Finite Group Databasebeta

← C41×#24218 #23800419

Subgroups — C41×#24218 #23800419

Order 10496.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#535C211yesmaximal, characteristic, complemented
2C2×C41×#463C211yesmaximal, characteristic, complemented
3C2×C41×#459C211yesmaximal, characteristic, complemented
4C2×C41×#449C211yesmaximal, characteristic, complemented
5C2×C41×#447C211yesmaximal, characteristic, complemented
6C41×#2324C211yesmaximal, characteristic, complemented
7C41×#2042C211yesmaximal, characteristic, complemented
8C41×#2041C211yesmaximal, characteristic, complemented
9C41×#2012C211yesmaximal, characteristic, complemented
10C41×#2011C211yesmaximal, characteristic, complemented
11C41×#1983C211yesmaximal, characteristic, complemented
12C41×#1982C211yesmaximal, characteristic, complemented
13C41×#1798C211yesmaximal, 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
21C22×D8×C41C2211yescharacteristic, complemented
22C41×#535—24no—
23C41×#535—24no—
24C2×#127×C41C2211yescharacteristic
25C2×#127×C41C2211yescharacteristic
26C2×#124×C41C2211yescharacteristic
27C2×#124×C41C2211yescharacteristic
28C2×#121×C41—21no—
29C2×#121×C41—21no—
30C2×#121×C41C2211yescharacteristic
31C2×#120×C41—21no—
32C2×#120×C41—21no—
33C2×C4×D4×C41C2211yescharacteristic, complemented
34C2×#117×C41C2211yescharacteristic
35C41×#463—24no—
36C41×#459—24no—
37C41×#449—24no—
38C41×#447—24no—
39C2×C4⋊C8×C41C2211yescharacteristic, complemented
40C2×C4⋊C8×C41C2211yescharacteristic, complemented
41C2×#103×C41C2211yescharacteristic, complemented
42C2×#103×C41C2211yescharacteristic, complemented
43C2×#103×C41C2211yescharacteristic, complemented
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#102×C41C2211yescharacteristic
49C2×#102×C41C2211yescharacteristic
50C2×#102×C41C2211yescharacteristic, complemented
51C2×#102×C41C2211yescharacteristic, complemented
52C2×#102×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic
54C2×C22⋊C8×C41C2211yescharacteristic
55C41×#390—21no—
56C41×#390C2211yescharacteristic, complemented
57C41×#389C2211yescharacteristic, complemented
58C41×#388—21no—
59C41×#386—21no—
60C41×#385—21no—
61C41×#380C2211yescharacteristic
62C4×C4⋊C4×C41C2211yescharacteristic, complemented
63C41×#336C2211yescharacteristic, complemented
64C41×#336C2211yescharacteristic, 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—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—21no—
82C22×D4×C41—22no—
83C22×D4×C41—22no—
84C22×D4×C41—41no—
85C22×D4×C41—41no—
86C22×D4×C41C2311yescharacteristic
87C22×D4×C41C2311yescharacteristic
88C22×D4×C41C2311yescharacteristic
89C22×D4×C41C2311yescharacteristic
90C23×C4×C41—21no—
91C23×C4×C41—21no—
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—22no—
101C2×D8×C41—22no—
102C2×D8×C41—41no—
103C2×D8×C41—41no—
104C2×D8×C41—41no—
105C22×C8×C41C2311yescharacteristic
106C22×C8×C41C2311yescharacteristic
107C22×C8×C41C2311yescharacteristic
108C22×C8×C41C2311yescharacteristic
109#127×C41—22no—
110#127×C41—22no—
111#127×C41—22no—
112#127×C41D414yescomplemented
113#124×C41—22no—
114#124×C41—22no—
115#124×C41—22no—
116#124×C41D414yescomplemented
117#121×C41—28no—
118#121×C41—28no—
119#121×C41—22no—
120#121×C41D414yescomplemented
121#120×C41—28no—
122#120×C41—28no—
123C4×D4×C41—22no—
124C4×D4×C41—22no—
125#117×C41—22no—
126#117×C41—22no—
127C2×C4⋊C4×C41—21no—
128C2×C4⋊C4×C41D411yescharacteristic
129C2×C4⋊C4×C41D411yescharacteristic
130C2×C4⋊C4×C41C2311yescharacteristic
