Finite Group Databasebeta

← C41×#23863 #23800064

Subgroups — C41×#23863 #23800064

Order 10496.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C41C211yesmaximal, characteristic, complemented
2C2×C41×#546C211yesmaximal, characteristic, complemented
3C2×C41×#452C211yesmaximal, characteristic, complemented
4C2×C41×#452C211yesmaximal, characteristic, complemented
5C2×C41×#449C211yesmaximal, characteristic, complemented
6C41×#2407C211yesmaximal, characteristic, complemented
7C41×#2015C211yesmaximal, characteristic, complemented
8C41×#2012C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1894C211yesmaximal, characteristic, complemented
12C41×#1879C211yesmaximal, characteristic, complemented
13C41×#1877C211yesmaximal, characteristic, complemented
14C41×#1870C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41—24no—
20C2×AGL(1,ℤ/8)×C41—24no—
21C2×AGL(1,ℤ/8)×C41—24no—
22C22×Q16×C41C2211yescharacteristic, complemented
23C22×SD16×C41C2211yescharacteristic
24C22×SD16×C41C2211yescharacteristic
25C22×SD16×C41C2211yescharacteristic, complemented
26C22×D8×C41C2211yescharacteristic
27C22×D8×C41C2211yescharacteristic
28C22×M16×C41C2211yescharacteristic
29C41×#546—24no—
30C41×#546—24no—
31C2×#124×C41C2211yescharacteristic
32C2×#123×C41—21no—
33C2×C22⋊Q8×C41C2211yescharacteristic
34C2×C22⋊Q8×C41C2211yescharacteristic, complemented
35C2×#121×C41—21no—
36C2×#121×C41C2211yescharacteristic
37C2×#121×C41C2211yescharacteristic, complemented
38C2×#120×C41—21no—
39C2×C4×D4×C41C2211yescharacteristic
40C2×C4×D4×C41C2211yescharacteristic
41C22×C22⋊C4×C41—21no—
42C41×#452—24no—
43C41×#452—24no—
44C41×#449—24no—
45C2×#103×C41C2211yescharacteristic, complemented
46C2×#103×C41C2211yescharacteristic, complemented
47C2×#103×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic
49C2×#102×C41C2211yescharacteristic
50C2×#102×C41C2211yescharacteristic
51C2×#102×C41C2211yescharacteristic
52C2×#102×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic
54C2×C22⋊C8×C41C2211yescharacteristic, complemented
55C2×C22⋊C8×C41C2211yescharacteristic, complemented
56C41×#394—21no—
57C41×#392—21no—
58C41×#391C2211yescharacteristic, complemented
59C41×#390C2211yescharacteristic, complemented
60C41×#386—21no—
61C41×#385—21no—
62C41×#380C2211yescharacteristic
63C41×#340C2211yescharacteristic, complemented
64C41×#340C2211yescharacteristic, complemented
65C41×#336C2211yescharacteristic, complemented
66C41×#336C2211yescharacteristic, complemented
67C25×C41—21no—
68C2×#41×C41—22no—
69C2×#41×C41—22no—
70C2×#41×C41—22no—
71C2×#41×C41—22no—
72C2×#41×C41—22no—
73C2×#41×C41—22no—
74C2×#41×C41—22no—
75C2×#41×C41—22no—
76C2×#41×C41—41no—
77C2×#41×C41—41no—
78C2×#41×C41—41no—
79C2×#41×C41—41no—
80C22×Q8×C41C2311yescharacteristic
81C22×Q8×C41C2311yescharacteristic
82C22×D4×C41—22no—
