Finite Group Databasebeta

← C41×#23889 #23800090

Subgroups — C41×#23889 #23800090

Order 10496.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#578C211yesmaximal, characteristic, complemented
2C2×C41×#577C211yesmaximal, characteristic, complemented
3C2×C41×#454C211yesmaximal, characteristic, complemented
4C2×C41×#455C211yesmaximal, characteristic, complemented
5C41×#3013C211yesmaximal, characteristic, complemented
6C41×#3012C211yesmaximal, characteristic, complemented
7C41×#2020C211yesmaximal, characteristic, complemented
8C41×#2019C211yesmaximal, characteristic, complemented
9C41×#2015C211yesmaximal, characteristic, complemented
10C41×#2007C211yesmaximal, characteristic, complemented
11C41×#1908C211yesmaximal, characteristic, complemented
12C41×#1907C211yesmaximal, characteristic, complemented
13C41×#1876C211yesmaximal, characteristic, complemented
14C41×#1876C211yesmaximal, characteristic, complemented
15C41×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C41C2211yescharacteristic
17C2×2−1+4×C41C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C41C2211yescharacteristic
19C41×#578—24no—
20C41×#578—24no—
21C41×#577—24no—
22C41×#577—24no—
23C2×#137×C41—21no—
24C2×#137×C41—21no—
25C2×#137×C41—21no—
26C2×#137×C41C2211yescharacteristic
27C2×#137×C41C2211yescharacteristic
28C2×#137×C41C2211yescharacteristic
29C2×#137×C41C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C41—21no—
31C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
33C2×#135×C41—21no—
34C2×#135×C41—21no—
35C2×#135×C41C2211yescharacteristic
36C2×#135×C41C2211yescharacteristic
37C22×Q16×C41—21no—
38C22×Q16×C41C2211yescharacteristic, complemented
39C22×SD16×C41—21no—
40C22×SD16×C41C2211yescharacteristic
41C2×#131×C41C2211yescharacteristic
42C2×#131×C41C2211yescharacteristic, complemented
43C41×#537C2211yescharacteristic
44C2×#124×C41C2211yescharacteristic
45C41×#455—24no—
46C41×#454—24no—
47C41×#452—21no—
48C41×#452—21no—
49C41×#451—21no—
50C41×#450—21no—
51C41×#449—21no—
52C41×#449—21no—
53C41×#448—21no—
54C41×#447—21no—
55C2×#104×C41C2211yescharacteristic
56C2×#104×C41C2211yescharacteristic
57C2×#104×C41C2211yescharacteristic, complemented
58C2×#104×C41C2211yescharacteristic, complemented
59C41×#417C2211yescharacteristic
60C41×#417C2211yescharacteristic, complemented
61C2×#103×C41C2211yescharacteristic, complemented
62C2×#102×C41C2211yescharacteristic
63C2×#101×C41C2211yescharacteristic, complemented
64C2×#101×C41C2211yescharacteristic, complemented
65C2×#100×C41C2211yescharacteristic
66C41×#408C2211yescharacteristic
67C41×#408C2211yescharacteristic, complemented
68C41×#391C2211yescharacteristic, complemented
69C41×#343C2211yescharacteristic, complemented
70C41×#341C2211yescharacteristic, complemented
71C41×#341C2211yescharacteristic, complemented
72C41×#336C2211yescharacteristic, complemented
732−1+4×C41—22no—
742−1+4×C41—22no—
752−1+4×C41—22no—
762−1+4×C41—22no—
772−1+4×C41—22no—
782−1+4×C41—41no—
792−1+4×C41—41no—
802−1+4×C41D414yescomplemented
81H(5,𝔽2)×C41—22no—
82H(5,𝔽2)×C41—22no—
83H(5,𝔽2)×C41—22no—
84H(5,𝔽2)×C41—41no—
85C2×#41×C41—21no—
86C2×#41×C41—21no—
87C2×#41×C41—21no—
88C2×#41×C41—21no—
89C2×#41×C41—21no—
90C2×#41×C41—21no—
91C2×#41×C41—41no—
92C2×#41×C41—41no—
93C2×#41×C41C2311yescharacteristic
