Finite Group Databasebeta

← C41×#23894 #23800095

Subgroups — C41×#23894 #23800095

Order 10496.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3586C211yesmaximal, characteristic, complemented
2C41×#3585C211yesmaximal, characteristic, complemented
3C41×#3020C211yesmaximal, characteristic, complemented
4C41×#3019C211yesmaximal, characteristic, complemented
5C41×#3010C211yesmaximal, characteristic, complemented
6C41×#3009C211yesmaximal, characteristic, complemented
7C41×#2019C211yesmaximal, characteristic, complemented
8C41×#2017C211yesmaximal, characteristic, complemented
9C41×#2009C211yesmaximal, characteristic, complemented
10C41×#2008C211yesmaximal, characteristic, complemented
11C41×#1903C211yesmaximal, characteristic, complemented
12C41×#1902C211yesmaximal, characteristic, complemented
13C41×#1881C211yesmaximal, characteristic, complemented
14C41×#1881C211yesmaximal, characteristic, complemented
15C41×#1794C211yesmaximal, characteristic, complemented
16C41×#585C2211yescharacteristic
17C2×2−1+4×C41C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C41C2211yescharacteristic
19C41×#578—22no—
20C41×#578—22no—
21C41×#577—22no—
22C41×#577—22no—
23C41×#577—22no—
24C41×#577—22no—
25C41×#576—22no—
26C41×#576—22no—
27C41×#575—22no—
28C41×#575—22no—
29C41×#575C2211yescharacteristic
30C41×#575C2211yescharacteristic
31C41×#575C2211yescharacteristic
32C41×#575C2211yescharacteristic, complemented
33C41×#575C2211yescharacteristic, complemented
34C2×#137×C41—22no—
35C2×#137×C41C2211yescharacteristic
36C2×#137×C41C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C41—22no—
38C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
40C22×SD16×C41C2211yescharacteristic, complemented
41C41×#568C2211yescharacteristic
42C41×#568C2211yescharacteristic, complemented
43C41×#536C2211yescharacteristic, complemented
44C41×#535C2211yescharacteristic, complemented
45C41×#456—22no—
46C41×#455—22no—
47C41×#454—22no—
48C41×#453—22no—
49C41×#452—22no—
50C41×#450—22no—
51C41×#449—22no—
52C41×#448—22no—
53C41×#421C2211yescharacteristic
54C41×#421C2211yescharacteristic, complemented
55C41×#421C2211yescharacteristic, complemented
56C41×#421C2211yescharacteristic, complemented
57C41×#419C2211yescharacteristic, complemented
58C41×#418C2211yescharacteristic, complemented
59C41×#416C2211yescharacteristic
60C41×#416C2211yescharacteristic, complemented
61C2×#101×C41C2211yescharacteristic, complemented
62C2×#100×C41C2211yescharacteristic, complemented
63C41×#410C2211yescharacteristic, complemented
64C41×#408C2211yescharacteristic, complemented
65C41×#408C2211yescharacteristic, complemented
66C41×#408C2211yescharacteristic, complemented
67C41×#344C2211yescharacteristic, complemented
68C41×#344C2211yescharacteristic, complemented
69C41×#341C2211yescharacteristic, complemented
70C41×#338C2211yescharacteristic, complemented
712−1+4×C41—22no—
722−1+4×C41—21no—
732−1+4×C41—22no—
742−1+4×C41—21no—
752−1+4×C41—22no—
762−1+4×C41—41no—
772−1+4×C41D412yescomplemented
78H(5,𝔽2)×C41—22no—
79H(5,𝔽2)×C41—21no—
80H(5,𝔽2)×C41—22no—
81H(5,𝔽2)×C41—21no—
82H(5,𝔽2)×C41—22no—
83H(5,𝔽2)×C41—41no—
84H(5,𝔽2)×C41—41no—
85H(5,𝔽2)×C41D412yescomplemented
86C2×#41×C41—22no—
87C2×#41×C41—22no—
88C2×#41×C41—21no—
89C2×#41×C41—21no—
90C2×#41×C41—21no—
