Finite Group Databasebeta

← C41×#23860 #23800061

Subgroups — C41×#23860 #23800061

Order 10496.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 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×D42×C41C211yesmaximal, characteristic, complemented
3C2×C41×#449C211yesmaximal, characteristic, complemented
4C2×C41×#450C211yesmaximal, characteristic, complemented
5C2×C41×#447C211yesmaximal, characteristic, complemented
6C41×#2407C211yesmaximal, characteristic, complemented
7C41×#2014C211yesmaximal, characteristic, complemented
8C41×#2011C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1895C211yesmaximal, characteristic, complemented
12C41×#1879C211yesmaximal, characteristic, complemented
13C41×#1877C211yesmaximal, characteristic, complemented
14C41×#1870C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic, complemented
17C23×D4×C41—21no—
18C23×D4×C41C2211yescharacteristic
19C23×D4×C41C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C41—24no—
21C2×AGL(1,ℤ/8)×C41—24no—
22C2×AGL(1,ℤ/8)×C41—24no—
23C22×SD16×C41C2211yescharacteristic
24C22×SD16×C41C2211yescharacteristic, complemented
25C22×SD16×C41C2211yescharacteristic, complemented
26C22×D8×C41C2211yescharacteristic
27C22×D8×C41C2211yescharacteristic, complemented
28C22×D8×C41C2211yescharacteristic, complemented
29C22×M16×C41C2211yescharacteristic, complemented
30D42×C41—24no—
31D42×C41—24no—
32C2×#127×C41C2211yescharacteristic
33C2×C22⋊Q8×C41C2211yescharacteristic, complemented
34C2×#121×C41—21no—
35C2×#121×C41C2211yescharacteristic
36C2×#121×C41C2211yescharacteristic
37C2×#121×C41C2211yescharacteristic, complemented
38C2×#120×C41—21no—
39C2×#120×C41—21no—
40C2×C4×D4×C41C2211yescharacteristic
41C2×C4×D4×C41C2211yescharacteristic
42C41×#450—24no—
43C41×#449—24no—
44C41×#447—24no—
45C2×#103×C41C2211yescharacteristic, complemented
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#102×C41C2211yescharacteristic, complemented
49C2×#102×C41C2211yescharacteristic, complemented
50C2×#102×C41C2211yescharacteristic, complemented
51C2×#102×C41C2211yescharacteristic, complemented
52C2×#102×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
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, complemented
63C41×#340C2211yescharacteristic, complemented
64C41×#340C2211yescharacteristic, complemented
65C41×#336C2211yescharacteristic, complemented
66C41×#336C2211yescharacteristic, complemented
67C25×C41—21no—
68C25×C41—21no—
69C2×#41×C41—22no—
70C2×#41×C41—22no—
71C2×#41×C41—22no—
72C2×#41×C41—22no—
73C2×#41×C41—41no—
74C2×#41×C41—41no—
75C22×Q8×C41C2311yescharacteristic
76C22×D4×C41—22no—
77C22×D4×C41—22no—
78C22×D4×C41—28no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—22no—
82C22×D4×C41—22no—
83C22×D4×C41—22no—
84C22×D4×C41—22no—
85C22×D4×C41—21no—
86C22×D4×C41—21no—
87C22×D4×C41—21no—
88C22×D4×C41—21no—
89C22×D4×C41—21no—
90C22×D4×C41—22no—
91C22×D4×C41—21no—
92C22×D4×C41—41no—
93C22×D4×C41—41no—
94C22×D4×C41—41no—