94C2×#41×C41C2311yescharacteristic
95C2×#41×C41C2311yescharacteristic
96C2×#41×C41C2311yescharacteristic
97C22×Q8×C41—21no—
98C22×Q8×C41—21no—
99C22×Q8×C41—21no—
100C22×Q8×C41—21no—
101C22×Q8×C41C2311yescharacteristic
102C22×Q8×C41C2311yescharacteristic
103C22×D4×C41—21no—
104C22×D4×C41—21no—
105C22×D4×C41—41no—
106C22×D4×C41C2311yescharacteristic
107#137×C41—28no—
108#137×C41—28no—
109#137×C41—28no—
110#137×C41—22no—
111#137×C41—22no—
112#137×C41—22no—
113#137×C41—22no—
114#137×C41—22no—
115#137×C41—22no—
116#137×C41—41no—
117#137×C41D414yescomplemented
118AGL(1,ℤ/8)×C41—28no—
119AGL(1,ℤ/8)×C41—22no—
120AGL(1,ℤ/8)×C41—22no—
121AGL(1,ℤ/8)×C41—41no—
122AGL(1,ℤ/8)×C41D414yescomplemented
123#135×C41—28no—
124#135×C41—28no—
125#135×C41—22no—
126#135×C41—22no—
127#135×C41—22no—
128#135×C41—22no—
129C2×Q16×C41—28no—
130C2×Q16×C41—21no—
131C2×Q16×C41—21no—
132C2×Q16×C41—22no—
133C2×Q16×C41—22no—
134C2×Q16×C41—21no—
135C2×Q16×C41—21no—
136C2×Q16×C41—21no—
137C2×Q16×C41—21no—
138C2×Q16×C41D411yescharacteristic
139C2×Q16×C41D411yescharacteristic
140C2×SD16×C41—28no—
141C2×SD16×C41—21no—
142C2×SD16×C41—22no—
143C2×SD16×C41—21no—
144C2×SD16×C41—22no—
145C2×SD16×C41—21no—
146C2×SD16×C41—21no—
147C2×SD16×C41—21no—
148C2×SD16×C41—21no—
149C2×SD16×C41—21no—
150C2×SD16×C41—21no—
151C2×SD16×C41D411yescharacteristic
152C2×SD16×C41D411yescharacteristic
153C2×SD16×C41D411yescharacteristic
154C2×SD16×C41D411yescharacteristic
155C2×D8×C41—21no—
156C2×D8×C41—21no—
157C2×D8×C41D411yescharacteristic
158C2×D8×C41D411yescharacteristic
159#131×C41—22no—
160#131×C41—22no—
161#131×C41—22no—
162#131×C41—22no—
163C2×M16×C41—21no—
164C2×M16×C41—21no—
165C2×M16×C41C2311yescharacteristic
166C2×M16×C41C2311yescharacteristic
167C2×M16×C41C2311yescharacteristic
168C2×M16×C41C2311yescharacteristic
169C22×C8×C41—21no—
170C22×C8×C41—21no—
171C22×C8×C41C2311yescharacteristic
172C22×C8×C41C2311yescharacteristic
173#124×C41—22no—
174#124×C41—22no—
175C22⋊Q8×C41—21no—
176C22⋊Q8×C41—21no—
177#121×C41—21no—
178#121×C41—21no—
179#121×C41—41no—
180C2×C4⋊C4×C41C2311yescharacteristic
181C2×C22⋊C4×C41—41no—
182C2×C42×C41C2311yescharacteristic
183#104×C41—22no—
184#104×C41—22no—
185#104×C41—22no—
186#104×C41—22no—
187#103×C41—21no—
188#103×C41—21no—
189#103×C41—21no—
190#103×C41—21no—
191#102×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194#102×C41—21no—
195#101×C41—22no—
196#101×C41—41no—
197#100×C41—22no—
198C22⋊C8×C41—21no—
199C22⋊C8×C41—21no—
200C22⋊C8×C41—21no—
201C22⋊C8×C41—21no—
202#95×C41—41no—
203C24×C41—21no—
204C24×C41—41no—
205#41×C41—21no—
206#41×C41—21no—
207#41×C41—21no—
208#41×C41—21no—
209#41×C41—24no—
210#41×C41—24no—
211#41×C41—24no—
212#41×C41—24no—
213#41×C41—21no—
214#41×C41—21no—
215#41×C41—21no—
216#41×C41—21no—
217#41×C41—21no—
218#41×C41—21no—
219#41×C41—21no—
220#41×C41—21no—
221#41×C41—44no—
222#41×C41—42no—
223#41×C41—42no—
224#41×C41—42no—
225#41×C41—44no—
226#41×C41—42no—
227#41×C41—44no—
228#41×C41—42no—
229#41×C41—42no—
230#41×C41—44no—
231#41×C41—42no—
232#41×C41—42no—
233#41×C41C2×D412yes—
234#41×C41C2×D412yes—
235#41×C41C2×D412yes—
236#41×C41C2×D412yes—
237C2×Q8×C41—21no—
238C2×Q8×C41—21no—
239C2×Q8×C41—24no—
240C2×Q8×C41—24no—
241C2×Q8×C41—24no—
242C2×Q8×C41—21no—
243C2×Q8×C41—21no—
244C2×Q8×C41—21no—
