Finite Group Databasebeta

← C2×C41×#2008 #23799611

Subgroups — C2×C41×#2008 #23799611

Order 10496.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C41C211yesmaximal, characteristic, complemented
3C2×C41×#535C211yesmaximal, characteristic, complemented
4C2×C41×#421C211yesmaximal, characteristic, complemented
5C2×C41×#418C211yesmaximal, characteristic, complemented
6C2×C41×#410C211yesmaximal, characteristic, complemented
7C41×#2008C218yesmaximal, direct product factor
8C2×C41×#344C211yesmaximal, characteristic, complemented
9C22×#41×C41C2211yescharacteristic
10C22×#41×C41C2211yescharacteristic
11C23×D4×C41C2211yescharacteristic
12C41×#575—22no—
13C41×#575—22no—
14C41×#575—22no—
15C41×#575C2214yescomplemented
16C2×#137×C41—21no—
17C2×#137×C41—21no—
18C2×AGL(1,ℤ/8)×C41—22no—
19C2×AGL(1,ℤ/8)×C41—22no—
20C2×AGL(1,ℤ/8)×C41—22no—
21C2×AGL(1,ℤ/8)×C41—21no—
22C2×AGL(1,ℤ/8)×C41—21no—
23C2×AGL(1,ℤ/8)×C41—22no—
24C2×AGL(1,ℤ/8)×C41—22no—
25C2×AGL(1,ℤ/8)×C41C2214yescomplemented
26C2×#135×C41—22no—
27C22×SD16×C41—21no—
28C22×D8×C41—21no—
29C22×M16×C41C2211yescharacteristic
30C22×M16×C41C2211yescharacteristic
31C41×#535—22no—
32C41×#535—22no—
33C41×#535—22no—
34C41×#535C2214yescomplemented
35C2×#127×C41—21no—
36C2×#124×C41—21no—
37C2×#121×C41—22no—
38C2×#120×C41—22no—
39C2×#117×C41C2211yescharacteristic
40C2×#117×C41C2211yescharacteristic
41C41×#421—22no—
42C41×#421C2214yescomplemented
43C2×#104×C41—22no—
44C41×#418—22no—
45C41×#418C2214yescomplemented
46C2×#102×C41—22no—
47C41×#410—22no—
48C41×#410C2214yescomplemented
49C2×#99×C41—22no—
50C41×#344C2214yescomplemented
51C25×C41—21no—
52C2×#41×C41—21no—
53C2×#41×C41—21no—
54C2×#41×C41—21no—
55C2×#41×C41—21no—
56C2×#41×C41—21no—
57C2×#41×C41—21no—
58C2×#41×C41—21no—
59C2×#41×C41—21no—
60C2×#41×C41—21no—
61C2×#41×C41—21no—
62C2×#41×C41—21no—
63C2×#41×C41—21no—
64C2×#41×C41—21no—
65C2×#41×C41—21no—
66C2×#41×C41—21no—
67C2×#41×C41—21no—
68C2×#41×C41—21no—
69C2×#41×C41—21no—
70C2×#41×C41—21no—
71C2×#41×C41—21no—
72C2×#41×C41D412yes—
73C2×#41×C41D412yescomplemented
74C2×#41×C41C2312yes—
75C2×#41×C41C2312yes—
76C22×Q8×C41D411yescharacteristic
77C22×Q8×C41D411yescharacteristic, complemented
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—24no—
81C22×D4×C41—21no—
82C22×D4×C41—21no—
83C22×D4×C41—21no—
84C22×D4×C41—21no—
85C22×D4×C41—21no—
86C22×D4×C41—21no—
87C22×D4×C41—21no—
88C22×D4×C41—21no—
89C22×D4×C41—21no—
90C22×D4×C41—21no—
91C22×D4×C41—21no—
92C22×D4×C41D412yes—
93C22×D4×C41D411yescharacteristic
94C22×D4×C41D412yes—
95C22×D4×C41D411yescharacteristic, complemented
96C22×D4×C41C2312yes—
97C23×C4×C41—21no—
98C23×C4×C41—21no—
99C23×C4×C41C2311yescharacteristic
100#137×C41—24no—
101#137×C41—24no—
102#137×C41—24no—
103#137×C41—24no—