91C2×#41×C41—21no—
92C2×#41×C41—41no—
93C2×#41×C41—41no—
94C2×#41×C41C2311yescharacteristic
95C2×#41×C41C2311yescharacteristic
96C2×#41×C41C2311yescharacteristic
97C2×#41×C41C2311yescharacteristic
98C2×#41×C41C2311yescharacteristic
99C22×Q8×C41—21no—
100C22×Q8×C41—21no—
101C22×Q8×C41C2311yescharacteristic
102C22×D4×C41—21no—
103C22×D4×C41—21no—
104C22×D4×C41—41no—
105C22×D4×C41C2311yescharacteristic
106#137×C41—24no—
107#137×C41—24no—
108#137×C41—24no—
109#137×C41—24no—
110#137×C41—22no—
111#137×C41—22no—
112#137×C41—21no—
113#137×C41—22no—
114#137×C41—21no—
115#137×C41—21no—
116#137×C41—21no—
117#137×C41—21no—
118#137×C41—21no—
119#137×C41—21no—
120#137×C41—21no—
121#137×C41—22no—
122#137×C41D412yes—
123#137×C41D412yescomplemented
124AGL(1,ℤ/8)×C41—24no—
125AGL(1,ℤ/8)×C41—24no—
126AGL(1,ℤ/8)×C41—24no—
127AGL(1,ℤ/8)×C41—24no—
128AGL(1,ℤ/8)×C41—22no—
129AGL(1,ℤ/8)×C41—22no—
130AGL(1,ℤ/8)×C41—21no—
131AGL(1,ℤ/8)×C41—22no—
132AGL(1,ℤ/8)×C41—21no—
133AGL(1,ℤ/8)×C41—21no—
134AGL(1,ℤ/8)×C41—21no—
135AGL(1,ℤ/8)×C41—21no—
136AGL(1,ℤ/8)×C41—21no—
137AGL(1,ℤ/8)×C41—21no—
138AGL(1,ℤ/8)×C41—21no—
139AGL(1,ℤ/8)×C41—22no—
140AGL(1,ℤ/8)×C41D412yes—
141AGL(1,ℤ/8)×C41D412yescomplemented
142#135×C41—24no—
143#135×C41—24no—
144#135×C41—24no—
145#135×C41—24no—
146#135×C41—22no—
147#135×C41—22no—
148#135×C41—22no—
149#135×C41—22no—
150#135×C41—41no—
151C2×Q16×C41—24no—
152C2×Q16×C41—21no—
153C2×Q16×C41D412yescomplemented
154C2×SD16×C41—24no—
155C2×SD16×C41—24no—
156C2×SD16×C41—21no—
157C2×SD16×C41—21no—
158C2×SD16×C41—22no—
159C2×SD16×C41—22no—
160C2×SD16×C41—41no—
161C2×SD16×C41D412yes—
162C2×SD16×C41D412yescomplemented
163C2×D8×C41—24no—
164C2×D8×C41—21no—
165C2×D8×C41D412yes—
166#131×C41—22no—
167#131×C41—22no—
168#131×C41—22no—
169#131×C41—22no—
170C2×M16×C41—22no—
171C2×M16×C41—22no—
172C2×M16×C41C2311yescharacteristic
173C2×M16×C41C2311yescharacteristic
174C2×M16×C41C2311yescharacteristic
175C2×M16×C41C2311yescharacteristic
176C2×M16×C41C2311yescharacteristic
177C22×C8×C41C2311yescharacteristic
178C4⋊Q8×C41—21no—
179#127×C41—21no—
180#124×C41—21no—
181#124×C41—21no—
182#123×C41—41no—
183C22⋊Q8×C41—22no—
184#121×C41—22no—
185#120×C41—41no—
186#117×C41C2311yescharacteristic
187#117×C41C2311yescharacteristic
188#104×C41—22no—
189#104×C41—22no—
190#104×C41—22no—
191#104×C41—22no—
192#103×C41—21no—
193#103×C41—21no—
194#103×C41—22no—
195#102×C41—21no—
196#102×C41—21no—
197#102×C41—22no—
198#101×C41—22no—
199#100×C41—22no—
200#99×C41—41no—
201C22⋊C8×C41—22no—
202C22⋊C8×C41—22no—
203C22⋊C8×C41—41no—
204C24×C41—21no—
205C24×C41—41no—
206#41×C41—21no—
207#41×C41—21no—
208#41×C41—21no—
209#41×C41—21no—
210#41×C41—24no—
211#41×C41—24no—
212#41×C41—22no—
213#41×C41—22no—
214#41×C41—22no—
215#41×C41—22no—
216#41×C41—21no—
217#41×C41—21no—
218#41×C41—21no—
219#41×C41—21no—
220#41×C41—21no—
221#41×C41—21no—
222#41×C41—21no—
223#41×C41—21no—
224#41×C41—21no—
225#41×C41—21no—
226#41×C41—21no—
227#41×C41—21no—
228#41×C41—42no—
229#41×C41—42no—
230#41×C41—42no—
231#41×C41—42no—
232#41×C41—42no—
233#41×C41—44no—
234#41×C41—42no—
235#41×C41—42no—
236#41×C41—42no—
237#41×C41—41no—
238#41×C41—41no—
239#41×C41—44no—
240#41×C41—42no—
241#41×C41—42no—
242#41×C41C2×D412yes—
243#41×C41C2×D412yes—
244#41×C41C2×D412yes—
