305. #1665C2×C41semidirect
306. #1569C2×C41semidirect
307. #1551C2×C41semidirect
308. #1550C2×C41semidirect
367. C41#19369direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32532
C41×#32352
C41×#31822
C41×#29352
C41×#17032
C41×#16972
C41×#16952
C41×#16852
C41×#16832
C41×#16772
C41×#16752
C41×#16652
C41×#15692
C41×#15512
C41×#15502
#1936941