Finite Group Databasebeta

← C41×#24257 #23800458

Subgroups — C41×#24257 #23800458

Order 10496.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#546C211yesmaximal, characteristic, complemented
2C2×C41×#463C211yesmaximal, characteristic, complemented
3C2×C41×#449C211yesmaximal, characteristic, complemented
4C2×C41×#447C211yesmaximal, characteristic, complemented
5C2×C41×#442C211yesmaximal, characteristic, complemented
6C41×#2537C211yesmaximal, characteristic, complemented
7C41×#2035C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1959C211yesmaximal, characteristic, complemented
12C41×#1955C211yesmaximal, characteristic, complemented
13C41×#1802C211yesmaximal, characteristic, complemented
14C41×#1788C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic, complemented
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C41×#546—24no—
22C41×#546—24no—
23C2×#124×C41C2211yescharacteristic
24C2×#123×C41—21no—
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41—21no—
27C2×#121×C41—21no—
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic, complemented
31C2×#120×C41—21no—
32C2×C4×D4×C41C2211yescharacteristic
33C2×C4×D4×C41C2211yescharacteristic
34C2×C4×D4×C41C2211yescharacteristic, complemented
35C22×C22⋊C4×C41—21no—
36C41×#463—24no—
37C41×#449—24no—
38C41×#447—24no—
39C41×#442—24no—
40C2×#106×C41C2211yescharacteristic, complemented
41C2×C4⋊C8×C41C2211yescharacteristic, complemented
42C2×#103×C41C2211yescharacteristic, complemented
43C2×#103×C41C2211yescharacteristic, complemented
44C2×#103×C41C2211yescharacteristic, complemented
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#102×C41C2211yescharacteristic
49C2×#102×C41C2211yescharacteristic
50C2×#102×C41C2211yescharacteristic
51C2×#102×C41C2211yescharacteristic, complemented
52C2×C22⋊C8×C41C2211yescharacteristic
53C2×C22⋊C8×C41C2211yescharacteristic
54C2×C22⋊C8×C41C2211yescharacteristic, complemented
55C2×C22⋊C8×C41C2211yescharacteristic, complemented
56C2×#97×C41C2211yescharacteristic, complemented
57C41×#394—21no—
58C41×#394—21no—
59C41×#384C2211yescharacteristic, complemented
60C41×#380—21no—
61C41×#380C2211yescharacteristic
62C41×#380C2211yescharacteristic, complemented
63C41×#340C2211yescharacteristic, complemented
64C41×#340C2211yescharacteristic, complemented
65C25×C41—21no—
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—22no—
69C2×#41×C41—22no—
70C2×#41×C41—41no—
71C2×#41×C41—41no—
72C22×Q8×C41C2311yescharacteristic
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—22no—
76C22×D4×C41—22no—
77C22×D4×C41—22no—
78C22×D4×C41—22no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—21no—
82C22×D4×C41—41no—
83C22×D4×C41—41no—
84C22×D4×C41D411yescharacteristic
85C22×D4×C41C2311yescharacteristic
86C22×D4×C41C2311yescharacteristic
87C22×D4×C41C2311yescharacteristic
88C23×C4×C41—21no—
89C23×C4×C41—21no—
90C23×C4×C41—21no—
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2311yescharacteristic
93C2×SD16×C41—22no—
94C2×SD16×C41—22no—
95C2×SD16×C41—41no—
96C2×D8×C41—22no—
97C2×D8×C41—22no—
98C2×D8×C41—22no—
99C2×D8×C41—22no—
100C2×D8×C41—41no—
101C2×D8×C41D414yescomplemented
102C22×C8×C41C2311yescharacteristic
103C22×C8×C41C2311yescharacteristic
104C22×C8×C41C2311yescharacteristic
105C22×C8×C41C2311yescharacteristic
106#124×C41—22no—
107#124×C41D414yescomplemented
108#123×C41—28no—
109C22⋊Q8×C41—22no—
110C22⋊Q8×C41—22no—
111#121×C41—28no—
112#121×C41—22no—
113#121×C41—22no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—41no—
117#121×C41—41no—
118#121×C41—44no—
119#120×C41—28no—
120C4×D4×C41—22no—
