Finite Group Databasebeta

← C41×#18428 #23794629

Subgroups — C41×#18428 #23794629

Order 10496.

1104 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3561C211yesmaximal, characteristic, complemented
2C41×#3217C211yesmaximal, characteristic, complemented
3C41×#3208C211yesmaximal, characteristic, complemented
4C41×#2657C211yesmaximal, characteristic, complemented
5C41×#1600C214yesmaximal, complemented
6C41×#1596C214yesmaximal, complemented
7C41×#1506C211yesmaximal, characteristic, complemented
8C41×#1500C211yesmaximal, characteristic, complemented
9C41×#1469C211yesmaximal, characteristic, complemented
10C41×#563—21no—
11C41×#562—21no—
12C41×#556—21no—
13C41×#551—22no—
14D4×Q8×C41—21no—
15C41×#548—21no—
16C41×#546—21no—
17C41×#543C2212yes—
18C41×#542—21no—
19C41×#542—22no—
20C41×#538C2212yes—
21C41×#536—21no—
22C41×#533C2211yescharacteristic
23C2×#127×C41—21no—
24C2×#127×C41C2211yescharacteristic
25C41×#529C2211yescharacteristic
26C2×#124×C41—21no—
27C2×#124×C41C2211yescharacteristic
28C41×#496—21no—
29C41×#492—21no—
30C41×#490—21no—
31C41×#486—21no—
32C41×#460—22no—
33C41×#460—21no—
34C41×#459—21no—
35C41×#450C2212yes—
36C41×#450C2214yes—
37C41×#447C2212yes—
38C41×#432C2211yescharacteristic
39C41×#431C2211yescharacteristic
40C41×#392—22no—
41C41×#392C2214yes—
42C41×#376C2211yescharacteristic
43C41×#328C2212yes—
44C41×#328C2214yes—
45C41×#327C2212yes—
46C41×#323C2214yes—
47C2×#41×C41—21no—
48C22×Q8×C41—21no—
49C22×Q8×C41D411yescharacteristic
50C22×D4×C41—24no—
51C22×D4×C41—21no—
52C22×D4×C41—21no—
53C22×D4×C41D411yescharacteristic
54C22×D4×C41C2312yes—
55C2×SD16×C41—24no—
56C2×SD16×C41—22no—
57C2×D8×C41—22no—
58C4⋊Q8×C41—21no—
59C4⋊Q8×C41—22no—
60C4⋊Q8×C41D411yescharacteristic, complemented
61C4⋊Q8×C41D411yescharacteristic, complemented
62#127×C41—21no—
63#127×C41—21no—
64#127×C41—21no—
65#127×C41—21no—
66#127×C41—44no—
67#126×C41—22no—
68#126×C41—22no—
69#126×C41—22no—
70#126×C41—21no—
71#125×C41—21no—
72#125×C41D411yescharacteristic, complemented
73#124×C41—21no—
74#124×C41—22no—
75#124×C41—22no—
76#124×C41—21no—
77#124×C41—21no—
78#124×C41—21no—
79#124×C41—21no—
80#124×C41—44no—
81#124×C41D411yescharacteristic, complemented
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—21no—
86#123×C41—22no—
87C22⋊Q8×C41—22no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—22no—
90C22⋊Q8×C41—22no—
91C22⋊Q8×C41—22no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41C2311yescharacteristic
97C22⋊Q8×C41C2312yes—
98#121×C41—21no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41C2311yescharacteristic
102#120×C41—22no—
103C4×Q8×C41—21no—
104C4×Q8×C41—21no—
105C4×Q8×C41D411yescharacteristic, complemented
106C4×Q8×C41D412yescomplemented
107C4×D4×C41—21no—
108C4×D4×C41—22no—
109C4×D4×C41—21no—
110C4×D4×C41—22no—
111C4×D4×C41D411yescharacteristic, complemented
112#117×C41—22no—
113#117×C41—21no—
114#117×C41—21no—
115C2×C22⋊C4×C41—22no—
116C2×C22⋊C4×C41—24no—
117C2×C22⋊C4×C41D412yes—
118C2×C22⋊C4×C41C2312yes—
119C2×C42×C41—21no—
120C2×C42×C41C2311yescharacteristic
121C4⋊C8×C41—21no—
122C4⋊C8×C41—21no—
123#102×C41—22no—
124#102×C41—22no—
125#102×C41—24no—
126C22⋊C8×C41C2312yes—
127C22⋊C8×C41C2312yes—
128#97×C41—21no—
