Finite Group Databasebeta

← C41×#25152 #23801353

Subgroups — C41×#25152 #23801353

Order 10496.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#463C211yesmaximal, characteristic, complemented
2C2×C41×#450C211yesmaximal, characteristic, complemented
3C2×C41×#447C211yesmaximal, characteristic
4C2×C4×SD16×C41C211yesmaximal, characteristic, complemented
5C41×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C41C211yesmaximal, characteristic, complemented
7C41×#2065C211yesmaximal, characteristic, complemented
8C41×#2036C211yesmaximal, characteristic, complemented
9C41×#2034C211yesmaximal, characteristic, complemented
10C41×#2012C211yesmaximal, characteristic, complemented
11C41×#1970C211yesmaximal, characteristic, complemented
12C41×#1923C211yesmaximal, characteristic, complemented
13C41×#1880C211yesmaximal, characteristic, complemented
14C41×#1879C211yesmaximal, characteristic, complemented
15C41×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C2×#124×C41C2211yescharacteristic, complemented
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×C4×Q8×C41C2211yescharacteristic, complemented
25C2×C4×D4×C41C2211yescharacteristic
26C2×C4×D4×C41C2211yescharacteristic
27C22×C22⋊C4×C41—21no—
28C41×#463—24no—
29C41×#450—24no—
30C41×#447—24no—
31C4×SD16×C41—24no—
32C2×#107×C41C2211yescharacteristic, complemented
33C2×#106×C41C2211yescharacteristic, complemented
34C2×C4⋊C8×C41C2211yescharacteristic, complemented
35C2×#103×C41C2211yescharacteristic, complemented
36C2×#103×C41C2211yescharacteristic, complemented
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic, complemented
42C2×#102×C41C2211yescharacteristic, complemented
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×C22⋊C8×C41C2211yescharacteristic
45C2×C4×C8×C41C2211yescharacteristic, complemented
46C41×#396—21no—
47C41×#394—21no—
48C41×#390—21no—
49C41×#390C2211yescharacteristic
50C41×#390C2211yescharacteristic
51C41×#390C2211yescharacteristic, complemented
52C41×#389C2211yescharacteristic, complemented
53C41×#388—21no—
54C41×#386—21no—
55C41×#386—21no—
56C41×#380C2211yescharacteristic
57C41×#379—21no—
58C4×C22⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic, complemented
60C41×#340C2211yescharacteristic, complemented
61C41×#336C2211yescharacteristic, complemented
62C41×#336C2211yescharacteristic, complemented
63C25×C41—21no—
64C22×Q8×C41C2311yescharacteristic
65C22×D4×C41—22no—
66C22×D4×C41—22no—
67C22×D4×C41—22no—
68C22×D4×C41—22no—
69C22×D4×C41—21no—
70C22×D4×C41—21no—
71C22×D4×C41—41no—
72C22×D4×C41—41no—
73C22×D4×C41C2311yescharacteristic
74C22×D4×C41C2311yescharacteristic
75C22×D4×C41C2311yescharacteristic
76C23×C4×C41—21no—
77C23×C4×C41—21no—
78C23×C4×C41C2311yescharacteristic
79C2×SD16×C41—22no—
80C2×SD16×C41—22no—
81C2×SD16×C41—22no—
82C2×SD16×C41—22no—
83C2×SD16×C41—41no—
84C2×SD16×C41D414yescomplemented
85C2×D8×C41—22no—
86C2×D8×C41—22no—
87C2×D8×C41—22no—
88C2×D8×C41—22no—
89C2×D8×C41—22no—
90C2×D8×C41—41no—
91C22×C8×C41C2311yescharacteristic
92C22×C8×C41C2311yescharacteristic
93C22×C8×C41C2311yescharacteristic
94C22×C8×C41C2311yescharacteristic
95#124×C41—22no—
96#124×C41—41no—
97C22⋊Q8×C41—22no—
98C22⋊Q8×C41—41no—
99#121×C41—22no—
100#121×C41—41no—
101C4×Q8×C41—22no—
102C4×Q8×C41—41no—
103C4×D4×C41—22no—
104C4×D4×C41—22no—
105C4×D4×C41—41no—
106C4×D4×C41—41no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41C2311yescharacteristic
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C22⋊C4×C41—21no—
115C2×C22⋊C4×C41—21no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—44no—
128C2×C22⋊C4×C41D411yescharacteristic
129C2×C22⋊C4×C41D411yescharacteristic
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132C2×C42×C41C2311yescharacteristic
133#107×C41—41no—
134#106×C41—22no—
135C4⋊C8×C41—22no—
136#103×C41—22no—
137#103×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—41no—
143#102×C41D414yes—