95C22×D4×C41—41no—
96C22×D4×C41—44no—
97C22×D4×C41—44no—
98C22×D4×C41D411yescharacteristic
99C22×D4×C41D414yescomplemented
100C22×D4×C41C2311yescharacteristic
101C22×D4×C41C2311yescharacteristic
102C22×D4×C41C2311yescharacteristic
103C22×D4×C41C2311yescharacteristic
104C23×C4×C41—21no—
105C23×C4×C41—21no—
106C23×C4×C41C2311yescharacteristic
107C23×C4×C41C2311yescharacteristic
108AGL(1,ℤ/8)×C41—232no—
109C2×SD16×C41—22no—
110C2×SD16×C41—22no—
111C2×SD16×C41—22no—
112C2×SD16×C41—22no—
113C2×SD16×C41—22no—
114C2×SD16×C41—22no—
115C2×SD16×C41—22no—
116C2×SD16×C41—41no—
117C2×SD16×C41D414yescomplemented
118C2×D8×C41—22no—
119C2×D8×C41—22no—
120C2×D8×C41—22no—
121C2×D8×C41—22no—
122C2×D8×C41—22no—
123C2×D8×C41—22no—
124C2×D8×C41—22no—
125C2×D8×C41—41no—
126C2×D8×C41D414yescomplemented
127C2×M16×C41—22no—
128C2×M16×C41—22no—
129C2×M16×C41—22no—
130C22×C8×C41C2311yescharacteristic
131C22×C8×C41C2311yescharacteristic
132C22×C8×C41C2311yescharacteristic
133C22×C8×C41C2311yescharacteristic
134#127×C41—22no—
135#127×C41—22no—
136C22⋊Q8×C41—22no—
137C22⋊Q8×C41—41no—
138#121×C41—28no—
139#121×C41—22no—
140#121×C41—22no—
141#121×C41—22no—
142#121×C41—22no—
143#121×C41—41no—
144#121×C41D414yescomplemented
145#120×C41—28no—
146#120×C41—28no—
147C4×D4×C41—22no—
148C4×D4×C41—22no—
149C4×D4×C41—22no—
150C4×D4×C41—22no—
151C2×C4⋊C4×C41—21no—
152C2×C4⋊C4×C41D411yescharacteristic
153C2×C4⋊C4×C41C2311yescharacteristic
154C2×C4⋊C4×C41C2311yescharacteristic
155C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
163C2×C22⋊C4×C41—21no—
164C2×C22⋊C4×C41D411yescharacteristic
165C2×C22⋊C4×C41D411yescharacteristic
166C2×C42×C41C2311yescharacteristic
167#103×C41—22no—
168#102×C41—22no—
169#102×C41—22no—
170#102×C41—22no—
171#102×C41—22no—
172#102×C41—22no—
173#102×C41—41no—
174#102×C41—41no—
175C22⋊C8×C41—22no—
176C22⋊C8×C41—22no—
177C22⋊C8×C41—22no—
178#95×C41—21no—
179#95×C41—21no—
180#95×C41—21no—
181C24×C41—21no—
182C24×C41—24no—
183C24×C41—21no—
184C24×C41—21no—
185C24×C41—21no—
186C24×C41—24no—
187C24×C41—42no—
188C24×C41—42no—
189C24×C41—42no—
190C24×C41—42no—
191C24×C41—42no—
192C24×C41—42no—
193C24×C41—42no—
194C24×C41—42no—
195C24×C41—81no—
196C24×C41—81no—
197C24×C41—81no—
198C24×C41—81no—
199C24×C41C2×D411yescharacteristic
200C24×C41C2×D411yescharacteristic
201#41×C41—28no—
202#41×C41—44no—
203#41×C41—44no—
204#41×C41—44no—
205C2×Q8×C41—21no—
206C2×Q8×C41—21no—
207C2×Q8×C41—21no—
208C2×Q8×C41—21no—
209C2×Q8×C41—21no—
210C2×Q8×C41C2×D412yescomplemented
211C2×D4×C41—22no—
212C2×D4×C41—22no—
213C2×D4×C41—28no—
214C2×D4×C41—24no—
215C2×D4×C41—24no—
216C2×D4×C41—24no—
217C2×D4×C41—24no—
218C2×D4×C41—24no—
219C2×D4×C41—24no—
220C2×D4×C41—22no—
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—21no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—21no—
239C2×D4×C41—44no—
240C2×D4×C41—44no—
241C2×D4×C41—44no—
242C2×D4×C41—42no—
243C2×D4×C41—42no—
244C2×D4×C41—42no—
245C2×D4×C41—42no—
246C2×D4×C41—42no—