131C2×C4⋊C4×C41C2311yescharacteristic
132C2×C4⋊C4×C41C2311yescharacteristic
133C2×C22⋊C4×C41—21no—
134C2×C22⋊C4×C41—21no—
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×C41D411yescharacteristic
143C2×C22⋊C4×C41D411yescharacteristic
144C2×C42×C41—21no—
145C2×C42×C41C2311yescharacteristic
146C2×C42×C41C2311yescharacteristic
147C4⋊C8×C41—22no—
148C4⋊C8×C41—22no—
149#103×C41—22no—
150#103×C41—22no—
151#103×C41—41no—
152#102×C41—22no—
153#102×C41—22no—
154#102×C41—22no—
155#102×C41—22no—
156#102×C41—22no—
157#102×C41—22no—
158#102×C41—41no—
159#102×C41—41no—
160#102×C41—41no—
161C22⋊C8×C41—22no—
162C22⋊C8×C41—22no—
163#95×C41—21no—
164#95×C41—21no—
165#95×C41—21no—
166C24×C41—24no—
167C24×C41—21no—
168C24×C41—21no—
169C24×C41—21no—
170C24×C41—21no—
171C24×C41—42no—
172C24×C41—42no—
173C24×C41—81no—
174C24×C41—81no—
175C24×C41—81no—
176C24×C41—81no—
177C24×C41C2×D411yescharacteristic
178#41×C41—44no—
179#41×C41—44no—
180#41×C41—44no—
181#41×C41—44no—
182C2×Q8×C41—21no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41C2×D412yes—
188C2×D4×C41—24no—
189C2×D4×C41—24no—
190C2×D4×C41—24no—
191C2×D4×C41—24no—
192C2×D4×C41—24no—
193C2×D4×C41—24no—
194C2×D4×C41—24no—
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—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—21no—
213C2×D4×C41—21no—
214C2×D4×C41—21no—
215C2×D4×C41—44no—
216C2×D4×C41—44no—
217C2×D4×C41—44no—
218C2×D4×C41—44no—
219C2×D4×C41—42no—
220C2×D4×C41—42no—
221C2×D4×C41—42no—
222C2×D4×C41—42no—
223C2×D4×C41—81no—
224C2×D4×C41—81no—
225C2×D4×C41—81no—
226C2×D4×C41—81no—
227C2×D4×C41—81no—
228C2×D4×C41—81no—
229C2×D4×C41—81no—
230C2×D4×C41—81no—
231C2×D4×C41—81no—
232C2×D4×C41—81no—
233C2×D4×C41C2×D412yes—
234C2×D4×C41C2×D412yes—
235C2×D4×C41C2×D412yes—
236C2×D4×C41C2×D412yes—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—24no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—42no—
247C22×C4×C41—42no—
248C22×C4×C41—42no—
249C22×C4×C41—81no—
250C22×C4×C41—81no—
251C22×C4×C41C2×D411yescharacteristic
252C22×C4×C41C2×D411yescharacteristic
253C22×C4×C41C2×D411yescharacteristic
254C22×C4×C41C2×D411yescharacteristic
255C22×C4×C41C2×D411yescharacteristic
256C22×C4×C41C2×D412yes—
257C22×C4×C41#4112yes—
258C22×C4×C41C2411yescharacteristic
259SD16×C41—44no—
260D8×C41—44no—
261D8×C41—44no—
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×C41—21no—
275C4⋊C4×C41—22no—
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—81no—
283C4⋊C4×C41C2×D412yes—
284C22⋊C4×C41—24no—
285C22⋊C4×C41—24no—
286C22⋊C4×C41—24no—
287C22⋊C4×C41—24no—
288C22⋊C4×C41—22no—
289C22⋊C4×C41—22no—
290C22⋊C4×C41—24no—
291C22⋊C4×C41—42no—
292C22⋊C4×C41—81no—
293C22⋊C4×C41—81no—
294C22⋊C4×C41—81no—
295C42×C41—21no—
296C42×C41—21no—
297C42×C41—81no—
298C42×C41C2×D412yes—
299C42×C41C2×D412yes—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—21no—
303C23×C41—21no—
304C23×C41—21no—
305C23×C41—21no—
306C23×C41—22no—
307C23×C41—22no—
308C23×C41—22no—
309C23×C41—22no—
310C23×C41—48no—
311C23×C41—41no—
312C23×C41—41no—
313C23×C41—41no—
314C23×C41—41no—
315C23×C41—41no—
316C23×C41—41no—
317C23×C41—41no—
318C23×C41—41no—
319C23×C41—41no—
320C23×C41—41no—
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—84no—
336C23×C41—84no—
337C23×C41—84no—
338C23×C41—84no—
339C23×C41—84no—
340C23×C41—84no—
341C23×C41#12112yes—
342C23×C41C22×D411yescharacteristic
343Q8×C41—22no—
344Q8×C41—22no—
345Q8×C41—41no—
346Q8×C41—41no—
347D4×C41—22no—
348D4×C41—22no—
349D4×C41—22no—