245C2×Q8×C41—21no—
246C2×Q8×C41—21no—
247C2×Q8×C41—21no—
248C2×Q8×C41—21no—
249C2×Q8×C41—21no—
250C2×Q8×C41—41no—
251C2×Q8×C41—41no—
252C2×Q8×C41—42no—
253C2×Q8×C41—42no—
254C2×Q8×C41—42no—
255C2×Q8×C41—42no—
256C2×Q8×C41—42no—
257C2×Q8×C41C2×D411yescharacteristic
258C2×Q8×C41C2×D411yescharacteristic
259C2×Q8×C41C2×D412yes—
260C2×Q8×C41C2×D412yes—
261C2×Q8×C41C2×D411yescharacteristic
262C2×Q8×C41C2×D411yescharacteristic
263C2×D4×C41—21no—
264C2×D4×C41—21no—
265C2×D4×C41—24no—
266C2×D4×C41—21no—
267C2×D4×C41—21no—
268C2×D4×C41—21no—
269C2×D4×C41—21no—
270C2×D4×C41—21no—
271C2×D4×C41—21no—
272C2×D4×C41—21no—
273C2×D4×C41—42no—
274C2×D4×C41—41no—
275C2×D4×C41—41no—
276C2×D4×C41—42no—
277C2×D4×C41—44no—
278C2×D4×C41—44no—
279C2×D4×C41—41no—
280C2×D4×C41—41no—
281C2×D4×C41—42no—
282C2×D4×C41—41no—
283C2×D4×C41C2×D411yescharacteristic
284C2×D4×C41C2×D411yescharacteristic
285C2×D4×C41C2×D412yes—
286C2×D4×C41C2×D411yescharacteristic
287C2×D4×C41C2×D411yescharacteristic
288C22×C4×C41—21no—
289C22×C4×C41—21no—
290C22×C4×C41—21no—
291C22×C4×C41—21no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—21no—
295C22×C4×C41—21no—
296C22×C4×C41—41no—
297C22×C4×C41—41no—
298C22×C4×C41—41no—
299C22×C4×C41—41no—
300C22×C4×C41—41no—
301C22×C4×C41C2411yescharacteristic
302Q16×C41—24no—
303Q16×C41—24no—
304Q16×C41—24no—
305Q16×C41—24no—
306Q16×C41—22no—
307Q16×C41—24no—
308Q16×C41—22no—
309Q16×C41—42no—
310SD16×C41—24no—
311SD16×C41—24no—
312SD16×C41—24no—
313SD16×C41—24no—
314SD16×C41—22no—
315SD16×C41—24no—
316SD16×C41—22no—
317SD16×C41—24no—
318SD16×C41—22no—
319SD16×C41—22no—
320SD16×C41—42no—
321SD16×C41—42no—
322D8×C41—24no—
323D8×C41—22no—
324D8×C41—22no—
325D8×C41—42no—
326M16×C41—24no—
327M16×C41—24no—
328M16×C41—21no—
329M16×C41—21no—
330M16×C41—21no—
331M16×C41—21no—
332M16×C41—21no—
333M16×C41—21no—
334M16×C41C2×D412yes—
335M16×C41C2×D412yes—
336C2×C8×C41—24no—
337C2×C8×C41—24no—
338C2×C8×C41—21no—
339C2×C8×C41—21no—
340C2×C8×C41—21no—
341C2×C8×C41—21no—
342C2×C8×C41—21no—
343C2×C8×C41—21no—
344C2×C8×C41—21no—
345C2×C8×C41—21no—
346C2×C8×C41C2×D411yescharacteristic
347C2×C8×C41C2×D411yescharacteristic
348C2×C8×C41C2×D411yescharacteristic
349C2×C8×C41C2×D411yescharacteristic
350C4⋊C4×C41—21no—
351C4⋊C4×C41—21no—
352C4⋊C4×C41—41no—
353C22⋊C4×C41—44no—
354C22⋊C4×C41—41no—
355C22⋊C4×C41—41no—
356C42×C41—21no—
357C42×C41—21no—
358C23×C41—21no—
359C23×C41—21no—
360C23×C41—21no—
361C23×C41—21no—
362C23×C41—22no—
363C23×C41—44no—
364C23×C41—41no—
365C23×C41—41no—
366C23×C41—81no—
367C23×C41—81no—
368C23×C41—161no—
369C23×C41—161no—
370C23×C41H(5,𝔽2)11yescharacteristic
371Q8×C41—21no—
372Q8×C41—21no—
373Q8×C41—22no—
374Q8×C41—22no—
375Q8×C41—22no—
376Q8×C41—21no—
377Q8×C41—21no—
378Q8×C41—21no—
379Q8×C41—22no—
380Q8×C41—21no—
381Q8×C41—44no—
382Q8×C41—44no—
383Q8×C41—41no—
384Q8×C41—41no—
385Q8×C41—41no—
386Q8×C41—41no—
387Q8×C41#12012yes—
388Q8×C41#12012yes—
389D4×C41—22no—
390D4×C41—22no—
391D4×C41—22no—
392D4×C41—22no—
393D4×C41—22no—
394D4×C41—21no—
395D4×C41—21no—
396D4×C41—21no—
397D4×C41—21no—
398D4×C41—21no—
399D4×C41—22no—
400D4×C41—21no—
401D4×C41—44no—
402D4×C41—44no—
403D4×C41—44no—
404D4×C41—44no—
405D4×C41—41no—
406D4×C41—41no—
407D4×C41—41no—
408D4×C41—41no—
409D4×C41—41no—
410D4×C41—41no—