247C2×D4×C41—42no—
248C2×D4×C41—44no—
249C2×D4×C41—44no—
250C2×D4×C41—432no—
251C2×D4×C41—44no—
252C2×D4×C41—42no—
253C2×D4×C41—42no—
254C2×D4×C41—42no—
255C2×D4×C41—42no—
256C2×D4×C41—42no—
257C2×D4×C41—42no—
258C2×D4×C41—44no—
259C2×D4×C41—42no—
260C2×D4×C41—42no—
261C2×D4×C41—42no—
262C2×D4×C41—81no—
263C2×D4×C41—81no—
264C2×D4×C41—81no—
265C2×D4×C41C2×D412yes—
266C2×D4×C41C2×D412yes—
267C2×D4×C41C2×D412yes—
268C2×D4×C41C2×D412yes—
269C2×D4×C41C2×D412yes—
270C2×D4×C41C2×D412yescomplemented
271C22×C4×C41—21no—
272C22×C4×C41—21no—
273C22×C4×C41—21no—
274C22×C4×C41—21no—
275C22×C4×C41—24no—
276C22×C4×C41—21no—
277C22×C4×C41—21no—
278C22×C4×C41—21no—
279C22×C4×C41—21no—
280C22×C4×C41—21no—
281C22×C4×C41—21no—
282C22×C4×C41—21no—
283C22×C4×C41—21no—
284C22×C4×C41—21no—
285C22×C4×C41—21no—
286C22×C4×C41—42no—
287C22×C4×C41—42no—
288C22×C4×C41—42no—
289C22×C4×C41—42no—
290C22×C4×C41—42no—
291C22×C4×C41C2×D411yescharacteristic
292C22×C4×C41C2×D411yescharacteristic
293C22×C4×C41C2×D411yescharacteristic
294C22×C4×C41C2×D412yes—
295C22×C4×C41C2×D412yes—
296C22×C4×C41C2×D411yescharacteristic
297C22×C4×C41C2411yescharacteristic
298SD16×C41—28no—
299SD16×C41—28no—
300SD16×C41—44no—
301D8×C41—28no—
302D8×C41—28no—
303D8×C41—44no—
304M16×C41—28no—
305C2×C8×C41—21no—
306C2×C8×C41—21no—
307C2×C8×C41—21no—
308C2×C8×C41—21no—
309C2×C8×C41—21no—
310C2×C8×C41—21no—
311C2×C8×C41—21no—
312C2×C8×C41—21no—
313C2×C8×C41—21no—
314C2×C8×C41—21no—
315C2×C8×C41C2×D412yescomplemented
316C2×C8×C41C2×D412yescomplemented
317C4⋊C4×C41—22no—
318C4⋊C4×C41—21no—
319C4⋊C4×C41—21no—
320C4⋊C4×C41—21no—
321C4⋊C4×C41—21no—
322C4⋊C4×C41—21no—
323C4⋊C4×C41—42no—
324C4⋊C4×C41C2×D412yes—
325C22⋊C4×C41—24no—
326C22⋊C4×C41—24no—
327C22⋊C4×C41—22no—
328C22⋊C4×C41—24no—
329C22⋊C4×C41—22no—
330C22⋊C4×C41—42no—
331C22⋊C4×C41—42no—
332C22⋊C4×C41—42no—
333C22⋊C4×C41—81no—
334C22⋊C4×C41—81no—
335C42×C41—21no—
336C42×C41—21no—
337C23×C41—21no—
338C23×C41—22no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—21no—
342C23×C41—21no—
343C23×C41—22no—
344C23×C41—22no—
345C23×C41—21no—
346C23×C41—21no—
347C23×C41—21no—
348C23×C41—21no—
349C23×C41—21no—
350C23×C41—21no—
351C23×C41—21no—
352C23×C41—22no—
353C23×C41—22no—
354C23×C41—22no—
355C23×C41—48no—
356C23×C41—48no—
357C23×C41—48no—
358C23×C41—48no—
359C23×C41—41no—
360C23×C41—41no—
361C23×C41—41no—
362C23×C41—41no—
363C23×C41—41no—
364C23×C41—41no—
365C23×C41—41no—
366C23×C41—41no—
367C23×C41—41no—
368C23×C41—41no—
369C23×C41—41no—
370C23×C41—41no—
371C23×C41—41no—
372C23×C41—41no—
373C23×C41—41no—
374C23×C41—41no—
375C23×C41—41no—
376C23×C41—41no—
377C23×C41—41no—
378C23×C41—41no—
379C23×C41—41no—
380C23×C41—41no—
381C23×C41—84no—
382C23×C41—84no—
383C23×C41—84no—
384C23×C41—84no—
385C23×C41—84no—
386C23×C41—84no—
387C23×C41—84no—
388C23×C41—84no—
389C23×C41—84no—
390C23×C41—84no—
391C23×C41#12012yes—
392C23×C41AGL(1,ℤ/8)12yescomplemented
393C23×C41C22×D411yescharacteristic
394Q8×C41—22no—
