Finite Group Databasebeta

← C41×#19038 #23795239

Subgroups — C41×#19038 #23795239

Order 10496.

876 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3568C211yesmaximal, characteristic, complemented
2C41×#3219C211yesmaximal, characteristic, complemented
3C41×#3180C211yesmaximal, characteristic, complemented
4C41×#3171C211yesmaximal, characteristic, complemented
5C41×#1664C211yesmaximal, characteristic, complemented
6C41×#1664C211yesmaximal, characteristic, complemented
7C41×#1660C211yesmaximal, characteristic, complemented
8C41×#1659C211yesmaximal, characteristic, complemented
9C41×#1657C211yesmaximal, characteristic, complemented
10C41×#1657C211yesmaximal, characteristic, complemented
11C41×#1657C211yesmaximal, characteristic, complemented
12C41×#1655C211yesmaximal, characteristic, complemented
13C41×#1532C211yesmaximal, characteristic, complemented
14C41×#1529C211yesmaximal, characteristic, complemented
15C41×#1524C211yesmaximal, characteristic, complemented
16C41×#563C2211yescharacteristic
17C41×#563C2211yescharacteristic
18C41×#563C2211yescharacteristic
19C41×H(3,𝔽4)C2211yescharacteristic
20C41×#556—21no—
21C41×#556—21no—
22C41×#556—21no—
23C41×#551—21no—
24C41×#551—21no—
25C41×#551—21no—
26C41×#542—21no—
27C41×#542—21no—
28C41×#542—21no—
29C41×#538—21no—
30C41×#538—21no—
31C41×#538—21no—
32C41×#532C2211yescharacteristic, complemented
33C41×#529C2211yescharacteristic
34C41×#529C2211yescharacteristic
35C41×#529C2211yescharacteristic
36C41×#501C2211yescharacteristic, complemented
37C41×#501C2211yescharacteristic, complemented
38C41×#497C2211yescharacteristic
39C41×#496C2211yescharacteristic
40C41×#496C2211yescharacteristic
41C41×#496C2211yescharacteristic
42C41×#491C2211yescharacteristic, complemented
43C41×#490C2211yescharacteristic, complemented
44C41×#490C2211yescharacteristic, complemented
45C41×#490C2211yescharacteristic, complemented
46C41×#489C2211yescharacteristic
47C41×#489C2211yescharacteristic
48C41×#469—21no—
49C41×#468—21no—
50C41×#466—21no—
51C41×#465—21no—
52C41×#464—21no—
53C41×#463—21no—
54C41×#452—21no—
55C41×#449—21no—
56C41×#442—21no—
57C41×#440—21no—
58C4×SD16×C41—21no—
59C4×D8×C41—21no—
60C41×#432C2211yescharacteristic, complemented
61C4×M16×C41C2211yescharacteristic, complemented
62C2×#97×C41C2211yescharacteristic, complemented
63C41×#330C2211yescharacteristic, complemented
64C41×#330C2211yescharacteristic, complemented
65C41×#330C2211yescharacteristic, complemented
66C41×#330C2211yescharacteristic, complemented
67C41×#330C2211yescharacteristic, complemented
68C41×#330C2211yescharacteristic, complemented
69C41×#329C2211yescharacteristic
70C41×#329C2211yescharacteristic
71C41×#329C2211yescharacteristic
72C41×#329C2211yescharacteristic
73C41×#329C2211yescharacteristic
74C41×#329C2211yescharacteristic
75C2×#41×C41—21no—
76C2×Q16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×D8×C41—21no—
82C2×D8×C41—21no—
83C2×D8×C41—21no—
84C2×M16×C41—21no—
85C22×C8×C41—21no—
86C4⋊Q8×C41—21no—
87C4⋊Q8×C41—21no—
88C4⋊Q8×C41—21no—
89C4⋊Q8×C41C2311yescharacteristic
90#127×C41C2311yescharacteristic
91#126×C41—21no—
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#126×C41—21no—
97#126×C41—21no—
98#126×C41—21no—
99#126×C41—21no—
100#126×C41—21no—
101#126×C41—21no—
102#126×C41—21no—
103#126×C41—21no—
104#125×C41C2311yescharacteristic
105#125×C41C2311yescharacteristic
106#125×C41C2311yescharacteristic
107#124×C41—21no—
108#124×C41—21no—
109#124×C41—21no—
110#124×C41—21no—
111#124×C41—21no—
