Finite Group Databasebeta

← C41×#33551 #23809752

Subgroups — C41×#33551 #23809752

Order 10496.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3532C211yesmaximal, characteristic, complemented
2C41×#3026C211yesmaximal, characteristic, complemented
3C2×C41×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C41×#3019C211yesmaximal, characteristic, complemented
5C41×#2200C212yesmaximal, complemented
6C41×#2199C212yesmaximal, complemented
7C41×#2197C212yesmaximal, complemented
8C41×#2196C212yesmaximal, complemented
9C41×#2127C211yesmaximal, characteristic, complemented
10C41×#2121C211yesmaximal, characteristic, complemented
11C2×C41×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C41C2211yescharacteristic, complemented
13C41×#575—21no—
14C41×H(3,𝔽4)C2211yescharacteristic, complemented
15C41×#560—21no—
16C41×#560C2211yescharacteristic, complemented
17C41×#551—21no—
18C41×#551C2211yescharacteristic, complemented
19C41×#546—21no—
20C41×#546—21no—
21C41×#546—21no—
22D42×C41—21no—
23D42×C41C2211yescharacteristic, complemented
24C41×#538—21no—
25C41×#538—21no—
26C41×#538—21no—
27C41×#535—21no—
28C41×#535C2211yescharacteristic
29C41×#534—21no—
30C41×#534—21no—
31C41×#534C2211yescharacteristic
32C2×#120×C41—21no—
33C2×#120×C41—21no—
34C2×#120×C41C2211yescharacteristic
35C41×#458—21no—
36C41×#458C2212yescomplemented
37C41×B(4,𝔽2)—21no—
38C41×B(4,𝔽2)—21no—
39C41×B(4,𝔽2)—21no—
40C41×B(4,𝔽2)C2212yes—
41C41×B(4,𝔽2)C2212yescomplemented
42C41×B(4,𝔽2)C2212yescomplemented
43C41×#455—21no—
44C41×#455C2212yescomplemented
45C41×#453—21no—
46C41×#453C2212yescomplemented
47C41×#421—21no—
48C2×#100×C41C2211yescharacteristic, complemented
49C2×#99×C41—21no—
50C2×#99×C41—21no—
51C2×#99×C41C2211yescharacteristic, complemented
52C2×#99×C41C2211yescharacteristic, complemented
53C41×#354C2212yescomplemented
54C41×#353C2212yescomplemented
55C41×#352C2212yescomplemented
56C41×AΣL(1,𝔽16)C2212yescomplemented
57C41×AΣL(1,𝔽16)C2212yescomplemented
58C41×AΣL(1,𝔽16)C2212yescomplemented
59C25×C41D411yescharacteristic, complemented
60H(5,𝔽2)×C41—21no—
61H(5,𝔽2)×C41—21no—
62H(5,𝔽2)×C41—21no—
63H(5,𝔽2)×C41—42no—
64H(5,𝔽2)×C41C2312yes—
65C2×#41×C41—21no—
66C2×#41×C41—21no—
67C2×#41×C41—41no—
68C2×#41×C41D411yescharacteristic, complemented
69C22×D4×C41—21no—
70C22×D4×C41—21no—
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—41no—
77C22×D4×C41—41no—
78C22×D4×C41D411yescharacteristic, complemented
79C22×D4×C41C2311yescharacteristic
80#137×C41—22no—
81#137×C41—41no—
82AGL(1,ℤ/8)×C41—22no—
83AGL(1,ℤ/8)×C41—41no—
84#135×C41—42no—
85C2×M16×C41—21no—
86#127×C41—21no—
87#127×C41D411yescharacteristic, complemented
88#127×C41C2311yescharacteristic
89#126×C41—21no—
90#126×C41—21no—
91#126×C41—21no—
92#126×C41—21no—
93#124×C41—21no—
94#124×C41—21no—
95#124×C41—21no—
96#124×C41—21no—
97#124×C41—21no—
98#124×C41D411yescharacteristic, complemented
99#124×C41C2311yescharacteristic
100#123×C41—21no—
101#123×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×C41—21no—
107#123×C41—21no—
108#123×C41—22no—
109#123×C41—41no—
110#123×C41D411yescharacteristic, complemented