121C4×D4×C41—22no—
122C4×D4×C41—22no—
123C4×D4×C41—22no—
124C4×D4×C41—22no—
125C4×D4×C41D414yescomplemented
126C2×C4⋊C4×C41—21no—
127C2×C4⋊C4×C41—21no—
128C2×C4⋊C4×C41—21no—
129C2×C4⋊C4×C41D411yescharacteristic
130C2×C4⋊C4×C41C2311yescharacteristic
131C2×C4⋊C4×C41C2311yescharacteristic
132C2×C4⋊C4×C41C2311yescharacteristic
133C2×C4⋊C4×C41C2311yescharacteristic
134C2×C22⋊C4×C41—28no—
135C2×C22⋊C4×C41—21no—
136C2×C22⋊C4×C41—21no—
137C2×C22⋊C4×C41—21no—
138C2×C22⋊C4×C41—21no—
139C2×C22⋊C4×C41—21no—
140C2×C22⋊C4×C41—21no—
141C2×C22⋊C4×C41—21no—
142C2×C22⋊C4×C41—21no—
143C2×C22⋊C4×C41—21no—
144C2×C22⋊C4×C41—21no—
145C2×C22⋊C4×C41D411yescharacteristic
146C2×C22⋊C4×C41D411yescharacteristic
147C2×C42×C41C2311yescharacteristic
148#106×C41—22no—
149C4⋊C8×C41—22no—
150#103×C41—22no—
151#103×C41—22no—
152#103×C41—41no—
153#102×C41—22no—
154#102×C41—22no—
155#102×C41—22no—
156#102×C41—22no—
157#102×C41—22no—
158#102×C41—22no—
159#102×C41—41no—
160C22⋊C8×C41—22no—
161C22⋊C8×C41—22no—
162C22⋊C8×C41—41no—
163C22⋊C8×C41—41no—
164#97×C41—22no—
165#95×C41—21no—
166#95×C41—21no—
167C24×C41—21no—
168C24×C41—24no—
169C24×C41—21no—
170C24×C41—21no—
171C24×C41—42no—
172C24×C41—42no—
173C24×C41—42no—
174C24×C41—42no—
175C24×C41—81no—
176C24×C41—81no—
177C24×C41C2×D411yescharacteristic
178C24×C41C2×D411yescharacteristic
179#41×C41—44no—
180#41×C41—44no—
181#41×C41—44no—
182#41×C41—44no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41C2×D412yes—
189C2×D4×C41—24no—
190C2×D4×C41—24no—
191C2×D4×C41—22no—
192C2×D4×C41—24no—
193C2×D4×C41—22no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—41no—
208C2×D4×C41—42no—
209C2×D4×C41—42no—
210C2×D4×C41—44no—
211C2×D4×C41—44no—
212C2×D4×C41—44no—
213C2×D4×C41—42no—
214C2×D4×C41—42no—
215C2×D4×C41—44no—
216C2×D4×C41—42no—
217C2×D4×C41—42no—
218C2×D4×C41—42no—
219C2×D4×C41—42no—
220C2×D4×C41—81no—
221C2×D4×C41—81no—
222C2×D4×C41—81no—
223C2×D4×C41—81no—
224C2×D4×C41C2×D412yes—
225C2×D4×C41C2×D412yes—
226C2×D4×C41C2×D412yes—
227C2×D4×C41C2×D412yes—
228C2×D4×C41#4112yes—
229C22×C4×C41—24no—
230C22×C4×C41—21no—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—24no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—42no—
249C22×C4×C41—42no—
250C22×C4×C41—42no—
251C22×C4×C41—42no—
252C22×C4×C41—42no—
253C22×C4×C41—81no—
254C22×C4×C41—81no—
255C22×C4×C41C2×D411yescharacteristic
256C22×C4×C41C2×D411yescharacteristic
257C22×C4×C41C2×D411yescharacteristic
258C22×C4×C41C2×D411yescharacteristic
259C22×C4×C41C2411yescharacteristic
260SD16×C41—44no—
261D8×C41—28no—
262D8×C41—44no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—21no—
271C2×C8×C41—21no—
272C2×C8×C41—21no—
273C2×C8×C41—21no—
274C2×C8×C41C2×D412yes—
275C4⋊C4×C41—24no—
276C4⋊C4×C41—22no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—42no—
285C4⋊C4×C41—81no—
286C4⋊C4×C41C2×D412yes—
287C22⋊C4×C41—24no—
288C22⋊C4×C41—24no—
289C22⋊C4×C41—22no—
290C22⋊C4×C41—24no—
291C22⋊C4×C41—24no—
292C22⋊C4×C41—24no—
293C22⋊C4×C41—22no—
294C22⋊C4×C41—42no—
295C22⋊C4×C41—42no—
296C22⋊C4×C41—42no—
297C22⋊C4×C41—42no—
298C22⋊C4×C41—42no—
299C42×C41C2×D412yes—
300C42×C41C2×D412yes—
301C23×C41—21no—
302C23×C41—22no—
303C23×C41—21no—
304C23×C41—22no—
305C23×C41—21no—
306C23×C41—22no—
307C23×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—22no—
311C23×C41—21no—
312C23×C41—22no—
313C23×C41—21no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—21no—
317C23×C41—21no—
318C23×C41—21no—
319C23×C41—48no—
320C23×C41—48no—
321C23×C41—41no—
322C23×C41—41no—
323C23×C41—41no—
324C23×C41—41no—
325C23×C41—41no—
326C23×C41—41no—
327C23×C41—41no—
