Finite Group Databasebeta

← C41×#24440 #23800641

Subgroups — C41×#24440 #23800641

Order 10496.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C41C211yesmaximal, characteristic, complemented
2C2×C41×#469C211yesmaximal, characteristic, complemented
3C2×C41×#447C211yesmaximal, characteristic, complemented
4C2×C41×#447C211yesmaximal, characteristic, complemented
5C2×C41×#418C211yesmaximal, characteristic, complemented
6C41×#2414C211yesmaximal, characteristic, complemented
7C41×#2041C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2011C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1879C211yesmaximal, characteristic, complemented
12C41×#1875C211yesmaximal, characteristic, complemented
13C41×#1870C211yesmaximal, characteristic, complemented
14C41×#1864C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C41—21no—
17C23×D4×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic, complemented
21C22×D8×C41C2211yescharacteristic, complemented
22C22×M16×C41C2211yescharacteristic, complemented
23D42×C41—24no—
24D42×C41—24no—
25C2×#127×C41C2211yescharacteristic
26C2×#121×C41—21no—
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic, complemented
30C2×#121×C41C2211yescharacteristic, complemented
31C2×#120×C41—21no—
32C2×#120×C41—21no—
33C2×C4×D4×C41C2211yescharacteristic
34C2×C4×D4×C41C2211yescharacteristic
35C2×#117×C41C2211yescharacteristic, complemented
36C41×#469—24no—
37C41×#447—24no—
38C41×#447—24no—
39C2×#106×C41C2211yescharacteristic, complemented
40C41×#418—24no—
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic, complemented
45C2×#102×C41C2211yescharacteristic, complemented
46C2×#102×C41C2211yescharacteristic, complemented
47C2×#102×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic, complemented
49C2×#102×C41C2211yescharacteristic, complemented
50C2×#102×C41C2211yescharacteristic, complemented
51C2×C22⋊C8×C41C2211yescharacteristic, complemented
52C2×C22⋊C8×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#394—21no—
55C41×#392—21no—
56C41×#390—21no—
57C41×#390C2211yescharacteristic, complemented
58C41×#389C2211yescharacteristic, complemented
59C41×#388—21no—
60C41×#380C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#336C2211yescharacteristic, complemented
64C41×#336C2211yescharacteristic, complemented
65C25×C41—21no—
66C25×C41—21no—
67C22×D4×C41—22no—
68C22×D4×C41—22no—
69C22×D4×C41—28no—
70C22×D4×C41—21no—
71C22×D4×C41—21no—
72C22×D4×C41—22no—
73C22×D4×C41—22no—
74C22×D4×C41—22no—
75C22×D4×C41—22no—
76C22×D4×C41—21no—
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—22no—
82C22×D4×C41—21no—
83C22×D4×C41—41no—
84C22×D4×C41—41no—
85C22×D4×C41—41no—
86C22×D4×C41—41no—
87C22×D4×C41—44no—
88C22×D4×C41—44no—
89C22×D4×C41D411yescharacteristic
90C22×D4×C41D414yescomplemented
91C22×D4×C41C2311yescharacteristic
92C22×D4×C41C2311yescharacteristic
93C22×D4×C41C2311yescharacteristic
94C22×D4×C41C2311yescharacteristic
95C23×C4×C41—21no—
96C23×C4×C41C2311yescharacteristic
97C23×C4×C41C2311yescharacteristic
98C2×D8×C41—22no—
99C2×D8×C41—22no—
100C2×D8×C41—22no—
101C2×D8×C41—22no—
102C2×D8×C41—22no—
103C2×D8×C41—22no—
104C2×D8×C41—41no—
105C2×D8×C41—41no—