111#123×C41C2311yescharacteristic
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41—21no—
114C22⋊Q8×C41—21no—
115#121×C41—21no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41—21no—
124#121×C41—21no—
125#121×C41—21no—
126#121×C41—21no—
127#121×C41—21no—
128#121×C41—21no—
129#121×C41—21no—
130#121×C41—42no—
131#120×C41—21no—
132#120×C41—21no—
133#120×C41—21no—
134#120×C41—21no—
135#120×C41—21no—
136#120×C41—21no—
137#120×C41—21no—
138#120×C41—21no—
139#120×C41—21no—
140#120×C41—21no—
141#120×C41—21no—
142#120×C41—21no—
143#120×C41—21no—
144#120×C41—21no—
145#120×C41—22no—
146#120×C41—22no—
147#120×C41—22no—
148#120×C41—42no—
149#120×C41—41no—
150#120×C41D411yescharacteristic, complemented
151#120×C41D411yescharacteristic, complemented
152#120×C41D411yescharacteristic, complemented
153#120×C41C2311yescharacteristic
154#120×C41C2311yescharacteristic
155#120×C41C2311yescharacteristic
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162#117×C41—21no—
163#117×C41D411yescharacteristic, complemented
164C2×C22⋊C4×C41—21no—
165C2×C22⋊C4×C41—21no—
166C2×C22⋊C4×C41—21no—
167C2×C22⋊C4×C41—21no—
168C2×C22⋊C4×C41—21no—
169C2×C22⋊C4×C41—21no—
170C2×C22⋊C4×C41—21no—
171C2×C22⋊C4×C41—41no—
172C2×C22⋊C4×C41D411yescharacteristic, complemented
173C2×C22⋊C4×C41D411yescharacteristic, complemented
174#104×C41—22no—
175#104×C41—22no—
176#100×C41—21no—
177#100×C41C2312yes—
178#99×C41—21no—
179#99×C41—21no—
180#99×C41—22no—
181#99×C41—22no—
182#99×C41—22no—
183#99×C41—22no—
184#99×C41C2312yes—
185#99×C41C2312yes—
186C24×C41—21no—
187C24×C41—21no—
188C24×C41—21no—
189C24×C41—21no—
190C24×C41—21no—
191C24×C41—41no—
192C24×C41—41no—
193C24×C41—82no—
194C24×C41C2×D411yescharacteristic
195C24×C41C2×D411yescharacteristic
196C24×C41C2×D411yescharacteristic
197C24×C41C2×D411yescharacteristic
198C24×C41C2×D411yescharacteristic, complemented
199#41×C41—22no—
200#41×C41—22no—
201#41×C41—42no—
202#41×C41—41no—
203#41×C41—42no—
204#41×C41—42no—
205#41×C41—41no—
206#41×C41—41no—
207#41×C41—42no—
208#41×C41—41no—
209#41×C41—82no—
210C2×Q8×C41—21no—
211C2×Q8×C41—21no—
212C2×Q8×C41C2×D411yescharacteristic, complemented
213C2×D4×C41—21no—
214C2×D4×C41—21no—
215C2×D4×C41—21no—
216C2×D4×C41—22no—
217C2×D4×C41—22no—
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—22no—
222C2×D4×C41—22no—
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—41no—
239C2×D4×C41—41no—
240C2×D4×C41—42no—
241C2×D4×C41—42no—
242C2×D4×C41—41no—
243C2×D4×C41—41no—
244C2×D4×C41—41no—
245C2×D4×C41—41no—
246C2×D4×C41—42no—
247C2×D4×C41—42no—
248C2×D4×C41—41no—
249C2×D4×C41—41no—
250C2×D4×C41—41no—
251C2×D4×C41—41no—
252C2×D4×C41—41no—
253C2×D4×C41—42no—
254C2×D4×C41—42no—
255C2×D4×C41—42no—
256C2×D4×C41—82no—
257C2×D4×C41—82no—
258C2×D4×C41—82no—
259C2×D4×C41—82no—
260C2×D4×C41—81no—
261C2×D4×C41—81no—
262C2×D4×C41—84no—
263C2×D4×C41C2×D411yescharacteristic
264C2×D4×C41C2×D411yescharacteristic
265C2×D4×C41C2×D411yescharacteristic
266C2×D4×C41C2×D411yescharacteristic, complemented
267C2×D4×C41C2411yescharacteristic
268C22×C4×C41—21no—
269C22×C4×C41—21no—
