Finite Group Databasebeta

← C41×#19068 #23795269

Subgroups — C41×#19068 #23795269

Order 10496.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3545C211yesmaximal, characteristic, complemented
2C41×#3219C211yesmaximal, characteristic, complemented
3C41×#3213C211yesmaximal, characteristic, complemented
4C41×#3171C211yesmaximal, 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×#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×#532C2211yescharacteristic, complemented
33C41×#529C2211yescharacteristic
34C41×#529C2211yescharacteristic
35C2×#124×C41C2211yescharacteristic
36C41×#501C2211yescharacteristic, complemented
37C41×#497C2211yescharacteristic, complemented
38C41×#496C2211yescharacteristic
39C41×#496C2211yescharacteristic, complemented
40C41×#496C2211yescharacteristic, complemented
41C41×#496C2211yescharacteristic, complemented
42C41×#491C2211yescharacteristic, complemented
43C41×#490C2211yescharacteristic, complemented
44C41×#490C2211yescharacteristic, complemented
45C41×#489C2211yescharacteristic
46C41×#489C2211yescharacteristic, complemented
47C41×#489C2211yescharacteristic, complemented
48C41×#469—21no—
49C41×#468—21no—
50C41×#464—21no—
51C41×#463—21no—
52C41×#463—21no—
53C41×#463—21no—
54C41×#452—21no—
55C41×#449—21no—
56C41×#448—21no—
57C41×#447—21no—
58C4×SD16×C41—21no—
59C4×D8×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—
76C2×#41×C41—21no—
77C22×Q8×C41D411yescharacteristic
78C22×D4×C41—21no—
79C22×D4×C41D411yescharacteristic
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—
90C2×M16×C41—21no—
91C4⋊Q8×C41—21no—
92C4⋊Q8×C41—21no—
93C4⋊Q8×C41C2311yescharacteristic
94#127×C41C2311yescharacteristic
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#125×C41C2311yescharacteristic
102#125×C41C2311yescharacteristic
103#124×C41—21no—
104#124×C41—21no—
105#124×C41—21no—
106#124×C41—21no—
107#124×C41—21no—
108#124×C41—21no—
109#124×C41—21no—
110#124×C41—21no—
111#124×C41—21no—
112#124×C41D411yescharacteristic
113#124×C41D411yescharacteristic
114#124×C41C2311yescharacteristic
115#124×C41C2311yescharacteristic
116#124×C41C2311yescharacteristic
117#124×C41C2311yescharacteristic
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—
128#123×C41—21no—
129#123×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
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×C41D411yescharacteristic
151#121×C41D411yescharacteristic
152#120×C41—21no—
153#120×C41—21no—
154#120×C41—21no—
155#120×C41—21no—
156#120×C41—21no—
157#120×C41—21no—
158C4×Q8×C41D411yescharacteristic
159C4×Q8×C41D411yescharacteristic
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×C41—21no—
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—
175C2×C22⋊C4×C41—21no—
176C2×C22⋊C4×C41—21no—
177C2×C22⋊C4×C41—21no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×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×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—
209#41×C41—81no—
210#41×C41—81no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41—21no—
214C2×Q8×C41—81no—
215C2×Q8×C41C2×D411yescharacteristic
216C2×Q8×C41C2×D411yescharacteristic
217C2×Q8×C41C2×D411yescharacteristic
218C2×Q8×C41C2×D411yescharacteristic
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—41no—
233C2×D4×C41—81no—
234C2×D4×C41—82no—
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—41no—
248C22×C4×C41C2×D411yescharacteristic
249C22×C4×C41C2×D411yescharacteristic
250C22×C4×C41C2×D411yescharacteristic
251Q16×C41—81no—
252SD16×C41—42no—
253SD16×C41—81no—
254SD16×C41—81no—
255SD16×C41—81no—
256SD16×C41—81no—
257D8×C41—42no—
258D8×C41—81no—
259D8×C41—81no—
260D8×C41—81no—
261M16×C41—42no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×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—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×C41C2×D411yescharacteristic
285C4⋊C4×C41C2×D411yescharacteristic
286C4⋊C4×C41C2×D411yescharacteristic
287C4⋊C4×C41C2×D411yescharacteristic
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—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—42no—
331C23×C41—41no—
332C23×C41—81no—
333C23×C41—81no—
334C23×C41—81no—
335C23×C41—81no—
336C23×C41—81no—
337C23×C41#12011yescharacteristic
338Q8×C41—41no—
339Q8×C41—41no—
340Q8×C41—41no—
341Q8×C41—41no—
342Q8×C41—41no—
343Q8×C41—41no—