106C2×D8×C41—41no—
107C2×M16×C41—22no—
108C2×M16×C41—22no—
109C2×M16×C41—41no—
110C22×C8×C41C2311yescharacteristic
111C22×C8×C41C2311yescharacteristic
112C22×C8×C41C2311yescharacteristic
113C22×C8×C41C2311yescharacteristic
114#127×C41—22no—
115#127×C41—22no—
116#121×C41—28no—
117#121×C41—22no—
118#121×C41—22no—
119#121×C41—22no—
120#121×C41—22no—
121#121×C41—22no—
122#121×C41—22no—
123#121×C41—41no—
124#121×C41D414yescomplemented
125#120×C41—28no—
126#120×C41—28no—
127C4×D4×C41—22no—
128C4×D4×C41—22no—
129C4×D4×C41—22no—
130C4×D4×C41—22no—
131#117×C41—22no—
132#117×C41—41no—
133C2×C4⋊C4×C41—21no—
134C2×C4⋊C4×C41D411yescharacteristic
135C2×C4⋊C4×C41C2311yescharacteristic
136C2×C4⋊C4×C41C2311yescharacteristic
137C2×C4⋊C4×C41C2311yescharacteristic
138C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
146C2×C22⋊C4×C41—21no—
147C2×C22⋊C4×C41—21no—
148C2×C22⋊C4×C41D411yescharacteristic
149C2×C22⋊C4×C41D411yescharacteristic
150C2×C42×C41—21no—
151C2×C42×C41C2311yescharacteristic
152#106×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—22no—
159#102×C41—22no—
160#102×C41—22no—
161#102×C41—41no—
162#102×C41D414yescomplemented
163C22⋊C8×C41—22no—
164C22⋊C8×C41—22no—
165C22⋊C8×C41—41no—
166#95×C41—21no—
167#95×C41—21no—
168C24×C41—21no—
169C24×C41—24no—
170C24×C41—21no—
171C24×C41—21no—
172C24×C41—24no—
173C24×C41—21no—
174C24×C41—42no—
175C24×C41—42no—
176C24×C41—42no—
177C24×C41—42no—
178C24×C41—42no—
179C24×C41—42no—
180C24×C41—42no—
181C24×C41—42no—
182C24×C41—81no—
183C24×C41—81no—
184C24×C41—81no—
185C24×C41—81no—
186C24×C41C2×D411yescharacteristic
187C24×C41C2×D411yescharacteristic
188C2×D4×C41—22no—
189C2×D4×C41—22no—
190C2×D4×C41—28no—
191C2×D4×C41—24no—
192C2×D4×C41—24no—
193C2×D4×C41—24no—
194C2×D4×C41—24no—
195C2×D4×C41—24no—
196C2×D4×C41—24no—
197C2×D4×C41—22no—
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—21no—
216C2×D4×C41—21no—
217C2×D4×C41—44no—
218C2×D4×C41—44no—
219C2×D4×C41—44no—
220C2×D4×C41—42no—
221C2×D4×C41—42no—
222C2×D4×C41—42no—
223C2×D4×C41—42no—
224C2×D4×C41—42no—
225C2×D4×C41—42no—
226C2×D4×C41—44no—
227C2×D4×C41—44no—
228C2×D4×C41—432no—
229C2×D4×C41—44no—
230C2×D4×C41—42no—
231C2×D4×C41—42no—
232C2×D4×C41—42no—
233C2×D4×C41—42no—
234C2×D4×C41—44no—
235C2×D4×C41—42no—
236C2×D4×C41—42no—
237C2×D4×C41—42no—
238C2×D4×C41—81no—
239C2×D4×C41—81no—
240C2×D4×C41—81no—
241C2×D4×C41—81no—
242C2×D4×C41—81no—
243C2×D4×C41C2×D412yes—
244C2×D4×C41C2×D412yes—
245C2×D4×C41C2×D412yes—
246C2×D4×C41C2×D412yes—
247C2×D4×C41#4112yes—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—24no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—21no—
259C22×C4×C41—21no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—42no—
264C22×C4×C41—42no—
265C22×C4×C41C2×D411yescharacteristic
266C22×C4×C41C2×D411yescharacteristic
267C22×C4×C41C2×D411yescharacteristic
268C22×C4×C41C2×D412yes—
269C22×C4×C41C2×D412yes—
270C22×C4×C41C2×D411yescharacteristic
271C22×C4×C41C2411yescharacteristic
272D8×C41—44no—
273D8×C41—44no—
274D8×C41—44no—
275M16×C41—44no—
276C2×C8×C41—21no—
277C2×C8×C41—21no—
278C2×C8×C41—21no—
279C2×C8×C41—21no—
280C2×C8×C41—21no—
281C2×C8×C41—21no—
282C2×C8×C41—21no—
