Finite Group Databasebeta

← C41×#19183 #23795384

Subgroups — C41×#19183 #23795384

Order 10496.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3182C211yesmaximal, characteristic, complemented
2C41×#3106C211yesmaximal, characteristic
3C41×#3076C211yesmaximal, characteristic, complemented
4C41×#2971C211yesmaximal, characteristic, complemented
5C41×#1703C211yesmaximal, characteristic, complemented
6C41×#1697C211yesmaximal, characteristic, complemented
7C41×#1695C211yesmaximal, characteristic, complemented
8C41×#1685C211yesmaximal, characteristic, complemented
9C41×#1684C211yesmaximal, characteristic, complemented
10C41×#1678C211yesmaximal, characteristic, complemented
11C41×#1676C211yesmaximal, characteristic, complemented
12C41×#1666C211yesmaximal, characteristic, complemented
13C41×#1565C211yesmaximal, characteristic, complemented
14C41×#1554C211yesmaximal, characteristic, complemented
15C41×#1551C211yesmaximal, characteristic, complemented
16C41×#533C2211yescharacteristic
17C41×#532C2211yescharacteristic
18C4×#41×C41C2211yescharacteristic
19C41×#500C2211yescharacteristic
20C41×#492C2211yescharacteristic
21C41×#487C2211yescharacteristic
22C41×#486C2211yescharacteristic
23C41×#482—21no—
24C41×#479—21no—
25C41×#478—21no—
26C41×#477C2211yescharacteristic
27C41×#477C2211yescharacteristic
28C41×#476C2211yescharacteristic
29C41×#476C2211yescharacteristic
30C41×#475C2211yescharacteristic
31C41×#474C2211yescharacteristic
32C41×#468—21no—
33C41×#468—21no—
34C41×#460C2211yescharacteristic
35C41×#459C2211yescharacteristic
36C41×#449—21no—
37C8×Q8×C41C2211yescharacteristic
38C8×Q8×C41C2211yescharacteristic
39C41×#440—21no—
40C41×#440—21no—
41C4×SD16×C41—21no—
42C4×D8×C41—21no—
43C41×#436—21no—
44C41×#436—21no—
45C41×#436C2211yescharacteristic
46C41×#436C2211yescharacteristic
47C41×#432—21no—
48C41×#432C2211yescharacteristic
49C41×#431C2211yescharacteristic
50C41×#427—21no—
51C2×C4⋊C8×C41C2211yescharacteristic
52C41×#416—21no—
53C4×M16×C41—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×C41D411yescharacteristic
69C2×SD16×C41—21no—
70C2×SD16×C41—21no—
71C2×SD16×C41—21no—
72C2×D8×C41—21no—
73C2×M16×C41—21no—
74C2×M16×C41—21no—
75C2×M16×C41D411yescharacteristic
76C2×M16×C41D411yescharacteristic
77C22×C8×C41—21no—
78C4⋊Q8×C41C2311yescharacteristic
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81#127×C41C2311yescharacteristic
82#125×C41—21no—
83#124×C41—21no—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—21no—
86#121×C41—21no—
87#121×C41—21no—
88C4×Q8×C41—21no—
89C4×Q8×C41—21no—
90C4×Q8×C41D411yescharacteristic
91C4×Q8×C41C2311yescharacteristic
92C4×D4×C41—21no—
93C4×D4×C41—21no—
94C4×D4×C41—21no—
95C4×D4×C41—21no—
96C4×D4×C41D411yescharacteristic
97C4×D4×C41C2311yescharacteristic
98#117×C41—21no—
99#117×C41—21no—
100#117×C41D411yescharacteristic
101C2×C42×C41—21no—
102C2×C42×C41C2311yescharacteristic
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#107×C41—21no—
107#107×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41—21no—
111C4⋊C8×C41—21no—
112C4⋊C8×C41—21no—
113C4⋊C8×C41—21no—
114C4⋊C8×C41C2311yescharacteristic
115C4⋊C8×C41C2311yescharacteristic
116C4⋊C8×C41C2311yescharacteristic
117C4⋊C8×C41C2311yescharacteristic
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120#103×C41—21no—
121#103×C41—21no—
122#103×C41—21no—
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—
132C22⋊C8×C41—21no—
133C22⋊C8×C41—21no—
134C22⋊C8×C41—21no—
135C22⋊C8×C41—21no—
136#97×C41—21no—
137#97×C41D411yescharacteristic
138#97×C41D411yescharacteristic
139C4×C8×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41—21no—
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144#41×C41—22no—
145#41×C41—41no—
146#41×C41—82no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41C2×D411yescharacteristic
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—41no—
156C2×D4×C41C2×D411yescharacteristic
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—41no—
161C22×C4×C41C2×D411yescharacteristic
162C22×C4×C41C2×D411yescharacteristic
163C22×C4×C41#4111yescharacteristic
164SD16×C41—42no—
165SD16×C41—42no—
166SD16×C41—42no—
167D8×C41—42no—
168M16×C41—22no—
