Finite Group Databasebeta

← C41×#19069 #23795270

Subgroups — C41×#19069 #23795270

Order 10496.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3545C211yesmaximal, characteristic
2C41×#3240C211yesmaximal, characteristic, complemented
3C41×#3215C211yesmaximal, characteristic, complemented
4C41×#3172C211yesmaximal, characteristic, complemented
5C41×#1664C211yesmaximal, characteristic, complemented
6C41×#1662C211yesmaximal, characteristic, complemented
7C41×#1661C211yesmaximal, characteristic, complemented
8C41×#1661C211yesmaximal, characteristic, complemented
9C41×#1661C211yesmaximal, characteristic, complemented
10C41×#1660C211yesmaximal, characteristic, complemented
11C41×#1659C211yesmaximal, characteristic, complemented
12C41×#1659C211yesmaximal, characteristic, complemented
13C41×#1535C211yesmaximal, characteristic, complemented
14C41×#1529C211yesmaximal, characteristic, complemented
15C41×#1527C211yesmaximal, characteristic, complemented
16C41×#563C2211yescharacteristic
17C41×#562C2211yescharacteristic
18C41×#562C2211yescharacteristic
19C41×H(3,𝔽4)C2211yescharacteristic
20C41×#555—21no—
21C41×#551—21no—
22C41×#551—21no—
23C41×#551—21no—
24C41×#546—21no—
25C41×#546—21no—
26C41×#542—21no—
27C41×#542—21no—
28C41×#538—21no—
29C41×#538—21no—
30C41×#536—21no—
31C41×#534—21no—
32C41×#533C2211yescharacteristic, complemented
33C41×#529C2211yescharacteristic
34C41×#529C2211yescharacteristic
35C2×#124×C41C2211yescharacteristic
36C41×#501C2211yescharacteristic, complemented
37C41×#501C2211yescharacteristic, complemented
38C41×#501C2211yescharacteristic, complemented
39C41×#497C2211yescharacteristic
40C41×#497C2211yescharacteristic, complemented
41C41×#497C2211yescharacteristic, complemented
42C41×#491C2211yescharacteristic, complemented
43C41×#489C2211yescharacteristic
44C41×#489C2211yescharacteristic, complemented
45C41×#489C2211yescharacteristic, complemented
46C41×#489C2211yescharacteristic, complemented
47C41×#489C2211yescharacteristic, complemented
48C41×#485—21no—
49C41×#482—21no—
50C41×#479—21no—
51C41×#478—21no—
52C41×#470—21no—
53C41×#468—21no—
54C41×#464—21no—
55C41×#464—21no—
56C41×#451—21no—
57C41×#450—21no—
58C4×Q16×C41—21no—
59C4×SD16×C41—21no—
60C41×#432C2211yescharacteristic, complemented
61C41×#432C2211yescharacteristic, complemented
62C4×M16×C41C2211yescharacteristic, complemented
63C41×#330C2211yescharacteristic, complemented
64C41×#330C2211yescharacteristic, complemented
65C41×#330C2211yescharacteristic, complemented
66C41×#330C2211yescharacteristic, complemented
67C41×#329C2211yescharacteristic
68C41×#329C2211yescharacteristic
69C41×#329C2211yescharacteristic, complemented
70C41×#329C2211yescharacteristic, complemented
71C41×#329C2211yescharacteristic, complemented
72C41×#329C2211yescharacteristic, complemented
73C41×#329C2211yescharacteristic, complemented
74C41×#329C2211yescharacteristic, complemented
75C2×#41×C41—21no—
76C22×Q8×C41D411yescharacteristic
77C22×D4×C41—21no—
78C22×D4×C41D411yescharacteristic
79C2×Q16×C41—21no—
80C2×Q16×C41—21no—
81C2×Q16×C41—21no—
82C2×SD16×C41—21no—
83C2×SD16×C41—21no—
84C2×SD16×C41—21no—
85C2×M16×C41—21no—