83C22×D4×C41—22no—
84C22×D4×C41—21no—
85C22×D4×C41—21no—
86C22×D4×C41—21no—
87C22×D4×C41—21no—
88C22×D4×C41—21no—
89C22×D4×C41—22no—
90C22×D4×C41—41no—
91C22×D4×C41—41no—
92C22×D4×C41D411yescharacteristic
93C22×D4×C41D414yescomplemented
94C22×D4×C41C2311yescharacteristic
95C22×D4×C41C2311yescharacteristic
96C22×D4×C41C2311yescharacteristic
97C23×C4×C41—21no—
98C23×C4×C41—21no—
99C23×C4×C41—21no—
100C23×C4×C41C2311yescharacteristic
101C23×C4×C41C2311yescharacteristic
102AGL(1,ℤ/8)×C41—232no—
103C2×Q16×C41—22no—
104C2×Q16×C41—22no—
105C2×Q16×C41—41no—
106C2×SD16×C41—22no—
107C2×SD16×C41—22no—
108C2×SD16×C41—22no—
109C2×SD16×C41—22no—
110C2×SD16×C41—22no—
111C2×SD16×C41—22no—
112C2×SD16×C41—22no—
113C2×SD16×C41—41no—
114C2×SD16×C41D414yescomplemented
115C2×D8×C41—22no—
116C2×D8×C41—22no—
117C2×D8×C41—22no—
118C2×D8×C41—22no—
119C2×D8×C41—22no—
120C2×D8×C41D414yescomplemented
121C2×M16×C41—22no—
122C2×M16×C41—22no—
123C2×M16×C41—22no—
124C22×C8×C41C2311yescharacteristic
125C22×C8×C41C2311yescharacteristic
126C22×C8×C41C2311yescharacteristic
127C22×C8×C41C2311yescharacteristic
128#124×C41—22no—
129#124×C41—22no—
130#123×C41—28no—
131C22⋊Q8×C41—22no—
132C22⋊Q8×C41—22no—
133C22⋊Q8×C41—41no—
134C22⋊Q8×C41D414yescomplemented
135#121×C41—28no—
136#121×C41—22no—
137#121×C41—22no—
138#121×C41—22no—
139#121×C41—41no—
140#120×C41—28no—
141C4×D4×C41—22no—
142C4×D4×C41—22no—
143C4×D4×C41—22no—
144C4×D4×C41—22no—
145C2×C4⋊C4×C41—21no—
146C2×C4⋊C4×C41—21no—
147C2×C4⋊C4×C41D411yescharacteristic
148C2×C4⋊C4×C41C2311yescharacteristic
149C2×C4⋊C4×C41C2311yescharacteristic
150C2×C4⋊C4×C41C2311yescharacteristic
151C2×C22⋊C4×C41—28no—
152C2×C22⋊C4×C41—21no—
153C2×C22⋊C4×C41—21no—
154C2×C22⋊C4×C41—21no—
155C2×C22⋊C4×C41—21no—
156C2×C22⋊C4×C41—21no—
157C2×C22⋊C4×C41—21no—
158C2×C22⋊C4×C41—21no—
159C2×C22⋊C4×C41—21no—
160C2×C22⋊C4×C41—21no—
161C2×C22⋊C4×C41—21no—
162C2×C22⋊C4×C41D411yescharacteristic
163C2×C22⋊C4×C41D411yescharacteristic
164C2×C42×C41C2311yescharacteristic
165#103×C41—22no—
166#103×C41—22no—
167#103×C41—22no—
168#102×C41—22no—
169#102×C41—22no—
170#102×C41—22no—
171#102×C41—41no—
172#102×C41—41no—
173C22⋊C8×C41—22no—
174C22⋊C8×C41—22no—
175C22⋊C8×C41—22no—
176#95×C41—21no—
177#95×C41—21no—
178#95×C41—21no—
179C24×C41—21no—
180C24×C41—21no—
181C24×C41—21no—
182C24×C41—24no—
183C24×C41—42no—
184C24×C41—42no—
185C24×C41—42no—
186C24×C41—42no—
187C24×C41—81no—
188C24×C41—81no—
189C24×C41C2×D411yescharacteristic
190C24×C41C2×D411yescharacteristic
191#41×C41—28no—
192#41×C41—44no—
193#41×C41—44no—
194#41×C41—44no—
195#41×C41—44no—
196#41×C41—44no—
197#41×C41—44no—
198#41×C41—44no—
199C2×Q8×C41—21no—
200C2×Q8×C41—21no—
201C2×Q8×C41—21no—
202C2×Q8×C41—21no—
203C2×Q8×C41—21no—
204C2×Q8×C41—21no—
205C2×Q8×C41—21no—
206C2×Q8×C41—21no—
207C2×Q8×C41—21no—