169M16×C41—41no—
170M16×C41—42no—
171M16×C41—42no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—42no—
179C2×C8×C41C2×D411yescharacteristic
180C2×C8×C41C2×D411yescharacteristic
181C2×C8×C41C2×D411yescharacteristic
182C2×C8×C41C2×D411yescharacteristic
183C4⋊C4×C41—21no—
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C22⋊C4×C41—21no—
196C22⋊C4×C41—21no—
197C22⋊C4×C41—21no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C42×C41—21no—
202C42×C41—21no—
203C42×C41—21no—
204C42×C41—41no—
205C42×C41C2×D411yescharacteristic
206C42×C41C2×D411yescharacteristic
207C42×C41#4111yescharacteristic
208C42×C41C2411yescharacteristic
209C23×C41—21no—
210C23×C41—41no—
211C23×C41#12111yescharacteristic
212Q8×C41—21no—
213Q8×C41—41no—
214Q8×C41—41no—
215Q8×C41—81no—
216Q8×C41—81no—
217Q8×C41#13712yes—
218D4×C41—21no—
219D4×C41—21no—
220D4×C41—42no—
221D4×C41—41no—
222D4×C41—41no—
223D4×C41—41no—
224D4×C41—41no—
225D4×C41—81no—
226D4×C41—82no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—41no—
235C2×C4×C41—42no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—81no—
242C2×C4×C41—82no—
243C2×C4×C41#12111yescharacteristic
244C2×C4×C41#12111yescharacteristic
245C2×C4×C41#12111yescharacteristic
246C2×C4×C41C22×D411yescharacteristic
247C2×C4×C41C22×D411yescharacteristic
248C2×C4×C41C2×#4111yescharacteristic
249C8×C41—21no—
250C8×C41—21no—
251C8×C41—21no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257C8×C41—41no—
258C8×C41#13512yes—
259#19183C4111yesmaximal, characteristic, direct product factor, Sylow
260C22×C41—21no—
261C22×C41—21no—
262C22×C41—21no—
263C22×C41—41no—
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—81no—
267C22×C41—81no—
268C22×C41—81no—
269C22×C41C2×#12111yescharacteristic
270C4×C41—21no—
271C4×C41—21no—
272C4×C41—22no—
273C4×C41—21no—
274C4×C41—21no—
275C4×C41—41no—
276C4×C41—41no—
277C4×C41—81no—
278C4×C41—81no—
279C4×C41—81no—
280C4×C41C2×#13511yescharacteristic
281C4×C41C2×#13711yescharacteristic
282C4×C41#57511yescharacteristic
283C4×C41#57511yescharacteristic
284#3182C2×C4111yescharacteristic, complemented
285#3106C2×C4111yescharacteristic
286#3076C2×C4111yescharacteristic, complemented
287#2971C2×C4111yescharacteristic, complemented
288#1703C2×C4111yescharacteristic, complemented
289#1697C2×C4111yescharacteristic, complemented
290#1695C2×C4111yescharacteristic, complemented
291#1685C2×C4111yescharacteristic, complemented
292#1684C2×C4111yescharacteristic, complemented
293#1678C2×C4111yescharacteristic, complemented
294#1676C2×C4111yescharacteristic, complemented
295#1666C2×C4111yescharacteristic, complemented
296#1565C2×C4111yescharacteristic, complemented
297#1554C2×C4111yescharacteristic, complemented
298#1551C2×C4111yescharacteristic, complemented
299C2×C41—41no—
300C2×C41—81no—
301C2×C41—161no—
302C2×C41#303511yescharacteristic
303C2×C41#305611yescharacteristic
304C2×C41#306811yescharacteristic
305#533C22×C4111yescharacteristic
306#532C22×C4111yescharacteristic
307C4×#41C22×C4111yescharacteristic
308#500C22×C4111yescharacteristic
309#492C22×C4111yescharacteristic
310#487C22×C4111yescharacteristic
311#486C22×C4111yescharacteristic
312#482—21no—
313#479—21no—
314#478—21no—
315#477C22×C4111yescharacteristic
316#477C22×C4111yescharacteristic
317#476C22×C4111yescharacteristic
318#476C22×C4111yescharacteristic
319#475C22×C4111yescharacteristic
320#474C22×C4111yescharacteristic
321#468—21no—
322#468—21no—
323#460C22×C4111yescharacteristic
324#459C22×C4111yescharacteristic
325#449—21no—
326C8×Q8C22×C4111yescharacteristic
327C8×Q8C22×C4111yescharacteristic
328#440—21no—
329#440—21no—
330C4×SD16—21no—
331C4×D8—21no—
332#436—21no—
333#436—21no—
334#436C22×C4111yescharacteristic
335#436C22×C4111yescharacteristic
336#432—21no—
337#432C22×C4111yescharacteristic
338#431C22×C4111yescharacteristic
339#427—21no—
340C2×C4⋊C8C22×C4111yescharacteristic
341#416—21no—
342C4×M16—21no—
343C4×M16C22×C4111yescharacteristic
344#335C22×C4111yescharacteristic
345#335C22×C4111yescharacteristic
346#334C22×C4111yescharacteristic
347#334C22×C4111yescharacteristic
348#333C22×C4111yescharacteristic
349#333C22×C4111yescharacteristic