86C4⋊Q8×C41—21no—
87C4⋊Q8×C41—21no—
88C4⋊Q8×C41C2311yescharacteristic
89C4⋊Q8×C41C2311yescharacteristic
90#126×C41—21no—
91#126×C41—21no—
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#125×C41—21no—
97#125×C41C2311yescharacteristic
98#125×C41C2311yescharacteristic
99#124×C41—21no—
100#124×C41—21no—
101#124×C41—21no—
102#124×C41—21no—
103#124×C41—21no—
104#124×C41—21no—
105#124×C41—21no—
106#124×C41—21no—
107#124×C41D411yescharacteristic
108#124×C41D411yescharacteristic
109#124×C41C2311yescharacteristic
110#124×C41C2311yescharacteristic
111#124×C41C2311yescharacteristic
112#124×C41C2311yescharacteristic
113#123×C41—21no—
114#123×C41—21no—
115#123×C41—21no—
116#123×C41—21no—
117#123×C41—21no—
118#123×C41—21no—
119#123×C41—21no—
120#123×C41—21no—
121#123×C41—21no—
122#123×C41—21no—
123#123×C41—21no—
124#123×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129C22⋊Q8×C41—21no—
130C22⋊Q8×C41—21no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41D411yescharacteristic
136C22⋊Q8×C41D411yescharacteristic
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41—21no—
141#121×C41—21no—
142#121×C41—21no—
143#121×C41—21no—
144#121×C41—21no—
145#121×C41D411yescharacteristic
146#121×C41D411yescharacteristic
147#120×C41—21no—
148#120×C41—21no—
149#120×C41—21no—
150#120×C41—21no—
151#120×C41—21no—
152#120×C41—21no—
153C4×Q8×C41—21no—
154C4×Q8×C41—21no—
155C4×Q8×C41D411yescharacteristic
156C4×Q8×C41D411yescharacteristic
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162C4×D4×C41—21no—
163C4×D4×C41D411yescharacteristic
164C4×D4×C41D411yescharacteristic
165#117×C41—21no—
166#117×C41—21no—
167#117×C41—21no—
168#117×C41—21no—
169#117×C41—21no—
170#117×C41—21no—
171C2×C22⋊C4×C41—21no—
172C2×C22⋊C4×C41—21no—
173C2×C22⋊C4×C41—21no—
174C2×C22⋊C4×C41—21no—
175C2×C22⋊C4×C41—21no—
176C2×C42×C41C2311yescharacteristic
177#107×C41—21no—
178#107×C41—21no—
179#107×C41—21no—
180#106×C41—21no—
181#106×C41—21no—
182#106×C41—21no—
183C4⋊C8×C41—21no—
184C4⋊C8×C41—21no—
185#103×C41—21no—
186#103×C41—21no—
187#103×C41—21no—
188#103×C41—21no—
189#103×C41—21no—
190#103×C41—21no—
191#103×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194#102×C41—21no—
195#102×C41—21no—
196#102×C41—21no—
197C22⋊C8×C41—21no—
198C22⋊C8×C41—21no—
199#97×C41C2311yescharacteristic
200#97×C41C2311yescharacteristic
201#97×C41C2311yescharacteristic
202#97×C41C2311yescharacteristic
203#97×C41C2311yescharacteristic
204#97×C41C2311yescharacteristic
205C4×C8×C41—21no—
206C24×C41—21no—
207C24×C41—21no—
208#41×C41—82no—
209C2×Q8×C41—21no—
210C2×Q8×C41—21no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41—81no—
214C2×Q8×C41C2×D411yescharacteristic
215C2×Q8×C41C2×D411yescharacteristic
216C2×Q8×C41C2×D411yescharacteristic
217C2×Q8×C41C2×D411yescharacteristic
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—21no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—21no—
227C2×D4×C41—21no—
228C2×D4×C41—81no—
229C2×D4×C41—82no—
230C2×D4×C41C2×D411yescharacteristic
231C2×D4×C41C2×D411yescharacteristic
232C2×D4×C41C2×D411yescharacteristic
233C2×D4×C41C2×D411yescharacteristic