208C2×Q8×C41—21no—
209C2×Q8×C41C2×D412yes—
210C2×Q8×C41C2×D412yes—
211C2×D4×C41—28no—
212C2×D4×C41—24no—
213C2×D4×C41—22no—
214C2×D4×C41—24no—
215C2×D4×C41—24no—
216C2×D4×C41—21no—
217C2×D4×C41—21no—
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—21no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—21no—
227C2×D4×C41—21no—
228C2×D4×C41—21no—
229C2×D4×C41—44no—
230C2×D4×C41—44no—
231C2×D4×C41—44no—
232C2×D4×C41—41no—
233C2×D4×C41—41no—
234C2×D4×C41—42no—
235C2×D4×C41—42no—
236C2×D4×C41—42no—
237C2×D4×C41—42no—
238C2×D4×C41—42no—
239C2×D4×C41—42no—
240C2×D4×C41—42no—
241C2×D4×C41—42no—
242C2×D4×C41—42no—
243C2×D4×C41—81no—
244C2×D4×C41—81no—
245C2×D4×C41—81no—
246C2×D4×C41C2×D412yes—
247C2×D4×C41C2×D412yes—
248C2×D4×C41C2×D412yes—
249C2×D4×C41C2×D412yes—
250C2×D4×C41C2×D412yes—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—24no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—21no—
259C22×C4×C41—24no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—21no—
264C22×C4×C41—21no—
265C22×C4×C41—21no—
266C22×C4×C41—21no—
267C22×C4×C41—21no—
268C22×C4×C41—42no—
269C22×C4×C41—42no—
270C22×C4×C41—42no—
271C22×C4×C41—42no—
272C22×C4×C41—42no—
273C22×C4×C41—81no—
274C22×C4×C41—81no—
275C22×C4×C41C2×D411yescharacteristic
276C22×C4×C41C2×D411yescharacteristic
277C22×C4×C41C2×D411yescharacteristic
278C22×C4×C41C2×D411yescharacteristic
279C22×C4×C41C2×D412yes—
280C22×C4×C41C2×D412yes—
281C22×C4×C41C2411yescharacteristic
282Q16×C41—44no—
283SD16×C41—28no—
284SD16×C41—28no—
285SD16×C41—44no—
286D8×C41—28no—
287D8×C41—28no—
288M16×C41—28no—
289C2×C8×C41—21no—
290C2×C8×C41—21no—
291C2×C8×C41—21no—
292C2×C8×C41—21no—
293C2×C8×C41—21no—
294C2×C8×C41—21no—
295C2×C8×C41—21no—
296C2×C8×C41—21no—
297C2×C8×C41—21no—
298C2×C8×C41—21no—
299C2×C8×C41C2×D412yes—
300C2×C8×C41C2×D412yes—
301C4⋊C4×C41—24no—
302C4⋊C4×C41—22no—
303C4⋊C4×C41—21no—
304C4⋊C4×C41—21no—
305C4⋊C4×C41—21no—
306C4⋊C4×C41—21no—
307C4⋊C4×C41—21no—
308C4⋊C4×C41—42no—
309C4⋊C4×C41C2×D412yes—
310C22⋊C4×C41—24no—
311C22⋊C4×C41—24no—
312C22⋊C4×C41—24no—
313C22⋊C4×C41—24no—
314C22⋊C4×C41—22no—
315C22⋊C4×C41—24no—
316C22⋊C4×C41—22no—
317C22⋊C4×C41—42no—
318C22⋊C4×C41—42no—
319C22⋊C4×C41—42no—
320C22⋊C4×C41—81no—
321C22⋊C4×C41—81no—
322C42×C41—21no—
323C42×C41—21no—
324C23×C41—22no—
325C23×C41—21no—
326C23×C41—21no—
327C23×C41—22no—
328C23×C41—22no—
329C23×C41—21no—
330C23×C41—21no—
331C23×C41—21no—
332C23×C41—21no—
333C23×C41—22no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—22no—
337C23×C41—21no—
338C23×C41—21no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—21no—
342C23×C41—48no—
343C23×C41—48no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—41no—
348C23×C41—41no—
349C23×C41—41no—
350C23×C41—41no—
351C23×C41—41no—
352C23×C41—41no—
353C23×C41—41no—
354C23×C41—41no—
