Finite Group Databasebeta

← C41×#24295 #23800496

Subgroups — C41×#24295 #23800496

Order 10496.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#577C211yesmaximal, characteristic, complemented
2C41×#3067C211yesmaximal, characteristic, complemented
3C41×#3057C211yesmaximal, characteristic, complemented
4C41×#3020C211yesmaximal, characteristic, complemented
5C41×#3019C211yesmaximal, characteristic, complemented
6C41×#2955C211yesmaximal, characteristic, complemented
7C41×#2049C211yesmaximal, characteristic, complemented
8C41×#2048C211yesmaximal, characteristic, complemented
9C41×#2009C211yesmaximal, characteristic, complemented
10C41×#2008C211yesmaximal, characteristic, complemented
11C41×#1977C211yesmaximal, characteristic, complemented
12C41×#1976C211yesmaximal, characteristic, complemented
13C41×#1814C211yesmaximal, characteristic, complemented
14C41×#1796C211yesmaximal, characteristic, complemented
15C41×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C41C2211yescharacteristic
17C2×H(5,𝔽2)×C41C2211yescharacteristic
18C41×#577—22no—
19C41×#577—22no—
20C41×#577—22no—
21C41×#577—22no—
22C41×#575C2211yescharacteristic
23C41×#575C2211yescharacteristic
24C41×#575C2211yescharacteristic, complemented
25C2×#137×C41—21no—
26C2×#137×C41C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C41—21no—
28C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
29C2×#135×C41—21no—
30C2×#135×C41C2211yescharacteristic
31C22×SD16×C41—21no—
32C22×SD16×C41C2211yescharacteristic
33C2×#131×C41C2211yescharacteristic
34C2×#131×C41C2211yescharacteristic, complemented
35C41×#536C2211yescharacteristic, complemented
36C41×#535C2211yescharacteristic
37C41×#473—21no—
38C41×#472—21no—
39C41×#471—21no—
40C41×#471—21no—
41C41×#468—22no—
42C41×#465—22no—
43C41×#456—22no—
44C41×#455—22no—
45C41×#454—22no—
46C41×#453—22no—
47C41×#444—22no—
48C41×#443—22no—
49C41×#430C2211yescharacteristic, complemented
50C2×#108×C41C2211yescharacteristic, complemented
51C41×#427C2211yescharacteristic, complemented
52C41×#421C2211yescharacteristic
53C41×#421C2211yescharacteristic
54C41×#421C2211yescharacteristic
55C41×#421C2211yescharacteristic
56C41×#421C2211yescharacteristic, complemented
57C41×#421C2211yescharacteristic, complemented
58C41×#419C2211yescharacteristic, complemented
59C41×#419C2211yescharacteristic, complemented
60C41×#418C2211yescharacteristic
61C41×#418C2211yescharacteristic
62C41×#413C2211yescharacteristic
63C41×#413C2211yescharacteristic, complemented
64C2×#101×C41C2211yescharacteristic, complemented
65C2×#100×C41C2211yescharacteristic
66C41×#410C2211yescharacteristic
67C41×#410C2211yescharacteristic, complemented
68C41×#405C2211yescharacteristic, complemented
69C41×#344C2211yescharacteristic, complemented
70C41×#344C2211yescharacteristic, complemented