104AGL(1,ℤ/8)×C41—28no—
105AGL(1,ℤ/8)×C41—28no—
106AGL(1,ℤ/8)×C41—24no—
107AGL(1,ℤ/8)×C41—24no—
108AGL(1,ℤ/8)×C41—28no—
109AGL(1,ℤ/8)×C41—24no—
110AGL(1,ℤ/8)×C41—24no—
111AGL(1,ℤ/8)×C41—28no—
112#135×C41—28no—
113#135×C41—28no—
114C2×Q16×C41—22no—
115C2×SD16×C41—24no—
116C2×SD16×C41—24no—
117C2×SD16×C41—22no—
118C2×SD16×C41—22no—
119C2×SD16×C41—24no—
120C2×D8×C41—24no—
121C2×D8×C41—24no—
122C2×D8×C41—22no—
123C2×D8×C41—24no—
124C2×M16×C41—21no—
125C2×M16×C41—21no—
126C2×M16×C41—21no—
127C2×M16×C41—21no—
128C2×M16×C41—21no—
129C2×M16×C41—21no—
130C2×M16×C41—21no—
131C2×M16×C41D412yescomplemented
132C2×M16×C41D412yescomplemented
133C2×M16×C41D412yescomplemented
134C2×M16×C41C2312yes—
135C2×M16×C41C2312yes—
136C22×C8×C41—21no—
137C22×C8×C41D412yescomplemented
138#127×C41—24no—
139#127×C41—24no—
140#124×C41—24no—
141#124×C41—24no—
142#121×C41—28no—
143#121×C41—28no—
144#120×C41—28no—
145#120×C41—28no—
146#117×C41—21no—
147#117×C41—21no—
148#117×C41—21no—
149#117×C41—21no—
150#117×C41—21no—
151#117×C41D412yes—
152#117×C41C2312yes—
153#117×C41C2312yes—
154C2×C4⋊C4×C41—21no—
155C2×C4⋊C4×C41—21no—
156C2×C22⋊C4×C41—24no—
157C2×C22⋊C4×C41—21no—
158C2×C22⋊C4×C41D412yes—
159C2×C42×C41—21no—
160C2×C42×C41—21no—
161#104×C41—28no—
162#102×C41—28no—
163#99×C41—28no—
164C24×C41—22no—
165C24×C41—21no—
166C24×C41—22no—
167C24×C41—21no—
168C24×C41—22no—
169C24×C41—41no—
170C24×C41—41no—
171C24×C41—41no—
172C24×C41—41no—
173C24×C41—84no—
174C24×C41C2×D411yescharacteristic
175#41×C41—22no—
176#41×C41—22no—
177#41×C41—22no—
178#41×C41—22no—
179#41×C41—22no—
180#41×C41—22no—
181#41×C41—22no—
182#41×C41—22no—
183#41×C41—22no—
184#41×C41—22no—
185#41×C41—22no—
186#41×C41—22no—
187#41×C41—22no—
188#41×C41—22no—
189#41×C41—22no—
190#41×C41—22no—
191#41×C41—41no—
192#41×C41—41no—
193#41×C41—41no—
194#41×C41—41no—
195#41×C41—41no—
196#41×C41—41no—
197#41×C41—41no—
198#41×C41—41no—
199#41×C41—41no—
200#41×C41—41no—
201#41×C41—41no—
202#41×C41—41no—
203#41×C41—41no—
204#41×C41—41no—
205#41×C41—41no—
206#41×C41—41no—
207C2×Q8×C41—21no—
208C2×Q8×C41—21no—
209C2×Q8×C41—21no—
210C2×Q8×C41—21no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41—21no—
214C2×Q8×C41—21no—
215C2×Q8×C41—21no—
216C2×Q8×C41—21no—
217C2×Q8×C41C2×D412yes—
218C2×Q8×C41C2×D412yescomplemented
219C2×D4×C41—22no—
220C2×D4×C41—22no—
221C2×D4×C41—22no—
222C2×D4×C41—22no—
223C2×D4×C41—216no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—22no—
227C2×D4×C41—22no—
228C2×D4×C41—21no—
229C2×D4×C41—21no—
230C2×D4×C41—22no—
231C2×D4×C41—22no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—22no—
235C2×D4×C41—22no—
236C2×D4×C41—21no—
237C2×D4×C41—22no—
238C2×D4×C41—22no—
239C2×D4×C41—22no—
240C2×D4×C41—22no—
241C2×D4×C41—21no—
