Finite Group Databasebeta

← C41×#24473 #23800674

Subgroups — C41×#24473 #23800674

Order 10496.

1314 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×#3586C211yesmaximal, characteristic, complemented
2C41×#3068C211yesmaximal, characteristic, complemented
3C41×#3040C211yesmaximal, characteristic, complemented
4C41×#3021C211yesmaximal, characteristic, complemented
5C2×C41×#454C211yesmaximal, characteristic, complemented
6C41×#2901C211yesmaximal, characteristic, complemented
7C41×#2050C211yesmaximal, characteristic, complemented
8C41×#2049C211yesmaximal, characteristic, complemented
9C41×#2008C211yesmaximal, characteristic, complemented
10C41×#2004C211yesmaximal, characteristic, complemented
11C41×#1906C211yesmaximal, characteristic, complemented
12C41×#1903C211yesmaximal, characteristic, complemented
13C41×#1902C211yesmaximal, characteristic, complemented
14C41×#1861C211yesmaximal, characteristic, complemented
15C41×#1796C211yesmaximal, characteristic, complemented
16C41×#585C2211yescharacteristic
17C2×2−1+4×C41C2211yescharacteristic
18C41×#578—22no—
19C41×#578—22no—
20C41×#577—22no—
21C41×#577—22no—
22C41×#575—22no—
23C41×#575C2211yescharacteristic
24C41×#575C2211yescharacteristic
25C2×#137×C41—22no—
26C2×#137×C41C2211yescharacteristic
27C2×#137×C41C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C41C2211yescharacteristic, complemented
31C41×#568C2211yescharacteristic
32C41×#568C2211yescharacteristic
33C41×#535C2211yescharacteristic
34C2×#124×C41C2211yescharacteristic, complemented
35C4×#41×C41C2211yescharacteristic
36C41×#472—22no—
37C41×#471—22no—
38C41×#464—22no—
39C41×#463—22no—
40C41×#454—22no—
41C41×#454—22no—
42C41×#454—22no—
43C41×#453—22no—
44C41×#430C2211yescharacteristic, complemented
45C41×#423C2211yescharacteristic, complemented
46C41×#421—22no—
47C41×#421C2211yescharacteristic
48C41×#421C2211yescharacteristic
49C41×#421C2211yescharacteristic
50C41×#421C2211yescharacteristic
51C2×#104×C41—22no—
52C2×#104×C41C2211yescharacteristic
53C2×#104×C41C2211yescharacteristic
54C2×#104×C41C2211yescharacteristic, complemented
55C41×#419C2211yescharacteristic, complemented
56C41×#419C2211yescharacteristic, complemented
57C41×#418C2211yescharacteristic, complemented
58C41×#413C2211yescharacteristic
59C41×#413C2211yescharacteristic, complemented
60C2×#101×C41C2211yescharacteristic, complemented
61C2×#100×C41C2211yescharacteristic, complemented
62C41×#410C2211yescharacteristic, complemented
63C41×#344C2211yescharacteristic, complemented
64C41×#344C2211yescharacteristic, complemented
65C41×#339C2211yescharacteristic, complemented
66C41×#338C2211yescharacteristic, complemented
672−1+4×C41—22no—
682−1+4×C41—22no—
692−1+4×C41—21no—
702−1+4×C41—21no—
712−1+4×C41—22no—
722−1+4×C41—41no—
732−1+4×C41D412yes—
74H(5,𝔽2)×C41—21no—
75H(5,𝔽2)×C41—21no—
76H(5,𝔽2)×C41—41no—
77H(5,𝔽2)×C41D412yes—
78C2×#41×C41—22no—
79C2×#41×C41—22no—
80C2×#41×C41—21no—
81C2×#41×C41—21no—
82C2×#41×C41—41no—
83C2×#41×C41—41no—
84C2×#41×C41C2311yescharacteristic