144C22⋊C8×C41—22no—
145C22⋊C8×C41—22no—
146C4×C8×C41—22no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41D411yescharacteristic
150#95×C41D411yescharacteristic
151C24×C41—21no—
152C24×C41—24no—
153C24×C41—21no—
154C24×C41—21no—
155C24×C41—42no—
156C24×C41—42no—
157C24×C41—42no—
158C24×C41—42no—
159C24×C41—81no—
160C24×C41—81no—
161C24×C41C2×D411yescharacteristic
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41—21no—
167C2×Q8×C41C2×D412yes—
168C2×D4×C41—24no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—21no—
179C2×D4×C41—21no—
180C2×D4×C41—21no—
181C2×D4×C41—21no—
182C2×D4×C41—21no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—42no—
186C2×D4×C41—44no—
187C2×D4×C41—44no—
188C2×D4×C41—44no—
189C2×D4×C41—44no—
190C2×D4×C41—42no—
191C2×D4×C41—81no—
192C2×D4×C41C2×D412yes—
193C2×D4×C41C2×D412yes—
194C2×D4×C41#4112yes—
195C2×D4×C41#4112yes—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—42no—
208C22×C4×C41—42no—
209C22×C4×C41—42no—
210C22×C4×C41—42no—
211C22×C4×C41—81no—
212C22×C4×C41—81no—
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2411yescharacteristic
219SD16×C41—28no—
220SD16×C41—44no—
221D8×C41—44no—
222D8×C41—44no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41C2×D412yes—
234C2×C8×C41C2×D412yes—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—42no—
243C4⋊C4×C41—42no—
244C4⋊C4×C41—81no—
245C4⋊C4×C41C2×D412yes—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41—42no—
254C22⋊C4×C41—42no—
255C22⋊C4×C41—42no—
256C22⋊C4×C41—42no—
257C22⋊C4×C41—42no—
258C22⋊C4×C41—81no—
259C22⋊C4×C41—81no—
260C22⋊C4×C41—81no—
261C42×C41—21no—
262C42×C41—21no—
263C42×C41—21no—
264C42×C41—21no—
265C42×C41—42no—
266C23×C41—21no—
267C23×C41—22no—
268C23×C41—21no—
269C23×C41—22no—
270C23×C41—22no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—21no—
274C23×C41—21no—
275C23×C41—22no—
276C23×C41—48no—
277C23×C41—48no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41—41no—
295C23×C41—84no—
296C23×C41—84no—
297C23×C41—84no—
298C23×C41—84no—
299C23×C41—84no—
300C23×C41#13512yes—
301C23×C41C22×D411yescharacteristic
302Q8×C41—22no—
303Q8×C41—22no—
304Q8×C41—41no—
305Q8×C41—41no—
306D4×C41—22no—
307D4×C41—22no—
308D4×C41—22no—
309D4×C41—22no—
310D4×C41—22no—
311D4×C41—48no—
312D4×C41—41no—
313D4×C41—41no—
314D4×C41—41no—
315D4×C41—41no—
316D4×C41—41no—
317D4×C41—41no—
318D4×C41—84no—
319D4×C41#12114yes—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—22no—
327C2×C4×C41—22no—
328C2×C4×C41—21no—
329C2×C4×C41—21no—
330C2×C4×C41—21no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—84no—
354C2×C4×C41—84no—
355C2×C4×C41AGL(1,ℤ/8)12yes—
356C2×C4×C41C22×D411yescharacteristic
357C2×C4×C41C22×D411yescharacteristic
358C2×C4×C41C2×#4111yescharacteristic
359C2×C4×C41C2×#4111yescharacteristic
360C2×C4×C41H(5,𝔽2)11yescharacteristic
361C2×C4×C41H(5,𝔽2)11yescharacteristic
362C8×C41—22no—
363C8×C41—22no—
364C8×C41—41no—
365C8×C41—41no—
366#25152C4111yesmaximal, characteristic, direct product factor, Sylow
367C22×C41—22no—
368C22×C41—24no—
369C22×C41—22no—
370C22×C41—22no—
371C22×C41—42no—
372C22×C41—41no—
373C22×C41—42no—
374C22×C41—41no—
375C22×C41—42no—
376C22×C41—41no—
377C22×C41—42no—
378C22×C41—41no—
379C22×C41—42no—
380C22×C41—42no—
381C22×C41—42no—
382C22×C41—42no—
383C22×C41—42no—
384C22×C41—816no—
385C22×C41—81no—
386C22×C41—81no—
387C22×C41—81no—
388C22×C41—81no—
389C22×C41—81no—
390C22×C41—81no—
391C22×C41—81no—
392C22×C41—81no—
393C22×C41—81no—
394C22×C41—81no—
395C22×C41—81no—
396C22×C41#52511yescharacteristic
397C22×C41D4211yescharacteristic
398C22×C41D4211yescharacteristic
399C22×C41C2×#13511yescharacteristic
400C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C41#57611yescharacteristic
402C22×C41#57711yescharacteristic
403C4×C41—22no—
404C4×C41—41no—
405C4×C41—42no—
406C4×C41—41no—
407C4×C41—41no—
408C4×C41—42no—
409C4×C41—41no—
410C4×C41—81no—