242C2×D4×C41—21no—
243C2×D4×C41—21no—
244C2×D4×C41—22no—
245C2×D4×C41—22no—
246C2×D4×C41—22no—
247C2×D4×C41—22no—
248C2×D4×C41—22no—
249C2×D4×C41—41no—
250C2×D4×C41—41no—
251C2×D4×C41—41no—
252C2×D4×C41—41no—
253C2×D4×C41—41no—
254C2×D4×C41—41no—
255C2×D4×C41—41no—
256C2×D4×C41—41no—
257C2×D4×C41—41no—
258C2×D4×C41—41no—
259C2×D4×C41—41no—
260C2×D4×C41—41no—
261C2×D4×C41—41no—
262C2×D4×C41—41no—
263C2×D4×C41—41no—
264C2×D4×C41—41no—
265C2×D4×C41—41no—
266C2×D4×C41—41no—
267C2×D4×C41—41no—
268C2×D4×C41—41no—
269C2×D4×C41—88no—
270C2×D4×C41C2×D414yes—
271C2×D4×C41C2×D412yes—
272C2×D4×C41C2×D412yescomplemented
273C22×C4×C41—22no—
274C22×C4×C41—21no—
275C22×C4×C41—21no—
276C22×C4×C41—22no—
277C22×C4×C41—22no—
278C22×C4×C41—22no—
279C22×C4×C41—22no—
280C22×C4×C41—41no—
281C22×C4×C41—41no—
282C22×C4×C41—41no—
283C22×C4×C41—41no—
284C22×C4×C41—41no—
285C22×C4×C41—41no—
286C22×C4×C41—41no—
287C22×C4×C41—41no—
288C22×C4×C41—41no—
289C22×C4×C41C2×D411yescharacteristic
290C22×C4×C41C2×D411yescharacteristic
291C22×C4×C41C2×D411yescharacteristic
292C22×C4×C41C2×D411yescharacteristic
293C22×C4×C41C2×D411yescharacteristic
294C22×C4×C41C2×D411yescharacteristic
295C22×C4×C41C2×D411yescharacteristic
296C22×C4×C41C2×D411yescharacteristic
297C22×C4×C41C2×D411yescharacteristic
298C22×C4×C41C2×D411yescharacteristic
299C22×C4×C41C2×D411yescharacteristic
300C22×C4×C41#4111yescharacteristic
301C22×C4×C41#4111yescharacteristic
302C22×C4×C41C2411yescharacteristic
303Q16×C41—28no—
304SD16×C41—216no—
305SD16×C41—28no—
306SD16×C41—28no—
307D8×C41—216no—
308D8×C41—28no—
309M16×C41—22no—
310M16×C41—22no—
311M16×C41—22no—
312M16×C41—22no—
313M16×C41—22no—
314M16×C41—22no—
315M16×C41—22no—
316M16×C41C2×D414yescomplemented
317C2×C8×C41—22no—
318C2×C8×C41—22no—
319C2×C8×C41—22no—
320C2×C8×C41—22no—
321C2×C8×C41—22no—
322C2×C8×C41C2×D414yescomplemented
323C4⋊C4×C41—22no—
324C4⋊C4×C41—22no—
325C4⋊C4×C41—22no—
326C4⋊C4×C41—41no—
327C22⋊C4×C41—216no—
328C22⋊C4×C41—22no—
329C22⋊C4×C41—22no—
330C22⋊C4×C41—41no—
331C22⋊C4×C41C2×D414yes—
332C42×C41—22no—
333C42×C41—22no—
334C42×C41—22no—
335C42×C41—41no—
336C23×C41—24no—
337C23×C41—22no—
338C23×C41—22no—
339C23×C41—42no—
340C23×C41—44no—
341C23×C41—48no—
342C23×C41—42no—
343C23×C41—42no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—42no—
347C23×C41—42no—
348C23×C41—42no—
349C23×C41—41no—
350C23×C41—41no—
351C23×C41—42no—
352C23×C41—82no—
353C23×C41—84no—
354C23×C41—84no—
355C23×C41—84no—
356C23×C41—84no—
357C23×C41—84no—
358C23×C41—84no—
359C23×C41#12011yescharacteristic
360C23×C41#12011yescharacteristic
361C23×C41#12111yescharacteristic
362C23×C41#12111yescharacteristic
363C23×C41#12711yescharacteristic
364C23×C41#12711yescharacteristic