85C2×#41×C41C2311yescharacteristic
86C2×#41×C41C2311yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C22×Q8×C41—21no—
89C22×Q8×C41—21no—
90C22×Q8×C41C2311yescharacteristic
91C22×D4×C41C2311yescharacteristic
92#137×C41—24no—
93#137×C41—24no—
94#137×C41—24no—
95#137×C41—22no—
96#137×C41—22no—
97#137×C41—21no—
98#137×C41—22no—
99#137×C41—21no—
100#137×C41—21no—
101#137×C41—22no—
102#137×C41D412yescomplemented
103AGL(1,ℤ/8)×C41—24no—
104AGL(1,ℤ/8)×C41—21no—
105AGL(1,ℤ/8)×C41—21no—
106AGL(1,ℤ/8)×C41—21no—
107AGL(1,ℤ/8)×C41—22no—
108AGL(1,ℤ/8)×C41—22no—
109AGL(1,ℤ/8)×C41—22no—
110AGL(1,ℤ/8)×C41—22no—
111AGL(1,ℤ/8)×C41—22no—
112AGL(1,ℤ/8)×C41—41no—
113AGL(1,ℤ/8)×C41D412yescomplemented
114#135×C41—24no—
115#135×C41—24no—
116#135×C41—22no—
117#135×C41—22no—
118C2×Q16×C41—24no—
119C2×Q16×C41—21no—
120C2×Q16×C41D412yescomplemented
121C2×SD16×C41—24no—
122C2×SD16×C41—21no—
123C2×SD16×C41—21no—
124C2×SD16×C41—21no—
125C2×SD16×C41—21no—
126C2×SD16×C41D412yescomplemented
127C2×D8×C41—21no—
128C2×D8×C41—21no—
129C2×D8×C41—21no—
130#131×C41—22no—
131#131×C41—22no—
132#131×C41—22no—
133#131×C41—41no—
134C2×M16×C41—22no—
135C2×M16×C41—22no—
136C2×M16×C41C2311yescharacteristic
137C2×M16×C41C2311yescharacteristic
138C2×M16×C41C2311yescharacteristic
139C2×M16×C41C2311yescharacteristic
140C2×M16×C41C2311yescharacteristic
141C2×M16×C41C2311yescharacteristic
142#127×C41—21no—
143#124×C41—22no—
144#124×C41—21no—
145#124×C41—21no—
146#124×C41—21no—
147#121×C41—41no—
148#120×C41—41no—
149C4×Q8×C41—21no—
150C4×D4×C41—21no—
151C4×D4×C41—41no—
152#117×C41—21no—
153#117×C41C2311yescharacteristic
154#117×C41C2311yescharacteristic
155C2×C22⋊C4×C41—41no—
156C2×C42×C41—21no—
157C2×C42×C41C2311yescharacteristic
158#108×C41—22no—
159C4⋊C8×C41—22no—
160#104×C41—22no—
161#104×C41—22no—
162#104×C41—22no—
163#104×C41—22no—
164#104×C41—21no—
165#104×C41—21no—
166#104×C41—21no—
167#104×C41—21no—
168#104×C41D412yescomplemented
169#104×C41D412yescomplemented
170#103×C41—22no—
171#103×C41—41no—
172#102×C41—22no—
173#101×C41—21no—
174#101×C41—21no—
175#101×C41—22no—
176#100×C41—21no—
177#100×C41—21no—
178#100×C41—22no—
179#99×C41—41no—
180C24×C41—21no—
181#41×C41—21no—
182#41×C41—21no—
183#41×C41—21no—
184#41×C41—21no—
185#41×C41—24no—
186#41×C41—22no—
187#41×C41—22no—
188#41×C41—22no—
189#41×C41—22no—
190#41×C41—21no—
191#41×C41—21no—
192#41×C41—21no—
193#41×C41—21no—
194#41×C41—21no—
195#41×C41—21no—
196#41×C41—21no—
197#41×C41—21no—
198#41×C41—42no—
199#41×C41—42no—
200#41×C41—42no—
201#41×C41—42no—
202#41×C41—42no—
203#41×C41—44no—
204#41×C41—42no—
205#41×C41—41no—
206#41×C41—41no—
207#41×C41—44no—
208#41×C41—42no—
209#41×C41C2×D412yes—
210#41×C41C2×D412yes—
211#41×C41C2×D412yes—
212#41×C41C2×D412yes—
213C2×Q8×C41—21no—
214C2×Q8×C41—24no—
215C2×Q8×C41—22no—
216C2×Q8×C41—22no—
217C2×Q8×C41—21no—
218C2×Q8×C41—21no—
219C2×Q8×C41—21no—
220C2×Q8×C41—21no—
221C2×Q8×C41—41no—
222C2×Q8×C41—42no—
223C2×Q8×C41—42no—
224C2×Q8×C41—41no—
225C2×Q8×C41—42no—