411D4×C41—161no—
412D4×C41#12012yes—
413D4×C41#12012yes—
414C2×C4×C41—21no—
415C2×C4×C41—21no—
416C2×C4×C41—22no—
417C2×C4×C41—22no—
418C2×C4×C41—22no—
419C2×C4×C41—22no—
420C2×C4×C41—22no—
421C2×C4×C41—22no—
422C2×C4×C41—21no—
423C2×C4×C41—21no—
424C2×C4×C41—44no—
425C2×C4×C41—44no—
426C2×C4×C41—44no—
427C2×C4×C41—44no—
428C2×C4×C41—44no—
429C2×C4×C41—41no—
430C2×C4×C41—41no—
431C2×C4×C41—41no—
432C2×C4×C41—41no—
433C2×C4×C41—41no—
434C2×C4×C41—41no—
435C2×C4×C41—41no—
436C2×C4×C41—41no—
437C2×C4×C41—41no—
438C2×C4×C41—41no—
439C2×C4×C41—41no—
440C2×C4×C41—41no—
441C2×C4×C41—81no—
442C2×C4×C41C22×D411yescharacteristic
443C2×C4×C41C22×D411yescharacteristic
444C2×C4×C41C22×D411yescharacteristic
445C2×C4×C41C22×D411yescharacteristic
446C2×C4×C41C22×D411yescharacteristic
447C2×C4×C41H(5,𝔽2)11yescharacteristic
448C8×C41—21no—
449C8×C41—21no—
450C8×C41—22no—
451C8×C41—22no—
452C8×C41—21no—
453C8×C41—21no—
454C8×C41—41no—
455C8×C41—41no—
456#23889C4111yesmaximal, characteristic, direct product factor, Sylow
457C22×C41—21no—
458C22×C41—21no—
459C22×C41—22no—
460C22×C41—22no—
461C22×C41—41no—
462C22×C41—41no—
463C22×C41—41no—
464C22×C41—41no—
465C22×C41—41no—
466C22×C41—41no—
467C22×C41—42no—
468C22×C41—41no—
469C22×C41—41no—
470C22×C41—41no—
471C22×C41—41no—
472C22×C41—82no—
473C22×C41—81no—
474C22×C41—81no—
475C22×C41—161no—
476C22×C41—164no—
477C22×C41#53411yescharacteristic
478C22×C41D4211yescharacteristic
479C22×C41D4211yescharacteristic
480C4×C41—22no—
481C4×C41—22no—
482C4×C41—41no—
483C4×C41—42no—
484C4×C41—42no—
485C4×C41—41no—
486C4×C41—81no—
487C4×C41—81no—
488C4×C41C2×#12011yescharacteristic
489C4×C41C2×#12011yescharacteristic
490C4×C41D4211yescharacteristic
491C4×C41D4211yescharacteristic
492C2×#578C2×C4111yescharacteristic, complemented
493C2×#577C2×C4111yescharacteristic, complemented
494C2×#454C2×C4111yescharacteristic, complemented
495C2×#455C2×C4111yescharacteristic, complemented
496#3013C2×C4111yescharacteristic, complemented
497#3012C2×C4111yescharacteristic, complemented
498#2020C2×C4111yescharacteristic, complemented
499#2019C2×C4111yescharacteristic, complemented
500#2015C2×C4111yescharacteristic, complemented
501#2007C2×C4111yescharacteristic, complemented
502#1908C2×C4111yescharacteristic, complemented
503#1907C2×C4111yescharacteristic, complemented
504#1876C2×C4111yescharacteristic, complemented
505#1876C2×C4111yescharacteristic, complemented
506#1793C2×C4111yescharacteristic, complemented
507C2×C41—21no—
508C2×C41—21no—
509C2×C41—42no—
510C2×C41—42no—
511C2×C41—81no—
512C2×C41—81no—
513C2×C41—82no—
514C2×C41#240311yescharacteristic
515C2×C41#328911yescharacteristic
516C2×C41#329011yescharacteristic
517C2×2−1+4C22×C4111yescharacteristic
518C2×2−1+4C22×C4111yescharacteristic, complemented
519C2×H(5,𝔽2)C22×C4111yescharacteristic
520#578—24no—
521#578—24no—
522#577—24no—
523#577—24no—
524C2×#137—21no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137C22×C4111yescharacteristic
528C2×#137C22×C4111yescharacteristic
529C2×#137C22×C4111yescharacteristic
530C2×#137C22×C4111yescharacteristic, complemented
531C2×AGL(1,ℤ/8)—21no—
532C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
533C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
534C2×#135—21no—
535C2×#135—21no—