245#41×C41C2×D412yes—
246C2×Q8×C41—21no—
247C2×Q8×C41—24no—
248C2×Q8×C41—22no—
249C2×Q8×C41—22no—
250C2×Q8×C41—21no—
251C2×Q8×C41—21no—
252C2×Q8×C41—21no—
253C2×Q8×C41—21no—
254C2×Q8×C41—41no—
255C2×Q8×C41—42no—
256C2×Q8×C41—42no—
257C2×Q8×C41—41no—
258C2×Q8×C41—42no—
259C2×Q8×C41C2×D412yes—
260C2×Q8×C41C2×D411yescharacteristic
261C2×Q8×C41C2×D411yescharacteristic
262C2×Q8×C41C2×D411yescharacteristic
263C2×Q8×C41C2×D411yescharacteristic
264C2×Q8×C41C2×D411yescharacteristic
265C2×D4×C41—21no—
266C2×D4×C41—21no—
267C2×D4×C41—24no—
268C2×D4×C41—22no—
269C2×D4×C41—22no—
270C2×D4×C41—21no—
271C2×D4×C41—21no—
272C2×D4×C41—21no—
273C2×D4×C41—21no—
274C2×D4×C41—21no—
275C2×D4×C41—21no—
276C2×D4×C41—21no—
277C2×D4×C41—21no—
278C2×D4×C41—42no—
279C2×D4×C41—41no—
280C2×D4×C41—41no—
281C2×D4×C41—42no—
282C2×D4×C41—42no—
283C2×D4×C41—41no—
284C2×D4×C41—44no—
285C2×D4×C41—42no—
286C2×D4×C41—42no—
287C2×D4×C41—44no—
288C2×D4×C41—41no—
289C2×D4×C41—42no—
290C2×D4×C41—42no—
291C2×D4×C41C2×D412yes—
292C2×D4×C41C2×D411yescharacteristic
293C2×D4×C41C2×D411yescharacteristic
294C2×D4×C41C2×D411yescharacteristic
295C2×D4×C41C2×D411yescharacteristic
296C2×D4×C41C2×D411yescharacteristic
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—41no—
304C22×C4×C41—42no—
305C22×C4×C41—41no—
306C22×C4×C41—41no—
307C22×C4×C41C2411yescharacteristic
308Q16×C41—24no—
309Q16×C41—22no—
310Q16×C41—22no—
311Q16×C41—22no—
312Q16×C41—24no—
313Q16×C41—22no—
314Q16×C41—41no—
315SD16×C41—24no—
316SD16×C41—22no—
317SD16×C41—24no—
318SD16×C41—22no—
319SD16×C41—22no—
320SD16×C41—22no—
321SD16×C41—22no—
322SD16×C41—24no—
323SD16×C41—22no—
324SD16×C41—22no—
325SD16×C41—24no—
326SD16×C41—22no—
327SD16×C41—44no—
328SD16×C41—41no—
329SD16×C41—41no—
330D8×C41—24no—
331D8×C41—22no—
332D8×C41—22no—
333D8×C41—22no—
334D8×C41—24no—
335D8×C41—22no—
336D8×C41—41no—
337M16×C41—24no—
338M16×C41—24no—
339M16×C41—21no—
340M16×C41—21no—
341M16×C41—21no—
342M16×C41—21no—
343M16×C41—21no—
344M16×C41—21no—
345M16×C41—21no—
346M16×C41—21no—
347M16×C41C2×D412yes—
348M16×C41C2×D412yes—
349C2×C8×C41—24no—
350C2×C8×C41—24no—
351C2×C8×C41—21no—
352C2×C8×C41—21no—
353C2×C8×C41—21no—
354C2×C8×C41—21no—
355C2×C8×C41—21no—
356C2×C8×C41—21no—
357C2×C8×C41C2×D412yes—
358C2×C8×C41C2×D412yes—
359C4⋊C4×C41—21no—
360C4⋊C4×C41—21no—
361C4⋊C4×C41—42no—
362C22⋊C4×C41—21no—
363C22⋊C4×C41—21no—
364C22⋊C4×C41—42no—
365C22⋊C4×C41—42no—
366C42×C41—21no—
367C42×C41—21no—
368C23×C41—21no—
369C23×C41—21no—
370C23×C41—21no—
371C23×C41—21no—
372C23×C41—21no—
373C23×C41—22no—
374C23×C41—42no—
375C23×C41—44no—
376C23×C41—41no—
377C23×C41—41no—
378C23×C41—161no—
379C23×C41—162no—
380C23×C41H(5,𝔽2)11yescharacteristic
381Q8×C41—21no—
382Q8×C41—21no—
383Q8×C41—21no—
384Q8×C41—21no—
385Q8×C41—22no—
386Q8×C41—21no—
387Q8×C41—21no—
388Q8×C41—22no—
389Q8×C41—21no—
390Q8×C41—21no—
391Q8×C41—42no—
392Q8×C41—44no—
393Q8×C41—41no—
394Q8×C41—41no—
395Q8×C41#12012yes—
396Q8×C41#12012yes—
397D4×C41—22no—
398D4×C41—22no—
399D4×C41—22no—
400D4×C41—22no—
401D4×C41—21no—
402D4×C41—21no—
403D4×C41—22no—
404D4×C41—21no—
405D4×C41—21no—
406D4×C41—21no—
407D4×C41—21no—
408D4×C41—21no—
409D4×C41—21no—
410D4×C41—22no—
411D4×C41—42no—
412D4×C41—42no—
413D4×C41—44no—
414D4×C41—42no—
415D4×C41—44no—
416D4×C41—44no—