112#124×C41—21no—
113#124×C41—21no—
114#124×C41—21no—
115#124×C41—21no—
116#124×C41—21no—
117#124×C41C2311yescharacteristic
118#124×C41C2311yescharacteristic
119#124×C41C2311yescharacteristic
120#123×C41—21no—
121#123×C41—21no—
122#123×C41—21no—
123#123×C41—21no—
124#123×C41—21no—
125#123×C41—21no—
126#123×C41—21no—
127#123×C41—21no—
128#123×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×C41—21no—
136C22⋊Q8×C41—21no—
137C22⋊Q8×C41—21no—
138C22⋊Q8×C41D411yescharacteristic
139C22⋊Q8×C41D411yescharacteristic
140C22⋊Q8×C41D411yescharacteristic
141#121×C41—21no—
142#121×C41—21no—
143#121×C41—21no—
144#121×C41—21no—
145#121×C41—21no—
146#121×C41D411yescharacteristic
147#121×C41D411yescharacteristic
148#121×C41D411yescharacteristic
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×C41—21no—
156C4×Q8×C41D411yescharacteristic
157C4×Q8×C41D411yescharacteristic
158C4×Q8×C41D411yescharacteristic
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162C4×D4×C41—21no—
163C4×D4×C41—21no—
164C4×D4×C41—21no—
165C4×D4×C41—21no—
166C4×D4×C41—21no—
167C4×D4×C41D411yescharacteristic
168C4×D4×C41D411yescharacteristic
169C4×D4×C41D411yescharacteristic
170#117×C41—21no—
171#117×C41—21no—
172#117×C41—21no—
173#117×C41—21no—
174#117×C41—21no—
175#117×C41—21no—
176C2×C22⋊C4×C41—21no—
177C2×C22⋊C4×C41—21no—
178C2×C22⋊C4×C41—21no—
179C2×C42×C41C2311yescharacteristic
180#107×C41—21no—
181#107×C41—21no—
182#106×C41—21no—
183#106×C41—21no—
184C4⋊C8×C41—21no—
185#103×C41—21no—
186#103×C41—21no—
187#103×C41—21no—
188#103×C41—21no—
189#102×C41—21no—
190#102×C41—21no—
191#102×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—
198#97×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—
207#41×C41—81no—
208#41×C41—81no—
209C2×Q8×C41—21no—
210C2×Q8×C41—21no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41C2×D411yescharacteristic
214C2×Q8×C41C2×D411yescharacteristic
215C2×Q8×C41C2×D411yescharacteristic
216C2×D4×C41—21no—
217C2×D4×C41—21no—
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—41no—
226C2×D4×C41C2×D411yescharacteristic
227C2×D4×C41C2×D411yescharacteristic
228C2×D4×C41C2×D411yescharacteristic
229C22×C4×C41—21no—
230C22×C4×C41—21no—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—41no—
236C22×C4×C41C2×D411yescharacteristic
237C22×C4×C41C2×D411yescharacteristic
238C22×C4×C41C2×D411yescharacteristic
239Q16×C41—81no—
240SD16×C41—42no—
241SD16×C41—42no—
242SD16×C41—81no—
243SD16×C41—81no—
244D8×C41—42no—
245D8×C41—42no—
246D8×C41—81no—
247M16×C41—42no—
248C2×C8×C41—21no—
249C2×C8×C41—21no—
250C2×C8×C41—21no—
251C2×C8×C41—21no—
252C2×C8×C41—21no—
253C2×C8×C41—21no—
254C2×C8×C41—42no—
255C4⋊C4×C41—21no—
256C4⋊C4×C41—21no—
257C4⋊C4×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×C41C2×D411yescharacteristic
276C4⋊C4×C41C2×D411yescharacteristic
277C4⋊C4×C41C2×D411yescharacteristic
278C4⋊C4×C41C2×D411yescharacteristic
279C4⋊C4×C41C2×D411yescharacteristic
280C4⋊C4×C41C2×D411yescharacteristic
281C22⋊C4×C41—21no—
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—41no—
309C22⋊C4×C41—41no—
310C42×C41—21no—
311C42×C41—21no—
312C42×C41—21no—
313C42×C41—21no—
314C42×C41—21no—
315C42×C41—21no—
316C42×C41—21no—
317C42×C41C2×D411yescharacteristic
318C42×C41C2×D411yescharacteristic
319C42×C41C2×D411yescharacteristic
320C42×C41C2411yescharacteristic
321C23×C41—21no—
322C23×C41—21no—
323C23×C41—21no—
324C23×C41—41no—
325C23×C41—81no—
326C23×C41—81no—
327C23×C41—81no—
328C23×C41#12011yescharacteristic
329Q8×C41—41no—