365C23×C41C22×D411yescharacteristic
366Q8×C41—22no—
367Q8×C41—22no—
368Q8×C41—22no—
369Q8×C41—22no—
370Q8×C41—41no—
371Q8×C41—41no—
372Q8×C41—41no—
373Q8×C41—41no—
374D4×C41—22no—
375D4×C41—24no—
376D4×C41—22no—
377D4×C41—22no—
378D4×C41—24no—
379D4×C41—22no—
380D4×C41—42no—
381D4×C41—42no—
382D4×C41—42no—
383D4×C41—42no—
384D4×C41—42no—
385D4×C41—42no—
386D4×C41—42no—
387D4×C41—42no—
388D4×C41—42no—
389D4×C41—42no—
390D4×C41—42no—
391D4×C41—42no—
392D4×C41—42no—
393D4×C41—42no—
394D4×C41—41no—
395D4×C41—41no—
396D4×C41—41no—
397D4×C41—41no—
398D4×C41—816no—
399C2×C4×C41—24no—
400C2×C4×C41—22no—
401C2×C4×C41—22no—
402C2×C4×C41—44no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—42no—
408C2×C4×C41—42no—
409C2×C4×C41—42no—
410C2×C4×C41—42no—
411C2×C4×C41—42no—
412C2×C4×C41—42no—
413C2×C4×C41—42no—
414C2×C4×C41—42no—
415C2×C4×C41—42no—
416C2×C4×C41—82no—
417C2×C4×C41#12011yescharacteristic
418C2×C4×C41#12011yescharacteristic
419C2×C4×C41#12011yescharacteristic
420C2×C4×C41#12011yescharacteristic
421C2×C4×C41#12011yescharacteristic
422C2×C4×C41#12011yescharacteristic
423C2×C4×C41#12011yescharacteristic
424C2×C4×C41#12011yescharacteristic
425C2×C4×C41#12011yescharacteristic
426C2×C4×C41#12011yescharacteristic
427C2×C4×C41#12111yescharacteristic
428C2×C4×C41#12111yescharacteristic
429C2×C4×C41#12111yescharacteristic
430C2×C4×C41#12111yescharacteristic
431C2×C4×C41#12111yescharacteristic
432C2×C4×C41#12111yescharacteristic
433C2×C4×C41#12111yescharacteristic
434C2×C4×C41#12111yescharacteristic
435C2×C4×C41#12111yescharacteristic
436C2×C4×C41#12111yescharacteristic
437C2×C4×C41#12711yescharacteristic
438C2×C4×C41#12711yescharacteristic
439C2×C4×C41C22×D411yescharacteristic
440C2×C4×C41C22×D411yescharacteristic
441C2×C4×C41C22×D411yescharacteristic
442C2×C4×C41C22×D411yescharacteristic
443C2×C4×C41C22×D411yescharacteristic
444C2×C4×C41C2×#4111yescharacteristic
445C8×C41—24no—
446C8×C41—24no—
447C2×#2008C4111yesmaximal, characteristic, direct product factor, Sylow
448C22×C41—22no—
449C22×C41—22no—
450C22×C41—22no—
451C22×C41—41no—
452C22×C41—41no—
453C22×C41—41no—
454C22×C41—41no—
455C22×C41—44no—
456C22×C41—48no—
457C22×C41—42no—
458C22×C41—42no—
459C22×C41—44no—
460C22×C41—82no—
461C22×C41—82no—
462C22×C41—84no—
463C22×C41—82no—
464C22×C41—84no—
465C22×C41—84no—
466C22×C41—84no—
467C22×C41—84no—
468C22×C41—82no—
469C22×C41—84no—
470C22×C41—82no—
471C22×C41#39211yescharacteristic
472C22×C41#39211yescharacteristic
473C22×C41#39211yescharacteristic
474C22×C41#39211yescharacteristic
475C22×C41C2×#12011yescharacteristic
476C22×C41C2×#12111yescharacteristic
477C22×C41C2×#12711yescharacteristic
478C4×C41—44no—
479C4×C41—42no—
480C4×C41—42no—
481C4×C41—82no—
482C4×C41#39211yescharacteristic