283C2×C8×C41—21no—
284C2×C8×C41—21no—
285C2×C8×C41—21no—
286C2×C8×C41—21no—
287C2×C8×C41C2×D412yescomplemented
288C4⋊C4×C41—22no—
289C4⋊C4×C41—21no—
290C4⋊C4×C41—21no—
291C4⋊C4×C41—21no—
292C4⋊C4×C41—21no—
293C4⋊C4×C41—21no—
294C4⋊C4×C41—21no—
295C4⋊C4×C41—81no—
296C4⋊C4×C41C2×D412yes—
297C4⋊C4×C41C2×D412yescomplemented
298C22⋊C4×C41—24no—
299C22⋊C4×C41—24no—
300C22⋊C4×C41—22no—
301C22⋊C4×C41—24no—
302C22⋊C4×C41—22no—
303C22⋊C4×C41—42no—
304C22⋊C4×C41—42no—
305C22⋊C4×C41—42no—
306C22⋊C4×C41—42no—
307C22⋊C4×C41—81no—
308C22⋊C4×C41—81no—
309C42×C41—21no—
310C42×C41—21no—
311C42×C41—42no—
312C23×C41—21no—
313C23×C41—22no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—22no—
317C23×C41—21no—
318C23×C41—21no—
319C23×C41—22no—
320C23×C41—21no—
321C23×C41—21no—
322C23×C41—21no—
323C23×C41—21no—
324C23×C41—21no—
325C23×C41—21no—
326C23×C41—21no—
327C23×C41—22no—
328C23×C41—22no—
329C23×C41—48no—
330C23×C41—48no—
331C23×C41—48no—
332C23×C41—48no—
333C23×C41—41no—
334C23×C41—41no—
335C23×C41—41no—
336C23×C41—41no—
337C23×C41—41no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—41no—
342C23×C41—41no—
343C23×C41—41no—
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—84no—
357C23×C41—84no—
358C23×C41—84no—
359C23×C41—84no—
360C23×C41—84no—
361C23×C41—84no—
362C23×C41—84no—
363C23×C41—84no—
364C23×C41—84no—
365C23×C41—84no—
366C23×C41#12012yes—
367C23×C41AGL(1,ℤ/8)12yes—
368C23×C41C22×D411yescharacteristic
369D4×C41—28no—
370D4×C41—22no—
371D4×C41—22no—
372D4×C41—22no—
373D4×C41—22no—
374D4×C41—22no—
375D4×C41—22no—
376D4×C41—22no—
377D4×C41—48no—
378D4×C41—48no—
379D4×C41—48no—
380D4×C41—48no—
381D4×C41—48no—
382D4×C41—41no—
383D4×C41—41no—
384D4×C41—41no—
385D4×C41—41no—
386D4×C41—41no—
387D4×C41—41no—
388D4×C41—41no—
389D4×C41—41no—
390D4×C41—84no—
391D4×C41—84no—
392D4×C41—84no—
393D4×C41#12114yes—
394C2×C4×C41—21no—
395C2×C4×C41—21no—
396C2×C4×C41—21no—
397C2×C4×C41—21no—
398C2×C4×C41—22no—
399C2×C4×C41—22no—
400C2×C4×C41—22no—
401C2×C4×C41—22no—
402C2×C4×C41—21no—
403C2×C4×C41—21no—
404C2×C4×C41—22no—
405C2×C4×C41—22no—
406C2×C4×C41—21no—
407C2×C4×C41—21no—
408C2×C4×C41—21no—
409C2×C4×C41—21no—
410C2×C4×C41—48no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
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#12012yes—
426C2×C4×C41AGL(1,ℤ/8)12yes—
427C2×C4×C41C22×D411yescharacteristic
428C2×C4×C41C22×D411yescharacteristic
429C2×C4×C41C22×D411yescharacteristic
430C2×C4×C41C2×#4111yescharacteristic
431C2×C4×C41H(5,𝔽2)11yescharacteristic
432C2×C4×C41H(5,𝔽2)11yescharacteristic
433C8×C41—22no—
434C8×C41—41no—
435C8×C41—41no—
436C8×C41—41no—
437#24440C4111yesmaximal, characteristic, direct product factor, Sylow
438C22×C41—22no—
439C22×C41—24no—
440C22×C41—22no—
441C22×C41—22no—
442C22×C41—22no—
443C22×C41—22no—
444C22×C41—22no—
445C22×C41—41no—
446C22×C41—42no—
447C22×C41—41no—
448C22×C41—42no—
449C22×C41—41no—
450C22×C41—42no—
451C22×C41—41no—
452C22×C41—41no—
453C22×C41—42no—
454C22×C41—41no—
455C22×C41—42no—
456C22×C41—41no—
457C22×C41—41no—
458C22×C41—42no—
459C22×C41—42no—
460C22×C41—42no—
461C22×C41—42no—
462C22×C41—42no—
463C22×C41—42no—
464C22×C41—42no—
465C22×C41—816no—
