Finite Group Databasebeta

← C41×#19036 #23795237

Subgroups — C41×#19036 #23795237

Order 10496.

880 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3559C211yesmaximal, characteristic
2C41×#3216C211yesmaximal, characteristic, complemented
3C41×#3172C211yesmaximal, characteristic, complemented
4C41×#3166C211yesmaximal, characteristic, complemented
5C41×#1664C212yesmaximal, complemented
6C41×#1661C212yesmaximal, complemented
7C41×#1661C212yesmaximal, complemented
8C41×#1660C212yesmaximal, complemented
9C41×#1529C211yesmaximal, characteristic, complemented
10C41×#1528C211yesmaximal, characteristic, complemented
11C41×#1525C211yesmaximal, characteristic, complemented
12C41×#563C2212yes—
13C41×#562C2212yes—
14C41×#554—21no—
15C41×#553—21no—
16C41×#553—21no—
17C41×#547—22no—
18C41×#547—21no—
19C41×#544—21no—
20C41×#540—21no—
21C41×#539—22no—
22C41×#539—21no—
23C41×#537—21no—
24C41×#533C2211yescharacteristic
25C41×#532C2211yescharacteristic
26C41×#529C2211yescharacteristic
27C2×#125×C41C2211yescharacteristic
28C41×#501C2212yes—
29C41×#501C2212yes—
30C41×#501C2211yescharacteristic
31C41×#499—22no—
32C41×#497C2211yescharacteristic
33C41×#497C2212yes—
34C41×#491C2211yescharacteristic
35C41×#489C2211yescharacteristic
36C41×#489C2212yes—
37C41×#470—21no—
38C41×#468—21no—
39C41×#462—21no—
40C41×#460—21no—
41C41×#452—22no—
42C4×Q16×C41—21no—
43C4×SD16×C41—21no—
44C41×#432C2211yescharacteristic
45C41×#428—21no—
46C41×#428—21no—
47C4×M16×C41C2211yescharacteristic
48C4×M16×C41C2211yescharacteristic
49C41×#330C2212yes—
50C41×#330C2212yes—
51C41×#330C2212yes—
52C41×#329C2212yes—
53C41×#329C2212yes—
54C41×#329C2212yes—
55C2×#41×C41—22no—
56C2×#41×C41D412yes—
57C2×Q16×C41—21no—
58C2×Q16×C41—22no—
59C2×SD16×C41—21no—
60C2×SD16×C41—22no—
61C2×M16×C41—21no—
62C2×M16×C41—21no—
63C4⋊Q8×C41—21no—
64C4⋊Q8×C41—22no—
65C4⋊Q8×C41D411yescharacteristic
66C4⋊Q8×C41C2311yescharacteristic
67C4⋊Q8×C41C2311yescharacteristic
68#127×C41D411yescharacteristic
69#126×C41—22no—
70#126×C41—22no—
71#126×C41—21no—
72#125×C41—22no—
73#125×C41—21no—
74#125×C41—21no—
75#125×C41—21no—
76#125×C41—21no—
77#125×C41D412yes—
78#125×C41C2312yes—
79#125×C41C2311yescharacteristic
80#124×C41C2311yescharacteristic
81#124×C41C2312yes—
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—22no—
86#123×C41—21no—
87#123×C41—22no—
88#123×C41—22no—
89C22⋊Q8×C41—22no—
90C22⋊Q8×C41—22no—
91C22⋊Q8×C41—22no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41D411yescharacteristic
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—21no—
101#121×C41—21no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—21no—
105#121×C41—21no—
106#121×C41D411yescharacteristic
107C4×Q8×C41—21no—
108C4×Q8×C41—21no—
109C4×Q8×C41D411yescharacteristic
110C4×D4×C41—22no—
111C4×D4×C41—22no—
112C4×D4×C41—21no—
113C4×D4×C41—21no—
114C4×D4×C41—21no—
115C4×D4×C41—21no—
116C4×D4×C41—21no—
117C4×D4×C41D411yescharacteristic
118#117×C41—21no—
119#117×C41—21no—
120#117×C41—21no—
121C2×C4⋊C4×C41—22no—
122C2×C4⋊C4×C41—21no—
123C2×C4⋊C4×C41—21no—
124C2×C4⋊C4×C41—21no—
125C2×C4⋊C4×C41D411yescharacteristic