483C4×C41#39211yescharacteristic
484C4×C41#39211yescharacteristic
485C4×C41#39211yescharacteristic
486C4×C41C2×#12011yescharacteristic
487C4×C41C2×#12011yescharacteristic
488C4×C41C2×#12111yescharacteristic
489C4×C41C2×#12111yescharacteristic
490C2×#575C2×C4111yescharacteristic, complemented
491C22×AGL(1,ℤ/8)C2×C4111yescharacteristic, complemented
492C2×#535C2×C4111yescharacteristic, complemented
493C2×#421C2×C4111yescharacteristic, complemented
494C2×#418C2×C4111yescharacteristic, complemented
495C2×#410C2×C4111yescharacteristic, complemented
496#2008C2×C4118yesdirect product factor
497C2×#344C2×C4111yescharacteristic, complemented
498C2×C41—21no—
499C2×C41—21no—
500C2×C41—21no—
501C2×C41—21no—
502C2×C41—21no—
503C2×C41—21no—
504C2×C41—82no—
505C2×C41—84no—
506C2×C41—82no—
507C2×C41#200812yesdirect product factor
508C2×C41C2×#39211yescharacteristic
509C22×#41C22×C4111yescharacteristic
510C22×#41C22×C4111yescharacteristic
511C23×D4C22×C4111yescharacteristic
512#575—22no—
513#575—22no—
514#575—22no—
515#575C22×C4114yescomplemented
516C2×#137—21no—
517C2×#137—21no—
518C2×AGL(1,ℤ/8)—22no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—21no—
522C2×AGL(1,ℤ/8)—21no—
523C2×AGL(1,ℤ/8)—22no—
524C2×AGL(1,ℤ/8)—22no—
525C2×AGL(1,ℤ/8)C22×C4114yescomplemented
526C2×#135—22no—
527C22×SD16—21no—
528C22×D8—21no—
529C22×M16C22×C4111yescharacteristic
530C22×M16C22×C4111yescharacteristic
531#535—22no—
532#535—22no—
533#535—22no—
534#535C22×C4114yescomplemented
535C2×#127—21no—
536C2×#124—21no—
537C2×#121—22no—
538C2×#120—22no—
539C2×#117C22×C4111yescharacteristic
540C2×#117C22×C4111yescharacteristic
541#421—22no—
542#421C22×C4114yescomplemented
543C2×#104—22no—
544#418—22no—
545#418C22×C4114yescomplemented
546C2×#102—22no—
547#410—22no—
548#410C22×C4114yescomplemented
549C2×#99—22no—
550#344C22×C4114yescomplemented
551C41C2×#200811yescharacteristic, direct product factor, Sylow
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41D4×C4112yes—
574C2×#41D4×C4112yescomplemented
575C2×#41C23×C4112yes—
576C2×#41C23×C4112yes—
577C22×Q8D4×C4111yescharacteristic
578C22×Q8D4×C4111yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—24no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4D4×C4112yes—
594C22×D4D4×C4111yescharacteristic
595C22×D4D4×C4112yes—
596C22×D4D4×C4111yescharacteristic, complemented
597C22×D4C23×C4112yes—
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C23×C4111yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—28no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—24no—
612AGL(1,ℤ/8)—28no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—24no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—22no—
624C2×D8—24no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16D4×C4112yescomplemented