466C22×C41—816no—
467C22×C41—81no—
468C22×C41—81no—
469C22×C41—81no—
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×C41—81no—
479C22×C41—81no—
480C22×C41—81no—
481C22×C41—81no—
482C22×C41C2×#12011yescharacteristic
483C22×C41D4211yescharacteristic
484C22×C41#54611yescharacteristic
485C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C41#57611yescharacteristic
488C22×C41#57611yescharacteristic
489C4×C41—22no—
490C4×C41—22no—
491C4×C41—41no—
492C4×C41—42no—
493C4×C41—41no—
494C4×C41—42no—
495C4×C41—81no—
496C4×C41—81no—
497C4×C41C2×#12111yescharacteristic
498C4×C41#53411yescharacteristic
499C4×C41D4211yescharacteristic
500C4×C41#54611yescharacteristic
501C2×D42C2×C4111yescharacteristic, complemented
502C2×#469C2×C4111yescharacteristic, complemented
503C2×#447C2×C4111yescharacteristic, complemented
504C2×#447C2×C4111yescharacteristic, complemented
505C2×#418C2×C4111yescharacteristic, complemented
506#2414C2×C4111yescharacteristic, complemented
507#2041C2×C4111yescharacteristic, complemented
508#2034C2×C4111yescharacteristic, complemented
509#2011C2×C4111yescharacteristic, complemented
510#1999C2×C4111yescharacteristic, complemented
511#1879C2×C4111yescharacteristic, complemented
512#1875C2×C4111yescharacteristic, complemented
513#1870C2×C4111yescharacteristic, complemented
514#1864C2×C4111yescharacteristic, complemented
515#1786C2×C4111yescharacteristic, complemented
516C2×C41—42no—
517C2×C41—42no—
518C2×C41—44no—
519C2×C41—82no—
520C2×C41—82no—
521C2×C41—161no—
522C2×C41#241011yescharacteristic
523C2×C41#300311yescharacteristic
524C2×C41#300811yescharacteristic
525C2×C41#326411yescharacteristic
526C2×C41#327411yescharacteristic
527C2×C41#331811yescharacteristic
528C2×C41#332511yescharacteristic
529C23×D4—21no—
530C23×D4C22×C4111yescharacteristic
531C23×D4C22×C4111yescharacteristic
532C22×D8C22×C4111yescharacteristic
533C22×D8C22×C4111yescharacteristic, complemented
534C22×D8C22×C4111yescharacteristic, complemented
535C22×M16C22×C4111yescharacteristic, complemented
536D42—24no—
537D42—24no—
538C2×#127C22×C4111yescharacteristic
539C2×#121—21no—
540C2×#121C22×C4111yescharacteristic
541C2×#121C22×C4111yescharacteristic
542C2×#121C22×C4111yescharacteristic, complemented
543C2×#121C22×C4111yescharacteristic, complemented
544C2×#120—21no—
545C2×#120—21no—
546C2×C4×D4C22×C4111yescharacteristic
547C2×C4×D4C22×C4111yescharacteristic
548C2×#117C22×C4111yescharacteristic, complemented
549#469—24no—
550#447—24no—
551#447—24no—
552C2×#106C22×C4111yescharacteristic, complemented
553#418—24no—
554C2×#102C22×C4111yescharacteristic
555C2×#102C22×C4111yescharacteristic
556C2×#102C22×C4111yescharacteristic
557C2×#102C22×C4111yescharacteristic, complemented
558C2×#102C22×C4111yescharacteristic, complemented
559C2×#102C22×C4111yescharacteristic, complemented
560C2×#102C22×C4111yescharacteristic, complemented
561C2×#102C22×C4111yescharacteristic, complemented
562C2×#102C22×C4111yescharacteristic, complemented
563C2×#102C22×C4111yescharacteristic, complemented
564C2×C22⋊C8C22×C4111yescharacteristic, complemented
565C2×C22⋊C8C22×C4111yescharacteristic, complemented
566C2×C22⋊C8C22×C4111yescharacteristic, complemented