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41C2×D411yescharacteristic
243C22×C4×C41C2×D411yescharacteristic
244C22×C4×C41C2×D411yescharacteristic
245Q16×C41—42no—
246Q16×C41—81no—
247Q16×C41—81no—
248SD16×C41—42no—
249SD16×C41—81no—
250SD16×C41—81no—
251M16×C41—42no—
252C2×C8×C41—21no—
253C2×C8×C41—21no—
254C2×C8×C41—21no—
255C2×C8×C41—21no—
256C2×C8×C41—21no—
257C2×C8×C41—21no—
258C4⋊C4×C41—21no—
259C4⋊C4×C41—21no—
260C4⋊C4×C41—21no—
261C4⋊C4×C41—21no—
262C4⋊C4×C41—21no—
263C4⋊C4×C41—21no—
264C4⋊C4×C41—21no—
265C4⋊C4×C41—21no—
266C4⋊C4×C41—21no—
267C4⋊C4×C41—21no—
268C4⋊C4×C41—21no—
269C4⋊C4×C41—21no—
270C4⋊C4×C41—21no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—41no—
277C4⋊C4×C41—41no—
278C4⋊C4×C41C2×D411yescharacteristic
279C4⋊C4×C41C2×D411yescharacteristic
280C4⋊C4×C41C2×D411yescharacteristic
281C4⋊C4×C41C2×D411yescharacteristic
282C22⋊C4×C41—21no—
283C22⋊C4×C41—21no—
284C22⋊C4×C41—21no—
285C22⋊C4×C41—21no—
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—21no—
292C22⋊C4×C41—21no—
293C22⋊C4×C41—21no—
294C22⋊C4×C41—21no—
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
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—41no—
311C42×C41—21no—
312C42×C41—21no—
313C42×C41—21no—
314C42×C41—21no—
315C42×C41—41no—
316C42×C41C2×D411yescharacteristic
317C42×C41C2×D411yescharacteristic
318C42×C41C2×D411yescharacteristic
319C42×C41C2411yescharacteristic
320C23×C41—21no—
321C23×C41—21no—
322C23×C41—21no—
323C23×C41—21no—
324C23×C41—42no—
325C23×C41—81no—
326C23×C41—81no—
327C23×C41—81no—
328C23×C41—81no—
329C23×C41—81no—
330C23×C41#12011yescharacteristic
331Q8×C41—41no—
332Q8×C41—41no—
333Q8×C41—41no—
334Q8×C41—41no—
335Q8×C41—41no—
336Q8×C41—41no—
337Q8×C41—41no—
338Q8×C41—41no—
339Q8×C41—81no—
340Q8×C41—81no—
341D4×C41—41no—
342D4×C41—41no—
343D4×C41—41no—
344D4×C41—41no—
345D4×C41—42no—
346D4×C41—42no—
347D4×C41—81no—
348D4×C41—81no—
349D4×C41—81no—
350D4×C41—81no—
351D4×C41—81no—
352D4×C41—81no—
353D4×C41—81no—
354D4×C41—81no—
355C2×C4×C41—21no—
356C2×C4×C41—21no—
357C2×C4×C41—21no—
358C2×C4×C41—21no—
359C2×C4×C41—21no—
360C2×C4×C41—21no—
361C2×C4×C41—21no—
362C2×C4×C41—21no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—41no—
366C2×C4×C41—42no—
367C2×C4×C41—41no—
368C2×C4×C41—41no—
369C2×C4×C41—81no—
370C2×C4×C41—81no—
371C2×C4×C41—81no—
372C2×C4×C41—81no—
373C2×C4×C41—81no—
374C2×C4×C41—81no—
375C2×C4×C41—81no—
376C2×C4×C41#12011yescharacteristic
377C2×C4×C41#12011yescharacteristic
378C2×C4×C41#12011yescharacteristic
379C2×C4×C41C22×D411yescharacteristic
380C2×C4×C41C22×D411yescharacteristic
381C2×C4×C41C22×D411yescharacteristic
382C8×C41—22no—
383C8×C41—41no—
384C8×C41—41no—
385C8×C41—41no—
386C8×C41—41no—
387C8×C41—41no—
388#19069C4111yesmaximal, characteristic, direct product factor, Sylow
389C22×C41—21no—
390C22×C41—21no—
391C22×C41—21no—
392C22×C41—41no—
393C22×C41—41no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—41no—
399C22×C41—41no—
400C22×C41—41no—
401C22×C41—41no—
402C22×C41—41no—
403C22×C41—41no—
404C22×C41—162no—
405C22×C41—162no—
406C22×C41C2×#12011yescharacteristic
407C4×C41—21no—
408C4×C41—21no—
409C4×C41—21no—
410C4×C41—21no—
411C4×C41—21no—