328C23×C41—41no—
329C23×C41—41no—
330C23×C41—41no—
331C23×C41—41no—
332C23×C41—41no—
333C23×C41—41no—
334C23×C41—41no—
335C23×C41—41no—
336C23×C41—41no—
337C23×C41—84no—
338C23×C41—84no—
339C23×C41—84no—
340C23×C41—84no—
341C23×C41—84no—
342C23×C41AGL(1,ℤ/8)12yes—
343C23×C41C22×D411yescharacteristic
344Q8×C41—22no—
345Q8×C41—22no—
346Q8×C41—41no—
347Q8×C41—41no—
348D4×C41—22no—
349D4×C41—22no—
350D4×C41—22no—
351D4×C41—22no—
352D4×C41—22no—
353D4×C41—22no—
354D4×C41—22no—
355D4×C41—44no—
356D4×C41—48no—
357D4×C41—48no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—41no—
361D4×C41—41no—
362D4×C41—84no—
363D4×C41—84no—
364D4×C41—84no—
365D4×C41#12114yescomplemented
366C2×C4×C41—21no—
367C2×C4×C41—21no—
368C2×C4×C41—21no—
369C2×C4×C41—21no—
370C2×C4×C41—22no—
371C2×C4×C41—21no—
372C2×C4×C41—22no—
373C2×C4×C41—21no—
374C2×C4×C41—21no—
375C2×C4×C41—21no—
376C2×C4×C41—21no—
377C2×C4×C41—21no—
378C2×C4×C41—48no—
379C2×C4×C41—41no—
380C2×C4×C41—41no—
381C2×C4×C41—41no—
382C2×C4×C41—41no—
383C2×C4×C41—41no—
384C2×C4×C41—41no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—41no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—41no—
396C2×C4×C41—41no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—84no—
401C2×C4×C41—84no—
402C2×C4×C41#12012yes—
403C2×C4×C41#12012yes—
404C2×C4×C41C22×D411yescharacteristic
405C2×C4×C41C22×D411yescharacteristic
406C2×C4×C41C22×D411yescharacteristic
407C2×C4×C41C2×#4111yescharacteristic
408C2×C4×C41H(5,𝔽2)11yescharacteristic
409C2×C4×C41H(5,𝔽2)11yescharacteristic
410C8×C41—22no—
411C8×C41—41no—
412C8×C41—41no—
413C8×C41—41no—
414#24257C4111yesmaximal, characteristic, direct product factor, Sylow
415C22×C41—24no—
416C22×C41—22no—
417C22×C41—22no—
418C22×C41—22no—
419C22×C41—41no—
420C22×C41—42no—
421C22×C41—42no—
422C22×C41—41no—
423C22×C41—42no—
424C22×C41—42no—
425C22×C41—41no—
426C22×C41—42no—
427C22×C41—41no—
428C22×C41—42no—
429C22×C41—41no—
430C22×C41—42no—
431C22×C41—42no—
432C22×C41—41no—
433C22×C41—42no—
434C22×C41—41no—
435C22×C41—42no—
436C22×C41—41no—
437C22×C41—42no—
438C22×C41—41no—
439C22×C41—42no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—816no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41—81no—
451C22×C41C2×#12011yescharacteristic
452C22×C41D4211yescharacteristic
453C22×C41#54611yescharacteristic
454C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C41#57511yescharacteristic
456C22×C41#57611yescharacteristic
457C22×C41#57711yescharacteristic
458C4×C41—22no—
459C4×C41—22no—
460C4×C41—41no—
461C4×C41—41no—
462C4×C41—42no—
463C4×C41—42no—
464C4×C41—81no—
465C4×C41—81no—
466C4×C41—81no—
467C4×C41C2×#12111yescharacteristic
468C4×C41#53511yescharacteristic
469C4×C41D4211yescharacteristic
470C4×C41#54611yescharacteristic
471C2×#546C2×C4111yescharacteristic, complemented
472C2×#463C2×C4111yescharacteristic, complemented
473C2×#449C2×C4111yescharacteristic, complemented
474C2×#447C2×C4111yescharacteristic, complemented
475C2×#442C2×C4111yescharacteristic, complemented
476#2537C2×C4111yescharacteristic, complemented
477#2035C2×C4111yescharacteristic, complemented
478#2034C2×C4111yescharacteristic, complemented
479#2000C2×C4111yescharacteristic, complemented
480#1999C2×C4111yescharacteristic, complemented
481#1959C2×C4111yescharacteristic, complemented
482#1955C2×C4111yescharacteristic, complemented
483#1802C2×C4111yescharacteristic, complemented
484#1788C2×C4111yescharacteristic, complemented
485#1786C2×C4111yescharacteristic, complemented
486C2×C41—42no—
487C2×C41—44no—
488C2×C41—81no—
489C2×C41—82no—
490C2×C41—82no—
