Finite Group Databasebeta

← C41×#19010 #23795211

Subgroups — C41×#19010 #23795211

Order 10496.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3529C211yesmaximal, characteristic, complemented
2C41×#3219C211yesmaximal, characteristic, complemented
3C41×#3214C211yesmaximal, characteristic, complemented
4C41×#3180C211yesmaximal, characteristic, complemented
5C41×#1664C211yesmaximal, characteristic, complemented
6C41×#1662C211yesmaximal, characteristic, complemented
7C41×#1661C211yesmaximal, characteristic, complemented
8C41×#1659C211yesmaximal, characteristic, complemented
9C41×#1657C211yesmaximal, characteristic, complemented
10C41×#1656C211yesmaximal, characteristic, complemented
11C41×#1656C211yesmaximal, characteristic, complemented
12C41×#1655C211yesmaximal, characteristic, complemented
13C41×#1535C211yesmaximal, characteristic, complemented
14C41×#1532C211yesmaximal, characteristic, complemented
15C41×#1530C211yesmaximal, characteristic, complemented
16C41×#563—21no—
17C41×#563C2211yescharacteristic
18C41×#562—21no—
19C41×#562—21no—
20C41×#562C2211yescharacteristic
21C41×#562C2211yescharacteristic
22C41×H(3,𝔽4)C2211yescharacteristic
23C41×#560—21no—
24C41×#560—21no—
25C41×#560—21no—
26C41×#532—21no—
27C41×#532C2211yescharacteristic
28C41×#532C2211yescharacteristic, complemented
29C41×#529—21no—
30C41×#529—21no—
31C41×#529C2211yescharacteristic
32C41×#529C2211yescharacteristic
33C41×#525—21no—
34C41×#525—21no—
35C41×#525—21no—
36C41×#501C2211yescharacteristic, complemented
37C41×#497C2211yescharacteristic
38C41×#496C2211yescharacteristic
39C41×#496C2211yescharacteristic
40C41×#496C2211yescharacteristic
41C41×#496C2211yescharacteristic, complemented
42C41×#491C2211yescharacteristic, complemented
43C41×#490C2211yescharacteristic, complemented
44C41×#490C2211yescharacteristic, complemented
45C41×#489C2211yescharacteristic
46C41×#489C2211yescharacteristic
47C41×#489C2211yescharacteristic, complemented
48C41×#466—21no—
49C41×#465—21no—
50C41×#464—21no—
51C41×#463—21no—
52C41×#461—21no—
53C41×#459—21no—
54C41×#452—21no—
55C41×#449—21no—
56C41×#449—21no—
57C41×#449—21no—
58C41×#442—21no—
59C41×#440—21no—
60C41×#432C2211yescharacteristic, complemented
61C41×#432C2211yescharacteristic, complemented
62C2×#97×C41C2211yescharacteristic, complemented
63C41×#330C2211yescharacteristic, complemented
64C41×#330C2211yescharacteristic, complemented
65C41×#330C2211yescharacteristic, complemented
66C41×#330C2211yescharacteristic, complemented
67C41×#329C2211yescharacteristic
68C41×#329C2211yescharacteristic
69C41×#329C2211yescharacteristic
70C41×#329C2211yescharacteristic
71C41×#329C2211yescharacteristic
72C41×#329C2211yescharacteristic
73C41×#329C2211yescharacteristic, complemented
74C41×#329C2211yescharacteristic, complemented
75C2×#41×C41—21no—
76C2×#41×C41—21no—
77C2×#41×C41D411yescharacteristic
78C2×#41×C41D411yescharacteristic
79C23×C4×C41—21no—
80C2×Q16×C41—21no—
81C2×SD16×C41—21no—
82C2×SD16×C41—21no—
83C2×SD16×C41—21no—
84C2×SD16×C41—21no—
85C2×SD16×C41—21no—
86C2×D8×C41—21no—
87C2×D8×C41—21no—
88C2×D8×C41—21no—
89C2×D8×C41—21no—
90C22×C8×C41—21no—
91C4⋊Q8×C41—21no—