344Q8×C41—81no—
345Q8×C41—81no—
346D4×C41—41no—
347D4×C41—41no—
348D4×C41—41no—
349D4×C41—41no—
350D4×C41—41no—
351D4×C41—41no—
352D4×C41—41no—
353D4×C41—41no—
354D4×C41—41no—
355D4×C41—41no—
356D4×C41—42no—
357D4×C41—42no—
358D4×C41—81no—
359D4×C41—81no—
360D4×C41—81no—
361D4×C41—81no—
362D4×C41—81no—
363D4×C41—81no—
364D4×C41—81no—
365D4×C41—81no—
366D4×C41—82no—
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—21no—
375C2×C4×C41—41no—
376C2×C4×C41—41no—
377C2×C4×C41—41no—
378C2×C4×C41—42no—
379C2×C4×C41—41no—
380C2×C4×C41—81no—
381C2×C4×C41—81no—
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#19068C4111yesmaximal, 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—81no—
417C22×C41—81no—
418C22×C41—81no—
419C22×C41—162no—
420C22×C41—162no—
421C22×C41C2×#12011yescharacteristic
422C4×C41—21no—
423C4×C41—21no—
424C4×C41—21no—
425C4×C41—21no—
426C4×C41—21no—
427C4×C41—21no—
428C4×C41—41no—
429C4×C41—41no—
430C4×C41—41no—
431C4×C41—41no—
432C4×C41—41no—
433C4×C41—41no—
434C4×C41—41no—
435C4×C41—41no—
436C4×C41—81no—
437#3545C2×C4111yescharacteristic, complemented
438#3219C2×C4111yescharacteristic, complemented
439#3213C2×C4111yescharacteristic, complemented
440#3171C2×C4111yescharacteristic, complemented
441#1664C2×C4111yescharacteristic, complemented
442#1662C2×C4111yescharacteristic, complemented
443#1661C2×C4111yescharacteristic, complemented
444#1659C2×C4111yescharacteristic, complemented
445#1657C2×C4111yescharacteristic, complemented
446#1656C2×C4111yescharacteristic, complemented
447#1656C2×C4111yescharacteristic, complemented
448#1655C2×C4111yescharacteristic, complemented
449#1535C2×C4111yescharacteristic, complemented
450#1529C2×C4111yescharacteristic, complemented
451#1527C2×C4111yescharacteristic, complemented
452C2×C41—41no—
453C2×C41—81no—
454C2×C41—81no—
455C2×C41—81no—
456C2×C41—81no—
457C2×C41—161no—
458C2×C41#301811yescharacteristic
459C2×C41#301911yescharacteristic
460C2×C41#302111yescharacteristic
461#563C22×C4111yescharacteristic
462#562C22×C4111yescharacteristic
463#562C22×C4111yescharacteristic
464H(3,𝔽4)C22×C4111yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468#551—21no—
469#546—21no—
470#546—21no—
471#542—21no—
472#542—21no—
473#538—21no—
474#538—21no—
475#536—21no—
476#534—21no—
477#532C22×C4111yescharacteristic, complemented
478#529C22×C4111yescharacteristic
479#529C22×C4111yescharacteristic
480C2×#124C22×C4111yescharacteristic
481#501C22×C4111yescharacteristic, complemented
482#497C22×C4111yescharacteristic, complemented
483#496C22×C4111yescharacteristic
484#496C22×C4111yescharacteristic, complemented
485#496C22×C4111yescharacteristic, complemented
486#496C22×C4111yescharacteristic, complemented
487#491C22×C4111yescharacteristic, complemented
488#490C22×C4111yescharacteristic, complemented
489#490C22×C4111yescharacteristic, complemented
490#489C22×C4111yescharacteristic
491#489C22×C4111yescharacteristic, complemented
492#489C22×C4111yescharacteristic, complemented
493#469—21no—
494#468—21no—
495#464—21no—
496#463—21no—
497#463—21no—
498#463—21no—
499#452—21no—
500#449—21no—
501#448—21no—
502#447—21no—
503C4×SD16—21no—
504C4×D8—21no—
505#432C22×C4111yescharacteristic, complemented
506#432C22×C4111yescharacteristic, complemented
507C4×M16C22×C4111yescharacteristic, complemented
508#330C22×C4111yescharacteristic, complemented
509#330C22×C4111yescharacteristic, complemented
510#330C22×C4111yescharacteristic, complemented
511#330C22×C4111yescharacteristic, complemented
512#329C22×C4111yescharacteristic
513#329C22×C4111yescharacteristic
514#329C22×C4111yescharacteristic, complemented
515#329C22×C4111yescharacteristic, complemented
516#329C22×C4111yescharacteristic, complemented
517#329C22×C4111yescharacteristic, complemented
518#329C22×C4111yescharacteristic, complemented
519#329C22×C4111yescharacteristic, complemented
520C41#1906811yescharacteristic, direct product factor, Sylow
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C4111yescharacteristic
524C22×D4—21no—
525C22×D4D4×C4111yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C4111yescharacteristic
540#127C23×C4111yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C4111yescharacteristic
548#125C23×C4111yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C4111yescharacteristic
559#124D4×C4111yescharacteristic