355C23×C41—41no—
356C23×C41—41no—
357C23×C41—41no—
358C23×C41—41no—
359C23×C41—41no—
360C23×C41—84no—
361C23×C41—84no—
362C23×C41—84no—
363C23×C41—84no—
364C23×C41—84no—
365C23×C41#12012yes—
366C23×C41C22×D411yescharacteristic
367Q8×C41—22no—
368Q8×C41—22no—
369Q8×C41—22no—
370Q8×C41—22no—
371Q8×C41—41no—
372Q8×C41—41no—
373Q8×C41—41no—
374Q8×C41—41no—
375D4×C41—22no—
376D4×C41—22no—
377D4×C41—22no—
378D4×C41—22no—
379D4×C41—22no—
380D4×C41—22no—
381D4×C41—22no—
382D4×C41—48no—
383D4×C41—44no—
384D4×C41—48no—
385D4×C41—48no—
386D4×C41—41no—
387D4×C41—41no—
388D4×C41—41no—
389D4×C41—41no—
390D4×C41—84no—
391D4×C41—84no—
392D4×C41#12014yes—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—22no—
396C2×C4×C41—22no—
397C2×C4×C41—22no—
398C2×C4×C41—22no—
399C2×C4×C41—21no—
400C2×C4×C41—21no—
401C2×C4×C41—22no—
402C2×C4×C41—21no—
403C2×C4×C41—22no—
404C2×C4×C41—21no—
405C2×C4×C41—22no—
406C2×C4×C41—21no—
407C2×C4×C41—21no—
408C2×C4×C41—21no—
409C2×C4×C41—21no—
410C2×C4×C41—21no—
411C2×C4×C41—48no—
412C2×C4×C41—48no—
413C2×C4×C41—41no—
414C2×C4×C41—41no—
415C2×C4×C41—41no—
416C2×C4×C41—41no—
417C2×C4×C41—41no—
418C2×C4×C41—41no—
419C2×C4×C41—41no—
420C2×C4×C41—41no—
421C2×C4×C41—41no—
422C2×C4×C41—41no—
423C2×C4×C41—41no—
424C2×C4×C41—41no—
425C2×C4×C41—41no—
426C2×C4×C41—41no—
427C2×C4×C41—41no—
428C2×C4×C41—41no—
429C2×C4×C41—84no—
430C2×C4×C41#12012yes—
431C2×C4×C41C22×D411yescharacteristic
432C2×C4×C41C22×D411yescharacteristic
433C2×C4×C41C22×D411yescharacteristic
434C2×C4×C41C22×D411yescharacteristic
435C2×C4×C41H(5,𝔽2)11yescharacteristic
436C2×C4×C41H(5,𝔽2)11yescharacteristic
437C8×C41—22no—
438C8×C41—22no—
439C8×C41—41no—
440C8×C41—41no—
441#23863C4111yesmaximal, characteristic, direct product factor, Sylow
442C22×C41—22no—
443C22×C41—24no—
444C22×C41—22no—
445C22×C41—22no—
446C22×C41—42no—
447C22×C41—41no—
448C22×C41—42no—
449C22×C41—42no—
450C22×C41—41no—
451C22×C41—42no—
452C22×C41—41no—
453C22×C41—42no—
454C22×C41—41no—
455C22×C41—42no—
456C22×C41—42no—
457C22×C41—41no—
458C22×C41—42no—
459C22×C41—41no—
460C22×C41—42no—
461C22×C41—41no—
462C22×C41—42no—
463C22×C41—41no—
464C22×C41—42no—
465C22×C41—41no—
466C22×C41—41no—
467C22×C41—42no—
468C22×C41—41no—
469C22×C41—816no—
470C22×C41—81no—
471C22×C41—81no—
472C22×C41—81no—
473C22×C41—81no—
474C22×C41—81no—
475C22×C41—81no—
476C22×C41—81no—
477C22×C41—81no—
478C22×C41C2×#12011yescharacteristic
479C22×C41D4211yescharacteristic
480C22×C41D4211yescharacteristic
481C22×C41#57511yescharacteristic
482C22×C41#57511yescharacteristic
483C22×C41#57611yescharacteristic
484C22×C41#57711yescharacteristic
485C4×C41—22no—
486C4×C41—41no—
487C4×C41—42no—
488C4×C41—42no—
489C4×C41—41no—
490C4×C41—41no—
491C4×C41—42no—
492C4×C41—81no—
493C4×C41—81no—
494C4×C41C2×#12011yescharacteristic
495C4×C41#53411yescharacteristic