92C4⋊Q8×C41D411yescharacteristic
93C4⋊Q8×C41C2311yescharacteristic
94#127×C41—21no—
95#127×C41D411yescharacteristic
96#127×C41C2311yescharacteristic
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#125×C41—21no—
104#125×C41—21no—
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×C41C2311yescharacteristic
113#124×C41C2311yescharacteristic
114#124×C41C2311yescharacteristic
115#124×C41C2311yescharacteristic
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—
125#123×C41—21no—
126#123×C41—21no—
127#123×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×C41—21no—
136C22⋊Q8×C41D411yescharacteristic
137C22⋊Q8×C41D411yescharacteristic
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×C41—21no—
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—21no—
151#121×C41—21no—
152#121×C41—21no—
153#121×C41—21no—
154#121×C41D411yescharacteristic
155#121×C41D411yescharacteristic
156#120×C41—21no—
157#120×C41—21no—
158#120×C41—21no—
159#120×C41—21no—
160#120×C41—21no—
161#120×C41—21no—
162C4×Q8×C41D411yescharacteristic
163C4×Q8×C41D411yescharacteristic
164C4×D4×C41—21no—
165C4×D4×C41—21no—
166C4×D4×C41—21no—
167C4×D4×C41—21no—
168C4×D4×C41—21no—
169C4×D4×C41—21no—
170C4×D4×C41—21no—
171C4×D4×C41—21no—
172C4×D4×C41—21no—
173C4×D4×C41—21no—
174C4×D4×C41D411yescharacteristic
175C4×D4×C41D411yescharacteristic
176#117×C41—21no—
177#117×C41—21no—
178#117×C41—21no—
179C2×C42×C41—21no—
180C2×C42×C41C2311yescharacteristic
181#107×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#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—
198C22⋊C8×C41—21no—
199#97×C41—21no—
200#97×C41C2311yescharacteristic
201#97×C41C2311yescharacteristic
202#97×C41C2311yescharacteristic
203#97×C41C2311yescharacteristic
204#97×C41C2311yescharacteristic
205#97×C41C2311yescharacteristic
206C24×C41—21no—
207#41×C41—81no—
208#41×C41—81no—
209#41×C41—82no—
210#41×C41—81no—
211#41×C41—81no—
212C2×Q8×C41—21no—
213C2×Q8×C41—21no—
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—21no—
229C2×D4×C41—21no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—41no—
235C2×D4×C41C2×D411yescharacteristic
236C2×D4×C41C2×D411yescharacteristic
237C2×D4×C41C2×D411yescharacteristic
238C2×D4×C41C2×D411yescharacteristic
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—41no—
249C22×C4×C41—82no—
250C22×C4×C41C2×D411yescharacteristic
251C22×C4×C41C2×D411yescharacteristic
252C22×C4×C41C2×D411yescharacteristic
253Q16×C41—81no—
254SD16×C41—42no—
255SD16×C41—81no—
256SD16×C41—81no—
257SD16×C41—81no—
258SD16×C41—81no—
259D8×C41—42no—
260D8×C41—81no—
261D8×C41—81no—
262D8×C41—81no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—42no—
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—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41C2×D411yescharacteristic
289C4⋊C4×C41C2×D411yescharacteristic
290C4⋊C4×C41C2×D411yescharacteristic
291C4⋊C4×C41C2×D411yescharacteristic
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—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—41no—
317C22⋊C4×C41—41no—
318C42×C41—21no—
319C42×C41—21no—
320C42×C41—21no—
321C42×C41—21no—
322C42×C41C2×D411yescharacteristic