560#124C23×C4111yescharacteristic
561#124C23×C4111yescharacteristic
562#124C23×C4111yescharacteristic
563#124C23×C4111yescharacteristic
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—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C4111yescharacteristic
585C22⋊Q8D4×C4111yescharacteristic
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#121D4×C4111yescharacteristic
597#121D4×C4111yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C4111yescharacteristic
605C4×Q8D4×C4111yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C4111yescharacteristic
615C4×D4D4×C4111yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C4111yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C4111yescharacteristic
646#97C23×C4111yescharacteristic
647#97C23×C4111yescharacteristic
648#97C23×C4111yescharacteristic
649#97C23×C4111yescharacteristic
650#97C23×C4111yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C4111yescharacteristic
662C2×Q8C2×D4×C4111yescharacteristic
663C2×Q8C2×D4×C4111yescharacteristic
664C2×Q8C2×D4×C4111yescharacteristic
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—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C4111yescharacteristic
682C2×D4C2×D4×C4111yescharacteristic
683C2×D4C2×D4×C4111yescharacteristic
684C2×D4C2×D4×C4111yescharacteristic
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×C4C2×D4×C4111yescharacteristic
695C22×C4C2×D4×C4111yescharacteristic
696C22×C4C2×D4×C4111yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
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⋊C4C2×D4×C4111yescharacteristic
731C4⋊C4C2×D4×C4111yescharacteristic
732C4⋊C4C2×D4×C4111yescharacteristic
733C4⋊C4C2×D4×C4111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
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—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C4111yescharacteristic
769C42C2×D4×C4111yescharacteristic
770C42C2×D4×C4111yescharacteristic
771C42C24×C4111yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C4111yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C4111yescharacteristic
835C2×C4#120×C4111yescharacteristic
836C2×C4#120×C4111yescharacteristic
837C2×C4C22×D4×C4111yescharacteristic
838C2×C4C22×D4×C4111yescharacteristic
839C2×C4C22×D4×C4111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C4111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C41×#301811yescharacteristic
889C2C41×#301911yescharacteristic
890C2C41×#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×#3545C2semidirect
2. C41×#3219C2semidirect
3. C41×#3213C2semidirect
4. C41×#3171C2semidirect
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×#1529C2semidirect
15. C41×#1527C2semidirect
32. C41×#532C22semidirect
36. C41×#501C22semidirect
37. C41×#497C22semidirect
39. C41×#496C22semidirect
40. C41×#496C22semidirect
41. C41×#496C22semidirect
42. C41×#491C22semidirect
43. C41×#490C22semidirect
44. C41×#490C22semidirect
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
400. #19068C41direct (N × H)
437. #3545C2×C41semidirect
438. #3219C2×C41semidirect
439. #3213C2×C41semidirect
440. #3171C2×C41semidirect
441. #1664C2×C41semidirect
442. #1662C2×C41semidirect
443. #1661C2×C41semidirect
444. #1659C2×C41semidirect
445. #1657C2×C41semidirect
446. #1656C2×C41semidirect
447. #1656C2×C41semidirect
448. #1655C2×C41semidirect
449. #1535C2×C41semidirect
450. #1529C2×C41semidirect
451. #1527C2×C41semidirect
477. #532C22×C41semidirect
481. #501C22×C41semidirect
482. #497C22×C41semidirect
484. #496C22×C41semidirect
485. #496C22×C41semidirect
486. #496C22×C41semidirect
487. #491C22×C41semidirect
488. #490C22×C41semidirect
489. #490C22×C41semidirect
491. #489C22×C41semidirect
492. #489C22×C41semidirect
505. #432C22×C41semidirect
506. #432C22×C41semidirect
507. C4×M16C22×C41semidirect
508. #330C22×C41semidirect
509. #330C22×C41semidirect
510. #330C22×C41semidirect
511. #330C22×C41semidirect
514. #329C22×C41semidirect
515. #329C22×C41semidirect
516. #329C22×C41semidirect
517. #329C22×C41semidirect
518. #329C22×C41semidirect
519. #329C22×C41semidirect
520. C41#19068direct (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×#32192
C41×#32132
C41×#31712
C41×#16642
C41×#16622
C41×#16612
C41×#16592
C41×#16572
C41×#16562
C41×#16552
C41×#15352
C41×#15292
C41×#15272
#1906841