417D4×C41—41no—
418D4×C41—41no—
419D4×C41—41no—
420D4×C41—41no—
421D4×C41—41no—
422D4×C41—41no—
423D4×C41—41no—
424D4×C41—41no—
425D4×C41—162no—
426D4×C41#12012yes—
427D4×C41#12012yes—
428C2×C4×C41—21no—
429C2×C4×C41—21no—
430C2×C4×C41—22no—
431C2×C4×C41—22no—
432C2×C4×C41—22no—
433C2×C4×C41—22no—
434C2×C4×C41—21no—
435C2×C4×C41—21no—
436C2×C4×C41—22no—
437C2×C4×C41—21no—
438C2×C4×C41—42no—
439C2×C4×C41—42no—
440C2×C4×C41—42no—
441C2×C4×C41—44no—
442C2×C4×C41—44no—
443C2×C4×C41—44no—
444C2×C4×C41—41no—
445C2×C4×C41—41no—
446C2×C4×C41—41no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—41no—
453C2×C4×C41—41no—
454C2×C4×C41C22×D411yescharacteristic
455C2×C4×C41C22×D411yescharacteristic
456C2×C4×C41C22×D411yescharacteristic
457C2×C4×C41C22×D411yescharacteristic
458C2×C4×C41C22×D411yescharacteristic
459C2×C4×C41H(5,𝔽2)11yescharacteristic
460C8×C41—22no—
461C8×C41—22no—
462C8×C41—22no—
463C8×C41—22no—
464C8×C41—41no—
465C8×C41—41no—
466#23894C4111yesmaximal, characteristic, direct product factor, Sylow
467C22×C41—22no—
468C22×C41—22no—
469C22×C41—41no—
470C22×C41—42no—
471C22×C41—42no—
472C22×C41—41no—
473C22×C41—41no—
474C22×C41—41no—
475C22×C41—42no—
476C22×C41—81no—
477C22×C41—81no—
478C22×C41—82no—
479C22×C41—81no—
480C22×C41—82no—
481C22×C41—161no—
482C22×C41—162no—
483C22×C41—164no—
484C22×C41#53411yescharacteristic
485C22×C41D4211yescharacteristic
486C22×C41D4211yescharacteristic
487C4×C41—22no—
488C4×C41—22no—
489C4×C41—41no—
490C4×C41—41no—
491C4×C41—41no—
492C4×C41—42no—
493C4×C41—81no—
494C4×C41—81no—
495C4×C41C2×#12011yescharacteristic
496C4×C41C2×#12011yescharacteristic
497C4×C41D4211yescharacteristic
498C4×C41D4211yescharacteristic
499#3586C2×C4111yescharacteristic, complemented
500#3585C2×C4111yescharacteristic, complemented
501#3020C2×C4111yescharacteristic, complemented
502#3019C2×C4111yescharacteristic, complemented
503#3010C2×C4111yescharacteristic, complemented
504#3009C2×C4111yescharacteristic, complemented
505#2019C2×C4111yescharacteristic, complemented
506#2017C2×C4111yescharacteristic, complemented
507#2009C2×C4111yescharacteristic, complemented
508#2008C2×C4111yescharacteristic, complemented
509#1903C2×C4111yescharacteristic, complemented
510#1902C2×C4111yescharacteristic, complemented
511#1881C2×C4111yescharacteristic, complemented
512#1881C2×C4111yescharacteristic, complemented
513#1794C2×C4111yescharacteristic, complemented
514C2×C41—21no—
515C2×C41—21no—
516C2×C41—21no—
517C2×C41—42no—
518C2×C41—42no—
519C2×C41—81no—
520C2×C41—81no—
521C2×C41—82no—
522C2×C41—81no—
523C2×C41#240311yescharacteristic
524#585C22×C4111yescharacteristic
525C2×2−1+4C22×C4111yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C4111yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C4111yescharacteristic
538#575C22×C4111yescharacteristic
539#575C22×C4111yescharacteristic
540#575C22×C4111yescharacteristic, complemented
541#575C22×C4111yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C4111yescharacteristic
544C2×#137C22×C4111yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
547C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
548C22×SD16C22×C4111yescharacteristic, complemented
549#568C22×C4111yescharacteristic
550#568C22×C4111yescharacteristic, complemented