323C42×C41C2×D411yescharacteristic
324C42×C41C2×D411yescharacteristic
325C42×C41C2411yescharacteristic
326C23×C41—21no—
327C23×C41—21no—
328C23×C41—21no—
329C23×C41—21no—
330C23×C41—41no—
331C23×C41—81no—
332C23×C41—81no—
333C23×C41—81no—
334C23×C41#12011yescharacteristic
335Q8×C41—41no—
336Q8×C41—41no—
337Q8×C41—41no—
338Q8×C41—41no—
339Q8×C41—41no—
340Q8×C41—41no—
341Q8×C41—81no—
342D4×C41—41no—
343D4×C41—41no—
344D4×C41—41no—
345D4×C41—41no—
346D4×C41—41no—
347D4×C41—41no—
348D4×C41—41no—
349D4×C41—41no—
350D4×C41—41no—
351D4×C41—41no—
352D4×C41—81no—
353D4×C41—81no—
354D4×C41—81no—
355D4×C41—81no—
356D4×C41—81no—
357D4×C41—81no—
358D4×C41—81no—
359D4×C41—81no—
360D4×C41—81no—
361D4×C41—81no—
362D4×C41—81no—
363D4×C41—81no—
364D4×C41—81no—
365D4×C41—82no—
366C2×C4×C41—21no—
367C2×C4×C41—21no—
368C2×C4×C41—21no—
369C2×C4×C41—21no—
370C2×C4×C41—21no—
371C2×C4×C41—21no—
372C2×C4×C41—21no—
373C2×C4×C41—21no—
374C2×C4×C41—41no—
375C2×C4×C41—41no—
376C2×C4×C41—41no—
377C2×C4×C41—42no—
378C2×C4×C41—42no—
379C2×C4×C41—42no—
380C2×C4×C41—42no—
381C2×C4×C41—41no—
382C2×C4×C41—82no—
383C2×C4×C41—81no—
384C2×C4×C41—81no—
385C2×C4×C41—81no—
386C2×C4×C41—81no—
387C2×C4×C41—81no—
388C2×C4×C41#12011yescharacteristic
389C2×C4×C41#12011yescharacteristic
390C2×C4×C41#12011yescharacteristic
391C2×C4×C41C22×D411yescharacteristic
392C2×C4×C41C22×D411yescharacteristic
393C2×C4×C41C22×D411yescharacteristic
394C8×C41—22no—
395C8×C41—41no—
396C8×C41—41no—
397C8×C41—41no—
398C8×C41—41no—
399C8×C41—41no—
400#19010C4111yesmaximal, characteristic, direct product factor, Sylow
401C22×C41—21no—
402C22×C41—21no—
403C22×C41—21no—
404C22×C41—41no—
405C22×C41—41no—
406C22×C41—41no—
407C22×C41—41no—
408C22×C41—41no—
409C22×C41—41no—
410C22×C41—41no—
411C22×C41—41no—
412C22×C41—41no—
413C22×C41—41no—
414C22×C41—41no—
415C22×C41—41no—
416C22×C41—84no—
417C22×C41—81no—
418C22×C41—81no—
419C22×C41—81no—
420C22×C41C2×#12011yescharacteristic
421C4×C41—21no—
422C4×C41—21no—
423C4×C41—21no—
424C4×C41—21no—
425C4×C41—21no—
426C4×C41—21no—
427C4×C41—41no—
428C4×C41—41no—
429C4×C41—41no—
430C4×C41—41no—
431C4×C41—41no—
432C4×C41—41no—
433C4×C41—41no—
434C4×C41—41no—
435C4×C41—81no—
436#3529C2×C4111yescharacteristic, complemented
437#3219C2×C4111yescharacteristic, complemented
438#3214C2×C4111yescharacteristic, complemented
439#3180C2×C4111yescharacteristic, complemented
440#1664C2×C4111yescharacteristic, complemented
441#1662C2×C4111yescharacteristic, complemented
442#1661C2×C4111yescharacteristic, complemented
443#1659C2×C4111yescharacteristic, complemented
444#1657C2×C4111yescharacteristic, complemented
445#1656C2×C4111yescharacteristic, complemented
446#1656C2×C4111yescharacteristic, complemented
447#1655C2×C4111yescharacteristic, complemented
448#1535C2×C4111yescharacteristic, complemented
449#1532C2×C4111yescharacteristic, complemented
450#1530C2×C4111yescharacteristic, complemented
451C2×C41—41no—
452C2×C41—81no—
453C2×C41—81no—
454C2×C41—81no—
455C2×C41—81no—
456C2×C41—161no—
457C2×C41#301811yescharacteristic
458C2×C41#301911yescharacteristic
459C2×C41#302111yescharacteristic