567#394—21no—
568#392—21no—
569#390—21no—
570#390C22×C4111yescharacteristic, complemented
571#389C22×C4111yescharacteristic, complemented
572#388—21no—
573#380C22×C4111yescharacteristic, complemented
574#340C22×C4111yescharacteristic, complemented
575#340C22×C4111yescharacteristic, complemented
576#336C22×C4111yescharacteristic, complemented
577#336C22×C4111yescharacteristic, complemented
578C41#2444011yescharacteristic, direct product factor, Sylow
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C4111yescharacteristic
604C22×D4D4×C4114yescomplemented
605C22×D4C23×C4111yescharacteristic
606C22×D4C23×C4111yescharacteristic
607C22×D4C23×C4111yescharacteristic
608C22×D4C23×C4111yescharacteristic
609C23×C4—21no—
610C23×C4C23×C4111yescharacteristic
611C23×C4C23×C4111yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C4111yescharacteristic
625C22×C8C23×C4111yescharacteristic
626C22×C8C23×C4111yescharacteristic
627C22×C8C23×C4111yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C4114yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C4111yescharacteristic
649C2×C4⋊C4C23×C4111yescharacteristic
650C2×C4⋊C4C23×C4111yescharacteristic
651C2×C4⋊C4C23×C4111yescharacteristic
652C2×C4⋊C4C23×C4111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C4111yescharacteristic
663C2×C22⋊C4D4×C4111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C4111yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C4114yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C4111yescharacteristic
701C24C2×D4×C4111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C4112yes—
758C2×D4C2×D4×C4112yes—
759C2×D4C2×D4×C4112yes—
760C2×D4C2×D4×C4112yes—
761C2×D4#41×C4112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C4111yescharacteristic
780C22×C4C2×D4×C4111yescharacteristic
781C22×C4C2×D4×C4111yescharacteristic
782C22×C4C2×D4×C4112yes—
783C22×C4C2×D4×C4112yes—
784C22×C4C2×D4×C4111yescharacteristic
785C22×C4C24×C4111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C4112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C4112yes—
811C4⋊C4C2×D4×C4112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
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—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C4112yes—
881C23AGL(1,ℤ/8)×C4112yes—
882C23C22×D4×C4111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C4114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
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#120×C4112yes—
940C2×C4AGL(1,ℤ/8)×C4112yes—
941C2×C4C22×D4×C4111yescharacteristic
942C2×C4C22×D4×C4111yescharacteristic
943C2×C4C22×D4×C4111yescharacteristic
944C2×C4C2×#41×C4111yescharacteristic
945C2×C4H(5,𝔽2)×C4111yescharacteristic
946C2×C4H(5,𝔽2)×C4111yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—24no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C4111yescharacteristic
996C22D42×C4111yescharacteristic
997C22C41×#54611yescharacteristic
998C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
999C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
1000C22C41×#57611yescharacteristic
1001C22C41×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C4111yescharacteristic