412C4×C41—21no—
413C4×C41—41no—
414C4×C41—41no—
415C4×C41—41no—
416C4×C41—41no—
417C4×C41—41no—
418C4×C41—41no—
419C4×C41—41no—
420C4×C41—41no—
421C4×C41—81no—
422C4×C41—81no—
423#3545C2×C4111yescharacteristic
424#3240C2×C4111yescharacteristic, complemented
425#3215C2×C4111yescharacteristic, complemented
426#3172C2×C4111yescharacteristic, complemented
427#1664C2×C4111yescharacteristic, complemented
428#1662C2×C4111yescharacteristic, complemented
429#1661C2×C4111yescharacteristic, complemented
430#1661C2×C4111yescharacteristic, complemented
431#1661C2×C4111yescharacteristic, complemented
432#1660C2×C4111yescharacteristic, complemented
433#1659C2×C4111yescharacteristic, complemented
434#1659C2×C4111yescharacteristic, complemented
435#1535C2×C4111yescharacteristic, complemented
436#1529C2×C4111yescharacteristic, complemented
437#1527C2×C4111yescharacteristic, complemented
438C2×C41—41no—
439C2×C41—81no—
440C2×C41—81no—
441C2×C41—81no—
442C2×C41—81no—
443C2×C41#301811yescharacteristic
444C2×C41#301911yescharacteristic
445C2×C41#302211yescharacteristic
446#563C22×C4111yescharacteristic
447#562C22×C4111yescharacteristic
448#562C22×C4111yescharacteristic
449H(3,𝔽4)C22×C4111yescharacteristic
450#555—21no—
451#551—21no—
452#551—21no—
453#551—21no—
454#546—21no—
455#546—21no—
456#542—21no—
457#542—21no—
458#538—21no—
459#538—21no—
460#536—21no—
461#534—21no—
462#533C22×C4111yescharacteristic, complemented
463#529C22×C4111yescharacteristic
464#529C22×C4111yescharacteristic
465C2×#124C22×C4111yescharacteristic
466#501C22×C4111yescharacteristic, complemented
467#501C22×C4111yescharacteristic, complemented
468#501C22×C4111yescharacteristic, complemented
469#497C22×C4111yescharacteristic
470#497C22×C4111yescharacteristic, complemented
471#497C22×C4111yescharacteristic, complemented
472#491C22×C4111yescharacteristic, complemented
473#489C22×C4111yescharacteristic
474#489C22×C4111yescharacteristic, complemented
475#489C22×C4111yescharacteristic, complemented
476#489C22×C4111yescharacteristic, complemented
477#489C22×C4111yescharacteristic, complemented
478#485—21no—
479#482—21no—
480#479—21no—
481#478—21no—
482#470—21no—
483#468—21no—
484#464—21no—
485#464—21no—
486#451—21no—
487#450—21no—
488C4×Q16—21no—
489C4×SD16—21no—
490#432C22×C4111yescharacteristic, complemented
491#432C22×C4111yescharacteristic, complemented
492C4×M16C22×C4111yescharacteristic, complemented
493#330C22×C4111yescharacteristic, complemented
494#330C22×C4111yescharacteristic, complemented
495#330C22×C4111yescharacteristic, complemented
496#330C22×C4111yescharacteristic, complemented
497#329C22×C4111yescharacteristic
498#329C22×C4111yescharacteristic
499#329C22×C4111yescharacteristic, complemented
500#329C22×C4111yescharacteristic, complemented
501#329C22×C4111yescharacteristic, complemented
502#329C22×C4111yescharacteristic, complemented
503#329C22×C4111yescharacteristic, complemented
504#329C22×C4111yescharacteristic, complemented
505C41#1906911yescharacteristic, direct product factor, Sylow
506C2×#41—21no—
507C22×Q8D4×C4111yescharacteristic
508C22×D4—21no—
509C22×D4D4×C4111yescharacteristic
510C2×Q16—21no—