395Q8×C41—22no—
396Q8×C41—41no—
397Q8×C41—41no—
398D4×C41—28no—
399D4×C41—22no—
400D4×C41—22no—
401D4×C41—22no—
402D4×C41—22no—
403D4×C41—22no—
404D4×C41—22no—
405D4×C41—22no—
406D4×C41—22no—
407D4×C41—22no—
408D4×C41—48no—
409D4×C41—48no—
410D4×C41—48no—
411D4×C41—48no—
412D4×C41—48no—
413D4×C41—48no—
414D4×C41—41no—
415D4×C41—41no—
416D4×C41—41no—
417D4×C41—41no—
418D4×C41—41no—
419D4×C41—41no—
420D4×C41—84no—
421D4×C41—84no—
422D4×C41#12014yes—
423C2×C4×C41—21no—
424C2×C4×C41—21no—
425C2×C4×C41—21no—
426C2×C4×C41—21no—
427C2×C4×C41—22no—
428C2×C4×C41—22no—
429C2×C4×C41—22no—
430C2×C4×C41—22no—
431C2×C4×C41—21no—
432C2×C4×C41—21no—
433C2×C4×C41—22no—
434C2×C4×C41—21no—
435C2×C4×C41—22no—
436C2×C4×C41—21no—
437C2×C4×C41—21no—
438C2×C4×C41—21no—
439C2×C4×C41—48no—
440C2×C4×C41—48no—
441C2×C4×C41—41no—
442C2×C4×C41—41no—
443C2×C4×C41—41no—
444C2×C4×C41—41no—
445C2×C4×C41—41no—
446C2×C4×C41—41no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—41no—
453C2×C4×C41—41no—
454C2×C4×C41—41no—
455C2×C4×C41#12012yes—
456C2×C4×C41AGL(1,ℤ/8)12yescomplemented
457C2×C4×C41C22×D411yescharacteristic
458C2×C4×C41C22×D411yescharacteristic
459C2×C4×C41C22×D411yescharacteristic
460C2×C4×C41C22×D411yescharacteristic
461C2×C4×C41H(5,𝔽2)11yescharacteristic
462C2×C4×C41H(5,𝔽2)11yescharacteristic
463C8×C41—22no—
464C8×C41—22no—
465C8×C41—41no—
466C8×C41—41no—
467#23860C4111yesmaximal, characteristic, direct product factor, Sylow
468C22×C41—22no—
469C22×C41—24no—
470C22×C41—22no—
471C22×C41—22no—
472C22×C41—22no—
473C22×C41—22no—
474C22×C41—22no—
475C22×C41—41no—
476C22×C41—42no—
477C22×C41—41no—
478C22×C41—42no—
479C22×C41—41no—
480C22×C41—42no—
481C22×C41—41no—
482C22×C41—42no—
483C22×C41—41no—
484C22×C41—41no—
485C22×C41—42no—
486C22×C41—41no—
487C22×C41—41no—
488C22×C41—42no—
489C22×C41—42no—
490C22×C41—42no—
491C22×C41—42no—
492C22×C41—42no—
493C22×C41—42no—
494C22×C41—42no—
495C22×C41—42no—
496C22×C41—42no—
497C22×C41—42no—
498C22×C41—816no—
499C22×C41—816no—
500C22×C41—81no—
501C22×C41—81no—
502C22×C41—81no—
503C22×C41—81no—
504C22×C41—81no—
505C22×C41—81no—
506C22×C41—81no—
507C22×C41—81no—
508C22×C41—81no—
509C22×C41—81no—
510C22×C41—81no—
511C22×C41—81no—
512C22×C41C2×#12011yescharacteristic
513C22×C41D4211yescharacteristic
514C22×C41D4211yescharacteristic
515C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
517C22×C41#57611yescharacteristic
518C22×C41#57711yescharacteristic
519C4×C41—22no—
520C4×C41—22no—
521C4×C41—41no—
522C4×C41—42no—
523C4×C41—42no—
524C4×C41—41no—
525C4×C41—81no—
526C4×C41—81no—
527C4×C41C2×#12011yescharacteristic
528C4×C41#53411yescharacteristic
529C4×C41D4211yescharacteristic
530C4×C41D4211yescharacteristic
531C22×AGL(1,ℤ/8)C2×C4111yescharacteristic, complemented
532C2×D42C2×C4111yescharacteristic, complemented
533C2×#449C2×C4111yescharacteristic, complemented
534C2×#450C2×C4111yescharacteristic, complemented
535C2×#447C2×C4111yescharacteristic, complemented