491C2×C41#240811yescharacteristic
492C2×C41#300611yescharacteristic
493C2×C41#301211yescharacteristic
494C2×C41#326411yescharacteristic
495C2×C41#326711yescharacteristic
496C2×C41#330611yescharacteristic
497C2×C41#331911yescharacteristic
498C22×#41C22×C4111yescharacteristic
499C23×D4C22×C4111yescharacteristic
500C22×SD16C22×C4111yescharacteristic, complemented
501C22×D8C22×C4111yescharacteristic
502C22×D8C22×C4111yescharacteristic
503#546—24no—
504#546—24no—
505C2×#124C22×C4111yescharacteristic
506C2×#123—21no—
507C2×C22⋊Q8C22×C4111yescharacteristic
508C2×#121—21no—
509C2×#121—21no—
510C2×#121C22×C4111yescharacteristic
511C2×#121C22×C4111yescharacteristic
512C2×#121C22×C4111yescharacteristic, complemented
513C2×#120—21no—
514C2×C4×D4C22×C4111yescharacteristic
515C2×C4×D4C22×C4111yescharacteristic
516C2×C4×D4C22×C4111yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#463—24no—
519#449—24no—
520#447—24no—
521#442—24no—
522C2×#106C22×C4111yescharacteristic, complemented
523C2×C4⋊C8C22×C4111yescharacteristic, complemented
524C2×#103C22×C4111yescharacteristic, complemented
525C2×#103C22×C4111yescharacteristic, complemented
526C2×#103C22×C4111yescharacteristic, complemented
527C2×#102C22×C4111yescharacteristic
528C2×#102C22×C4111yescharacteristic
529C2×#102C22×C4111yescharacteristic
530C2×#102C22×C4111yescharacteristic
531C2×#102C22×C4111yescharacteristic
532C2×#102C22×C4111yescharacteristic
533C2×#102C22×C4111yescharacteristic, complemented
534C2×C22⋊C8C22×C4111yescharacteristic
535C2×C22⋊C8C22×C4111yescharacteristic
536C2×C22⋊C8C22×C4111yescharacteristic, complemented
537C2×C22⋊C8C22×C4111yescharacteristic, complemented
538C2×#97C22×C4111yescharacteristic, complemented
539#394—21no—
540#394—21no—
541#384C22×C4111yescharacteristic, complemented
542#380—21no—
543#380C22×C4111yescharacteristic
544#380C22×C4111yescharacteristic, complemented
545#340C22×C4111yescharacteristic, complemented
546#340C22×C4111yescharacteristic, complemented
547C41#2425711yescharacteristic, direct product factor, Sylow
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C4111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C4111yescharacteristic
568C22×D4C23×C4111yescharacteristic
569C22×D4C23×C4111yescharacteristic
570C22×D4C23×C4111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C4111yescharacteristic
575C23×C4C23×C4111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C4114yescomplemented
585C22×C8C23×C4111yescharacteristic
586C22×C8C23×C4111yescharacteristic
587C22×C8C23×C4111yescharacteristic
588C22×C8C23×C4111yescharacteristic
589#124—22no—
590#124D4×C4114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C4114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C4111yescharacteristic
613C2×C4⋊C4C23×C4111yescharacteristic
614C2×C4⋊C4C23×C4111yescharacteristic
615C2×C4⋊C4C23×C4111yescharacteristic
616C2×C4⋊C4C23×C4111yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C4111yescharacteristic
629C2×C22⋊C4D4×C4111yescharacteristic
630C2×C42C23×C4111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C4111yescharacteristic
661C24C2×D4×C4111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C4112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C4112yes—
708C2×D4C2×D4×C4112yes—
709C2×D4C2×D4×C4112yes—
710C2×D4C2×D4×C4112yes—
711C2×D4#41×C4112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C4111yescharacteristic
739C22×C4C2×D4×C4111yescharacteristic
740C22×C4C2×D4×C4111yescharacteristic
741C22×C4C2×D4×C4111yescharacteristic
