Finite Group Databasebeta

← C41×#24474 #23800675

Subgroups — C41×#24474 #23800675

Order 10496.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3586C211yesmaximal, characteristic
2C41×#3069C211yesmaximal, characteristic, complemented
3C41×#3039C211yesmaximal, characteristic, complemented
4C41×#3022C211yesmaximal, characteristic, complemented
5C2×C41×#456C211yesmaximal, characteristic, complemented
6C41×#2901C211yesmaximal, characteristic, complemented
7C41×#2050C211yesmaximal, characteristic, complemented
8C41×#2049C211yesmaximal, characteristic, complemented
9C41×#2009C211yesmaximal, characteristic, complemented
10C41×#2005C211yesmaximal, characteristic, complemented
11C41×#1906C211yesmaximal, characteristic, complemented
12C41×#1902C211yesmaximal, 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×#137×C41C2211yescharacteristic
29C2×#137×C41C2211yescharacteristic
30C2×#137×C41C2211yescharacteristic, complemented
31C41×#568C2211yescharacteristic
32C41×#568C2211yescharacteristic
33C41×#536C2211yescharacteristic
34C2×C4⋊Q8×C41C2211yescharacteristic, complemented
35C4×#41×C41C2211yescharacteristic
36C41×#473—22no—
37C41×#471—22no—
38C41×#462—22no—
39C41×#461—22no—
40C41×#456—22no—
41C41×#456—22no—
42C41×#456—22no—
43C41×#455—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×#419C2211yescharacteristic, complemented
58C41×#413C2211yescharacteristic
59C41×#413C2211yescharacteristic, complemented
60C2×#101×C41C2211yescharacteristic, complemented
61C2×#101×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×Q8×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×C41—22no—
103#137×C41—22no—
104#137×C41—22no—
105#137×C41—22no—
106#137×C41—22no—
107#137×C41—41no—
108#137×C41D412yes—
109AGL(1,ℤ/8)×C41—24no—
110AGL(1,ℤ/8)×C41—21no—
111AGL(1,ℤ/8)×C41—21no—
112AGL(1,ℤ/8)×C41—21no—
113AGL(1,ℤ/8)×C41D412yes—
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×C41—21no—
121C2×Q16×C41—21no—
122C2×Q16×C41—21no—
123C2×Q16×C41D412yes—
124C2×SD16×C41—24no—
125C2×SD16×C41—21no—
126C2×SD16×C41—21no—
127C2×SD16×C41—21no—
128C2×SD16×C41—21no—
129C2×SD16×C41D412yes—
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
142C4⋊Q8×C41—22no—
143C4⋊Q8×C41—21no—
144C4⋊Q8×C41—21no—
145C4⋊Q8×C41—21no—
146#124×C41—21no—
147#123×C41—41no—
148C22⋊Q8×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×C4⋊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×C41D412yes—
169#104×C41D412yes—
170#103×C41—22no—
171#103×C41—22no—
172#103×C41—41no—
173#101×C41—21no—
174#101×C41—21no—
175#101×C41—22no—
176#101×C41—22no—
177#100×C41—21no—
178#100×C41—21no—
179#99×C41—41no—
180#41×C41—21no—
181#41×C41—21no—
182#41×C41—21no—
183#41×C41—21no—
184#41×C41—24no—
185#41×C41—22no—
186#41×C41—22no—
187#41×C41—22no—
188#41×C41—22no—
189#41×C41—21no—
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—42no—
198#41×C41—42no—
199#41×C41—42no—
200#41×C41—42no—
201#41×C41—42no—
202#41×C41—44no—
203#41×C41—42no—
204#41×C41—41no—
205#41×C41—41no—
206#41×C41—44no—
207#41×C41—42no—
208#41×C41C2×D412yes—
209#41×C41C2×D412yes—
210#41×C41C2×D412yes—
211#41×C41C2×D412yes—
212C2×Q8×C41—21no—
213C2×Q8×C41—24no—
214C2×Q8×C41—22no—
215C2×Q8×C41—22no—
216C2×Q8×C41—21no—
217C2×Q8×C41—21no—
218C2×Q8×C41—21no—
219C2×Q8×C41—21no—
220C2×Q8×C41—21no—
221C2×Q8×C41—21no—
222C2×Q8×C41—21no—
223C2×Q8×C41—21no—
224C2×Q8×C41—21no—
225C2×Q8×C41—21no—
226C2×Q8×C41—41no—
227C2×Q8×C41—42no—
228C2×Q8×C41—42no—
229C2×Q8×C41—41no—
230C2×Q8×C41—42no—
231C2×Q8×C41C2×D411yescharacteristic
232C2×Q8×C41C2×D411yescharacteristic