536#2407C2×C4111yescharacteristic, complemented
537#2014C2×C4111yescharacteristic, complemented
538#2011C2×C4111yescharacteristic, complemented
539#2000C2×C4111yescharacteristic, complemented
540#1999C2×C4111yescharacteristic, complemented
541#1895C2×C4111yescharacteristic, complemented
542#1879C2×C4111yescharacteristic, complemented
543#1877C2×C4111yescharacteristic, complemented
544#1870C2×C4111yescharacteristic, complemented
545#1786C2×C4111yescharacteristic, complemented
546C2×C41—42no—
547C2×C41—42no—
548C2×C41—44no—
549C2×C41—82no—
550C2×C41—82no—
551C2×C41—82no—
552C2×C41#240311yescharacteristic
553C2×C41#300311yescharacteristic
554C2×C41#301211yescharacteristic
555C2×C41#326411yescharacteristic
556C2×C41#326511yescharacteristic
557C2×C41#327211yescharacteristic
558C2×C41#327411yescharacteristic
559C22×#41C22×C4111yescharacteristic, complemented
560C23×D4—21no—
561C23×D4C22×C4111yescharacteristic
562C23×D4C22×C4111yescharacteristic
563C2×AGL(1,ℤ/8)—24no—
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C22×SD16C22×C4111yescharacteristic
567C22×SD16C22×C4111yescharacteristic, complemented
568C22×SD16C22×C4111yescharacteristic, complemented
569C22×D8C22×C4111yescharacteristic
570C22×D8C22×C4111yescharacteristic, complemented
571C22×D8C22×C4111yescharacteristic, complemented
572C22×M16C22×C4111yescharacteristic, complemented
573D42—24no—
574D42—24no—
575C2×#127C22×C4111yescharacteristic
576C2×C22⋊Q8C22×C4111yescharacteristic, complemented
577C2×#121—21no—
578C2×#121C22×C4111yescharacteristic
579C2×#121C22×C4111yescharacteristic
580C2×#121C22×C4111yescharacteristic, complemented
581C2×#120—21no—
582C2×#120—21no—
583C2×C4×D4C22×C4111yescharacteristic
584C2×C4×D4C22×C4111yescharacteristic
585#450—24no—
586#449—24no—
587#447—24no—
588C2×#103C22×C4111yescharacteristic, complemented
589C2×#102C22×C4111yescharacteristic
590C2×#102C22×C4111yescharacteristic
591C2×#102C22×C4111yescharacteristic, complemented
592C2×#102C22×C4111yescharacteristic, complemented
593C2×#102C22×C4111yescharacteristic, complemented
594C2×#102C22×C4111yescharacteristic, complemented
595C2×#102C22×C4111yescharacteristic, complemented
596C2×C22⋊C8C22×C4111yescharacteristic, complemented
597C2×C22⋊C8C22×C4111yescharacteristic, complemented
598C2×C22⋊C8C22×C4111yescharacteristic, complemented
599#394—21no—
600#392—21no—
601#391C22×C4111yescharacteristic, complemented
602#390C22×C4111yescharacteristic, complemented
603#386—21no—
604#385—21no—
605#380C22×C4111yescharacteristic, complemented
606#340C22×C4111yescharacteristic, complemented
607#340C22×C4111yescharacteristic, complemented
608#336C22×C4111yescharacteristic, complemented
609#336C22×C4111yescharacteristic, complemented
610C41#2386011yescharacteristic, direct product factor, Sylow
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C4111yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C4111yescharacteristic
643C22×D4D4×C4114yescomplemented