270C22×C4×C41—21no—
271C22×C4×C41—21no—
272C22×C4×C41—21no—
273C22×C4×C41—21no—
274C22×C4×C41—21no—
275C22×C4×C41—21no—
276C22×C4×C41—21no—
277C22×C4×C41—21no—
278C22×C4×C41—41no—
279C22×C4×C41—41no—
280C22×C4×C41—41no—
281C22×C4×C41C2×D411yescharacteristic
282C22×C4×C41C2×D411yescharacteristic, complemented
283Q16×C41—42no—
284SD16×C41—42no—
285SD16×C41—42no—
286D8×C41—42no—
287M16×C41—22no—
288M16×C41—41no—
289C2×C8×C41—41no—
290C4⋊C4×C41—21no—
291C4⋊C4×C41—21no—
292C4⋊C4×C41—21no—
293C4⋊C4×C41—21no—
294C4⋊C4×C41—21no—
295C4⋊C4×C41—21no—
296C4⋊C4×C41—21no—
297C4⋊C4×C41—21no—
298C4⋊C4×C41—21no—
299C4⋊C4×C41—42no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—21no—
305C22⋊C4×C41—21no—
306C22⋊C4×C41—21no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—21no—
317C22⋊C4×C41—21no—
318C22⋊C4×C41—21no—
319C22⋊C4×C41—21no—
320C22⋊C4×C41—21no—
321C22⋊C4×C41—21no—
322C22⋊C4×C41—21no—
323C22⋊C4×C41—21no—
324C22⋊C4×C41—21no—
325C22⋊C4×C41—22no—
326C22⋊C4×C41—22no—
327C22⋊C4×C41—42no—
328C22⋊C4×C41—42no—
329C22⋊C4×C41—42no—
330C22⋊C4×C41—41no—
331C22⋊C4×C41—41no—
332C22⋊C4×C41—42no—
333C22⋊C4×C41C2×D411yescharacteristic
334C22⋊C4×C41C2×D411yescharacteristic
335C22⋊C4×C41C2×D411yescharacteristic, complemented
336C22⋊C4×C41C2×D411yescharacteristic, complemented
337C42×C41—21no—
338C42×C41—21no—
339C42×C41C2×D411yescharacteristic, complemented
340C42×C41C2×D411yescharacteristic, complemented
341C23×C41—21no—
342C23×C41—21no—
343C23×C41—21no—
344C23×C41—21no—
345C23×C41—21no—
346C23×C41—22no—
347C23×C41—22no—
348C23×C41—21no—
349C23×C41—21no—
350C23×C41—21no—
351C23×C41—41no—
352C23×C41—41no—
353C23×C41—42no—
354C23×C41—42no—
355C23×C41—42no—
356C23×C41—41no—
357C23×C41—41no—
358C23×C41—42no—
359C23×C41—41no—
360C23×C41—44no—
361C23×C41—41no—
362C23×C41—41no—
363C23×C41—41no—
364C23×C41—81no—
365C23×C41—81no—
366C23×C41—81no—
367C23×C41—81no—
368C23×C41—81no—
369C23×C41—81no—
370C23×C41—81no—
371C23×C41—81no—
372C23×C41—81no—
373C23×C41—82no—
374C23×C41—82no—
375C23×C41—82no—
376C23×C41—82no—
377C23×C41—161no—
378C23×C41#12011yescharacteristic
379C23×C41#12011yescharacteristic
380C23×C41#12011yescharacteristic
381C23×C41C22×D411yescharacteristic
382C23×C41C22×D411yescharacteristic
383Q8×C41—22no—
384Q8×C41—41no—
385Q8×C41—41no—
386Q8×C41—81no—
387D4×C41—22no—
388D4×C41—41no—
389D4×C41—41no—
390D4×C41—41no—
391D4×C41—41no—
392D4×C41—41no—
393D4×C41—41no—
394D4×C41—42no—
395D4×C41—42no—
396D4×C41—42no—
397D4×C41—42no—
398D4×C41—42no—
399D4×C41—42no—
400D4×C41—42no—
401D4×C41—42no—
402D4×C41—42no—
403D4×C41—42no—
404D4×C41—41no—
405D4×C41—41no—
406D4×C41—41no—
407D4×C41—41no—
408D4×C41—81no—
409D4×C41—81no—
410D4×C41—81no—
411D4×C41—81no—
412D4×C41—81no—
413D4×C41—81no—
414D4×C41—81no—
415D4×C41—81no—
416D4×C41—81no—
417D4×C41—81no—
418D4×C41—81no—
419D4×C41—81no—
420D4×C41—81no—
421D4×C41—81no—
422D4×C41—84no—
423D4×C41—84no—
424D4×C41—162no—
425C2×C4×C41—21no—
426C2×C4×C41—21no—
427C2×C4×C41—22no—
428C2×C4×C41—22no—
429C2×C4×C41—21no—
430C2×C4×C41—21no—
431C2×C4×C41—21no—
432C2×C4×C41—21no—
433C2×C4×C41—21no—