330Q8×C41—41no—
331Q8×C41—41no—
332Q8×C41—41no—
333Q8×C41—41no—
334Q8×C41—81no—
335Q8×C41—81no—
336Q8×C41—81no—
337D4×C41—41no—
338D4×C41—41no—
339D4×C41—41no—
340D4×C41—41no—
341D4×C41—41no—
342D4×C41—41no—
343D4×C41—41no—
344D4×C41—41no—
345D4×C41—41no—
346D4×C41—81no—
347D4×C41—81no—
348D4×C41—81no—
349D4×C41—81no—
350D4×C41—81no—
351D4×C41—81no—
352D4×C41—82no—
353C2×C4×C41—21no—
354C2×C4×C41—21no—
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—41no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—41no—
366C2×C4×C41—81no—
367C2×C4×C41—81no—
368C2×C4×C41—81no—
369C2×C4×C41—82no—
370C2×C4×C41—81no—
371C2×C4×C41—81no—
372C2×C4×C41—81no—
373C2×C4×C41#12011yescharacteristic
374C2×C4×C41#12011yescharacteristic
375C2×C4×C41#12011yescharacteristic
376C2×C4×C41C22×D411yescharacteristic
377C2×C4×C41C22×D411yescharacteristic
378C2×C4×C41C22×D411yescharacteristic
379C8×C41—22no—
380C8×C41—22no—
381C8×C41—41no—
382C8×C41—41no—
383C8×C41—41no—
384C8×C41—41no—
385#19038C4111yesmaximal, characteristic, direct product factor, Sylow
386C22×C41—21no—
387C22×C41—21no—
388C22×C41—21no—
389C22×C41—41no—
390C22×C41—41no—
391C22×C41—41no—
392C22×C41—41no—
393C22×C41—41no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—81no—
399C22×C41—81no—
400C22×C41—81no—
401C22×C41—162no—
402C22×C41C2×#12011yescharacteristic
403C4×C41—21no—
404C4×C41—21no—
405C4×C41—21no—
406C4×C41—21no—
407C4×C41—21no—
408C4×C41—21no—
409C4×C41—41no—
410C4×C41—41no—
411C4×C41—41no—
412C4×C41—41no—
413C4×C41—41no—
414C4×C41—41no—
415C4×C41—41no—
416C4×C41—41no—
417C4×C41—41no—
418C4×C41—81no—
419#3568C2×C4111yescharacteristic, complemented
420#3219C2×C4111yescharacteristic, complemented
421#3180C2×C4111yescharacteristic, complemented
422#3171C2×C4111yescharacteristic, complemented
423#1664C2×C4111yescharacteristic, complemented
424#1664C2×C4111yescharacteristic, complemented
425#1660C2×C4111yescharacteristic, complemented
426#1659C2×C4111yescharacteristic, complemented
427#1657C2×C4111yescharacteristic, complemented
428#1657C2×C4111yescharacteristic, complemented
429#1657C2×C4111yescharacteristic, complemented
430#1655C2×C4111yescharacteristic, complemented
431#1532C2×C4111yescharacteristic, complemented
432#1529C2×C4111yescharacteristic, complemented
433#1524C2×C4111yescharacteristic, complemented
434C2×C41—41no—
435C2×C41—81no—
436C2×C41—81no—
437C2×C41—81no—
438C2×C41—161no—
439C2×C41#301811yescharacteristic
440C2×C41#301811yescharacteristic
441C2×C41#302111yescharacteristic
442#563C22×C4111yescharacteristic
443#563C22×C4111yescharacteristic
444#563C22×C4111yescharacteristic
445H(3,𝔽4)C22×C4111yescharacteristic
446#556—21no—
447#556—21no—
448#556—21no—
449#551—21no—
450#551—21no—
451#551—21no—
452#542—21no—
453#542—21no—
454#542—21no—
455#538—21no—
456#538—21no—
457#538—21no—
458#532C22×C4111yescharacteristic, complemented
459#529C22×C4111yescharacteristic
460#529C22×C4111yescharacteristic
461#529C22×C4111yescharacteristic
462#501C22×C4111yescharacteristic, complemented
463#501C22×C4111yescharacteristic, complemented
464#497C22×C4111yescharacteristic
465#496C22×C4111yescharacteristic
466#496C22×C4111yescharacteristic
467#496C22×C4111yescharacteristic
468#491C22×C4111yescharacteristic, complemented
469#490C22×C4111yescharacteristic, complemented
470#490C22×C4111yescharacteristic, complemented
471#490C22×C4111yescharacteristic, complemented
472#489C22×C4111yescharacteristic
473#489C22×C4111yescharacteristic
474#469—21no—
475#468—21no—
476#466—21no—