350D4×C41—22no—
351D4×C41—22no—
352D4×C41—22no—
353D4×C41—22no—
354D4×C41—22no—
355D4×C41—48no—
356D4×C41—48no—
357D4×C41—41no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—41no—
361D4×C41—41no—
362D4×C41—41no—
363D4×C41—41no—
364D4×C41—41no—
365D4×C41—84no—
366D4×C41—84no—
367D4×C41—84no—
368D4×C41—84no—
369D4×C41—84no—
370C2×C4×C41—21no—
371C2×C4×C41—21no—
372C2×C4×C41—21no—
373C2×C4×C41—21no—
374C2×C4×C41—21no—
375C2×C4×C41—21no—
376C2×C4×C41—22no—
377C2×C4×C41—22no—
378C2×C4×C41—22no—
379C2×C4×C41—22no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—22no—
383C2×C4×C41—22no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—21no—
387C2×C4×C41—21no—
388C2×C4×C41—48no—
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—84no—
400C2×C4×C41#12012yes—
401C2×C4×C41#12012yes—
402C2×C4×C41#12112yes—
403C2×C4×C41C22×D411yescharacteristic
404C2×C4×C41C22×D411yescharacteristic
405C2×C4×C41C22×D411yescharacteristic
406C2×C4×C41C2×#4111yescharacteristic
407C2×C4×C41H(5,𝔽2)11yescharacteristic
408C2×C4×C41H(5,𝔽2)11yescharacteristic
409C8×C41—41no—
410C8×C41—41no—
411C8×C41—41no—
412C8×C41—41no—
413#24218C4111yesmaximal, characteristic, direct product factor, Sylow
414C22×C41—22no—
415C22×C41—22no—
416C22×C41—22no—
417C22×C41—41no—
418C22×C41—41no—
419C22×C41—41no—
420C22×C41—41no—
421C22×C41—42no—
422C22×C41—42no—
423C22×C41—42no—
424C22×C41—42no—
425C22×C41—42no—
426C22×C41—42no—
427C22×C41—42no—
428C22×C41—42no—
429C22×C41—42no—
430C22×C41—42no—
431C22×C41—42no—
432C22×C41—42no—
433C22×C41—816no—
434C22×C41—81no—
435C22×C41—81no—
436C22×C41—81no—
437C22×C41—81no—
438C22×C41—81no—
439C22×C41—81no—
440C22×C41—81no—
441C22×C41—81no—
442C22×C41—81no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41C2×#12011yescharacteristic
451C22×C41C2×#12111yescharacteristic
452C22×C41#53511yescharacteristic
453C22×C41#57611yescharacteristic
454C22×C41#57611yescharacteristic
455C22×C41#57611yescharacteristic
456C22×C41#57711yescharacteristic
457C4×C41—22no—
458C4×C41—22no—
459C4×C41—22no—
460C4×C41—42no—
461C4×C41—41no—
462C4×C41—41no—
463C4×C41—42no—
464C4×C41—81no—
465C4×C41—81no—
466C4×C41D4211yescharacteristic
467C4×C41D4211yescharacteristic
468C4×C41#54611yescharacteristic
469C4×C41#54611yescharacteristic
470C2×#535C2×C4111yescharacteristic, complemented
471C2×#463C2×C4111yescharacteristic, complemented
472C2×#459C2×C4111yescharacteristic, complemented
473C2×#449C2×C4111yescharacteristic, complemented
474C2×#447C2×C4111yescharacteristic, complemented
475#2324C2×C4111yescharacteristic, complemented
476#2042C2×C4111yescharacteristic, complemented
477#2041C2×C4111yescharacteristic, complemented
478#2012C2×C4111yescharacteristic, complemented
479#2011C2×C4111yescharacteristic, complemented
480#1983C2×C4111yescharacteristic, complemented
481#1982C2×C4111yescharacteristic, complemented
482#1798C2×C4111yescharacteristic, complemented
483#1788C2×C4111yescharacteristic, complemented
484#1786C2×C4111yescharacteristic, complemented
485C2×C41—42no—
486C2×C41—82no—
487C2×C41—82no—
488C2×C41—82no—
489C2×C41—82no—
490C2×C41#240811yescharacteristic
491C2×C41#300811yescharacteristic
492C2×C41#301211yescharacteristic
493C2×C41#304111yescharacteristic
494C2×C41#304511yescharacteristic
495C2×C41#322011yescharacteristic
496C2×C41#322411yescharacteristic
497C22×#41C22×C4111yescharacteristic
498C23×D4C22×C4111yescharacteristic
499C22×SD16C22×C4111yescharacteristic, complemented
500C22×D8C22×C4111yescharacteristic