434C2×C4×C41—21no—
435C2×C4×C41—21no—
436C2×C4×C41—21no—
437C2×C4×C41—42no—
438C2×C4×C41—42no—
439C2×C4×C41—41no—
440C2×C4×C41—41no—
441C2×C4×C41—42no—
442C2×C4×C41—41no—
443C2×C4×C41—41no—
444C2×C4×C41—42no—
445C2×C4×C41—42no—
446C2×C4×C41—81no—
447C2×C4×C41—81no—
448C2×C4×C41—81no—
449C2×C4×C41—81no—
450C2×C4×C41—81no—
451C2×C4×C41—81no—
452C2×C4×C41—81no—
453C2×C4×C41—82no—
454C2×C4×C41—161no—
455C2×C4×C41#12011yescharacteristic
456C2×C4×C41C22×D411yescharacteristic
457C8×C41—42no—
458#33551C4111yesmaximal, characteristic, direct product factor, Sylow
459C22×C41—22no—
460C22×C41—21no—
461C22×C41—21no—
462C22×C41—21no—
463C22×C41—21no—
464C22×C41—41no—
465C22×C41—41no—
466C22×C41—41no—
467C22×C41—41no—
468C22×C41—41no—
469C22×C41—41no—
470C22×C41—42no—
471C22×C41—41no—
472C22×C41—41no—
473C22×C41—41no—
474C22×C41—41no—
475C22×C41—41no—
476C22×C41—41no—
477C22×C41—42no—
478C22×C41—41no—
479C22×C41—42no—
480C22×C41—42no—
481C22×C41—41no—
482C22×C41—41no—
483C22×C41—41no—
484C22×C41—81no—
485C22×C41—81no—
486C22×C41—81no—
487C22×C41—82no—
488C22×C41—82no—
489C22×C41—82no—
490C22×C41—81no—
491C22×C41—84no—
492C22×C41—82no—
493C22×C41—82no—
494C22×C41—82no—
495C22×C41—81no—
496C22×C41—162no—
497C22×C41—161no—
498C22×C41—161no—
499C22×C41B(4,𝔽2)11yescharacteristic
500C22×C41B(4,𝔽2)11yescharacteristic
501C22×C41C2×#12011yescharacteristic
502C4×C41—21no—
503C4×C41—21no—
504C4×C41—41no—
505C4×C41—41no—
506C4×C41—41no—
507C4×C41—41no—
508C4×C41—41no—
509C4×C41—41no—
510C4×C41—42no—
511C4×C41—41no—
512C4×C41—41no—
513C4×C41—82no—
514C4×C41—82no—
515#3532C2×C4111yescharacteristic, complemented
516#3026C2×C4111yescharacteristic, complemented
517C2×B(4,𝔽2)C2×C4111yescharacteristic, complemented
518#3019C2×C4111yescharacteristic, complemented
519#2200C2×C4112yescomplemented
520#2199C2×C4112yescomplemented
521#2197C2×C4112yescomplemented
522#2196C2×C4112yescomplemented
523#2127C2×C4111yescharacteristic, complemented
524#2121C2×C4111yescharacteristic, complemented
525C2×AΣL(1,𝔽16)C2×C4111yescharacteristic, complemented
526C2×C41—21no—
527C2×C41—21no—
528C2×C41—21no—
529C2×C41—41no—
530C2×C41—41no—
531C2×C41—42no—
532C2×C41—41no—
533C2×C41—41no—
534C2×C41—81no—
535C2×C41—81no—
536C2×C41—81no—
537C2×C41—82no—
538C2×C41C2×B(4,𝔽2)11yescharacteristic
539C2×H(5,𝔽2)C22×C4111yescharacteristic, complemented
540#575—21no—
541H(3,𝔽4)C22×C4111yescharacteristic, complemented
542#560—21no—
543#560C22×C4111yescharacteristic, complemented
544#551—21no—
545#551C22×C4111yescharacteristic, complemented
546#546—21no—
547#546—21no—
548#546—21no—
549D42—21no—
550D42C22×C4111yescharacteristic, complemented
551#538—21no—
552#538—21no—
553#538—21no—
554#535—21no—
555#535C22×C4111yescharacteristic
556#534—21no—
557#534—21no—
558#534C22×C4111yescharacteristic
559C2×#120—21no—
560C2×#120—21no—
561C2×#120C22×C4111yescharacteristic
562#458—21no—
563#458C22×C4112yescomplemented
564B(4,𝔽2)—21no—
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)C22×C4112yes—
568B(4,𝔽2)C22×C4112yescomplemented
569B(4,𝔽2)C22×C4112yescomplemented
570#455—21no—