477#465—21no—
478#464—21no—
479#463—21no—
480#452—21no—
481#449—21no—
482#442—21no—
483#440—21no—
484C4×SD16—21no—
485C4×D8—21no—
486#432C22×C4111yescharacteristic, complemented
487C4×M16C22×C4111yescharacteristic, complemented
488C2×#97C22×C4111yescharacteristic, complemented
489#330C22×C4111yescharacteristic, complemented
490#330C22×C4111yescharacteristic, complemented
491#330C22×C4111yescharacteristic, complemented
492#330C22×C4111yescharacteristic, complemented
493#330C22×C4111yescharacteristic, complemented
494#330C22×C4111yescharacteristic, complemented
495#329C22×C4111yescharacteristic
496#329C22×C4111yescharacteristic
497#329C22×C4111yescharacteristic
498#329C22×C4111yescharacteristic
499#329C22×C4111yescharacteristic
500#329C22×C4111yescharacteristic
501C41#1903811yescharacteristic, direct product factor, Sylow
502C2×#41—21no—
503C2×Q16—21no—
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×D8—21no—
509C2×D8—21no—
510C2×D8—21no—
511C2×M16—21no—
512C22×C8—21no—
513C4⋊Q8—21no—
514C4⋊Q8—21no—
515C4⋊Q8—21no—
516C4⋊Q8C23×C4111yescharacteristic
517#127C23×C4111yescharacteristic
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#126—21no—
528#126—21no—
529#126—21no—
530#126—21no—
531#125C23×C4111yescharacteristic
532#125C23×C4111yescharacteristic
533#125C23×C4111yescharacteristic
534#124—21no—
535#124—21no—
536#124—21no—
537#124—21no—
538#124—21no—
539#124—21no—
540#124—21no—
541#124—21no—
542#124—21no—
543#124—21no—
544#124C23×C4111yescharacteristic
545#124C23×C4111yescharacteristic
546#124C23×C4111yescharacteristic
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⋊Q8D4×C4111yescharacteristic
566C22⋊Q8D4×C4111yescharacteristic
567C22⋊Q8D4×C4111yescharacteristic
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121D4×C4111yescharacteristic
574#121D4×C4111yescharacteristic
575#121D4×C4111yescharacteristic
576#120—21no—
577#120—21no—
578#120—21no—
579#120—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8D4×C4111yescharacteristic
584C4×Q8D4×C4111yescharacteristic
585C4×Q8D4×C4111yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4D4×C4111yescharacteristic
595C4×D4D4×C4111yescharacteristic
596C4×D4D4×C4111yescharacteristic
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C42C23×C4111yescharacteristic
607#107—21no—
608#107—21no—
609#106—21no—
610#106—21no—
611C4⋊C8—21no—
612#103—21no—
613#103—21no—
614#103—21no—
615#103—21no—
616#102—21no—
617#102—21no—
618#102—21no—
619#102—21no—
620#102—21no—
621#102—21no—
622#102—21no—
623#102—21no—
624C22⋊C8—21no—
625#97—21no—
626#97C23×C4111yescharacteristic
627#97C23×C4111yescharacteristic
628#97C23×C4111yescharacteristic
629#97C23×C4111yescharacteristic
630#97C23×C4111yescharacteristic
631#97C23×C4111yescharacteristic
632C4×C8—21no—
633C24—21no—
634#41—81no—
635#41—81no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8C2×D4×C4111yescharacteristic
641C2×Q8C2×D4×C4111yescharacteristic
642C2×Q8C2×D4×C4111yescharacteristic
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—41no—
653C2×D4C2×D4×C4111yescharacteristic
654C2×D4C2×D4×C4111yescharacteristic
655C2×D4C2×D4×C4111yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—41no—
663C22×C4C2×D4×C4111yescharacteristic
664C22×C4C2×D4×C4111yescharacteristic
665C22×C4C2×D4×C4111yescharacteristic
666Q16—81no—
667SD16—42no—
668SD16—42no—
669SD16—81no—
670SD16—81no—
671D8—42no—
672D8—42no—
673D8—81no—