233C2×Q8×C41C2×D412yes—
234C2×Q8×C41C2×D411yescharacteristic
235C2×Q8×C41#4111yescharacteristic
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—22no—
239C2×D4×C41—22no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—42no—
243C2×D4×C41—41no—
244C2×D4×C41—42no—
245C2×D4×C41—42no—
246C2×D4×C41—41no—
247C2×D4×C41C2×D411yescharacteristic
248C2×D4×C41C2×D411yescharacteristic
249C2×D4×C41C2×D411yescharacteristic
250C2×D4×C41#4111yescharacteristic
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—42no—
259C22×C4×C41—41no—
260C22×C4×C41—41no—
261C22×C4×C41—41no—
262C22×C4×C41C2411yescharacteristic
263Q16×C41—24no—
264Q16×C41—22no—
265Q16×C41—22no—
266Q16×C41—24no—
267Q16×C41—42no—
268Q16×C41—42no—
269Q16×C41—42no—
270SD16×C41—24no—
271SD16×C41—22no—
272SD16×C41—22no—
273SD16×C41—22no—
274SD16×C41—22no—
275SD16×C41—24no—
276SD16×C41—42no—
277SD16×C41—42no—
278SD16×C41—42no—
279D8×C41—22no—
280D8×C41—22no—
281M16×C41—24no—
282M16×C41—21no—
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—42no—
293M16×C41C2×D412yes—
294M16×C41C2×D412yes—
295C2×C8×C41—24no—
296C2×C8×C41—21no—
297C2×C8×C41—21no—
298C2×C8×C41—21no—
299C2×C8×C41—21no—
300C2×C8×C41—21no—
301C2×C8×C41—42no—
302C2×C8×C41C2×D412yes—
303C4⋊C4×C41—21no—
304C4⋊C4×C41—21no—
305C4⋊C4×C41—42no—
306C4⋊C4×C41—42no—
307C4⋊C4×C41—41no—
308C4⋊C4×C41—42no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
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×C41H(5,𝔽2)11yescharacteristic
325Q8×C41—21no—
326Q8×C41—21no—
327Q8×C41—21no—
328Q8×C41—22no—
329Q8×C41—21no—
330Q8×C41—21no—
331Q8×C41—21no—
332Q8×C41—22no—
333Q8×C41—42no—
334Q8×C41—44no—
335Q8×C41—41no—
336Q8×C41—41no—
337Q8×C41—41no—
338Q8×C41—41no—
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#12012yes—
362D4×C41#12112yes—
363C2×C4×C41—21no—
364C2×C4×C41—21no—
365C2×C4×C41—21no—
366C2×C4×C41—22no—
367C2×C4×C41—22no—
368C2×C4×C41—22no—
369C2×C4×C41—22no—
370C2×C4×C41—21no—
371C2×C4×C41—21no—
372C2×C4×C41—22no—
373C2×C4×C41—21no—
374C2×C4×C41—42no—
375C2×C4×C41—42no—
376C2×C4×C41—42no—
377C2×C4×C41—42no—
378C2×C4×C41—44no—
379C2×C4×C41—44no—
380C2×C4×C41—41no—
381C2×C4×C41—41no—
382C2×C4×C41—41no—
383C2×C4×C41—41no—
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—82no—
392C2×C4×C41C22×D411yescharacteristic
393C2×C4×C41C22×D411yescharacteristic
394C2×C4×C41C22×D411yescharacteristic
395C2×C4×C41C22×D411yescharacteristic
396C2×C4×C41C2×#4111yescharacteristic
397C2×C4×C41H(5,𝔽2)11yescharacteristic
398C8×C41—22no—
399C8×C41—22no—
400C8×C41—22no—
401C8×C41—41no—
402C8×C41—41no—
403C8×C41—41no—
404#24474C4111yesmaximal, characteristic, direct product factor, Sylow
405C22×C41—22no—
406C22×C41—22no—
407C22×C41—41no—
408C22×C41—41no—
409C22×C41—41no—
410C22×C41—81no—
411C22×C41—81no—
412C22×C41—81no—
413C22×C41—81no—
414C22×C41—162no—
415C22×C41#53411yescharacteristic
416C22×C41D4211yescharacteristic
417C22×C41#54611yescharacteristic
418C4×C41—22no—
419C4×C41—22no—
420C4×C41—22no—
421C4×C41—41no—
422C4×C41—41no—
423C4×C41—42no—
424C4×C41—41no—
425C4×C41—81no—
426C4×C41—81no—
427C4×C41—81no—
428C4×C41C2×#12011yescharacteristic
429C4×C41C2×#12111yescharacteristic
430C4×C41D4211yescharacteristic
431C4×C41#54611yescharacteristic
432#3586C2×C4111yescharacteristic
433#3069C2×C4111yescharacteristic, complemented
434#3039C2×C4111yescharacteristic, complemented
435#3022C2×C4111yescharacteristic, complemented
436C2×#456C2×C4111yescharacteristic, complemented
437#2901C2×C4111yescharacteristic, complemented
438#2050C2×C4111yescharacteristic, complemented