742C22×C4C24×C4111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C4112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C4112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C4112yes—
783C42C2×D4×C4112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C4112yes—
826C23C22×D4×C4111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C4114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C4112yes—
886C2×C4#120×C4112yes—
887C2×C4C22×D4×C4111yescharacteristic
888C2×C4C22×D4×C4111yescharacteristic
889C2×C4C22×D4×C4111yescharacteristic
890C2×C4C2×#41×C4111yescharacteristic
891C2×C4H(5,𝔽2)×C4111yescharacteristic
892C2×C4H(5,𝔽2)×C4111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C4111yescharacteristic
934C22D42×C4111yescharacteristic
935C22C41×#54611yescharacteristic
936C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
937C22C41×#57511yescharacteristic
938C22C41×#57611yescharacteristic
939C22C41×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C4111yescharacteristic
950C4C41×#53511yescharacteristic
951C4D42×C4111yescharacteristic
952C4C41×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C41×#240811yescharacteristic
959C2C41×#300611yescharacteristic
960C2C41×#301211yescharacteristic
961C2C41×#326411yescharacteristic
962C2C41×#326711yescharacteristic
963C2C41×#330611yescharacteristic
964C2C41×#331911yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#546C2semidirect
2. C2×C41×#463C2semidirect
3. C2×C41×#449C2semidirect
4. C2×C41×#447C2semidirect
5. C2×C41×#442C2semidirect
6. C41×#2537C2semidirect
7. C41×#2035C2semidirect
8. C41×#2034C2semidirect
9. C41×#2000C2semidirect
10. C41×#1999C2semidirect
11. C41×#1959C2semidirect
12. C41×#1955C2semidirect
13. C41×#1802C2semidirect
14. C41×#1788C2semidirect
15. C41×#1786C2semidirect
18. C22×SD16×C41C22semidirect
30. C2×#121×C41C22semidirect
34. C2×C4×D4×C41C22semidirect
40. C2×#106×C41C22semidirect
41. C2×C4⋊C8×C41C22semidirect
42. C2×#103×C41C22semidirect
43. C2×#103×C41C22semidirect
44. C2×#103×C41C22semidirect
51. C2×#102×C41C22semidirect
54. C2×C22⋊C8×C41C22semidirect
55. C2×C22⋊C8×C41C22semidirect
56. C2×#97×C41C22semidirect
59. C41×#384C22semidirect
62. C41×#380C22semidirect
63. C41×#340C22semidirect
64. C41×#340C22semidirect
101. C2×D8×C41D4semidirect
107. #124×C41D4semidirect
125. C4×D4×C41D4semidirect
365. D4×C41#121semidirect
414. #24257C41direct (N × H)
471. C2×#546C2×C41semidirect
472. C2×#463C2×C41semidirect
473. C2×#449C2×C41semidirect
474. C2×#447C2×C41semidirect
475. C2×#442C2×C41semidirect
476. #2537C2×C41semidirect
477. #2035C2×C41semidirect
478. #2034C2×C41semidirect
479. #2000C2×C41semidirect
480. #1999C2×C41semidirect
481. #1959C2×C41semidirect
482. #1955C2×C41semidirect
483. #1802C2×C41semidirect
484. #1788C2×C41semidirect
485. #1786C2×C41semidirect
500. C22×SD16C22×C41semidirect
512. C2×#121C22×C41semidirect
516. C2×C4×D4C22×C41semidirect
522. C2×#106C22×C41semidirect
523. C2×C4⋊C8C22×C41semidirect
524. C2×#103C22×C41semidirect
525. C2×#103C22×C41semidirect
526. C2×#103C22×C41semidirect
533. C2×#102C22×C41semidirect
536. C2×C22⋊C8C22×C41semidirect
537. C2×C22⋊C8C22×C41semidirect
538. C2×#97C22×C41semidirect
541. #384C22×C41semidirect
544. #380C22×C41semidirect
545. #340C22×C41semidirect
546. #340C22×C41semidirect
547. C41#24257direct (N × H)
584. C2×D8D4×C41semidirect
590. #124D4×C41semidirect
608. C4×D4D4×C41semidirect
848. D4#121×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5462
C2×C41×#4632
C2×C41×#4492
C2×C41×#4472
C2×C41×#4422
C41×#25372
C41×#20352
C41×#20342
C41×#20002
C41×#19992
C41×#19592
C41×#19552
C41×#18022
C41×#17882
C41×#17862
#2425741