536C2×#135C22×C4111yescharacteristic
537C2×#135C22×C4111yescharacteristic
538C22×Q16—21no—
539C22×Q16C22×C4111yescharacteristic, complemented
540C22×SD16—21no—
541C22×SD16C22×C4111yescharacteristic
542C2×#131C22×C4111yescharacteristic
543C2×#131C22×C4111yescharacteristic, complemented
544#537C22×C4111yescharacteristic
545C2×#124C22×C4111yescharacteristic
546#455—24no—
547#454—24no—
548#452—21no—
549#452—21no—
550#451—21no—
551#450—21no—
552#449—21no—
553#449—21no—
554#448—21no—
555#447—21no—
556C2×#104C22×C4111yescharacteristic
557C2×#104C22×C4111yescharacteristic
558C2×#104C22×C4111yescharacteristic, complemented
559C2×#104C22×C4111yescharacteristic, complemented
560#417C22×C4111yescharacteristic
561#417C22×C4111yescharacteristic, complemented
562C2×#103C22×C4111yescharacteristic, complemented
563C2×#102C22×C4111yescharacteristic
564C2×#101C22×C4111yescharacteristic, complemented
565C2×#101C22×C4111yescharacteristic, complemented
566C2×#100C22×C4111yescharacteristic
567#408C22×C4111yescharacteristic
568#408C22×C4111yescharacteristic, complemented
569#391C22×C4111yescharacteristic, complemented
570#343C22×C4111yescharacteristic, complemented
571#341C22×C4111yescharacteristic, complemented
572#341C22×C4111yescharacteristic, complemented
573#336C22×C4111yescharacteristic, complemented
574C41#2388911yescharacteristic, direct product factor, Sylow
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C4114yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C4111yescharacteristic
596C2×#41C23×C4111yescharacteristic
597C2×#41C23×C4111yescharacteristic
598C2×#41C23×C4111yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C4111yescharacteristic
604C22×Q8C23×C4111yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C4111yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C4114yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C4114yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C4111yescharacteristic
641C2×Q16D4×C4111yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C4111yescharacteristic
654C2×SD16D4×C4111yescharacteristic
655C2×SD16D4×C4111yescharacteristic
656C2×SD16D4×C4111yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C4111yescharacteristic
660C2×D8D4×C4111yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C4111yescharacteristic
668C2×M16C23×C4111yescharacteristic
669C2×M16C23×C4111yescharacteristic
670C2×M16C23×C4111yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C4111yescharacteristic
674C22×C8C23×C4111yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C4111yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C4111yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C4112yes—
736#41C2×D4×C4112yes—
737#41C2×D4×C4112yes—
738#41C2×D4×C4112yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C4111yescharacteristic
760C2×Q8C2×D4×C4111yescharacteristic
761C2×Q8C2×D4×C4112yes—
762C2×Q8C2×D4×C4112yes—
763C2×Q8C2×D4×C4111yescharacteristic
764C2×Q8C2×D4×C4111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C4111yescharacteristic
786C2×D4C2×D4×C4111yescharacteristic
787C2×D4C2×D4×C4112yes—
788C2×D4C2×D4×C4111yescharacteristic
789C2×D4C2×D4×C4111yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C4111yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C4112yes—