126C2×C4⋊C4×C41D411yescharacteristic
127C2×C42×C41C2311yescharacteristic
128#107×C41—22no—
129#107×C41—22no—
130#107×C41—21no—
131#106×C41—22no—
132#106×C41—22no—
133#106×C41—21no—
134C4⋊C8×C41—21no—
135#103×C41—21no—
136#103×C41—22no—
137#103×C41—21no—
138#103×C41—21no—
139#102×C41—21no—
140#102×C41—22no—
141C22⋊C8×C41—21no—
142#97×C41C2312yes—
143#97×C41C2311yescharacteristic
144#97×C41C2311yescharacteristic
145#97×C41C2312yes—
146C4×C8×C41—21no—
147C4×C8×C41—21no—
148#41×C41—84no—
149#41×C41—82no—
150C2×Q8×C41—22no—
151C2×Q8×C41—21no—
152C2×Q8×C41—21no—
153C2×Q8×C41C2×D411yescharacteristic
154C2×Q8×C41C2×D412yes—
155C2×D4×C41—22no—
156C2×D4×C41—21no—
157C2×D4×C41—22no—
158C2×D4×C41—22no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41C2×D411yescharacteristic
162C2×D4×C41C2×D412yes—
163C22×C4×C41—21no—
164C22×C4×C41—22no—
165C22×C4×C41—22no—
166C22×C4×C41—22no—
167C22×C4×C41—21no—
168C22×C4×C41—21no—
169C22×C4×C41—22no—
170C22×C4×C41C2×D411yescharacteristic
171C22×C4×C41C2×D411yescharacteristic
172C22×C4×C41C2×D411yescharacteristic
173Q16×C41—42no—
174Q16×C41—82no—
175SD16×C41—42no—
176SD16×C41—82no—
177M16×C41—24no—
178M16×C41—42no—
179C2×C8×C41—22no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—22no—
183C4⋊C4×C41—22no—
184C4⋊C4×C41—22no—
185C4⋊C4×C41—22no—
186C4⋊C4×C41—22no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—22no—
196C4⋊C4×C41—22no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—21no—
203C4⋊C4×C41—41no—
204C4⋊C4×C41—41no—
205C4⋊C4×C41C2×D411yescharacteristic
206C4⋊C4×C41C2×D411yescharacteristic
207C4⋊C4×C41C2×D412yes—
208C4⋊C4×C41C2×D412yes—
209C22⋊C4×C41—22no—
210C22⋊C4×C41—22no—
211C22⋊C4×C41—22no—
212C22⋊C4×C41—22no—
213C22⋊C4×C41—22no—
214C22⋊C4×C41—21no—
215C22⋊C4×C41—21no—
216C22⋊C4×C41—21no—
217C22⋊C4×C41—21no—
218C22⋊C4×C41—22no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—21no—
221C22⋊C4×C41—41no—
222C42×C41—22no—
223C42×C41—21no—
224C42×C41—41no—
225C42×C41C2×D411yescharacteristic
226C42×C41C2×D411yescharacteristic
227C42×C41C2×D411yescharacteristic
228C42×C41C2411yescharacteristic
229C23×C41—21no—
230C23×C41—22no—
231C23×C41#12011yescharacteristic
232Q8×C41—41no—
233Q8×C41—42no—
234Q8×C41—41no—
235Q8×C41—41no—
236Q8×C41—41no—
237Q8×C41—41no—
238Q8×C41—82no—
239D4×C41—41no—
240D4×C41—42no—
241D4×C41—44no—
242D4×C41—42no—
243D4×C41—42no—
244D4×C41—81no—
245D4×C41—82no—
246D4×C41—82no—
247C2×C4×C41—22no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—22no—
251C2×C4×C41—22no—
252C2×C4×C41—21no—
253C2×C4×C41—22no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—42no—
257C2×C4×C41—42no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—82no—
261C2×C4×C41—81no—
262C2×C4×C41—82no—
263C2×C4×C41—82no—
264C2×C4×C41—82no—
265C2×C4×C41#12011yescharacteristic
266C2×C4×C41#12011yescharacteristic
267C2×C4×C41#12011yescharacteristic
268C2×C4×C41C22×D411yescharacteristic
269C2×C4×C41C22×D411yescharacteristic
270C2×C4×C41C22×D411yescharacteristic
271C8×C41—24no—
272C8×C41—22no—
273C8×C41—41no—
274C8×C41—42no—
275#19036C4111yesmaximal, characteristic, direct product factor, Sylow