571#455C22×C4112yescomplemented
572#453—21no—
573#453C22×C4112yescomplemented
574#421—21no—
575C2×#100C22×C4111yescharacteristic, complemented
576C2×#99—21no—
577C2×#99—21no—
578C2×#99C22×C4111yescharacteristic, complemented
579C2×#99C22×C4111yescharacteristic, complemented
580#354C22×C4112yescomplemented
581#353C22×C4112yescomplemented
582#352C22×C4112yescomplemented
583AΣL(1,𝔽16)C22×C4112yescomplemented
584AΣL(1,𝔽16)C22×C4112yescomplemented
585AΣL(1,𝔽16)C22×C4112yescomplemented
586C41#3355111yescharacteristic, direct product factor, Sylow
587C25D4×C4111yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C4112yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C4111yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C4111yescharacteristic, complemented
607C22×D4C23×C4111yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C4111yescharacteristic, complemented
616#127C23×C4111yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C4111yescharacteristic, complemented
627#124C23×C4111yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C4111yescharacteristic, complemented
639#123C23×C4111yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C4111yescharacteristic, complemented
679#120D4×C4111yescharacteristic, complemented
680#120D4×C4111yescharacteristic, complemented
681#120C23×C4111yescharacteristic
682#120C23×C4111yescharacteristic
683#120C23×C4111yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C4111yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C4111yescharacteristic, complemented
701C2×C22⋊C4D4×C4111yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C4112yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C4112yes—
713#99C23×C4112yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C4111yescharacteristic
723C24C2×D4×C4111yescharacteristic
724C24C2×D4×C4111yescharacteristic
725C24C2×D4×C4111yescharacteristic
726C24C2×D4×C4111yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C4111yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C4111yescharacteristic
792C2×D4C2×D4×C4111yescharacteristic
793C2×D4C2×D4×C4111yescharacteristic
794C2×D4C2×D4×C4111yescharacteristic, complemented
795C2×D4C24×C4111yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C4111yescharacteristic
810C22×C4C2×D4×C4111yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C4111yescharacteristic
862C22⋊C4C2×D4×C4111yescharacteristic
863C22⋊C4C2×D4×C4111yescharacteristic, complemented
864C22⋊C4C2×D4×C4111yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C4111yescharacteristic, complemented
868C42C2×D4×C4111yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C4111yescharacteristic
907C23#120×C4111yescharacteristic
908C23#120×C4111yescharacteristic
909C23C22×D4×C4111yescharacteristic
910C23C22×D4×C4111yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C4111yescharacteristic
984C2×C4C22×D4×C4111yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22C41×B(4,𝔽2)11yescharacteristic
1027C22C41×B(4,𝔽2)11yescharacteristic
1028C22C2×#120×C4111yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C41C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3532C2semidirect