460#563—21no—
461#563C22×C4111yescharacteristic
462#562—21no—
463#562—21no—
464#562C22×C4111yescharacteristic
465#562C22×C4111yescharacteristic
466H(3,𝔽4)C22×C4111yescharacteristic
467#560—21no—
468#560—21no—
469#560—21no—
470#532—21no—
471#532C22×C4111yescharacteristic
472#532C22×C4111yescharacteristic, complemented
473#529—21no—
474#529—21no—
475#529C22×C4111yescharacteristic
476#529C22×C4111yescharacteristic
477#525—21no—
478#525—21no—
479#525—21no—
480#501C22×C4111yescharacteristic, complemented
481#497C22×C4111yescharacteristic
482#496C22×C4111yescharacteristic
483#496C22×C4111yescharacteristic
484#496C22×C4111yescharacteristic
485#496C22×C4111yescharacteristic, complemented
486#491C22×C4111yescharacteristic, complemented
487#490C22×C4111yescharacteristic, complemented
488#490C22×C4111yescharacteristic, complemented
489#489C22×C4111yescharacteristic
490#489C22×C4111yescharacteristic
491#489C22×C4111yescharacteristic, complemented
492#466—21no—
493#465—21no—
494#464—21no—
495#463—21no—
496#461—21no—
497#459—21no—
498#452—21no—
499#449—21no—
500#449—21no—
501#449—21no—
502#442—21no—
503#440—21no—
504#432C22×C4111yescharacteristic, complemented
505#432C22×C4111yescharacteristic, complemented
506C2×#97C22×C4111yescharacteristic, complemented
507#330C22×C4111yescharacteristic, complemented
508#330C22×C4111yescharacteristic, complemented
509#330C22×C4111yescharacteristic, complemented
510#330C22×C4111yescharacteristic, complemented
511#329C22×C4111yescharacteristic
512#329C22×C4111yescharacteristic
513#329C22×C4111yescharacteristic
514#329C22×C4111yescharacteristic
515#329C22×C4111yescharacteristic
516#329C22×C4111yescharacteristic
517#329C22×C4111yescharacteristic, complemented
518#329C22×C4111yescharacteristic, complemented
519C41#1901011yescharacteristic, direct product factor, Sylow
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C4111yescharacteristic
523C2×#41D4×C4111yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C4111yescharacteristic
538C4⋊Q8C23×C4111yescharacteristic
539#127—21no—
540#127D4×C4111yescharacteristic
541#127C23×C4111yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C4111yescharacteristic
551#125C23×C4111yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C4111yescharacteristic
558#124C23×C4111yescharacteristic
559#124C23×C4111yescharacteristic
560#124C23×C4111yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C4111yescharacteristic
582C22⋊Q8D4×C4111yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C4111yescharacteristic
600#121D4×C4111yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C4111yescharacteristic
608C4×Q8D4×C4111yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C4111yescharacteristic
620C4×D4D4×C4111yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C4111yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C4111yescharacteristic
646#97C23×C4111yescharacteristic
647#97C23×C4111yescharacteristic
648#97C23×C4111yescharacteristic
649#97C23×C4111yescharacteristic
650#97C23×C4111yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C4111yescharacteristic
660C2×Q8C2×D4×C4111yescharacteristic