644C22×D4C23×C4111yescharacteristic
645C22×D4C23×C4111yescharacteristic
646C22×D4C23×C4111yescharacteristic
647C22×D4C23×C4111yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C4111yescharacteristic
651C23×C4C23×C4111yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C4114yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C4114yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C4111yescharacteristic
675C22×C8C23×C4111yescharacteristic
676C22×C8C23×C4111yescharacteristic
677C22×C8C23×C4111yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C4114yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C4111yescharacteristic
697C2×C4⋊C4C23×C4111yescharacteristic
698C2×C4⋊C4C23×C4111yescharacteristic
699C2×C4⋊C4C23×C4111yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C4111yescharacteristic
709C2×C22⋊C4D4×C4111yescharacteristic
710C2×C42C23×C4111yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C4111yescharacteristic
744C24C2×D4×C4111yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C4112yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C4112yes—
810C2×D4C2×D4×C4112yes—
811C2×D4C2×D4×C4112yes—
812C2×D4C2×D4×C4112yes—
813C2×D4C2×D4×C4112yes—
814C2×D4C2×D4×C4112yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C4111yescharacteristic
836C22×C4C2×D4×C4111yescharacteristic
837C22×C4C2×D4×C4111yescharacteristic
838C22×C4C2×D4×C4112yes—
839C22×C4C2×D4×C4112yes—
840C22×C4C2×D4×C4111yescharacteristic
841C22×C4C24×C4111yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C4112yescomplemented
860C2×C8C2×D4×C4112yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C4112yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C4112yes—
936C23AGL(1,ℤ/8)×C4112yescomplemented
937C23C22×D4×C4111yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C4114yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C4112yes—
1000C2×C4AGL(1,ℤ/8)×C4112yescomplemented
1001C2×C4C22×D4×C4111yescharacteristic
1002C2×C4C22×D4×C4111yescharacteristic
1003C2×C4C22×D4×C4111yescharacteristic
1004C2×C4C22×D4×C4111yescharacteristic
1005C2×C4H(5,𝔽2)×C4111yescharacteristic
1006C2×C4H(5,𝔽2)×C4111yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C4111yescharacteristic
1056C22D42×C4111yescharacteristic
1057C22D42×C4111yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
1060C22C41×#57611yescharacteristic
1061C22C41×#57711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C4111yescharacteristic
1071C4C41×#53411yescharacteristic
1072C4D42×C4111yescharacteristic
1073C4D42×C4111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C41×#240311yescharacteristic
1081C2C41×#300311yescharacteristic
1082C2C41×#301211yescharacteristic
1083C2C41×#326411yescharacteristic
1084C2C41×#326511yescharacteristic
1085C2C41×#327211yescharacteristic
1086C2C41×#327411yescharacteristic
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×D42×C41C2semidirect
3. C2×C41×#449C2semidirect
4. C2×C41×#450C2semidirect
5. C2×C41×#447C2semidirect