2. C41×#3026C2semidirect
3. C2×C41×B(4,𝔽2)C2semidirect
4. C41×#3019C2semidirect
5. C41×#2200C2semidirect
6. C41×#2199C2semidirect
7. C41×#2197C2semidirect
8. C41×#2196C2semidirect
9. C41×#2127C2semidirect
10. C41×#2121C2semidirect
11. C2×C41×AΣL(1,𝔽16)C2semidirect
12. C2×H(5,𝔽2)×C41C22semidirect
14. C41×H(3,𝔽4)C22semidirect
16. C41×#560C22semidirect
18. C41×#551C22semidirect
23. D42×C41C22semidirect
36. C41×#458C22semidirect
41. C41×B(4,𝔽2)C22semidirect
42. C41×B(4,𝔽2)C22semidirect
44. C41×#455C22semidirect
46. C41×#453C22semidirect
48. C2×#100×C41C22semidirect
51. C2×#99×C41C22semidirect
52. C2×#99×C41C22semidirect
53. C41×#354C22semidirect
54. C41×#353C22semidirect
55. C41×#352C22semidirect
56. C41×AΣL(1,𝔽16)C22semidirect
57. C41×AΣL(1,𝔽16)C22semidirect
58. C41×AΣL(1,𝔽16)C22semidirect
59. C25×C41D4semidirect
68. C2×#41×C41D4semidirect
78. C22×D4×C41D4semidirect
87. #127×C41D4semidirect
98. #124×C41D4semidirect
110. #123×C41D4semidirect
150. #120×C41D4semidirect
151. #120×C41D4semidirect
152. #120×C41D4semidirect
163. #117×C41D4semidirect
172. C2×C22⋊C4×C41D4semidirect
173. C2×C22⋊C4×C41D4semidirect
198. C24×C41C2×D4semidirect
212. C2×Q8×C41C2×D4semidirect
266. C2×D4×C41C2×D4semidirect
282. C22×C4×C41C2×D4semidirect
335. C22⋊C4×C41C2×D4semidirect
336. C22⋊C4×C41C2×D4semidirect
339. C42×C41C2×D4semidirect
340. C42×C41C2×D4semidirect
458. #33551C41direct (N × H)
515. #3532C2×C41semidirect
516. #3026C2×C41semidirect
517. C2×B(4,𝔽2)C2×C41semidirect
518. #3019C2×C41semidirect
519. #2200C2×C41semidirect
520. #2199C2×C41semidirect
521. #2197C2×C41semidirect
522. #2196C2×C41semidirect
523. #2127C2×C41semidirect
524. #2121C2×C41semidirect
525. C2×AΣL(1,𝔽16)C2×C41semidirect
539. C2×H(5,𝔽2)C22×C41semidirect
541. H(3,𝔽4)C22×C41semidirect
543. #560C22×C41semidirect
545. #551C22×C41semidirect
550. D42C22×C41semidirect
563. #458C22×C41semidirect
568. B(4,𝔽2)C22×C41semidirect
569. B(4,𝔽2)C22×C41semidirect
571. #455C22×C41semidirect
573. #453C22×C41semidirect
575. C2×#100C22×C41semidirect
578. C2×#99C22×C41semidirect
579. C2×#99C22×C41semidirect
580. #354C22×C41semidirect
581. #353C22×C41semidirect
582. #352C22×C41semidirect
583. AΣL(1,𝔽16)C22×C41semidirect
584. AΣL(1,𝔽16)C22×C41semidirect
585. AΣL(1,𝔽16)C22×C41semidirect
586. C41#33551direct (N × H)
587. C25D4×C41semidirect
596. C2×#41D4×C41semidirect
606. C22×D4D4×C41semidirect
615. #127D4×C41semidirect
626. #124D4×C41semidirect
638. #123D4×C41semidirect
678. #120D4×C41semidirect
679. #120D4×C41semidirect
680. #120D4×C41semidirect
691. #117D4×C41semidirect
700. C2×C22⋊C4D4×C41semidirect
701. C2×C22⋊C4D4×C41semidirect
726. C24C2×D4×C41semidirect
740. C2×Q8C2×D4×C41semidirect
794. C2×D4C2×D4×C41semidirect
810. C22×C4C2×D4×C41semidirect
863. C22⋊C4C2×D4×C41semidirect
864. C22⋊C4C2×D4×C41semidirect
867. C42C2×D4×C41semidirect
868. C42C2×D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35322
C41×#30262
C2×C41×B(4,𝔽2)2
C41×#30192
C41×#22002
C41×#21992
C41×#21972
C41×#21962
C41×#21272
C41×#21212
C2×C41×AΣL(1,𝔽16)2
#3355141