226C2×Q8×C41C2×D411yescharacteristic
227C2×Q8×C41C2×D411yescharacteristic
228C2×Q8×C41C2×D412yes—
229C2×Q8×C41C2×D411yescharacteristic
230C2×Q8×C41#4111yescharacteristic
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—22no—
234C2×D4×C41—22no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—21no—
239C2×D4×C41—21no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—21no—
243C2×D4×C41—42no—
244C2×D4×C41—41no—
245C2×D4×C41—42no—
246C2×D4×C41—42no—
247C2×D4×C41—41no—
248C2×D4×C41—42no—
249C2×D4×C41C2×D411yescharacteristic
250C2×D4×C41C2×D411yescharacteristic
251C2×D4×C41C2×D411yescharacteristic
252C2×D4×C41#4111yescharacteristic
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—21no—
259C22×C4×C41—42no—
260C22×C4×C41—41no—
261C22×C4×C41—41no—
262C22×C4×C41—41no—
263C22×C4×C41C2411yescharacteristic
264Q16×C41—24no—
265Q16×C41—22no—
266Q16×C41—22no—
267Q16×C41—24no—
268SD16×C41—24no—
269SD16×C41—22no—
270SD16×C41—22no—
271SD16×C41—22no—
272SD16×C41—22no—
273SD16×C41—24no—
274SD16×C41—42no—
275SD16×C41—42no—
276SD16×C41—42no—
277D8×C41—22no—
278D8×C41—22no—
279D8×C41—42no—
280D8×C41—42no—
281D8×C41—42no—
282M16×C41—24no—
283M16×C41—21no—
284M16×C41—21no—
285M16×C41—21no—
286M16×C41—21no—
287M16×C41—21no—
288M16×C41—21no—
289M16×C41—21no—
290M16×C41—21no—
291M16×C41—21no—
292M16×C41—21no—
293M16×C41—42no—
294M16×C41C2×D412yes—
295M16×C41C2×D412yes—
296C2×C8×C41—24no—
297C2×C8×C41—21no—
298C2×C8×C41—21no—
299C2×C8×C41—21no—
300C2×C8×C41—21no—
301C2×C8×C41—21no—
302C2×C8×C41—42no—
303C2×C8×C41C2×D412yes—
304C4⋊C4×C41—21no—
305C4⋊C4×C41—21no—
306C4⋊C4×C41—41no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—42no—
310C22⋊C4×C41—42no—
311C22⋊C4×C41—41no—
312C22⋊C4×C41—42no—
313C42×C41—21no—
314C42×C41—21no—
315C42×C41—21no—
316C42×C41—41no—
317C42×C41C2×D411yescharacteristic
318C42×C41C2×D411yescharacteristic
319C23×C41—21no—
320C23×C41—21no—
321C23×C41—21no—
322C23×C41—21no—
323C23×C41—42no—
324C23×C41—41no—
325C23×C41—41no—
326C23×C41—41no—
327C23×C41—82no—
328C23×C41H(5,𝔽2)11yescharacteristic
329Q8×C41—21no—
330Q8×C41—21no—
331Q8×C41—21no—
332Q8×C41—22no—
333Q8×C41—21no—
334Q8×C41—21no—
335Q8×C41—21no—
336Q8×C41—22no—
337Q8×C41—42no—
338Q8×C41—44no—
339Q8×C41—41no—
340Q8×C41—41no—
341Q8×C41#12012yes—
342Q8×C41#12112yes—
343D4×C41—22no—
344D4×C41—22no—
345D4×C41—22no—
346D4×C41—22no—
347D4×C41—21no—
348D4×C41—21no—
349D4×C41—21no—
350D4×C41—21no—
351D4×C41—21no—
352D4×C41—21no—
353D4×C41—42no—
354D4×C41—42no—
355D4×C41—42no—
356D4×C41—44no—
357D4×C41—41no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—41no—
361D4×C41—41no—
362D4×C41—41no—
363D4×C41—41no—
364D4×C41—41no—
365D4×C41—162no—
366D4×C41#12012yes—
367D4×C41#12112yes—
368C2×C4×C41—21no—
369C2×C4×C41—21no—
370C2×C4×C41—22no—
371C2×C4×C41—22no—
372C2×C4×C41—22no—
373C2×C4×C41—22no—
374C2×C4×C41—21no—
375C2×C4×C41—21no—
376C2×C4×C41—21no—
377C2×C4×C41—22no—
378C2×C4×C41—21no—
379C2×C4×C41—42no—
380C2×C4×C41—42no—
381C2×C4×C41—42no—
382C2×C4×C41—44no—
383C2×C4×C41—44no—