1011C4C41×#53411yescharacteristic
1012C4D42×C4111yescharacteristic
1013C4C41×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C41×#241011yescharacteristic
1021C2C41×#300311yescharacteristic
1022C2C41×#300811yescharacteristic
1023C2C41×#326411yescharacteristic
1024C2C41×#327411yescharacteristic
1025C2C41×#331811yescharacteristic
1026C2C41×#332511yescharacteristic
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×D42×C41C2semidirect
2. C2×C41×#469C2semidirect
3. C2×C41×#447C2semidirect
4. C2×C41×#447C2semidirect
5. C2×C41×#418C2semidirect
6. C41×#2414C2semidirect
7. C41×#2041C2semidirect
8. C41×#2034C2semidirect
9. C41×#2011C2semidirect
10. C41×#1999C2semidirect
11. C41×#1879C2semidirect
12. C41×#1875C2semidirect
13. C41×#1870C2semidirect
14. C41×#1864C2semidirect
15. C41×#1786C2semidirect
20. C22×D8×C41C22semidirect
21. C22×D8×C41C22semidirect
22. C22×M16×C41C22semidirect
29. C2×#121×C41C22semidirect
30. C2×#121×C41C22semidirect
35. C2×#117×C41C22semidirect
39. C2×#106×C41C22semidirect
44. C2×#102×C41C22semidirect
45. C2×#102×C41C22semidirect
46. C2×#102×C41C22semidirect
47. C2×#102×C41C22semidirect
48. C2×#102×C41C22semidirect
49. C2×#102×C41C22semidirect
50. C2×#102×C41C22semidirect
51. C2×C22⋊C8×C41C22semidirect
52. C2×C22⋊C8×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
57. C41×#390C22semidirect
58. C41×#389C22semidirect
60. C41×#380C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#336C22semidirect
64. C41×#336C22semidirect
90. C22×D4×C41D4semidirect
124. #121×C41D4semidirect
162. #102×C41D4semidirect
287. C2×C8×C41C2×D4semidirect
297. C4⋊C4×C41C2×D4semidirect
437. #24440C41direct (N × H)
501. C2×D42C2×C41semidirect
502. C2×#469C2×C41semidirect
503. C2×#447C2×C41semidirect
504. C2×#447C2×C41semidirect
505. C2×#418C2×C41semidirect
506. #2414C2×C41semidirect
507. #2041C2×C41semidirect
508. #2034C2×C41semidirect
509. #2011C2×C41semidirect
510. #1999C2×C41semidirect
511. #1879C2×C41semidirect
512. #1875C2×C41semidirect
513. #1870C2×C41semidirect
514. #1864C2×C41semidirect
515. #1786C2×C41semidirect
533. C22×D8C22×C41semidirect
534. C22×D8C22×C41semidirect
535. C22×M16C22×C41semidirect
542. C2×#121C22×C41semidirect
543. C2×#121C22×C41semidirect
548. C2×#117C22×C41semidirect
552. C2×#106C22×C41semidirect
557. C2×#102C22×C41semidirect
558. C2×#102C22×C41semidirect
559. C2×#102C22×C41semidirect
560. C2×#102C22×C41semidirect
561. C2×#102C22×C41semidirect
562. C2×#102C22×C41semidirect
563. C2×#102C22×C41semidirect
564. C2×C22⋊C8C22×C41semidirect
565. C2×C22⋊C8C22×C41semidirect
566. C2×C22⋊C8C22×C41semidirect
570. #390C22×C41semidirect
571. #389C22×C41semidirect
573. #380C22×C41semidirect
574. #340C22×C41semidirect
575. #340C22×C41semidirect
576. #336C22×C41semidirect
577. #336C22×C41semidirect
578. C41#24440direct (N × H)
604. C22×D4D4×C41semidirect
638. #121D4×C41semidirect
676. #102D4×C41semidirect
801. C2×C8C2×D4×C41semidirect
811. C4⋊C4C2×D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C412
C2×C41×#4692
C2×C41×#4472
C2×C41×#4182
C41×#24142
C41×#20412
C41×#20342
C41×#20112
C41×#19992
C41×#18792
C41×#18752
C41×#18702
C41×#18642
C41×#17862
#2444041