Finite Group Databasebeta

← C41×#19092 #23795293

Subgroups — C41×#19092 #23795293

Order 10496.

816 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3563C211yesmaximal, characteristic, complemented
2C41×#3235C211yesmaximal, characteristic, complemented
3C41×#3234C211yesmaximal, characteristic, complemented
4C41×#3219C211yesmaximal, characteristic
5C41×#1663C212yesmaximal, complemented
6C41×#1660C212yesmaximal, complemented
7C41×#1658C212yesmaximal, complemented
8C41×#1657C212yesmaximal, complemented
9C41×#1537C211yesmaximal, characteristic, complemented
10C41×#1535C211yesmaximal, characteristic, complemented
11C41×#1534C211yesmaximal, characteristic, complemented
12C41×#564C2212yes—
13C41×#563C2212yes—
14C41×#557—21no—
15C41×#554—21no—
16C41×#552—21no—
17C41×#552—22no—
18C41×#552—21no—
19C41×#544—21no—
20C41×#544—21no—
21C41×#541—21no—
22C41×#541—22no—
23C41×#539—21no—
24C41×#533C2211yescharacteristic
25C41×#532C2211yescharacteristic
26C41×#529C2211yescharacteristic
27C2×#125×C41C2211yescharacteristic
28C41×#501C2212yes—
29C41×#501C2212yes—
30C41×#497C2211yescharacteristic
31C41×#496C2211yescharacteristic
32C41×#491C2211yescharacteristic
33C41×#490C2212yes—
34C41×#490C2212yes—
35C41×#490C2211yescharacteristic
36C41×#482—22no—
37C41×#481—21no—
38C41×#480—21no—
39C41×#478—22no—
40C41×#476—21no—
41C41×#474—21no—
42C41×#464—21no—
43C41×#463—21no—
44C41×#452—21no—
45C41×#449—21no—
46C41×#432C2211yescharacteristic
47C41×#432C2211yescharacteristic
48C41×#432C2211yescharacteristic
49C41×#330C2212yes—
50C41×#330C2212yes—
51C41×#330C2212yes—
52C41×#330C2212yes—
53C41×#330C2212yes—
54C41×#329C2212yes—
55C2×#41×C41—21no—
56C2×Q16×C41—21no—
57C2×SD16×C41—21no—
58C2×SD16×C41—21no—
59C2×D8×C41—21no—
60C4⋊Q8×C41—22no—
61C4⋊Q8×C41—21no—
62C4⋊Q8×C41—22no—
63C4⋊Q8×C41D411yescharacteristic
64C4⋊Q8×C41D411yescharacteristic
65C4⋊Q8×C41C2311yescharacteristic
66#127×C41C2311yescharacteristic
67#126×C41—22no—
68#126×C41—22no—
69#126×C41—22no—
70#126×C41—22no—
71#126×C41—21no—
72#125×C41—22no—
73#125×C41—22no—
74#125×C41—21no—
75#125×C41—22no—
76#125×C41—22no—
77#125×C41—22no—
78#125×C41—22no—
79#125×C41—22no—
80#125×C41—22no—
81#125×C41—21no—
82#125×C41—21no—
83#125×C41D412yes—
84#125×C41C2312yes—
85#125×C41C2312yes—
86#125×C41C2311yescharacteristic
87#124×C41—21no—
88#124×C41C2311yescharacteristic
89#123×C41—22no—
90#123×C41—22no—
91#123×C41—21no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—22no—
99C22⋊Q8×C41—22no—
100C22⋊Q8×C41D411yescharacteristic
101#121×C41—21no—
102#121×C41—21no—
103#121×C41D411yescharacteristic
104C4×Q8×C41—21no—
105C4×Q8×C41—22no—
106C4×Q8×C41—21no—
107C4×Q8×C41—21no—
108C4×Q8×C41—21no—
109C4×Q8×C41D411yescharacteristic
110C4×D4×C41—22no—
111C4×D4×C41—21no—
112C4×D4×C41—21no—
113C4×D4×C41—21no—
114C4×D4×C41D411yescharacteristic
115#117×C41—22no—
116#117×C41—21no—
117#117×C41—22no—
118#117×C41—21no—
119#117×C41D412yes—
120C2×C4⋊C4×C41—21no—
121C2×C4⋊C4×C41—21no—
122C2×C4⋊C4×C41—21no—
123C2×C4⋊C4×C41D411yescharacteristic
124C2×C4⋊C4×C41D411yescharacteristic