551#536C22×C4111yescharacteristic, complemented
552#535C22×C4111yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C4111yescharacteristic
562#421C22×C4111yescharacteristic, complemented
563#421C22×C4111yescharacteristic, complemented
564#421C22×C4111yescharacteristic, complemented
565#419C22×C4111yescharacteristic, complemented
566#418C22×C4111yescharacteristic, complemented
567#416C22×C4111yescharacteristic
568#416C22×C4111yescharacteristic, complemented
569C2×#101C22×C4111yescharacteristic, complemented
570C2×#100C22×C4111yescharacteristic, complemented
571#410C22×C4111yescharacteristic, complemented
572#408C22×C4111yescharacteristic, complemented
573#408C22×C4111yescharacteristic, complemented
574#408C22×C4111yescharacteristic, complemented
575#344C22×C4111yescharacteristic, complemented
576#344C22×C4111yescharacteristic, complemented
577#341C22×C4111yescharacteristic, complemented
578#338C22×C4111yescharacteristic, complemented
579C41#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C4112yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C4112yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C4111yescharacteristic
604C2×#41C23×C4111yescharacteristic
605C2×#41C23×C4111yescharacteristic
606C2×#41C23×C4111yescharacteristic
607C2×#41C23×C4111yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C4111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C4111yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C4112yes—
632#137D4×C4112yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C4112yes—
650AGL(1,ℤ/8)D4×C4112yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C4112yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C4112yes—
671C2×SD16D4×C4112yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C4112yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C4111yescharacteristic
682C2×M16C23×C4111yescharacteristic
683C2×M16C23×C4111yescharacteristic
684C2×M16C23×C4111yescharacteristic
685C2×M16C23×C4111yescharacteristic
686C22×C8C23×C4111yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C4111yescharacteristic
696#117C23×C4111yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C4112yes—
752#41C2×D4×C4112yes—
753#41C2×D4×C4112yes—
754#41C2×D4×C4112yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C4112yes—
769C2×Q8C2×D4×C4111yescharacteristic
770C2×Q8C2×D4×C4111yescharacteristic
771C2×Q8C2×D4×C4111yescharacteristic
772C2×Q8C2×D4×C4111yescharacteristic
773C2×Q8C2×D4×C4111yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C4112yes—
801C2×D4C2×D4×C4111yescharacteristic
802C2×D4C2×D4×C4111yescharacteristic
803C2×D4C2×D4×C4111yescharacteristic
804C2×D4C2×D4×C4111yescharacteristic
805C2×D4C2×D4×C4111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C4111yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C4112yes—
857M16C2×D4×C4112yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C4112yes—
867C2×C8C2×D4×C4112yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C4111yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C4112yes—
905Q8#120×C4112yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C4112yes—
936D4#120×C4112yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C4111yescharacteristic
964C2×C4C22×D4×C4111yescharacteristic
965C2×C4C22×D4×C4111yescharacteristic