350#333C22×C4111yescharacteristic
351#333C22×C4111yescharacteristic
352#332C22×C4111yescharacteristic
353#332C22×C4111yescharacteristic
354#331C22×C4111yescharacteristic
355#331C22×C4111yescharacteristic
356C41#1918311yescharacteristic, direct product factor, Sylow
357C2×#41—21no—
358C2×#41D4×C4111yescharacteristic
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16D4×C4111yescharacteristic
366C2×M16D4×C4111yescharacteristic
367C22×C8—21no—
368C4⋊Q8C23×C4111yescharacteristic
369C4⋊Q8C23×C4111yescharacteristic
370C4⋊Q8C23×C4111yescharacteristic
371#127C23×C4111yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C4111yescharacteristic
381C4×Q8C23×C4111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C4111yescharacteristic
387C4×D4C23×C4111yescharacteristic
388#117—21no—
389#117—21no—
390#117D4×C4111yescharacteristic
391C2×C42—21no—
392C2×C42C23×C4111yescharacteristic
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C4111yescharacteristic
405C4⋊C8C23×C4111yescharacteristic
406C4⋊C8C23×C4111yescharacteristic
407C4⋊C8C23×C4111yescharacteristic
408C4⋊C8C23×C4111yescharacteristic
409C4⋊C8C23×C4111yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97D4×C4111yescharacteristic
428#97D4×C4111yescharacteristic
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C4111yescharacteristic
433C4×C8C23×C4111yescharacteristic
434#41—22no—
435#41—41no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D4×C4111yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×D4×C4111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C4111yescharacteristic
452C22×C4C2×D4×C4111yescharacteristic
453C22×C4#41×C4111yescharacteristic
454SD16—42no—
455SD16—42no—
456SD16—42no—
457D8—42no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—42no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8C2×D4×C4111yescharacteristic
470C2×C8C2×D4×C4111yescharacteristic
471C2×C8C2×D4×C4111yescharacteristic
472C2×C8C2×D4×C4111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×D4×C4111yescharacteristic
484C4⋊C4C2×D4×C4111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42C2×D4×C4111yescharacteristic
496C42C2×D4×C4111yescharacteristic
497C42#41×C4111yescharacteristic
498C42C24×C4111yescharacteristic
499C23—21no—
500C23—41no—
501C23#121×C4111yescharacteristic
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—81no—
507Q8#137×C4112yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4#121×C4111yescharacteristic
534C2×C4#121×C4111yescharacteristic
535C2×C4#121×C4111yescharacteristic
536C2×C4C22×D4×C4111yescharacteristic
537C2×C4C22×D4×C4111yescharacteristic
538C2×C4C2×#41×C4111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8#135×C4112yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×#121×C4111yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×#135×C4111yescharacteristic
570C4C2×#137×C4111yescharacteristic
571C4C41×#57511yescharacteristic
572C4C41×#57511yescharacteristic
573C2—41no—
574C2—81no—
575C2—161no—
576C2C41×#303511yescharacteristic
577C2C41×#305611yescharacteristic
578C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3106C2
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×#3182C2semidirect
3. C41×#3076C2semidirect
4. C41×#2971C2semidirect
5. C41×#1703C2semidirect
6. C41×#1697C2semidirect
7. C41×#1695C2semidirect
8. C41×#1685C2semidirect
9. C41×#1684C2semidirect
10. C41×#1678C2semidirect
11. C41×#1676C2semidirect
12. C41×#1666C2semidirect
13. C41×#1565C2semidirect
14. C41×#1554C2semidirect
15. C41×#1551C2semidirect
259. #19183C41direct (N × H)
284. #3182C2×C41semidirect
286. #3076C2×C41semidirect
287. #2971C2×C41semidirect
288. #1703C2×C41semidirect
289. #1697C2×C41semidirect
290. #1695C2×C41semidirect
291. #1685C2×C41semidirect
292. #1684C2×C41semidirect
293. #1678C2×C41semidirect
294. #1676C2×C41semidirect
295. #1666C2×C41semidirect
296. #1565C2×C41semidirect
297. #1554C2×C41semidirect
298. #1551C2×C41semidirect
356. C41#19183direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31822
C41×#31062
C41×#30762
C41×#29712
C41×#17032
C41×#16972
C41×#16952
C41×#16852
C41×#16842
C41×#16782
C41×#16762
C41×#16662
C41×#15652
C41×#15542
C41×#15512
#1918341