674M16—42no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—42no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—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⋊C4C2×D4×C4111yescharacteristic
703C4⋊C4C2×D4×C4111yescharacteristic
704C4⋊C4C2×D4×C4111yescharacteristic
705C4⋊C4C2×D4×C4111yescharacteristic
706C4⋊C4C2×D4×C4111yescharacteristic
707C4⋊C4C2×D4×C4111yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
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—41no—
736C22⋊C4—41no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42C2×D4×C4111yescharacteristic
745C42C2×D4×C4111yescharacteristic
746C42C2×D4×C4111yescharacteristic
747C42C24×C4111yescharacteristic
748C23—21no—
749C23—21no—
750C23—21no—
751C23—41no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23#120×C4111yescharacteristic
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—81no—
762Q8—81no—
763Q8—81no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—82no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—82no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4#120×C4111yescharacteristic
801C2×C4#120×C4111yescharacteristic
802C2×C4#120×C4111yescharacteristic
803C2×C4C22×D4×C4111yescharacteristic
804C2×C4C22×D4×C4111yescharacteristic
805C2×C4C22×D4×C4111yescharacteristic
806C8—22no—
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—162no—
828C22C2×#120×C4111yescharacteristic
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C2—41no—
846C2—81no—
847C2—81no—
848C2—81no—
849C2—161no—
850C2C41×#301811yescharacteristic
851C2C41×#301811yescharacteristic
852C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
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
1. C41×#3568C2semidirect
2. C41×#3219C2semidirect
3. C41×#3180C2semidirect
4. C41×#3171C2semidirect
5. C41×#1664C2semidirect
6. C41×#1664C2semidirect
7. C41×#1660C2semidirect
8. C41×#1659C2semidirect
9. C41×#1657C2semidirect
10. C41×#1657C2semidirect
11. C41×#1657C2semidirect
12. C41×#1655C2semidirect
13. C41×#1532C2semidirect
14. C41×#1529C2semidirect
15. C41×#1524C2semidirect
32. C41×#532C22semidirect
36. C41×#501C22semidirect
37. C41×#501C22semidirect
42. C41×#491C22semidirect
43. C41×#490C22semidirect
44. C41×#490C22semidirect
45. C41×#490C22semidirect
60. C41×#432C22semidirect
61. C4×M16×C41C22semidirect
62. C2×#97×C41C22semidirect
63. C41×#330C22semidirect
64. C41×#330C22semidirect
65. C41×#330C22semidirect
66. C41×#330C22semidirect
67. C41×#330C22semidirect
68. C41×#330C22semidirect
385. #19038C41direct (N × H)
419. #3568C2×C41semidirect
420. #3219C2×C41semidirect
421. #3180C2×C41semidirect
422. #3171C2×C41semidirect
423. #1664C2×C41semidirect
424. #1664C2×C41semidirect
425. #1660C2×C41semidirect
426. #1659C2×C41semidirect
427. #1657C2×C41semidirect
428. #1657C2×C41semidirect
429. #1657C2×C41semidirect
430. #1655C2×C41semidirect
431. #1532C2×C41semidirect
432. #1529C2×C41semidirect
433. #1524C2×C41semidirect
458. #532C22×C41semidirect
462. #501C22×C41semidirect
463. #501C22×C41semidirect
468. #491C22×C41semidirect
469. #490C22×C41semidirect
470. #490C22×C41semidirect
471. #490C22×C41semidirect
486. #432C22×C41semidirect
487. C4×M16C22×C41semidirect
488. C2×#97C22×C41semidirect
489. #330C22×C41semidirect
490. #330C22×C41semidirect
491. #330C22×C41semidirect
492. #330C22×C41semidirect
493. #330C22×C41semidirect
494. #330C22×C41semidirect
501. C41#19038direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35682
C41×#32192
C41×#31802
C41×#31712
C41×#16642
C41×#16602
C41×#16592
C41×#16572
C41×#16552
C41×#15322
C41×#15292
C41×#15242
#1903841