411C4×C41—81no—
412C4×C41—81no—
413C4×C41C2×#12111yescharacteristic
414C4×C41#53811yescharacteristic
415C4×C41#54611yescharacteristic
416C4×C41#54611yescharacteristic
417C2×#463C2×C4111yescharacteristic, complemented
418C2×#450C2×C4111yescharacteristic, complemented
419C2×#447C2×C4111yescharacteristic
420C2×C4×SD16C2×C4111yescharacteristic, complemented
421#2426C2×C4111yescharacteristic, complemented
422D4×C22⋊C4C2×C4111yescharacteristic, complemented
423#2065C2×C4111yescharacteristic, complemented
424#2036C2×C4111yescharacteristic, complemented
425#2034C2×C4111yescharacteristic, complemented
426#2012C2×C4111yescharacteristic, complemented
427#1970C2×C4111yescharacteristic, complemented
428#1923C2×C4111yescharacteristic, complemented
429#1880C2×C4111yescharacteristic, complemented
430#1879C2×C4111yescharacteristic, complemented
431#1862C2×C4111yescharacteristic, complemented
432C2×C41—42no—
433C2×C41—44no—
434C2×C41—82no—
435C2×C41—161no—
436C2×C41#242411yescharacteristic
437C2×C41#310511yescharacteristic
438C2×C41#311811yescharacteristic
439C2×C41#326511yescharacteristic
440C2×C41#327411yescharacteristic
441C2×C41#328011yescharacteristic
442C2×C41#328211yescharacteristic
443C23×D4C22×C4111yescharacteristic
444C22×SD16C22×C4111yescharacteristic
445C22×SD16C22×C4111yescharacteristic
446C22×D8C22×C4111yescharacteristic
447C22×D8C22×C4111yescharacteristic
448C2×#124C22×C4111yescharacteristic, complemented
449C2×C22⋊Q8C22×C4111yescharacteristic
450C2×#121C22×C4111yescharacteristic
451C2×C4×Q8C22×C4111yescharacteristic, complemented
452C2×C4×D4C22×C4111yescharacteristic
453C2×C4×D4C22×C4111yescharacteristic
454C22×C22⋊C4—21no—
455#463—24no—
456#450—24no—
457#447—24no—
458C4×SD16—24no—
459C2×#107C22×C4111yescharacteristic, complemented
460C2×#106C22×C4111yescharacteristic, complemented
461C2×C4⋊C8C22×C4111yescharacteristic, complemented
462C2×#103C22×C4111yescharacteristic, complemented
463C2×#103C22×C4111yescharacteristic, complemented
464C2×#102C22×C4111yescharacteristic
465C2×#102C22×C4111yescharacteristic
466C2×#102C22×C4111yescharacteristic
467C2×#102C22×C4111yescharacteristic
468C2×#102C22×C4111yescharacteristic, complemented
469C2×#102C22×C4111yescharacteristic, complemented
470C2×C22⋊C8C22×C4111yescharacteristic
471C2×C22⋊C8C22×C4111yescharacteristic
472C2×C4×C8C22×C4111yescharacteristic, complemented
473#396—21no—
474#394—21no—
475#390—21no—
476#390C22×C4111yescharacteristic
477#390C22×C4111yescharacteristic
478#390C22×C4111yescharacteristic, complemented
479#389C22×C4111yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#386—21no—
483#380C22×C4111yescharacteristic
484#379—21no—
485C4×C22⋊C4C22×C4111yescharacteristic
486#340C22×C4111yescharacteristic, complemented
487#340C22×C4111yescharacteristic, complemented
488#336C22×C4111yescharacteristic, complemented
489#336C22×C4111yescharacteristic, complemented
490C41#2515211yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C4111yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C4111yescharacteristic
502C22×D4C23×C4111yescharacteristic
503C22×D4C23×C4111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C4111yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C4114yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C4111yescharacteristic
520C22×C8C23×C4111yescharacteristic
521C22×C8C23×C4111yescharacteristic
522C22×C8C23×C4111yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C4111yescharacteristic
539C2×C4⋊C4C23×C4111yescharacteristic
540C2×C4⋊C4C23×C4111yescharacteristic
541C2×C4⋊C4C23×C4111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C4111yescharacteristic
557C2×C22⋊C4D4×C4111yescharacteristic
558C2×C42—21no—
559C2×C42C23×C4111yescharacteristic
560C2×C42C23×C4111yescharacteristic
561#107—41no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C4114yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C4111yescharacteristic