439#2049C2×C4111yescharacteristic, complemented
440#2009C2×C4111yescharacteristic, complemented
441#2005C2×C4111yescharacteristic, complemented
442#1906C2×C4111yescharacteristic, complemented
443#1902C2×C4111yescharacteristic, complemented
444#1902C2×C4111yescharacteristic, complemented
445#1861C2×C4111yescharacteristic, complemented
446#1796C2×C4111yescharacteristic, complemented
447C2×C41—21no—
448C2×C41—21no—
449C2×C41—21no—
450C2×C41—42no—
451C2×C41—42no—
452C2×C41—81no—
453C2×C41—81no—
454C2×C41#241011yescharacteristic
455#585C22×C4111yescharacteristic
456C2×2−1+4C22×C4111yescharacteristic
457#578—22no—
458#578—22no—
459#577—22no—
460#577—22no—
461#575—22no—
462#575C22×C4111yescharacteristic
463#575C22×C4111yescharacteristic
464C2×#137—22no—
465C2×#137C22×C4111yescharacteristic
466C2×#137C22×C4111yescharacteristic
467C2×#137C22×C4111yescharacteristic
468C2×#137C22×C4111yescharacteristic
469C2×#137C22×C4111yescharacteristic, complemented
470#568C22×C4111yescharacteristic
471#568C22×C4111yescharacteristic
472#536C22×C4111yescharacteristic
473C2×C4⋊Q8C22×C4111yescharacteristic, complemented
474C4×#41C22×C4111yescharacteristic
475#473—22no—
476#471—22no—
477#462—22no—
478#461—22no—
479#456—22no—
480#456—22no—
481#456—22no—
482#455—22no—
483#430C22×C4111yescharacteristic, complemented
484#423C22×C4111yescharacteristic, complemented
485#421—22no—
486#421C22×C4111yescharacteristic
487#421C22×C4111yescharacteristic
488#421C22×C4111yescharacteristic
489#421C22×C4111yescharacteristic
490C2×#104—22no—
491C2×#104C22×C4111yescharacteristic
492C2×#104C22×C4111yescharacteristic
493C2×#104C22×C4111yescharacteristic, complemented
494#419C22×C4111yescharacteristic, complemented
495#419C22×C4111yescharacteristic, complemented
496#419C22×C4111yescharacteristic, complemented
497#413C22×C4111yescharacteristic
498#413C22×C4111yescharacteristic, complemented
499C2×#101C22×C4111yescharacteristic, complemented
500C2×#101C22×C4111yescharacteristic, complemented
501#410C22×C4111yescharacteristic, complemented
502#344C22×C4111yescharacteristic, complemented
503#344C22×C4111yescharacteristic, complemented
504#339C22×C4111yescharacteristic, complemented
505#338C22×C4111yescharacteristic, complemented
506C41#2447411yescharacteristic, direct product factor, Sylow
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C4112yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C4112yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C4111yescharacteristic
525C2×#41C23×C4111yescharacteristic
526C2×#41C23×C4111yescharacteristic
527C2×#41C23×C4111yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C4111yescharacteristic
531C22×Q8C23×C4111yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C4112yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C4112yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C4112yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C4112yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C4111yescharacteristic
577C2×M16C23×C4111yescharacteristic
578C2×M16C23×C4111yescharacteristic
579C2×M16C23×C4111yescharacteristic
580C2×M16C23×C4111yescharacteristic
581C2×M16C23×C4111yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C4111yescharacteristic
594#117C23×C4111yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C4111yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C4112yes—
609#104D4×C4112yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C4112yes—
649#41C2×D4×C4112yes—
650#41C2×D4×C4112yes—