125C2×C42×C41C2311yescharacteristic
126#107×C41—22no—
127#107×C41—22no—
128#106×C41—22no—
129#106×C41—22no—
130C4⋊C8×C41—21no—
131C4⋊C8×C41—21no—
132C4⋊C8×C41—21no—
133#103×C41—21no—
134#103×C41—21no—
135#102×C41—21no—
136#102×C41—21no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141C22⋊C8×C41—21no—
142C22⋊C8×C41—21no—
143C22⋊C8×C41—21no—
144#97×C41C2312yes—
145#97×C41C2312yes—
146#97×C41C2311yescharacteristic
147#97×C41C2311yescharacteristic
148#41×C41—81no—
149#41×C41—81no—
150C2×Q8×C41—22no—
151C2×Q8×C41—21no—
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
154C2×Q8×C41C2×D411yescharacteristic
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—41no—
160C2×D4×C41C2×D411yescharacteristic
161C22×C4×C41—21no—
162C22×C4×C41—22no—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—41no—
166C22×C4×C41C2×D411yescharacteristic
167C22×C4×C41C2×D411yescharacteristic
168C22×C4×C41C2×D411yescharacteristic
169Q16×C41—81no—
170SD16×C41—81no—
171SD16×C41—81no—
172D8×C41—81no—
173C2×C8×C41—22no—
174C2×C8×C41—22no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C4⋊C4×C41—22no—
178C4⋊C4×C41—22no—
179C4⋊C4×C41—22no—
180C4⋊C4×C41—22no—
181C4⋊C4×C41—22no—
182C4⋊C4×C41—22no—
183C4⋊C4×C41—22no—
184C4⋊C4×C41—22no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—22no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—22no—
194C4⋊C4×C41—22no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—22no—
198C4⋊C4×C41—22no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41C2×D411yescharacteristic
202C4⋊C4×C41C2×D411yescharacteristic
203C4⋊C4×C41C2×D412yes—
204C4⋊C4×C41C2×D412yes—
205C4⋊C4×C41C2×D412yes—
206C4⋊C4×C41C2×D412yes—
207C22⋊C4×C41—22no—
208C22⋊C4×C41—22no—
209C22⋊C4×C41—22no—
210C22⋊C4×C41—21no—
211C22⋊C4×C41—22no—
212C22⋊C4×C41—21no—
213C22⋊C4×C41—21no—
214C22⋊C4×C41—21no—
215C22⋊C4×C41—21no—
216C22⋊C4×C41—41no—
217C22⋊C4×C41—41no—
218C42×C41—22no—
219C42×C41—22no—
220C42×C41—22no—
221C42×C41—22no—
222C42×C41—21no—
223C42×C41C2×D411yescharacteristic
224C42×C41C2×D411yescharacteristic
225C42×C41C2×D411yescharacteristic
226C42×C41C2411yescharacteristic
227C23×C41—21no—
228C23×C41—41no—
229C23×C41#12011yescharacteristic
230Q8×C41—41no—
231Q8×C41—42no—
232Q8×C41—41no—
233Q8×C41—41no—
234Q8×C41—81no—
235Q8×C41—82no—
236D4×C41—41no—
237D4×C41—41no—
238D4×C41—41no—
239D4×C41—42no—
240D4×C41—42no—
241D4×C41—42no—
242D4×C41—82no—
243C2×C4×C41—22no—
244C2×C4×C41—21no—
245C2×C4×C41—21no—
246C2×C4×C41—21no—
247C2×C4×C41—22no—
248C2×C4×C41—22no—
249C2×C4×C41—22no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—42no—
254C2×C4×C41—42no—
255C2×C4×C41—41no—
256C2×C4×C41—82no—
257C2×C4×C41—81no—
258C2×C4×C41—82no—
259C2×C4×C41#12011yescharacteristic
260C2×C4×C41#12011yescharacteristic
261C2×C4×C41#12011yescharacteristic
262C2×C4×C41C22×D411yescharacteristic
263C2×C4×C41C22×D411yescharacteristic
264C2×C4×C41C22×D411yescharacteristic
265C8×C41—42no—
266C8×C41—42no—
267C8×C41—41no—
268C8×C41—41no—
269#19092C4111yesmaximal, characteristic, direct product factor, Sylow