712−1+4×C41—22no—
722−1+4×C41—22no—
732−1+4×C41—22no—
742−1+4×C41—41no—
75H(5,𝔽2)×C41—22no—
76H(5,𝔽2)×C41—22no—
77H(5,𝔽2)×C41—22no—
78H(5,𝔽2)×C41—41no—
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—21no—
82C2×#41×C41—21no—
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×C41—21no—
92C22×D4×C41—21no—
93C22×D4×C41—41no—
94C22×D4×C41C2311yescharacteristic
95#137×C41—24no—
96#137×C41—24no—
97#137×C41—22no—
98#137×C41—21no—
99#137×C41—21no—
100#137×C41—21no—
101#137×C41—21no—
102#137×C41—21no—
103#137×C41—22no—
104#137×C41D412yes—
105AGL(1,ℤ/8)×C41—24no—
106AGL(1,ℤ/8)×C41—24no—
107AGL(1,ℤ/8)×C41—22no—
108AGL(1,ℤ/8)×C41—21no—
109AGL(1,ℤ/8)×C41—21no—
110AGL(1,ℤ/8)×C41—21no—
111AGL(1,ℤ/8)×C41—21no—
112AGL(1,ℤ/8)×C41—21no—
113AGL(1,ℤ/8)×C41—22no—
114AGL(1,ℤ/8)×C41D412yes—
115#135×C41—24no—
116#135×C41—24no—
117#135×C41—22no—
118#135×C41—21no—
119#135×C41—21no—
120#135×C41—21no—
121#135×C41—21no—
122#135×C41—41no—
123#135×C41—41no—
124C2×Q16×C41—21no—
125C2×Q16×C41D411yescharacteristic, complemented
126C2×SD16×C41—24no—
127C2×SD16×C41—24no—
128C2×SD16×C41—21no—
129C2×SD16×C41—21no—
130C2×SD16×C41—21no—
131C2×SD16×C41—21no—
132C2×SD16×C41—21no—
133C2×SD16×C41—21no—
134C2×SD16×C41D412yes—
135C2×SD16×C41D412yes—
136C2×SD16×C41D411yescharacteristic, complemented
137C2×SD16×C41D411yescharacteristic, complemented
138C2×D8×C41—21no—
139C2×D8×C41D411yescharacteristic, complemented
140#131×C41—21no—
141#131×C41—21no—
142#131×C41—21no—
143#131×C41—21no—
144#131×C41—21no—
145#131×C41—21no—
146#131×C41D412yescomplemented
147#131×C41D412yescomplemented
148C2×M16×C41—21no—
149C2×M16×C41—21no—
150C2×M16×C41C2311yescharacteristic
151C2×M16×C41C2311yescharacteristic
152C2×M16×C41C2311yescharacteristic
153C2×M16×C41C2311yescharacteristic
154C2×M16×C41C2311yescharacteristic
155C22×C8×C41—21no—
156C22×C8×C41—21no—
157C22×C8×C41C2311yescharacteristic
158C4⋊Q8×C41—21no—
159#127×C41—21no—
160#124×C41—21no—
161#124×C41—21no—
162#123×C41—41no—
163C22⋊Q8×C41—22no—
164#121×C41—22no—
165#120×C41—41no—
166#117×C41C2311yescharacteristic
167#117×C41C2311yescharacteristic
168#117×C41C2311yescharacteristic
169#108×C41—22no—
170#108×C41—21no—
171#108×C41—21no—
172#107×C41—21no—
173#106×C41—21no—
174#104×C41—22no—
175#104×C41—22no—
176#104×C41—22no—
177#104×C41—22no—
178#104×C41—22no—
179#104×C41—22no—
180#103×C41—22no—
181#103×C41—41no—
182#102×C41—22no—
183#102×C41—41no—
184#101×C41—21no—
185#101×C41—21no—
186#101×C41—22no—
187#100×C41—21no—
188#100×C41—21no—
189#100×C41—22no—
190#99×C41—41no—
191#99×C41—41no—
192#97×C41—21no—
193C4×C8×C41—21no—
194C24×C41—21no—
195C24×C41—41no—
196#41×C41—21no—
197#41×C41—21no—
198#41×C41—24no—
199#41×C41—24no—
200#41×C41—21no—
201#41×C41—21no—
202#41×C41—21no—
203#41×C41—21no—
204#41×C41—21no—
205#41×C41—21no—