384C2×C4×C41—41no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—41no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—81no—
393C2×C4×C41—82no—
394C2×C4×C41C22×D411yescharacteristic
395C2×C4×C41C22×D411yescharacteristic
396C2×C4×C41C22×D411yescharacteristic
397C2×C4×C41C22×D411yescharacteristic
398C2×C4×C41C2×#4111yescharacteristic
399C2×C4×C41H(5,𝔽2)11yescharacteristic
400C8×C41—22no—
401C8×C41—22no—
402C8×C41—22no—
403C8×C41—41no—
404C8×C41—41no—
405C8×C41—41no—
406#24473C4111yesmaximal, characteristic, direct product factor, Sylow
407C22×C41—22no—
408C22×C41—22no—
409C22×C41—41no—
410C22×C41—41no—
411C22×C41—41no—
412C22×C41—81no—
413C22×C41—81no—
414C22×C41—81no—
415C22×C41—81no—
416C22×C41—82no—
417C22×C41—82no—
418C22×C41—81no—
419C22×C41—161no—
420C22×C41—162no—
421C22×C41#53411yescharacteristic
422C22×C41D4211yescharacteristic
423C22×C41#54611yescharacteristic
424C4×C41—22no—
425C4×C41—22no—
426C4×C41—41no—
427C4×C41—41no—
428C4×C41—41no—
429C4×C41—42no—
430C4×C41—41no—
431C4×C41—81no—
432C4×C41—81no—
433C4×C41C2×#12011yescharacteristic
434C4×C41C2×#12111yescharacteristic
435C4×C41D4211yescharacteristic
436C4×C41#54611yescharacteristic
437#3586C2×C4111yescharacteristic, complemented
438#3068C2×C4111yescharacteristic, complemented
439#3040C2×C4111yescharacteristic, complemented
440#3021C2×C4111yescharacteristic, complemented
441C2×#454C2×C4111yescharacteristic, complemented
442#2901C2×C4111yescharacteristic, complemented
443#2050C2×C4111yescharacteristic, complemented
444#2049C2×C4111yescharacteristic, complemented
445#2008C2×C4111yescharacteristic, complemented
446#2004C2×C4111yescharacteristic, complemented
447#1906C2×C4111yescharacteristic, complemented
448#1903C2×C4111yescharacteristic, complemented
449#1902C2×C4111yescharacteristic, complemented
450#1861C2×C4111yescharacteristic, complemented
451#1796C2×C4111yescharacteristic, complemented
452C2×C41—21no—
453C2×C41—21no—
454C2×C41—21no—
455C2×C41—42no—
456C2×C41—42no—
457C2×C41—81no—
458C2×C41—81no—
459C2×C41—161no—
460C2×C41#241011yescharacteristic
461#585C22×C4111yescharacteristic
462C2×2−1+4C22×C4111yescharacteristic
463#578—22no—
464#578—22no—
465#577—22no—
466#577—22no—
467#575—22no—
468#575C22×C4111yescharacteristic
469#575C22×C4111yescharacteristic
470C2×#137—22no—
471C2×#137C22×C4111yescharacteristic
472C2×#137C22×C4111yescharacteristic
473C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
474C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
475C2×AGL(1,ℤ/8)C22×C4111yescharacteristic, complemented
476#568C22×C4111yescharacteristic
477#568C22×C4111yescharacteristic
478#535C22×C4111yescharacteristic
479C2×#124C22×C4111yescharacteristic, complemented
480C4×#41C22×C4111yescharacteristic
481#472—22no—
482#471—22no—
483#464—22no—
484#463—22no—
485#454—22no—
486#454—22no—
487#454—22no—
488#453—22no—
489#430C22×C4111yescharacteristic, complemented
490#423C22×C4111yescharacteristic, complemented
491#421—22no—
492#421C22×C4111yescharacteristic