129C4×C8×C41—21no—
130#95×C41—21no—
131#95×C41C2312yes—
132C24×C41—22no—
133C24×C41C2×D412yes—
134#41×C41—82no—
135C2×Q8×C41—22no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—42no—
140C2×Q8×C41—82no—
141C2×Q8×C41C2×D411yescharacteristic
142C2×Q8×C41C2×D412yes—
143C2×D4×C41—21no—
144C2×D4×C41—22no—
145C2×D4×C41—22no—
146C2×D4×C41—21no—
147C2×D4×C41—21no—
148C2×D4×C41—22no—
149C2×D4×C41—22no—
150C2×D4×C41—42no—
151C2×D4×C41—42no—
152C2×D4×C41—42no—
153C2×D4×C41—48no—
154C2×D4×C41—41no—
155C2×D4×C41—41no—
156C2×D4×C41—41no—
157C2×D4×C41—41no—
158C2×D4×C41—82no—
159C2×D4×C41—82no—
160C2×D4×C41—84no—
161C2×D4×C41—84no—
162C2×D4×C41C2×D411yescharacteristic
163C22×C4×C41—22no—
164C22×C4×C41—22no—
165C22×C4×C41—22no—
166C22×C4×C41—22no—
167C22×C4×C41—21no—
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D411yescharacteristic
170C22×C4×C41C2×D412yes—
171C22×C4×C41C2411yescharacteristic
172SD16×C41—82no—
173SD16×C41—84no—
174D8×C41—82no—
175C2×C8×C41—22no—
176C2×C8×C41—22no—
177C4⋊C4×C41—22no—
178C4⋊C4×C41—22no—
179C4⋊C4×C41—22no—
180C4⋊C4×C41—22no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—21no—
183C4⋊C4×C41—21no—
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—22no—
190C4⋊C4×C41C2×D411yescharacteristic
191C4⋊C4×C41C2×D411yescharacteristic
192C4⋊C4×C41C2×D412yes—
193C22⋊C4×C41—22no—
194C22⋊C4×C41—22no—
195C22⋊C4×C41—22no—
196C22⋊C4×C41—22no—
197C22⋊C4×C41—22no—
198C22⋊C4×C41—21no—
199C22⋊C4×C41—22no—
200C22⋊C4×C41—22no—
201C22⋊C4×C41—22no—
202C22⋊C4×C41—21no—
203C22⋊C4×C41—21no—
204C22⋊C4×C41—21no—
205C22⋊C4×C41—22no—
206C22⋊C4×C41—22no—
207C22⋊C4×C41—21no—
208C22⋊C4×C41—48no—
209C42×C41—24no—
210C42×C41—22no—
211C42×C41—22no—
212C42×C41—21no—
213C42×C41C2×D411yescharacteristic
214C42×C41C2×D411yescharacteristic
215C42×C41C2×D411yescharacteristic
216C42×C41C2×D411yescharacteristic
217C23×C41—22no—
218C23×C41—21no—
219C23×C41—24no—
220C23×C41—42no—
221C23×C41—42no—
222C23×C41—42no—
223C23×C41—42no—
224C23×C41—44no—
225C23×C41—42no—
226C23×C41—44no—
227C23×C41C22×D411yescharacteristic
228Q8×C41—41no—
229Q8×C41—42no—
230Q8×C41—42no—
231Q8×C41—42no—
232Q8×C41—81no—
233Q8×C41—82no—
234D4×C41—41no—
235D4×C41—42no—
236D4×C41—42no—
237D4×C41—44no—
238D4×C41—42no—
239D4×C41—42no—
240D4×C41—81no—
241D4×C41—82no—
242D4×C41—82no—
243D4×C41—82no—
244D4×C41—82no—
245D4×C41—82no—
246D4×C41—816no—
247D4×C41—82no—
248C2×C4×C41—22no—
249C2×C4×C41—22no—
250C2×C4×C41—24no—
251C2×C4×C41—21no—
252C2×C4×C41—22no—
253C2×C4×C41—21no—
254C2×C4×C41—22no—
255C2×C4×C41—22no—
256C2×C4×C41—21no—
257C2×C4×C41—41no—
258C2×C4×C41—42no—
259C2×C4×C41—42no—
260C2×C4×C41—42no—
261C2×C4×C41—42no—
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×C41#12011yescharacteristic
269C2×C4×C41C22×D411yescharacteristic
270C2×C4×C41C22×D411yescharacteristic
271C8×C41—42no—
272C8×C41—42no—
273#18428C4111yesmaximal, characteristic, direct product factor, Sylow
274C22×C41—21no—
275C22×C41—21no—
276C22×C41—41no—
277C22×C41—42no—
278C22×C41—41no—
279C22×C41—42no—
280C22×C41—42no—
281C22×C41—41no—
282C22×C41—84no—
283C22×C41—84no—
284C22×C41—84no—
285C22×C41—82no—
286C22×C41—82no—
287C22×C41—82no—
288C22×C41C2×#12011yescharacteristic
289C22×C41#57712yes—
290C4×C41—21no—