501C22×D8C22×C4111yescharacteristic
502C22×D8C22×C4111yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127C22×C4111yescharacteristic
506C2×#127C22×C4111yescharacteristic
507C2×#124C22×C4111yescharacteristic
508C2×#124C22×C4111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C4111yescharacteristic
512C2×#120—21no—
513C2×#120—21no—
514C2×C4×D4C22×C4111yescharacteristic, complemented
515C2×#117C22×C4111yescharacteristic
516#463—24no—
517#459—24no—
518#449—24no—
519#447—24no—
520C2×C4⋊C8C22×C4111yescharacteristic, complemented
521C2×C4⋊C8C22×C4111yescharacteristic, complemented
522C2×#103C22×C4111yescharacteristic, complemented
523C2×#103C22×C4111yescharacteristic, complemented
524C2×#103C22×C4111yescharacteristic, complemented
525C2×#102C22×C4111yescharacteristic
526C2×#102C22×C4111yescharacteristic
527C2×#102C22×C4111yescharacteristic
528C2×#102C22×C4111yescharacteristic
529C2×#102C22×C4111yescharacteristic
530C2×#102C22×C4111yescharacteristic
531C2×#102C22×C4111yescharacteristic, complemented
532C2×#102C22×C4111yescharacteristic, complemented
533C2×#102C22×C4111yescharacteristic, complemented
534C2×C22⋊C8C22×C4111yescharacteristic
535C2×C22⋊C8C22×C4111yescharacteristic
536#390—21no—
537#390C22×C4111yescharacteristic, complemented
538#389C22×C4111yescharacteristic, complemented
539#388—21no—
540#386—21no—
541#385—21no—
542#380C22×C4111yescharacteristic
543C4×C4⋊C4C22×C4111yescharacteristic, complemented
544#336C22×C4111yescharacteristic, complemented
545#336C22×C4111yescharacteristic, complemented
546C41#2421811yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C4111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C4111yescharacteristic
569C22×D4C23×C4111yescharacteristic
570C22×D4C23×C4111yescharacteristic
571C22×D4C23×C4111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C4111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C4111yescharacteristic
588C22×C8C23×C4111yescharacteristic
589C22×C8C23×C4111yescharacteristic
590C22×C8C23×C4111yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C4114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C4114yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C4114yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C4111yescharacteristic
611C2×C4⋊C4D4×C4111yescharacteristic
612C2×C4⋊C4C23×C4111yescharacteristic
613C2×C4⋊C4C23×C4111yescharacteristic
614C2×C4⋊C4C23×C4111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
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⋊C4D4×C4111yescharacteristic
625C2×C22⋊C4D4×C4111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C4111yescharacteristic
628C2×C42C23×C4111yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C4111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C4112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C4112yes—
716C2×D4C2×D4×C4112yes—
717C2×D4C2×D4×C4112yes—
718C2×D4C2×D4×C4112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C4111yescharacteristic
734C22×C4C2×D4×C4111yescharacteristic
735C22×C4C2×D4×C4111yescharacteristic
736C22×C4C2×D4×C4111yescharacteristic
737C22×C4C2×D4×C4111yescharacteristic
738C22×C4C2×D4×C4112yes—
739C22×C4#41×C4112yes—
740C22×C4C24×C4111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
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—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C4112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C4112yes—
781C42C2×D4×C4112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