493#421C22×C4111yescharacteristic
494#421C22×C4111yescharacteristic
495#421C22×C4111yescharacteristic
496C2×#104—22no—
497C2×#104C22×C4111yescharacteristic
498C2×#104C22×C4111yescharacteristic
499C2×#104C22×C4111yescharacteristic, complemented
500#419C22×C4111yescharacteristic, complemented
501#419C22×C4111yescharacteristic, complemented
502#418C22×C4111yescharacteristic, complemented
503#413C22×C4111yescharacteristic
504#413C22×C4111yescharacteristic, complemented
505C2×#101C22×C4111yescharacteristic, complemented
506C2×#100C22×C4111yescharacteristic, complemented
507#410C22×C4111yescharacteristic, complemented
508#344C22×C4111yescharacteristic, complemented
509#344C22×C4111yescharacteristic, complemented
510#339C22×C4111yescharacteristic, complemented
511#338C22×C4111yescharacteristic, complemented
512C41#2447311yescharacteristic, direct product factor, Sylow
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C4112yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C4112yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C4111yescharacteristic
531C2×#41C23×C4111yescharacteristic
532C2×#41C23×C4111yescharacteristic
533C2×#41C23×C4111yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C4111yescharacteristic
537C22×D4C23×C4111yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C4112yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C4112yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C4112yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C4112yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C4111yescharacteristic
583C2×M16C23×C4111yescharacteristic
584C2×M16C23×C4111yescharacteristic
585C2×M16C23×C4111yescharacteristic
586C2×M16C23×C4111yescharacteristic
587C2×M16C23×C4111yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C4111yescharacteristic
600#117C23×C4111yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C4111yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C4112yescomplemented
615#104D4×C4112yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C4112yes—
656#41C2×D4×C4112yes—
657#41C2×D4×C4112yes—
658#41C2×D4×C4112yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C4111yescharacteristic
673C2×Q8C2×D4×C4111yescharacteristic
674C2×Q8C2×D4×C4112yes—
675C2×Q8C2×D4×C4111yescharacteristic
676C2×Q8#41×C4111yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C4111yescharacteristic
696C2×D4C2×D4×C4111yescharacteristic
697C2×D4C2×D4×C4111yescharacteristic
698C2×D4#41×C4111yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C4111yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C4112yes—
741M16C2×D4×C4112yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C4112yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C4111yescharacteristic
764C42C2×D4×C4111yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C4111yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C4112yes—
788Q8#121×C4112yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C4112yes—