651#41C2×D4×C4112yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C4111yescharacteristic
672C2×Q8C2×D4×C4111yescharacteristic
673C2×Q8C2×D4×C4112yes—
674C2×Q8C2×D4×C4111yescharacteristic
675C2×Q8#41×C4111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C4111yescharacteristic
688C2×D4C2×D4×C4111yescharacteristic
689C2×D4C2×D4×C4111yescharacteristic
690C2×D4#41×C4111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C4111yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C4112yes—
734M16C2×D4×C4112yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C4112yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C4111yescharacteristic
758C42C2×D4×C4111yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C4111yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C4112yes—
782Q8#121×C4112yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C4112yes—
802D4#121×C4112yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C4111yescharacteristic
833C2×C4C22×D4×C4111yescharacteristic
834C2×C4C22×D4×C4111yescharacteristic
835C2×C4C22×D4×C4111yescharacteristic
836C2×C4C2×#41×C4111yescharacteristic
837C2×C4H(5,𝔽2)×C4111yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22C41×#53411yescharacteristic
855C22D42×C4111yescharacteristic
856C22C41×#54611yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C4111yescharacteristic
868C4C2×#121×C4111yescharacteristic
869C4D42×C4111yescharacteristic
870C4C41×#54611yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C41×#241011yescharacteristic
subgroupG/H
center, socleC2×C41#2410
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3586C2
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
2. C41×#3069C2semidirect
3. C41×#3039C2semidirect
4. C41×#3022C2semidirect
5. C2×C41×#456C2semidirect
6. C41×#2901C2semidirect
7. C41×#2050C2semidirect
8. C41×#2049C2semidirect
9. C41×#2009C2semidirect
10. C41×#2005C2semidirect
11. C41×#1906C2semidirect
12. C41×#1902C2semidirect
13. C41×#1902C2semidirect
14. C41×#1861C2semidirect
15. C41×#1796C2semidirect
30. C2×#137×C41C22semidirect
34. C2×C4⋊Q8×C41C22semidirect
44. C41×#430C22semidirect
45. C41×#423C22semidirect
54. C2×#104×C41C22semidirect
55. C41×#419C22semidirect
56. C41×#419C22semidirect
57. C41×#419C22semidirect
59. C41×#413C22semidirect
60. C2×#101×C41C22semidirect
61. C2×#101×C41C22semidirect
62. C41×#410C22semidirect
63. C41×#344C22semidirect
64. C41×#344C22semidirect
65. C41×#339C22semidirect
66. C41×#338C22semidirect
404. #24474C41direct (N × H)
433. #3069C2×C41semidirect
434. #3039C2×C41semidirect
435. #3022C2×C41semidirect
436. C2×#456C2×C41semidirect
437. #2901C2×C41semidirect
438. #2050C2×C41semidirect
439. #2049C2×C41semidirect
440. #2009C2×C41semidirect
441. #2005C2×C41semidirect
442. #1906C2×C41semidirect
443. #1902C2×C41semidirect
444. #1902C2×C41semidirect
445. #1861C2×C41semidirect
446. #1796C2×C41semidirect
469. C2×#137C22×C41semidirect
473. C2×C4⋊Q8C22×C41semidirect
483. #430C22×C41semidirect
484. #423C22×C41semidirect
493. C2×#104C22×C41semidirect
494. #419C22×C41semidirect
495. #419C22×C41semidirect
496. #419C22×C41semidirect
498. #413C22×C41semidirect
499. C2×#101C22×C41semidirect
500. C2×#101C22×C41semidirect
501. #410C22×C41semidirect
502. #344C22×C41semidirect
503. #344C22×C41semidirect
504. #339C22×C41semidirect
505. #338C22×C41semidirect
506. C41#24474direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35862
C41×#30692
C41×#30392
C41×#30222
C2×C41×#4562
C41×#29012
C41×#20502
C41×#20492
C41×#20092
C41×#20052
C41×#19062
C41×#19022
C41×#18612
C41×#17962
#2447441