511C2×Q16—21no—
512C2×Q16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×M16—21no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8C23×C4111yescharacteristic
520C4⋊Q8C23×C4111yescharacteristic
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#125—21no—
528#125C23×C4111yescharacteristic
529#125C23×C4111yescharacteristic
530#124—21no—
531#124—21no—
532#124—21no—
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#124—21no—
538#124D4×C4111yescharacteristic
539#124D4×C4111yescharacteristic
540#124C23×C4111yescharacteristic
541#124C23×C4111yescharacteristic
542#124C23×C4111yescharacteristic
543#124C23×C4111yescharacteristic
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8D4×C4111yescharacteristic
567C22⋊Q8D4×C4111yescharacteristic
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121D4×C4111yescharacteristic
577#121D4×C4111yescharacteristic
578#120—21no—
579#120—21no—
580#120—21no—
581#120—21no—
582#120—21no—
583#120—21no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8D4×C4111yescharacteristic
587C4×Q8D4×C4111yescharacteristic
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4D4×C4111yescharacteristic
595C4×D4D4×C4111yescharacteristic
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C42C23×C4111yescharacteristic
608#107—21no—
609#107—21no—
610#107—21no—
611#106—21no—
612#106—21no—
613#106—21no—
614C4⋊C8—21no—
615C4⋊C8—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#103—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628C22⋊C8—21no—
629C22⋊C8—21no—
630#97C23×C4111yescharacteristic
631#97C23×C4111yescharacteristic
632#97C23×C4111yescharacteristic
633#97C23×C4111yescharacteristic
634#97C23×C4111yescharacteristic
635#97C23×C4111yescharacteristic
636C4×C8—21no—
637C24—21no—
638C24—21no—
639#41—82no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—81no—
645C2×Q8C2×D4×C4111yescharacteristic
646C2×Q8C2×D4×C4111yescharacteristic
647C2×Q8C2×D4×C4111yescharacteristic
648C2×Q8C2×D4×C4111yescharacteristic
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—81no—
660C2×D4—82no—
661C2×D4C2×D4×C4111yescharacteristic
662C2×D4C2×D4×C4111yescharacteristic
663C2×D4C2×D4×C4111yescharacteristic
664C2×D4C2×D4×C4111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4C2×D4×C4111yescharacteristic
674C22×C4C2×D4×C4111yescharacteristic
675C22×C4C2×D4×C4111yescharacteristic
676Q16—42no—
677Q16—81no—
678Q16—81no—
679SD16—42no—
680SD16—81no—
681SD16—81no—
682M16—42no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—41no—
708C4⋊C4—41no—
709C4⋊C4C2×D4×C4111yescharacteristic
710C4⋊C4C2×D4×C4111yescharacteristic
711C4⋊C4C2×D4×C4111yescharacteristic
712C4⋊C4C2×D4×C4111yescharacteristic
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—41no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—21no—
746C42—41no—
747C42C2×D4×C4111yescharacteristic
748C42C2×D4×C4111yescharacteristic
749C42C2×D4×C4111yescharacteristic
750C42C24×C4111yescharacteristic
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—42no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23#120×C4111yescharacteristic
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8—41no—