813D4#121×C4112yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—82no—
840C2×C4C22×D4×C4111yescharacteristic
841C2×C4C22×D4×C4111yescharacteristic
842C2×C4C22×D4×C4111yescharacteristic
843C2×C4C22×D4×C4111yescharacteristic
844C2×C4C2×#41×C4111yescharacteristic
845C2×C4H(5,𝔽2)×C4111yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22C41×#53411yescharacteristic
867C22D42×C4111yescharacteristic
868C22C41×#54611yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C4111yescharacteristic
879C4C2×#121×C4111yescharacteristic
880C4D42×C4111yescharacteristic
881C4C41×#54611yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2C41×#241011yescharacteristic
subgroupG/H
center, socleC2×C41#2410
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×#3068C2semidirect
3. C41×#3040C2semidirect
4. C41×#3021C2semidirect
5. C2×C41×#454C2semidirect
6. C41×#2901C2semidirect
7. C41×#2050C2semidirect
8. C41×#2049C2semidirect
9. C41×#2008C2semidirect
10. C41×#2004C2semidirect
11. C41×#1906C2semidirect
12. C41×#1903C2semidirect
13. C41×#1902C2semidirect
14. C41×#1861C2semidirect
15. C41×#1796C2semidirect
30. C2×AGL(1,ℤ/8)×C41C22semidirect
34. C2×#124×C41C22semidirect
44. C41×#430C22semidirect
45. C41×#423C22semidirect
54. C2×#104×C41C22semidirect
55. C41×#419C22semidirect
56. C41×#419C22semidirect
57. C41×#418C22semidirect
59. C41×#413C22semidirect
60. C2×#101×C41C22semidirect
61. C2×#100×C41C22semidirect
62. C41×#410C22semidirect
63. C41×#344C22semidirect
64. C41×#344C22semidirect
65. C41×#339C22semidirect
66. C41×#338C22semidirect
102. #137×C41D4semidirect
113. AGL(1,ℤ/8)×C41D4semidirect
120. C2×Q16×C41D4semidirect
126. C2×SD16×C41D4semidirect
168. #104×C41D4semidirect
169. #104×C41D4semidirect
406. #24473C41direct (N × H)
437. #3586C2×C41semidirect
438. #3068C2×C41semidirect
439. #3040C2×C41semidirect
440. #3021C2×C41semidirect
441. C2×#454C2×C41semidirect
442. #2901C2×C41semidirect
443. #2050C2×C41semidirect
444. #2049C2×C41semidirect
445. #2008C2×C41semidirect
446. #2004C2×C41semidirect
447. #1906C2×C41semidirect
448. #1903C2×C41semidirect
449. #1902C2×C41semidirect
450. #1861C2×C41semidirect
451. #1796C2×C41semidirect
475. C2×AGL(1,ℤ/8)C22×C41semidirect
479. C2×#124C22×C41semidirect
489. #430C22×C41semidirect
490. #423C22×C41semidirect
499. C2×#104C22×C41semidirect
500. #419C22×C41semidirect
501. #419C22×C41semidirect
502. #418C22×C41semidirect
504. #413C22×C41semidirect
505. C2×#101C22×C41semidirect
506. C2×#100C22×C41semidirect
507. #410C22×C41semidirect
508. #344C22×C41semidirect
509. #344C22×C41semidirect
510. #339C22×C41semidirect
511. #338C22×C41semidirect
512. C41#24473direct (N × H)
548. #137D4×C41semidirect
559. AGL(1,ℤ/8)D4×C41semidirect
566. C2×Q16D4×C41semidirect
572. C2×SD16D4×C41semidirect
614. #104D4×C41semidirect
615. #104D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35862
C41×#30682
C41×#30402
C41×#30212
C2×C41×#4542
C41×#29012
C41×#20502
C41×#20492
C41×#20082
C41×#20042
C41×#19062
C41×#19032
C41×#19022
C41×#18612
C41×#17962
#2447341