633C2×M16D4×C4112yescomplemented
634C2×M16D4×C4112yescomplemented
635C2×M16C23×C4112yes—
636C2×M16C23×C4112yes—
637C22×C8—21no—
638C22×C8D4×C4112yescomplemented
639#127—24no—
640#127—24no—
641#124—24no—
642#124—24no—
643#121—28no—
644#121—28no—
645#120—28no—
646#120—28no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117D4×C4112yes—
653#117C23×C4112yes—
654#117C23×C4112yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4D4×C4112yes—
660C2×C42—21no—
661C2×C42—21no—
662#104—28no—
663#102—28no—
664#99—28no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C4111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C4112yes—
719C2×Q8C2×D4×C4112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C4114yes—
772C2×D4C2×D4×C4112yes—
773C2×D4C2×D4×C4112yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C4111yescharacteristic
791C22×C4C2×D4×C4111yescharacteristic
792C22×C4C2×D4×C4111yescharacteristic
793C22×C4C2×D4×C4111yescharacteristic
794C22×C4C2×D4×C4111yescharacteristic
795C22×C4C2×D4×C4111yescharacteristic
796C22×C4C2×D4×C4111yescharacteristic
797C22×C4C2×D4×C4111yescharacteristic
798C22×C4C2×D4×C4111yescharacteristic
799C22×C4C2×D4×C4111yescharacteristic
800C22×C4C2×D4×C4111yescharacteristic
801C22×C4#41×C4111yescharacteristic
802C22×C4#41×C4111yescharacteristic
803C22×C4C24×C4111yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C4114yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C4114yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C4114yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—42no—
844C23—42no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23#120×C4111yescharacteristic
861C23#120×C4111yescharacteristic
862C23#121×C4111yescharacteristic
863C23#121×C4111yescharacteristic
864C23#127×C4111yescharacteristic
865C23#127×C4111yescharacteristic
866C23C22×D4×C4111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—42no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4#120×C4111yescharacteristic
919C2×C4#120×C4111yescharacteristic
920C2×C4#120×C4111yescharacteristic
921C2×C4#120×C4111yescharacteristic
922C2×C4#120×C4111yescharacteristic
923C2×C4#120×C4111yescharacteristic
924C2×C4#120×C4111yescharacteristic
925C2×C4#120×C4111yescharacteristic
926C2×C4#120×C4111yescharacteristic
927C2×C4#120×C4111yescharacteristic
928C2×C4#121×C4111yescharacteristic
929C2×C4#121×C4111yescharacteristic
930C2×C4#121×C4111yescharacteristic
931C2×C4#121×C4111yescharacteristic
932C2×C4#121×C4111yescharacteristic
933C2×C4#121×C4111yescharacteristic
934C2×C4#121×C4111yescharacteristic
935C2×C4#121×C4111yescharacteristic
936C2×C4#121×C4111yescharacteristic
937C2×C4#121×C4111yescharacteristic
938C2×C4#127×C4111yescharacteristic