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—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C4112yes—
824C23C22×D4×C4111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
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—84no—
882C2×C4#120×C4112yes—
883C2×C4#120×C4112yes—
884C2×C4#121×C4112yes—
885C2×C4C22×D4×C4111yescharacteristic
886C2×C4C22×D4×C4111yescharacteristic
887C2×C4C22×D4×C4111yescharacteristic
888C2×C4C2×#41×C4111yescharacteristic
889C2×C4H(5,𝔽2)×C4111yescharacteristic
890C2×C4H(5,𝔽2)×C4111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C4111yescharacteristic
932C22C2×#121×C4111yescharacteristic
933C22C41×#53511yescharacteristic
934C22C41×#57611yescharacteristic
935C22C41×#57611yescharacteristic
936C22C41×#57611yescharacteristic
937C22C41×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—81no—
946C4—81no—
947C4D42×C4111yescharacteristic
948C4D42×C4111yescharacteristic
949C4C41×#54611yescharacteristic
950C4C41×#54611yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C41×#240811yescharacteristic
957C2C41×#300811yescharacteristic
958C2C41×#301211yescharacteristic
959C2C41×#304111yescharacteristic
960C2C41×#304511yescharacteristic
961C2C41×#322011yescharacteristic
962C2C41×#322411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#535C2semidirect
2. C2×C41×#463C2semidirect
3. C2×C41×#459C2semidirect
4. C2×C41×#449C2semidirect
5. C2×C41×#447C2semidirect
6. C41×#2324C2semidirect
7. C41×#2042C2semidirect
8. C41×#2041C2semidirect
9. C41×#2012C2semidirect
10. C41×#2011C2semidirect
11. C41×#1983C2semidirect
12. C41×#1982C2semidirect
13. C41×#1798C2semidirect
14. C41×#1788C2semidirect
15. C41×#1786C2semidirect
18. C22×SD16×C41C22semidirect
21. C22×D8×C41C22semidirect
33. C2×C4×D4×C41C22semidirect
39. C2×C4⋊C8×C41C22semidirect
40. C2×C4⋊C8×C41C22semidirect
41. C2×#103×C41C22semidirect
42. C2×#103×C41C22semidirect
43. C2×#103×C41C22semidirect
50. C2×#102×C41C22semidirect
51. C2×#102×C41C22semidirect
52. C2×#102×C41C22semidirect
56. C41×#390C22semidirect
57. C41×#389C22semidirect
62. C4×C4⋊C4×C41C22semidirect
63. C41×#336C22semidirect
64. C41×#336C22semidirect
112. #127×C41D4semidirect
116. #124×C41D4semidirect
120. #121×C41D4semidirect
413. #24218C41direct (N × H)
470. C2×#535C2×C41semidirect
471. C2×#463C2×C41semidirect
472. C2×#459C2×C41semidirect
473. C2×#449C2×C41semidirect
474. C2×#447C2×C41semidirect
475. #2324C2×C41semidirect
476. #2042C2×C41semidirect
477. #2041C2×C41semidirect
478. #2012C2×C41semidirect
479. #2011C2×C41semidirect
480. #1983C2×C41semidirect
481. #1982C2×C41semidirect
482. #1798C2×C41semidirect
483. #1788C2×C41semidirect
484. #1786C2×C41semidirect
499. C22×SD16C22×C41semidirect
502. C22×D8C22×C41semidirect
514. C2×C4×D4C22×C41semidirect
520. C2×C4⋊C8C22×C41semidirect
521. C2×C4⋊C8C22×C41semidirect
522. C2×#103C22×C41semidirect
523. C2×#103C22×C41semidirect
524. C2×#103C22×C41semidirect
531. C2×#102C22×C41semidirect
532. C2×#102C22×C41semidirect
533. C2×#102C22×C41semidirect
537. #390C22×C41semidirect
538. #389C22×C41semidirect
543. C4×C4⋊C4C22×C41semidirect
544. #336C22×C41semidirect
545. #336C22×C41semidirect
546. C41#24218direct (N × H)
594. #127D4×C41semidirect
598. #124D4×C41semidirect
602. #121D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5352
C2×C41×#4632
C2×C41×#4592
C2×C41×#4492
C2×C41×#4472
C41×#23242
C41×#20422
C41×#20412
C41×#20122
C41×#20112
C41×#19832
C41×#19822
C41×#17982
C41×#17882
C41×#17862
#2421841