276C22×C41—21no—
277C22×C41—21no—
278C22×C41—21no—
279C22×C41—41no—
280C22×C41—42no—
281C22×C41—42no—
282C22×C41—41no—
283C22×C41—42no—
284C22×C41—41no—
285C22×C41C2×#12011yescharacteristic
286C4×C41—21no—
287C4×C41—21no—
288C4×C41—21no—
289C4×C41—21no—
290C4×C41—21no—
291C4×C41—41no—
292C4×C41—42no—
293C4×C41—41no—
294C4×C41—42no—
295C4×C41—42no—
296C4×C41—41no—
297C4×C41—81no—
298C4×C41—81no—
299C4×C41#45612yes—
300#3559C2×C4111yescharacteristic
301#3216C2×C4111yescharacteristic, complemented
302#3172C2×C4111yescharacteristic, complemented
303#3166C2×C4111yescharacteristic, complemented
304#1664C2×C4112yescomplemented
305#1661C2×C4112yescomplemented
306#1661C2×C4112yescomplemented
307#1660C2×C4112yescomplemented
308#1529C2×C4111yescharacteristic, complemented
309#1528C2×C4111yescharacteristic, complemented
310#1525C2×C4111yescharacteristic, complemented
311C2×C41—41no—
312C2×C41—81no—
313C2×C41—82no—
314C2×C41C2×#45611yescharacteristic
315C2×C41#301811yescharacteristic
316C2×C41#301911yescharacteristic
317#563C22×C4112yes—
318#562C22×C4112yes—
319#554—21no—
320#553—21no—
321#553—21no—
322#547—22no—
323#547—21no—
324#544—21no—
325#540—21no—
326#539—22no—
327#539—21no—
328#537—21no—
329#533C22×C4111yescharacteristic
330#532C22×C4111yescharacteristic
331#529C22×C4111yescharacteristic
332C2×#125C22×C4111yescharacteristic
333#501C22×C4112yes—
334#501C22×C4112yes—
335#501C22×C4111yescharacteristic
336#499—22no—
337#497C22×C4111yescharacteristic
338#497C22×C4112yes—
339#491C22×C4111yescharacteristic
340#489C22×C4111yescharacteristic
341#489C22×C4112yes—
342#470—21no—
343#468—21no—
344#462—21no—
345#460—21no—
346#452—22no—
347C4×Q16—21no—
348C4×SD16—21no—
349#432C22×C4111yescharacteristic
350#428—21no—
351#428—21no—
352C4×M16C22×C4111yescharacteristic
353C4×M16C22×C4111yescharacteristic
354#330C22×C4112yes—
355#330C22×C4112yes—
356#330C22×C4112yes—
357#329C22×C4112yes—
358#329C22×C4112yes—
359#329C22×C4112yes—
360C41#1903611yescharacteristic, direct product factor, Sylow
361C2×#41—22no—
362C2×#41D4×C4112yes—
363C2×Q16—21no—
364C2×Q16—22no—
365C2×SD16—21no—
366C2×SD16—22no—
367C2×M16—21no—
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—22no—
371C4⋊Q8D4×C4111yescharacteristic
372C4⋊Q8C23×C4111yescharacteristic
373C4⋊Q8C23×C4111yescharacteristic
374#127D4×C4111yescharacteristic
375#126—22no—
376#126—22no—
377#126—21no—
378#125—22no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C4112yes—
384#125C23×C4112yes—
385#125C23×C4111yescharacteristic
386#124C23×C4111yescharacteristic
387#124C23×C4112yes—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—21no—
393#123—22no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8D4×C4111yescharacteristic
404#121—22no—
405#121—22no—
406#121—21no—
407#121—21no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121—21no—
412#121D4×C4111yescharacteristic
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8D4×C4111yescharacteristic
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4D4×C4111yescharacteristic
424#117—21no—
425#117—21no—