768Q8—41no—
769Q8—41no—
770Q8—81no—
771Q8—81no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—42no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4#120×C4111yescharacteristic
808C2×C4#120×C4111yescharacteristic
809C2×C4#120×C4111yescharacteristic
810C2×C4C22×D4×C4111yescharacteristic
811C2×C4C22×D4×C4111yescharacteristic
812C2×C4C22×D4×C4111yescharacteristic
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C8—41no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—162no—
835C22—162no—
836C22C2×#120×C4111yescharacteristic
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—81no—
852C4—81no—
853C2—41no—
854C2—81no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2C41×#301811yescharacteristic
859C2C41×#301911yescharacteristic
860C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3545C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3240C2semidirect
3. C41×#3215C2semidirect
4. C41×#3172C2semidirect
5. C41×#1664C2semidirect
6. C41×#1662C2semidirect
7. C41×#1661C2semidirect
8. C41×#1661C2semidirect
9. C41×#1661C2semidirect
10. C41×#1660C2semidirect
11. C41×#1659C2semidirect
12. C41×#1659C2semidirect
13. C41×#1535C2semidirect
14. C41×#1529C2semidirect
15. C41×#1527C2semidirect
32. C41×#533C22semidirect
36. C41×#501C22semidirect
37. C41×#501C22semidirect
38. C41×#501C22semidirect
40. C41×#497C22semidirect
41. C41×#497C22semidirect
42. C41×#491C22semidirect
44. C41×#489C22semidirect
45. C41×#489C22semidirect
46. C41×#489C22semidirect
47. C41×#489C22semidirect
60. C41×#432C22semidirect
61. C41×#432C22semidirect
62. C4×M16×C41C22semidirect
63. C41×#330C22semidirect
64. C41×#330C22semidirect
65. C41×#330C22semidirect
66. C41×#330C22semidirect
69. C41×#329C22semidirect
70. C41×#329C22semidirect
71. C41×#329C22semidirect
72. C41×#329C22semidirect
73. C41×#329C22semidirect
74. C41×#329C22semidirect
388. #19069C41direct (N × H)
424. #3240C2×C41semidirect
425. #3215C2×C41semidirect
426. #3172C2×C41semidirect
427. #1664C2×C41semidirect
428. #1662C2×C41semidirect
429. #1661C2×C41semidirect
430. #1661C2×C41semidirect
431. #1661C2×C41semidirect
432. #1660C2×C41semidirect
433. #1659C2×C41semidirect
434. #1659C2×C41semidirect
435. #1535C2×C41semidirect
436. #1529C2×C41semidirect
437. #1527C2×C41semidirect
462. #533C22×C41semidirect
466. #501C22×C41semidirect
467. #501C22×C41semidirect
468. #501C22×C41semidirect
470. #497C22×C41semidirect
471. #497C22×C41semidirect
472. #491C22×C41semidirect
474. #489C22×C41semidirect
475. #489C22×C41semidirect
476. #489C22×C41semidirect
477. #489C22×C41semidirect
490. #432C22×C41semidirect
491. #432C22×C41semidirect
492. C4×M16C22×C41semidirect
493. #330C22×C41semidirect
494. #330C22×C41semidirect
495. #330C22×C41semidirect
496. #330C22×C41semidirect
499. #329C22×C41semidirect
500. #329C22×C41semidirect
501. #329C22×C41semidirect
502. #329C22×C41semidirect
503. #329C22×C41semidirect
504. #329C22×C41semidirect
505. C41#19069direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35452
C41×#32402
C41×#32152
C41×#31722
C41×#16642
C41×#16622
C41×#16612
C41×#16602
C41×#16592
C41×#15352
C41×#15292
C41×#15272
#1906941