496C4×C41D4211yescharacteristic
497C4×C41D4211yescharacteristic
498C22×AGL(1,ℤ/8)C2×C4111yescharacteristic, complemented
499C2×#546C2×C4111yescharacteristic, complemented
500C2×#452C2×C4111yescharacteristic, complemented
501C2×#452C2×C4111yescharacteristic, complemented
502C2×#449C2×C4111yescharacteristic, complemented
503#2407C2×C4111yescharacteristic, complemented
504#2015C2×C4111yescharacteristic, complemented
505#2012C2×C4111yescharacteristic, complemented
506#2000C2×C4111yescharacteristic, complemented
507#1999C2×C4111yescharacteristic, complemented
508#1894C2×C4111yescharacteristic, complemented
509#1879C2×C4111yescharacteristic, complemented
510#1877C2×C4111yescharacteristic, complemented
511#1870C2×C4111yescharacteristic, complemented
512#1786C2×C4111yescharacteristic, complemented
513C2×C41—42no—
514C2×C41—44no—
515C2×C41—81no—
516C2×C41—82no—
517C2×C41—82no—
518C2×C41#240311yescharacteristic
519C2×C41#300511yescharacteristic
520C2×C41#301211yescharacteristic
521C2×C41#326711yescharacteristic
522C2×C41#326811yescharacteristic
523C2×C41#327311yescharacteristic
524C2×C41#327511yescharacteristic
525C22×#41C22×C4111yescharacteristic
526C22×#41C22×C4111yescharacteristic
527C23×D4C22×C4111yescharacteristic
528C2×AGL(1,ℤ/8)—24no—
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C22×Q16C22×C4111yescharacteristic, complemented
532C22×SD16C22×C4111yescharacteristic
533C22×SD16C22×C4111yescharacteristic
534C22×SD16C22×C4111yescharacteristic, complemented
535C22×D8C22×C4111yescharacteristic
536C22×D8C22×C4111yescharacteristic
537C22×M16C22×C4111yescharacteristic
538#546—24no—
539#546—24no—
540C2×#124C22×C4111yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8C22×C4111yescharacteristic
543C2×C22⋊Q8C22×C4111yescharacteristic, complemented
544C2×#121—21no—
545C2×#121C22×C4111yescharacteristic
546C2×#121C22×C4111yescharacteristic, complemented
547C2×#120—21no—
548C2×C4×D4C22×C4111yescharacteristic
549C2×C4×D4C22×C4111yescharacteristic
550C22×C22⋊C4—21no—
551#452—24no—
552#452—24no—
553#449—24no—
554C2×#103C22×C4111yescharacteristic, complemented
555C2×#103C22×C4111yescharacteristic, complemented
556C2×#103C22×C4111yescharacteristic, complemented
557C2×#102C22×C4111yescharacteristic
558C2×#102C22×C4111yescharacteristic
559C2×#102C22×C4111yescharacteristic
560C2×#102C22×C4111yescharacteristic
561C2×#102C22×C4111yescharacteristic, complemented
562C2×C22⋊C8C22×C4111yescharacteristic
563C2×C22⋊C8C22×C4111yescharacteristic, complemented
564C2×C22⋊C8C22×C4111yescharacteristic, complemented
565#394—21no—
566#392—21no—
567#391C22×C4111yescharacteristic, complemented
568#390C22×C4111yescharacteristic, complemented
569#386—21no—
570#385—21no—
571#380C22×C4111yescharacteristic
572#340C22×C4111yescharacteristic, complemented