291C4×C41—21no—
292C4×C41—21no—
293C4×C41—21no—
294C4×C41—21no—
295C4×C41—44no—
296C4×C41—41no—
297C4×C41—41no—
298C4×C41—42no—
299C4×C41—42no—
300C4×C41—41no—
301C4×C41—42no—
302C4×C41#45312yes—
303#3561C2×C4111yescharacteristic, complemented
304#3217C2×C4111yescharacteristic, complemented
305#3208C2×C4111yescharacteristic, complemented
306#2657C2×C4111yescharacteristic, complemented
307#1600C2×C4114yescomplemented
308#1596C2×C4114yescomplemented
309#1506C2×C4111yescharacteristic, complemented
310#1500C2×C4111yescharacteristic, complemented
311#1469C2×C4111yescharacteristic, complemented
312C2×C41—22no—
313C2×C41—81no—
314C2×C41—82no—
315C2×C41—162no—
316C2×C41#301011yescharacteristic
317C2×C41C2×#45311yescharacteristic
318C2×C41#302711yescharacteristic
319#563—21no—
320#562—21no—
321#556—21no—
322#551—22no—
323D4×Q8—21no—
324#548—21no—
325#546—21no—
326#543C22×C4112yes—
327#542—21no—
328#542—22no—
329#538C22×C4112yes—
330#536—21no—
331#533C22×C4111yescharacteristic
332C2×#127—21no—
333C2×#127C22×C4111yescharacteristic
334#529C22×C4111yescharacteristic
335C2×#124—21no—
336C2×#124C22×C4111yescharacteristic
337#496—21no—
338#492—21no—
339#490—21no—
340#486—21no—
341#460—22no—
342#460—21no—
343#459—21no—
344#450C22×C4112yes—
345#450C22×C4114yes—
346#447C22×C4112yes—
347#432C22×C4111yescharacteristic
348#431C22×C4111yescharacteristic
349#392—22no—
350#392C22×C4114yes—
351#376C22×C4111yescharacteristic
352#328C22×C4112yes—
353#328C22×C4114yes—
354#327C22×C4112yes—
355#323C22×C4114yes—
356C41#1842811yescharacteristic, direct product factor, Sylow
357C2×#41—21no—
358C22×Q8—21no—
359C22×Q8D4×C4111yescharacteristic
360C22×D4—24no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4D4×C4111yescharacteristic
364C22×D4C23×C4112yes—
365C2×SD16—24no—
366C2×SD16—22no—
367C2×D8—22no—
368C4⋊Q8—21no—
369C4⋊Q8—22no—
370C4⋊Q8D4×C4111yescharacteristic, complemented
371C4⋊Q8D4×C4111yescharacteristic, complemented
372#127—21no—
373#127—21no—
374#127—21no—
375#127—21no—
376#127—44no—
377#126—22no—
378#126—22no—
379#126—22no—
380#126—21no—
381#125—21no—
382#125D4×C4111yescharacteristic, complemented
383#124—21no—
384#124—22no—
385#124—22no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124—21no—
390#124—44no—
391#124D4×C4111yescharacteristic, complemented
392#123—22no—
393#123—22no—
394#123—22no—
395#123—21no—
396#123—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8C23×C4111yescharacteristic
407C22⋊Q8C23×C4112yes—
408#121—21no—
409#121—22no—
410#121—22no—
411#121C23×C4111yescharacteristic
412#120—22no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8D4×C4111yescharacteristic, complemented
416C4×Q8D4×C4112yescomplemented
417C4×D4—21no—
418C4×D4—22no—
419C4×D4—21no—
420C4×D4—22no—
421C4×D4D4×C4111yescharacteristic, complemented
422#117—22no—
423#117—21no—
424#117—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4D4×C4112yes—
428C2×C22⋊C4C23×C4112yes—
429C2×C42—21no—
430C2×C42C23×C4111yescharacteristic
431C4⋊C8—21no—
432C4⋊C8—21no—
433#102—22no—
434#102—22no—
435#102—24no—
436C22⋊C8C23×C4112yes—
437C22⋊C8C23×C4112yes—
438#97—21no—
439C4×C8—21no—
440#95—21no—
441#95C23×C4112yes—
442C24—22no—
443C24C2×D4×C4112yes—