837M16C2×D4×C4112yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C4111yescharacteristic
849C2×C8C2×D4×C4111yescharacteristic
850C2×C8C2×D4×C4111yescharacteristic
851C2×C8C2×D4×C4111yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C4111yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C4112yes—
890Q8#120×C4112yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C4112yes—
915D4#120×C4112yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C4111yescharacteristic
945C2×C4C22×D4×C4111yescharacteristic
946C2×C4C22×D4×C4111yescharacteristic
947C2×C4C22×D4×C4111yescharacteristic
948C2×C4C22×D4×C4111yescharacteristic
949C2×C4H(5,𝔽2)×C4111yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22C41×#53411yescharacteristic
979C22D42×C4111yescharacteristic
980C22D42×C4111yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C4111yescharacteristic
990C4C2×#120×C4111yescharacteristic
991C4D42×C4111yescharacteristic
992C4D42×C4111yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C41×#240311yescharacteristic
1001C2C41×#328911yescharacteristic
1002C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#578C2semidirect
2. C2×C41×#577C2semidirect
3. C2×C41×#454C2semidirect
4. C2×C41×#455C2semidirect
5. C41×#3013C2semidirect
6. C41×#3012C2semidirect
7. C41×#2020C2semidirect
8. C41×#2019C2semidirect
9. C41×#2015C2semidirect
10. C41×#2007C2semidirect
11. C41×#1908C2semidirect
12. C41×#1907C2semidirect
13. C41×#1876C2semidirect
14. C41×#1876C2semidirect
15. C41×#1793C2semidirect
17. C2×2−1+4×C41C22semidirect
29. C2×#137×C41C22semidirect
38. C22×Q16×C41C22semidirect
42. C2×#131×C41C22semidirect
57. C2×#104×C41C22semidirect
58. C2×#104×C41C22semidirect
60. C41×#417C22semidirect
61. C2×#103×C41C22semidirect
63. C2×#101×C41C22semidirect
64. C2×#101×C41C22semidirect
67. C41×#408C22semidirect
68. C41×#391C22semidirect
69. C41×#343C22semidirect
70. C41×#341C22semidirect
71. C41×#341C22semidirect
72. C41×#336C22semidirect
80. 2−1+4×C41D4semidirect
117. #137×C41D4semidirect
122. AGL(1,ℤ/8)×C41D4semidirect
456. #23889C41direct (N × H)
492. C2×#578C2×C41semidirect
493. C2×#577C2×C41semidirect
494. C2×#454C2×C41semidirect
495. C2×#455C2×C41semidirect
496. #3013C2×C41semidirect
497. #3012C2×C41semidirect
498. #2020C2×C41semidirect
499. #2019C2×C41semidirect
500. #2015C2×C41semidirect
501. #2007C2×C41semidirect
502. #1908C2×C41semidirect
503. #1907C2×C41semidirect
504. #1876C2×C41semidirect
505. #1876C2×C41semidirect
506. #1793C2×C41semidirect
518. C2×2−1+4C22×C41semidirect
530. C2×#137C22×C41semidirect
539. C22×Q16C22×C41semidirect
543. C2×#131C22×C41semidirect
558. C2×#104C22×C41semidirect
559. C2×#104C22×C41semidirect
561. #417C22×C41semidirect
562. C2×#103C22×C41semidirect
564. C2×#101C22×C41semidirect
565. C2×#101C22×C41semidirect
568. #408C22×C41semidirect
569. #391C22×C41semidirect
570. #343C22×C41semidirect
571. #341C22×C41semidirect
572. #341C22×C41semidirect
573. #336C22×C41semidirect
574. C41#23889direct (N × H)
582. 2−1+4D4×C41semidirect
619. #137D4×C41semidirect
624. AGL(1,ℤ/8)D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5782
C2×C41×#5772
C2×C41×#4542
C2×C41×#4552
C41×#30132
C41×#30122
C41×#20202
C41×#20192
C41×#20152
C41×#20072
C41×#19082
C41×#19072
C41×#18762
C41×#17932
#2388941