6. C41×#2407C2semidirect
7. C41×#2014C2semidirect
8. C41×#2011C2semidirect
9. C41×#2000C2semidirect
10. C41×#1999C2semidirect
11. C41×#1895C2semidirect
12. C41×#1879C2semidirect
13. C41×#1877C2semidirect
14. C41×#1870C2semidirect
15. C41×#1786C2semidirect
16. C22×#41×C41C22semidirect
24. C22×SD16×C41C22semidirect
25. C22×SD16×C41C22semidirect
27. C22×D8×C41C22semidirect
28. C22×D8×C41C22semidirect
29. C22×M16×C41C22semidirect
33. C2×C22⋊Q8×C41C22semidirect
37. C2×#121×C41C22semidirect
45. C2×#103×C41C22semidirect
48. C2×#102×C41C22semidirect
49. C2×#102×C41C22semidirect
50. C2×#102×C41C22semidirect
51. C2×#102×C41C22semidirect
52. C2×#102×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
54. C2×C22⋊C8×C41C22semidirect
55. C2×C22⋊C8×C41C22semidirect
58. C41×#391C22semidirect
59. C41×#390C22semidirect
62. C41×#380C22semidirect
63. C41×#340C22semidirect
64. C41×#340C22semidirect
65. C41×#336C22semidirect
66. C41×#336C22semidirect
99. C22×D4×C41D4semidirect
117. C2×SD16×C41D4semidirect
126. C2×D8×C41D4semidirect
144. #121×C41D4semidirect
210. C2×Q8×C41C2×D4semidirect
270. C2×D4×C41C2×D4semidirect
315. C2×C8×C41C2×D4semidirect
316. C2×C8×C41C2×D4semidirect
392. C23×C41AGL(1,ℤ/8)semidirect
456. C2×C4×C41AGL(1,ℤ/8)semidirect
467. #23860C41direct (N × H)
531. C22×AGL(1,ℤ/8)C2×C41semidirect
532. C2×D42C2×C41semidirect
533. C2×#449C2×C41semidirect
534. C2×#450C2×C41semidirect
535. C2×#447C2×C41semidirect
536. #2407C2×C41semidirect
537. #2014C2×C41semidirect
538. #2011C2×C41semidirect
539. #2000C2×C41semidirect
540. #1999C2×C41semidirect
541. #1895C2×C41semidirect
542. #1879C2×C41semidirect
543. #1877C2×C41semidirect
544. #1870C2×C41semidirect
545. #1786C2×C41semidirect
559. C22×#41C22×C41semidirect
567. C22×SD16C22×C41semidirect
568. C22×SD16C22×C41semidirect
570. C22×D8C22×C41semidirect
571. C22×D8C22×C41semidirect
572. C22×M16C22×C41semidirect
576. C2×C22⋊Q8C22×C41semidirect
580. C2×#121C22×C41semidirect
588. C2×#103C22×C41semidirect
591. C2×#102C22×C41semidirect
592. C2×#102C22×C41semidirect
593. C2×#102C22×C41semidirect
594. C2×#102C22×C41semidirect
595. C2×#102C22×C41semidirect
596. C2×C22⋊C8C22×C41semidirect
597. C2×C22⋊C8C22×C41semidirect
598. C2×C22⋊C8C22×C41semidirect
601. #391C22×C41semidirect
602. #390C22×C41semidirect
605. #380C22×C41semidirect
606. #340C22×C41semidirect
607. #340C22×C41semidirect
608. #336C22×C41semidirect
609. #336C22×C41semidirect
610. C41#23860direct (N × H)
643. C22×D4D4×C41semidirect
661. C2×SD16D4×C41semidirect
670. C2×D8D4×C41semidirect
688. #121D4×C41semidirect
754. C2×Q8C2×D4×C41semidirect
814. C2×D4C2×D4×C41semidirect
859. C2×C8C2×D4×C41semidirect
860. C2×C8C2×D4×C41semidirect
936. C23AGL(1,ℤ/8)×C41semidirect
1000. C2×C4AGL(1,ℤ/8)×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×D42×C412
C2×C41×#4492
C2×C41×#4502
C2×C41×#4472
C41×#24072
C41×#20142
C41×#20112
C41×#20002
C41×#19992
C41×#18952
C41×#18792
C41×#18772
C41×#18702
C41×#17862
#2386041