661C2×Q8C2×D4×C4111yescharacteristic
662C2×Q8C2×D4×C4111yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C4111yescharacteristic
681C2×D4C2×D4×C4111yescharacteristic
682C2×D4C2×D4×C4111yescharacteristic
683C2×D4C2×D4×C4111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C4111yescharacteristic
696C22×C4C2×D4×C4111yescharacteristic
697C22×C4C2×D4×C4111yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C4111yescharacteristic
734C4⋊C4C2×D4×C4111yescharacteristic
735C4⋊C4C2×D4×C4111yescharacteristic
736C4⋊C4C2×D4×C4111yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C4111yescharacteristic
768C42C2×D4×C4111yescharacteristic
769C42C2×D4×C4111yescharacteristic
770C42C24×C4111yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C4111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C4111yescharacteristic
834C2×C4#120×C4111yescharacteristic
835C2×C4#120×C4111yescharacteristic
836C2×C4C22×D4×C4111yescharacteristic
837C2×C4C22×D4×C4111yescharacteristic
838C2×C4C22×D4×C4111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C4111yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C41×#301811yescharacteristic
887C2C41×#301911yescharacteristic
888C2C41×#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×#3529C2semidirect
2. C41×#3219C2semidirect
3. C41×#3214C2semidirect
4. C41×#3180C2semidirect
5. C41×#1664C2semidirect
6. C41×#1662C2semidirect
7. C41×#1661C2semidirect
8. C41×#1659C2semidirect
9. C41×#1657C2semidirect
10. C41×#1656C2semidirect
11. C41×#1656C2semidirect
12. C41×#1655C2semidirect
13. C41×#1535C2semidirect
14. C41×#1532C2semidirect
15. C41×#1530C2semidirect
28. C41×#532C22semidirect
36. C41×#501C22semidirect
41. C41×#496C22semidirect
42. C41×#491C22semidirect
43. C41×#490C22semidirect
44. C41×#490C22semidirect
47. C41×#489C22semidirect
60. C41×#432C22semidirect
61. C41×#432C22semidirect
62. C2×#97×C41C22semidirect
63. C41×#330C22semidirect
64. C41×#330C22semidirect
65. C41×#330C22semidirect
66. C41×#330C22semidirect
73. C41×#329C22semidirect
74. C41×#329C22semidirect
400. #19010C41direct (N × H)
436. #3529C2×C41semidirect
437. #3219C2×C41semidirect
438. #3214C2×C41semidirect
439. #3180C2×C41semidirect
440. #1664C2×C41semidirect
441. #1662C2×C41semidirect
442. #1661C2×C41semidirect
443. #1659C2×C41semidirect
444. #1657C2×C41semidirect
445. #1656C2×C41semidirect
446. #1656C2×C41semidirect
447. #1655C2×C41semidirect
448. #1535C2×C41semidirect
449. #1532C2×C41semidirect
450. #1530C2×C41semidirect
472. #532C22×C41semidirect
480. #501C22×C41semidirect
485. #496C22×C41semidirect
486. #491C22×C41semidirect
487. #490C22×C41semidirect
488. #490C22×C41semidirect
491. #489C22×C41semidirect
504. #432C22×C41semidirect
505. #432C22×C41semidirect
506. C2×#97C22×C41semidirect
507. #330C22×C41semidirect
508. #330C22×C41semidirect
509. #330C22×C41semidirect
510. #330C22×C41semidirect
517. #329C22×C41semidirect
518. #329C22×C41semidirect
519. C41#19010direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35292
C41×#32192
C41×#32142
C41×#31802
C41×#16642
C41×#16622
C41×#16612
C41×#16592
C41×#16572
C41×#16562
C41×#16552
C41×#15352
C41×#15322
C41×#15302
#1901041