444#41—82no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—42no—
450C2×Q8—82no—
451C2×Q8C2×D4×C4111yescharacteristic
452C2×Q8C2×D4×C4112yes—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—48no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—82no—
469C2×D4—82no—
470C2×D4—84no—
471C2×D4—84no—
472C2×D4C2×D4×C4111yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4C2×D4×C4111yescharacteristic
479C22×C4C2×D4×C4111yescharacteristic
480C22×C4C2×D4×C4112yes—
481C22×C4C24×C4111yescharacteristic
482SD16—82no—
483SD16—84no—
484D8—82no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4C2×D4×C4111yescharacteristic
501C4⋊C4C2×D4×C4111yescharacteristic
502C4⋊C4C2×D4×C4112yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—48no—
519C42—24no—
520C42—22no—
521C42—22no—
522C42—21no—
523C42C2×D4×C4111yescharacteristic
524C42C2×D4×C4111yescharacteristic
525C42C2×D4×C4111yescharacteristic
526C42C2×D4×C4111yescharacteristic
527C23—22no—
528C23—21no—
529C23—24no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—42no—
536C23—44no—
537C23C22×D4×C4111yescharacteristic
538Q8—41no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544D4—41no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—42no—
549D4—42no—
550D4—81no—
551D4—82no—
552D4—82no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4—816no—
557D4—82no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4#120×C4111yescharacteristic
576C2×C4#120×C4111yescharacteristic
577C2×C4#120×C4111yescharacteristic
578C2×C4#120×C4111yescharacteristic
579C2×C4C22×D4×C4111yescharacteristic
580C2×C4C22×D4×C4111yescharacteristic
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—84no—
592C22—84no—
593C22—84no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×#120×C4111yescharacteristic
598C22C41×#57712yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—44no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—42no—
611C4C41×#45312yes—
612C2—22no—
613C2—82no—
614C2—81no—
615C2—162no—
616C2C41×#301011yescharacteristic
617C2C2×C41×#45311yescharacteristic
618C2C41×#302711yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ 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×#3561C2semidirect
2. C41×#3217C2semidirect
3. C41×#3208C2semidirect
4. C41×#2657C2semidirect
5. C41×#1600C2semidirect
6. C41×#1596C2semidirect
7. C41×#1506C2semidirect
8. C41×#1500C2semidirect
9. C41×#1469C2semidirect
60. C4⋊Q8×C41D4semidirect
61. C4⋊Q8×C41D4semidirect
72. #125×C41D4semidirect
81. #124×C41D4semidirect
105. C4×Q8×C41D4semidirect
106. C4×Q8×C41D4semidirect
111. C4×D4×C41D4semidirect
273. #18428C41direct (N × H)
303. #3561C2×C41semidirect
304. #3217C2×C41semidirect
305. #3208C2×C41semidirect
306. #2657C2×C41semidirect
307. #1600C2×C41semidirect
308. #1596C2×C41semidirect
309. #1506C2×C41semidirect
310. #1500C2×C41semidirect
311. #1469C2×C41semidirect
356. C41#18428direct (N × H)
370. C4⋊Q8D4×C41semidirect
371. C4⋊Q8D4×C41semidirect
382. #125D4×C41semidirect
391. #124D4×C41semidirect
415. C4×Q8D4×C41semidirect
416. C4×Q8D4×C41semidirect
421. C4×D4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35612
C41×#32172
C41×#32082
C41×#26572
C41×#16002
C41×#15962
C41×#15062
C41×#15002
C41×#14692
#1842841