206#41×C41—21no—
207#41×C41—21no—
208#41×C41—21no—
209#41×C41—21no—
210#41×C41—21no—
211#41×C41—21no—
212#41×C41—42no—
213#41×C41—44no—
214#41×C41—42no—
215#41×C41—42no—
216#41×C41—42no—
217#41×C41—44no—
218#41×C41—42no—
219#41×C41—42no—
220#41×C41C2×D412yes—
221#41×C41C2×D412yes—
222C2×Q8×C41—21no—
223C2×Q8×C41—24no—
224C2×Q8×C41—21no—
225C2×Q8×C41—21no—
226C2×Q8×C41—21no—
227C2×Q8×C41—21no—
228C2×Q8×C41—41no—
229C2×Q8×C41—42no—
230C2×Q8×C41—42no—
231C2×Q8×C41—42no—
232C2×Q8×C41C2×D411yescharacteristic
233C2×Q8×C41C2×D411yescharacteristic
234C2×Q8×C41C2×D412yes—
235C2×Q8×C41C2×D411yescharacteristic
236C2×Q8×C41#4111yescharacteristic
237C2×D4×C41—21no—
238C2×D4×C41—24no—
239C2×D4×C41—21no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—21no—
243C2×D4×C41—21no—
244C2×D4×C41—21no—
245C2×D4×C41—21no—
246C2×D4×C41—21no—
247C2×D4×C41—42no—
248C2×D4×C41—41no—
249C2×D4×C41—41no—
250C2×D4×C41—42no—
251C2×D4×C41—44no—
252C2×D4×C41—44no—
253C2×D4×C41—41no—
254C2×D4×C41—42no—
255C2×D4×C41—42no—
256C2×D4×C41C2×D411yescharacteristic
257C2×D4×C41C2×D411yescharacteristic
258C2×D4×C41C2×D412yes—
259C2×D4×C41C2×D411yescharacteristic
260C2×D4×C41#4111yescharacteristic
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—21no—
264C22×C4×C41—21no—
265C22×C4×C41—21no—
266C22×C4×C41—41no—
267C22×C4×C41—41no—
268C22×C4×C41—41no—
269C22×C4×C41C2411yescharacteristic
270Q16×C41—24no—
271Q16×C41—22no—
272Q16×C41—21no—
273Q16×C41—21no—
274Q16×C41—41no—
275Q16×C41—41no—
276SD16×C41—24no—
277SD16×C41—24no—
278SD16×C41—22no—
279SD16×C41—22no—
280SD16×C41—22no—
281SD16×C41—22no—
282SD16×C41—21no—
283SD16×C41—21no—
284SD16×C41—22no—
285SD16×C41—22no—
286SD16×C41—21no—
287SD16×C41—21no—
288SD16×C41—41no—
289SD16×C41—41no—
290SD16×C41—41no—
291SD16×C41—41no—
292D8×C41—24no—
293D8×C41—22no—
294D8×C41—21no—
295D8×C41—21no—
296D8×C41—41no—
297D8×C41—41no—
298M16×C41—21no—
299M16×C41—21no—
300M16×C41—22no—
301M16×C41—22no—
302M16×C41—21no—
303M16×C41—21no—
304M16×C41—21no—
305M16×C41—21no—
306M16×C41—21no—
307M16×C41—21no—
308M16×C41—41no—
309M16×C41—41no—
310M16×C41C2×D412yes—
311M16×C41C2×D412yes—
312C2×C8×C41—21no—
313C2×C8×C41—21no—
314C2×C8×C41—22no—
315C2×C8×C41—22no—
316C2×C8×C41—21no—
317C2×C8×C41—21no—
318C2×C8×C41—21no—
319C2×C8×C41—41no—
320C2×C8×C41—41no—
321C2×C8×C41C2×D411yescharacteristic
322C2×C8×C41C2×D411yescharacteristic
323C2×C8×C41C2×D411yescharacteristic
324C2×C8×C41C2×D411yescharacteristic
325C2×C8×C41C2×D411yescharacteristic
326C2×C8×C41C2×D411yescharacteristic
327C4⋊C4×C41—21no—
328C4⋊C4×C41—21no—
329C4⋊C4×C41—21no—
330C4⋊C4×C41—42no—
331C22⋊C4×C41—21no—
332C22⋊C4×C41—21no—
333C22⋊C4×C41—21no—
334C22⋊C4×C41—42no—
335C22⋊C4×C41—42no—
336C42×C41—21no—
337C42×C41—21no—
338C42×C41—21no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—22no—