573#340C22×C4111yescharacteristic, complemented
574#336C22×C4111yescharacteristic, complemented
575#336C22×C4111yescharacteristic, complemented
576C41#2386311yescharacteristic, direct product factor, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C4111yescharacteristic
591C22×Q8C23×C4111yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C4111yescharacteristic
603C22×D4D4×C4114yescomplemented
604C22×D4C23×C4111yescharacteristic
605C22×D4C23×C4111yescharacteristic
606C22×D4C23×C4111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C4111yescharacteristic
611C23×C4C23×C4111yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C4114yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C4114yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C4111yescharacteristic
635C22×C8C23×C4111yescharacteristic
636C22×C8C23×C4111yescharacteristic
637C22×C8C23×C4111yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C4114yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C4111yescharacteristic
658C2×C4⋊C4C23×C4111yescharacteristic
659C2×C4⋊C4C23×C4111yescharacteristic
660C2×C4⋊C4C23×C4111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C4111yescharacteristic
673C2×C22⋊C4D4×C4111yescharacteristic
674C2×C42C23×C4111yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C4111yescharacteristic
700C24C2×D4×C4111yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
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×Q8—21no—
719C2×Q8C2×D4×C4112yes—
720C2×Q8C2×D4×C4112yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C4112yes—
757C2×D4C2×D4×C4112yes—
758C2×D4C2×D4×C4112yes—
759C2×D4C2×D4×C4112yes—
760C2×D4C2×D4×C4112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C4111yescharacteristic
786C22×C4C2×D4×C4111yescharacteristic
787C22×C4C2×D4×C4111yescharacteristic
788C22×C4C2×D4×C4111yescharacteristic
789C22×C4C2×D4×C4112yes—
790C22×C4C2×D4×C4112yes—
791C22×C4C24×C4111yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C4112yes—
810C2×C8C2×D4×C4112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C4112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C4112yes—
876C23C22×D4×C4111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—44no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C4114yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
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—84no—
940C2×C4#120×C4112yes—
941C2×C4C22×D4×C4111yescharacteristic
942C2×C4C22×D4×C4111yescharacteristic
943C2×C4C22×D4×C4111yescharacteristic
944C2×C4C22×D4×C4111yescharacteristic
945C2×C4H(5,𝔽2)×C4111yescharacteristic
946C2×C4H(5,𝔽2)×C4111yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C4111yescharacteristic
988C22D42×C4111yescharacteristic
989C22D42×C4111yescharacteristic
990C22C41×#57511yescharacteristic
991C22C41×#57511yescharacteristic