578#95D4×C4111yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C4111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C4112yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C4112yes—
621C2×D4C2×D4×C4112yes—
622C2×D4#41×C4112yes—
623C2×D4#41×C4112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C4111yescharacteristic
642C22×C4C2×D4×C4111yescharacteristic
643C22×C4C2×D4×C4111yescharacteristic
644C22×C4C2×D4×C4111yescharacteristic
645C22×C4C2×D4×C4111yescharacteristic
646C22×C4C24×C4111yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C4112yes—
662C2×C8C2×D4×C4112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C4112yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#135×C4112yes—
729C23C22×D4×C4111yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C4114yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4AGL(1,ℤ/8)×C4112yes—
784C2×C4C22×D4×C4111yescharacteristic
785C2×C4C22×D4×C4111yescharacteristic
786C2×C4C2×#41×C4111yescharacteristic
787C2×C4C2×#41×C4111yescharacteristic
788C2×C4H(5,𝔽2)×C4111yescharacteristic
789C2×C4H(5,𝔽2)×C4111yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C41×#52511yescharacteristic
824C22D42×C4111yescharacteristic
825C22D42×C4111yescharacteristic
826C22C2×#135×C4111yescharacteristic
827C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
828C22C41×#57611yescharacteristic
829C22C41×#57711yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C4111yescharacteristic
841C4C41×#53811yescharacteristic
842C4C41×#54611yescharacteristic
843C4C41×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C41×#242411yescharacteristic
849C2C41×#310511yescharacteristic
850C2C41×#311811yescharacteristic
851C2C41×#326511yescharacteristic
852C2C41×#327411yescharacteristic
853C2C41×#328011yescharacteristic
854C2C41×#328211yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#463C2semidirect
2. C2×C41×#450C2semidirect
4. C2×C4×SD16×C41C2semidirect
5. C41×#2426C2semidirect
6. D4×C22⋊C4×C41C2semidirect
7. C41×#2065C2semidirect
8. C41×#2036C2semidirect
9. C41×#2034C2semidirect
10. C41×#2012C2semidirect
11. C41×#1970C2semidirect
12. C41×#1923C2semidirect
13. C41×#1880C2semidirect
14. C41×#1879C2semidirect
15. C41×#1862C2semidirect
21. C2×#124×C41C22semidirect
24. C2×C4×Q8×C41C22semidirect
32. C2×#107×C41C22semidirect
33. C2×#106×C41C22semidirect
34. C2×C4⋊C8×C41C22semidirect
35. C2×#103×C41C22semidirect
36. C2×#103×C41C22semidirect
41. C2×#102×C41C22semidirect
42. C2×#102×C41C22semidirect
45. C2×C4×C8×C41C22semidirect
51. C41×#390C22semidirect
52. C41×#389C22semidirect
59. C41×#340C22semidirect
60. C41×#340C22semidirect
61. C41×#336C22semidirect
62. C41×#336C22semidirect
84. C2×SD16×C41D4semidirect
366. #25152C41direct (N × H)
417. C2×#463C2×C41semidirect
418. C2×#450C2×C41semidirect
420. C2×C4×SD16C2×C41semidirect
421. #2426C2×C41semidirect
422. D4×C22⋊C4C2×C41semidirect
423. #2065C2×C41semidirect
424. #2036C2×C41semidirect
425. #2034C2×C41semidirect
426. #2012C2×C41semidirect
427. #1970C2×C41semidirect
428. #1923C2×C41semidirect
429. #1880C2×C41semidirect
430. #1879C2×C41semidirect
431. #1862C2×C41semidirect
448. C2×#124C22×C41semidirect
451. C2×C4×Q8C22×C41semidirect
459. C2×#107C22×C41semidirect
460. C2×#106C22×C41semidirect
461. C2×C4⋊C8C22×C41semidirect
462. C2×#103C22×C41semidirect
463. C2×#103C22×C41semidirect
468. C2×#102C22×C41semidirect
469. C2×#102C22×C41semidirect
472. C2×C4×C8C22×C41semidirect
478. #390C22×C41semidirect
479. #389C22×C41semidirect
486. #340C22×C41semidirect
487. #340C22×C41semidirect
488. #336C22×C41semidirect
489. #336C22×C41semidirect
490. C41#25152direct (N × H)
512. C2×SD16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4632
C2×C41×#4502
C2×C41×#4472
C2×C4×SD16×C412
C41×#24262
D4×C22⋊C4×C412
C41×#20652
C41×#20362
C41×#20342
C41×#20122
C41×#19702
C41×#19232
C41×#18802
C41×#18792
C41×#18622
#2515241