270C22×C41—21no—
271C22×C41—21no—
272C22×C41—21no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—41no—
276C22×C41—81no—
277C22×C41—81no—
278C22×C41—81no—
279C22×C41C2×#12011yescharacteristic
280C4×C41—21no—
281C4×C41—21no—
282C4×C41—21no—
283C4×C41—21no—
284C4×C41—21no—
285C4×C41—21no—
286C4×C41—41no—
287C4×C41—42no—
288C4×C41—41no—
289C4×C41—42no—
290C4×C41—42no—
291C4×C41—42no—
292C4×C41—41no—
293C4×C41—81no—
294#3563C2×C4111yescharacteristic, complemented
295#3235C2×C4111yescharacteristic, complemented
296#3234C2×C4111yescharacteristic, complemented
297#3219C2×C4111yescharacteristic
298#1663C2×C4112yescomplemented
299#1660C2×C4112yescomplemented
300#1658C2×C4112yescomplemented
301#1657C2×C4112yescomplemented
302#1537C2×C4111yescharacteristic, complemented
303#1535C2×C4111yescharacteristic, complemented
304#1534C2×C4111yescharacteristic, complemented
305C2×C41—41no—
306C2×C41—81no—
307C2×C41—161no—
308C2×C41#302011yescharacteristic
309C2×C41#302011yescharacteristic
310C2×C41#302111yescharacteristic
311#564C22×C4112yes—
312#563C22×C4112yes—
313#557—21no—
314#554—21no—
315#552—21no—
316#552—22no—
317#552—21no—
318#544—21no—
319#544—21no—
320#541—21no—
321#541—22no—
322#539—21no—
323#533C22×C4111yescharacteristic
324#532C22×C4111yescharacteristic
325#529C22×C4111yescharacteristic
326C2×#125C22×C4111yescharacteristic
327#501C22×C4112yes—
328#501C22×C4112yes—
329#497C22×C4111yescharacteristic
330#496C22×C4111yescharacteristic
331#491C22×C4111yescharacteristic
332#490C22×C4112yes—
333#490C22×C4112yes—
334#490C22×C4111yescharacteristic
335#482—22no—
336#481—21no—
337#480—21no—
338#478—22no—
339#476—21no—
340#474—21no—
341#464—21no—
342#463—21no—
343#452—21no—
344#449—21no—
345#432C22×C4111yescharacteristic
346#432C22×C4111yescharacteristic
347#432C22×C4111yescharacteristic
348#330C22×C4112yes—
349#330C22×C4112yes—
350#330C22×C4112yes—
351#330C22×C4112yes—
352#330C22×C4112yes—
353#329C22×C4112yes—
354C41#1909211yescharacteristic, direct product factor, Sylow
355C2×#41—21no—
356C2×Q16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—21no—
362C4⋊Q8—22no—
363C4⋊Q8D4×C4111yescharacteristic
364C4⋊Q8D4×C4111yescharacteristic
365C4⋊Q8C23×C4111yescharacteristic
366#127C23×C4111yescharacteristic
367#126—22no—
368#126—22no—
369#126—22no—
370#126—22no—
371#126—21no—
372#125—22no—
373#125—22no—
374#125—21no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—22no—
379#125—22no—
380#125—22no—
381#125—21no—
382#125—21no—
383#125D4×C4112yes—
384#125C23×C4112yes—
385#125C23×C4111yescharacteristic
386#125C23×C4112yes—
387#124—21no—
388#124C23×C4111yescharacteristic
389#123—22no—
390#123—22no—
391#123—21no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8D4×C4111yescharacteristic
401#121—21no—
402#121—21no—
403#121D4×C4111yescharacteristic
404C4×Q8—21no—
405C4×Q8—22no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8D4×C4111yescharacteristic
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4D4×C4111yescharacteristic
415#117—22no—