992C22C41×#57611yescharacteristic
993C22C41×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C4111yescharacteristic
1004C4C41×#53411yescharacteristic
1005C4D42×C4111yescharacteristic
1006C4D42×C4111yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2C41×#240311yescharacteristic
1013C2C41×#300511yescharacteristic
1014C2C41×#301211yescharacteristic
1015C2C41×#326711yescharacteristic
1016C2C41×#326811yescharacteristic
1017C2C41×#327311yescharacteristic
1018C2C41×#327511yescharacteristic
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. C22×AGL(1,ℤ/8)×C41C2semidirect
2. C2×C41×#546C2semidirect
3. C2×C41×#452C2semidirect
4. C2×C41×#452C2semidirect
5. C2×C41×#449C2semidirect
6. C41×#2407C2semidirect
7. C41×#2015C2semidirect
8. C41×#2012C2semidirect
9. C41×#2000C2semidirect
10. C41×#1999C2semidirect
11. C41×#1894C2semidirect
12. C41×#1879C2semidirect
13. C41×#1877C2semidirect
14. C41×#1870C2semidirect
15. C41×#1786C2semidirect
22. C22×Q16×C41C22semidirect
25. C22×SD16×C41C22semidirect
34. C2×C22⋊Q8×C41C22semidirect
37. C2×#121×C41C22semidirect
45. C2×#103×C41C22semidirect
46. C2×#103×C41C22semidirect
47. C2×#103×C41C22semidirect
52. C2×#102×C41C22semidirect
54. C2×C22⋊C8×C41C22semidirect
55. C2×C22⋊C8×C41C22semidirect
58. C41×#391C22semidirect
59. C41×#390C22semidirect
63. C41×#340C22semidirect
64. C41×#340C22semidirect
65. C41×#336C22semidirect
66. C41×#336C22semidirect
93. C22×D4×C41D4semidirect
114. C2×SD16×C41D4semidirect
120. C2×D8×C41D4semidirect
134. C22⋊Q8×C41D4semidirect
441. #23863C41direct (N × H)
498. C22×AGL(1,ℤ/8)C2×C41semidirect
499. C2×#546C2×C41semidirect
500. C2×#452C2×C41semidirect
501. C2×#452C2×C41semidirect
502. C2×#449C2×C41semidirect
503. #2407C2×C41semidirect
504. #2015C2×C41semidirect
505. #2012C2×C41semidirect
506. #2000C2×C41semidirect
507. #1999C2×C41semidirect
508. #1894C2×C41semidirect
509. #1879C2×C41semidirect
510. #1877C2×C41semidirect
511. #1870C2×C41semidirect
512. #1786C2×C41semidirect
531. C22×Q16C22×C41semidirect
534. C22×SD16C22×C41semidirect
543. C2×C22⋊Q8C22×C41semidirect
546. C2×#121C22×C41semidirect
554. C2×#103C22×C41semidirect
555. C2×#103C22×C41semidirect
556. C2×#103C22×C41semidirect
561. C2×#102C22×C41semidirect
563. C2×C22⋊C8C22×C41semidirect
564. C2×C22⋊C8C22×C41semidirect
567. #391C22×C41semidirect
568. #390C22×C41semidirect
572. #340C22×C41semidirect
573. #340C22×C41semidirect
574. #336C22×C41semidirect
575. #336C22×C41semidirect
576. C41#23863direct (N × H)
603. C22×D4D4×C41semidirect
624. C2×SD16D4×C41semidirect
630. C2×D8D4×C41semidirect
644. C22⋊Q8D4×C41semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C412
C2×C41×#5462
C2×C41×#4522
C2×C41×#4492
C41×#24072
C41×#20152
C41×#20122
C41×#20002
C41×#19992
C41×#18942
C41×#18792
C41×#18772
C41×#18702
C41×#17862
#2386341