426#117—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C4111yescharacteristic
432C2×C4⋊C4D4×C4111yescharacteristic
433C2×C42C23×C4111yescharacteristic
434#107—22no—
435#107—22no—
436#107—21no—
437#106—22no—
438#106—22no—
439#106—21no—
440C4⋊C8—21no—
441#103—21no—
442#103—22no—
443#103—21no—
444#103—21no—
445#102—21no—
446#102—22no—
447C22⋊C8—21no—
448#97C23×C4112yes—
449#97C23×C4111yescharacteristic
450#97C23×C4111yescharacteristic
451#97C23×C4112yes—
452C4×C8—21no—
453C4×C8—21no—
454#41—84no—
455#41—82no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8C2×D4×C4111yescharacteristic
460C2×Q8C2×D4×C4112yes—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×D4×C4111yescharacteristic
468C2×D4C2×D4×C4112yes—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4C2×D4×C4111yescharacteristic
477C22×C4C2×D4×C4111yescharacteristic
478C22×C4C2×D4×C4111yescharacteristic
479Q16—42no—
480Q16—82no—
481SD16—42no—
482SD16—82no—
483M16—24no—
484M16—42no—
485C2×C8—22no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C4111yescharacteristic
512C4⋊C4C2×D4×C4111yescharacteristic
513C4⋊C4C2×D4×C4112yes—
514C4⋊C4C2×D4×C4112yes—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—41no—
528C42—22no—
529C42—21no—
530C42—41no—
531C42C2×D4×C4111yescharacteristic
532C42C2×D4×C4111yescharacteristic
533C42C2×D4×C4111yescharacteristic
534C42C24×C4111yescharacteristic
535C23—21no—
536C23—22no—
537C23#120×C4111yescharacteristic
538Q8—41no—
539Q8—42no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—82no—
545D4—41no—
546D4—42no—
547D4—44no—
548D4—42no—
549D4—42no—
550D4—81no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4—81no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4#120×C4111yescharacteristic
572C2×C4#120×C4111yescharacteristic
573C2×C4#120×C4111yescharacteristic
574C2×C4C22×D4×C4111yescharacteristic
575C2×C4C22×D4×C4111yescharacteristic
576C2×C4C22×D4×C4111yescharacteristic
577C8—24no—
578C8—22no—
579C8—41no—
580C8—42no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22C2×#120×C4111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4C41×#45612yes—
605C2—41no—
606C2—81no—
607C2—82no—
608C2C2×C41×#45611yescharacteristic
609C2C41×#301811yescharacteristic
610C2C41×#301911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3559C2
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×#3216C2semidirect
3. C41×#3172C2semidirect
4. C41×#3166C2semidirect
5. C41×#1664C2semidirect
6. C41×#1661C2semidirect
7. C41×#1661C2semidirect
8. C41×#1660C2semidirect
9. C41×#1529C2semidirect
10. C41×#1528C2semidirect
11. C41×#1525C2semidirect
275. #19036C41direct (N × H)
301. #3216C2×C41semidirect
302. #3172C2×C41semidirect
303. #3166C2×C41semidirect
304. #1664C2×C41semidirect
305. #1661C2×C41semidirect
306. #1661C2×C41semidirect
307. #1660C2×C41semidirect
308. #1529C2×C41semidirect
309. #1528C2×C41semidirect
310. #1525C2×C41semidirect
360. C41#19036direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35592
C41×#32162
C41×#31722
C41×#31662
C41×#16642
C41×#16612
C41×#16602
C41×#15292
C41×#15282
C41×#15252
#1903641