939C2×C4#127×C4111yescharacteristic
940C2×C4C22×D4×C4111yescharacteristic
941C2×C4C22×D4×C4111yescharacteristic
942C2×C4C22×D4×C4111yescharacteristic
943C2×C4C22×D4×C4111yescharacteristic
944C2×C4C22×D4×C4111yescharacteristic
945C2×C4C2×#41×C4111yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C41×#39211yescharacteristic
972C22C41×#39211yescharacteristic
973C22C41×#39211yescharacteristic
974C22C41×#39211yescharacteristic
975C22C2×#120×C4111yescharacteristic
976C22C2×#121×C4111yescharacteristic
977C22C2×#127×C4111yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C41×#39211yescharacteristic
983C4C41×#39211yescharacteristic
984C4C41×#39211yescharacteristic
985C4C41×#39211yescharacteristic
986C4C2×#120×C4111yescharacteristic
987C4C2×#120×C4111yescharacteristic
988C4C2×#121×C4111yescharacteristic
989C4C2×#121×C4111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C41×#200812yesdirect product factor
1000C2C2×C41×#39211yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C41C2semidirect
3. C2×C41×#535C2semidirect
4. C2×C41×#421C2semidirect
5. C2×C41×#418C2semidirect
6. C2×C41×#410C2semidirect
7. C41×#2008C2direct (N × H)
8. C2×C41×#344C2semidirect
15. C41×#575C22semidirect
25. C2×AGL(1,ℤ/8)×C41C22semidirect
34. C41×#535C22semidirect
42. C41×#421C22semidirect
45. C41×#418C22semidirect
48. C41×#410C22semidirect
50. C41×#344C22semidirect
73. C2×#41×C41D4semidirect
77. C22×Q8×C41D4semidirect
95. C22×D4×C41D4semidirect
131. C2×M16×C41D4semidirect
132. C2×M16×C41D4semidirect
133. C2×M16×C41D4semidirect
137. C22×C8×C41D4semidirect
218. C2×Q8×C41C2×D4semidirect
272. C2×D4×C41C2×D4semidirect
316. M16×C41C2×D4semidirect
322. C2×C8×C41C2×D4semidirect
447. C2×#2008C41direct (N × H)
490. C2×#575C2×C41semidirect
491. C22×AGL(1,ℤ/8)C2×C41semidirect
492. C2×#535C2×C41semidirect
493. C2×#421C2×C41semidirect
494. C2×#418C2×C41semidirect
495. C2×#410C2×C41semidirect
496. #2008C2×C41direct (N × H)
497. C2×#344C2×C41semidirect
507. C2×C41#2008direct (N × H)
515. #575C22×C41semidirect
525. C2×AGL(1,ℤ/8)C22×C41semidirect
534. #535C22×C41semidirect
542. #421C22×C41semidirect
545. #418C22×C41semidirect
548. #410C22×C41semidirect
550. #344C22×C41semidirect
551. C41C2×#2008direct (N × H)
574. C2×#41D4×C41semidirect
578. C22×Q8D4×C41semidirect
596. C22×D4D4×C41semidirect
632. C2×M16D4×C41semidirect
633. C2×M16D4×C41semidirect
634. C2×M16D4×C41semidirect
638. C22×C8D4×C41semidirect
719. C2×Q8C2×D4×C41semidirect
773. C2×D4C2×D4×C41semidirect
817. M16C2×D4×C41semidirect
823. C2×C8C2×D4×C41semidirect
999. C2C41×#2008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5752
C22×AGL(1,ℤ/8)×C412
C2×C41×#5352
C2×C41×#4212
C2×C41×#4182
C2×C41×#4102
C41×#20082
C2×C41×#3442
C2×#200841