416#117—21no—
417#117—22no—
418#117—21no—
419#117D4×C4112yes—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C4111yescharacteristic
424C2×C4⋊C4D4×C4111yescharacteristic
425C2×C42C23×C4111yescharacteristic
426#107—22no—
427#107—22no—
428#106—22no—
429#106—22no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433#103—21no—
434#103—21no—
435#102—21no—
436#102—21no—
437#102—22no—
438#102—22no—
439#102—22no—
440#102—22no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97C23×C4112yes—
445#97C23×C4112yes—
446#97C23×C4111yescharacteristic
447#97C23×C4111yescharacteristic
448#41—81no—
449#41—81no—
450C2×Q8—22no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4C2×D4×C4111yescharacteristic
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C4111yescharacteristic
467C22×C4C2×D4×C4111yescharacteristic
468C22×C4C2×D4×C4111yescharacteristic
469Q16—81no—
470SD16—81no—
471SD16—81no—
472D8—81no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—21no—
476C2×C8—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4C2×D4×C4111yescharacteristic
502C4⋊C4C2×D4×C4111yescharacteristic
503C4⋊C4C2×D4×C4112yes—
504C4⋊C4C2×D4×C4112yes—
505C4⋊C4C2×D4×C4112yes—
506C4⋊C4C2×D4×C4112yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42—21no—
523C42C2×D4×C4111yescharacteristic
524C42C2×D4×C4111yescharacteristic
525C42C2×D4×C4111yescharacteristic
526C42C24×C4111yescharacteristic
527C23—21no—
528C23—41no—
529C23#120×C4111yescharacteristic
530Q8—41no—
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—82no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—82no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4#120×C4111yescharacteristic
560C2×C4#120×C4111yescharacteristic
561C2×C4#120×C4111yescharacteristic
562C2×C4C22×D4×C4111yescharacteristic
563C2×C4C22×D4×C4111yescharacteristic
564C2×C4C22×D4×C4111yescharacteristic
565C8—41no—
566C8—41no—
567C8—42no—
568C8—42no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22C2×#120×C4111yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—41no—
592C4—81no—
593C2—41no—
594C2—81no—
595C2—161no—
596C2C41×#302011yescharacteristic
597C2C41×#302011yescharacteristic
598C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3219C2
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
1. C41×#3563C2semidirect
2. C41×#3235C2semidirect
3. C41×#3234C2semidirect
5. C41×#1663C2semidirect
6. C41×#1660C2semidirect
7. C41×#1658C2semidirect
8. C41×#1657C2semidirect
9. C41×#1537C2semidirect
10. C41×#1535C2semidirect
11. C41×#1534C2semidirect
269. #19092C41direct (N × H)
294. #3563C2×C41semidirect
295. #3235C2×C41semidirect
296. #3234C2×C41semidirect
298. #1663C2×C41semidirect
299. #1660C2×C41semidirect
300. #1658C2×C41semidirect
301. #1657C2×C41semidirect
302. #1537C2×C41semidirect
303. #1535C2×C41semidirect
304. #1534C2×C41semidirect
354. C41#19092direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35632
C41×#32352
C41×#32342
C41×#32192
C41×#16632
C41×#16602
C41×#16582
C41×#16572
C41×#15372
C41×#15352
C41×#15342
#1909241