966C2×C4C22×D4×C4111yescharacteristic
967C2×C4C22×D4×C4111yescharacteristic
968C2×C4H(5,𝔽2)×C4111yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C41×#53411yescharacteristic
993C22D42×C4111yescharacteristic
994C22D42×C4111yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C4111yescharacteristic
1004C4C2×#120×C4111yescharacteristic
1005C4D42×C4111yescharacteristic
1006C4D42×C4111yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C41×#240311yescharacteristic
subgroupG/H
center, socleC2×C41#2403
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3586C2semidirect
2. C41×#3585C2semidirect
3. C41×#3020C2semidirect
4. C41×#3019C2semidirect
5. C41×#3010C2semidirect
6. C41×#3009C2semidirect
7. C41×#2019C2semidirect
8. C41×#2017C2semidirect
9. C41×#2009C2semidirect
10. C41×#2008C2semidirect
11. C41×#1903C2semidirect
12. C41×#1902C2semidirect
13. C41×#1881C2semidirect
14. C41×#1881C2semidirect
15. C41×#1794C2semidirect
17. C2×2−1+4×C41C22semidirect
32. C41×#575C22semidirect
33. C41×#575C22semidirect
36. C2×#137×C41C22semidirect
40. C22×SD16×C41C22semidirect
42. C41×#568C22semidirect
43. C41×#536C22semidirect
44. C41×#535C22semidirect
54. C41×#421C22semidirect
55. C41×#421C22semidirect
56. C41×#421C22semidirect
57. C41×#419C22semidirect
58. C41×#418C22semidirect
60. C41×#416C22semidirect
61. C2×#101×C41C22semidirect
62. C2×#100×C41C22semidirect
63. C41×#410C22semidirect
64. C41×#408C22semidirect
65. C41×#408C22semidirect
66. C41×#408C22semidirect
67. C41×#344C22semidirect
68. C41×#344C22semidirect
69. C41×#341C22semidirect
70. C41×#338C22semidirect
77. 2−1+4×C41D4semidirect
85. H(5,𝔽2)×C41D4semidirect
123. #137×C41D4semidirect
141. AGL(1,ℤ/8)×C41D4semidirect
153. C2×Q16×C41D4semidirect
162. C2×SD16×C41D4semidirect
466. #23894C41direct (N × H)
499. #3586C2×C41semidirect
500. #3585C2×C41semidirect
501. #3020C2×C41semidirect
502. #3019C2×C41semidirect
503. #3010C2×C41semidirect
504. #3009C2×C41semidirect
505. #2019C2×C41semidirect
506. #2017C2×C41semidirect
507. #2009C2×C41semidirect
508. #2008C2×C41semidirect
509. #1903C2×C41semidirect
510. #1902C2×C41semidirect
511. #1881C2×C41semidirect
512. #1881C2×C41semidirect
513. #1794C2×C41semidirect
525. C2×2−1+4C22×C41semidirect
540. #575C22×C41semidirect
541. #575C22×C41semidirect
544. C2×#137C22×C41semidirect
548. C22×SD16C22×C41semidirect
550. #568C22×C41semidirect
551. #536C22×C41semidirect
552. #535C22×C41semidirect
562. #421C22×C41semidirect
563. #421C22×C41semidirect
564. #421C22×C41semidirect
565. #419C22×C41semidirect
566. #418C22×C41semidirect
568. #416C22×C41semidirect
569. C2×#101C22×C41semidirect
570. C2×#100C22×C41semidirect
571. #410C22×C41semidirect
572. #408C22×C41semidirect
573. #408C22×C41semidirect
574. #408C22×C41semidirect
575. #344C22×C41semidirect
576. #344C22×C41semidirect
577. #341C22×C41semidirect
578. #338C22×C41semidirect
579. C41#23894direct (N × H)
586. 2−1+4D4×C41semidirect
594. H(5,𝔽2)D4×C41semidirect
632. #137D4×C41semidirect
650. AGL(1,ℤ/8)D4×C41semidirect
662. C2×Q16D4×C41semidirect
671. C2×SD16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35862
C41×#35852
C41×#30202
C41×#30192
C41×#30102
C41×#30092
C41×#20192
C41×#20172
C41×#20092
C41×#20082
C41×#19032
C41×#19022
C41×#18812
C41×#17942
#2389441