342C23×C41—21no—
343C23×C41—21no—
344C23×C41—44no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—161no—
348C23×C41—162no—
349C23×C41H(5,𝔽2)11yescharacteristic
350Q8×C41—21no—
351Q8×C41—21no—
352Q8×C41—22no—
353Q8×C41—21no—
354Q8×C41—21no—
355Q8×C41—21no—
356Q8×C41—21no—
357Q8×C41—21no—
358Q8×C41—22no—
359Q8×C41—44no—
360Q8×C41—41no—
361Q8×C41—41no—
362Q8×C41#12112yes—
363D4×C41—22no—
364D4×C41—22no—
365D4×C41—21no—
366D4×C41—22no—
367D4×C41—21no—
368D4×C41—21no—
369D4×C41—21no—
370D4×C41—21no—
371D4×C41—21no—
372D4×C41—21no—
373D4×C41—22no—
374D4×C41—44no—
375D4×C41—44no—
376D4×C41—44no—
377D4×C41—41no—
378D4×C41—41no—
379D4×C41—41no—
380D4×C41—41no—
381D4×C41—41no—
382D4×C41—41no—
383D4×C41—41no—
384D4×C41—41no—
385D4×C41—162no—
386D4×C41#12112yes—
387C2×C4×C41—21no—
388C2×C4×C41—22no—
389C2×C4×C41—22no—
390C2×C4×C41—21no—
391C2×C4×C41—22no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—44no—
395C2×C4×C41—44no—
396C2×C4×C41—44no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41C22×D411yescharacteristic
409C2×C4×C41C22×D411yescharacteristic
410C2×C4×C41C22×D411yescharacteristic
411C2×C4×C41C22×D411yescharacteristic
412C2×C4×C41C2×#4111yescharacteristic
413C2×C4×C41H(5,𝔽2)11yescharacteristic
414C8×C41—22no—
415C8×C41—22no—
416C8×C41—41no—
417C8×C41—41no—
418C8×C41—41no—
419C8×C41#12011yescharacteristic
420C8×C41#12011yescharacteristic
421C8×C41#12011yescharacteristic
422C8×C41#12011yescharacteristic
423#24295C4111yesmaximal, characteristic, direct product factor, Sylow
424C22×C41—22no—
425C22×C41—41no—
426C22×C41—42no—
427C22×C41—42no—
428C22×C41—41no—
429C22×C41—42no—
430C22×C41—41no—
431C22×C41—41no—
432C22×C41—82no—
433C22×C41—81no—
434C22×C41—81no—
435C22×C41—82no—
436C22×C41—161no—
437C22×C41—164no—
438C22×C41#53511yescharacteristic
439C22×C41D4211yescharacteristic
440C22×C41#54611yescharacteristic
441C4×C41—22no—
442C4×C41—41no—
443C4×C41—42no—
444C4×C41—41no—
445C4×C41—41no—
446C4×C41—81no—
447C4×C41—81no—
448C4×C41—81no—
449C4×C41C2×#12011yescharacteristic
450C4×C41C2×#12111yescharacteristic
451C4×C41D4211yescharacteristic
452C4×C41#54611yescharacteristic
453C2×#577C2×C4111yescharacteristic, complemented
454#3067C2×C4111yescharacteristic, complemented
455#3057C2×C4111yescharacteristic, complemented
456#3020C2×C4111yescharacteristic, complemented
457#3019C2×C4111yescharacteristic, complemented
458#2955C2×C4111yescharacteristic, complemented
459#2049C2×C4111yescharacteristic, complemented
460#2048C2×C4111yescharacteristic, complemented
461#2009C2×C4111yescharacteristic, complemented
462#2008C2×C4111yescharacteristic, complemented
463#1977C2×C4111yescharacteristic, complemented
464#1976C2×C4111yescharacteristic, complemented
465#1814C2×C4111yescharacteristic, complemented
466#1796C2×C4111yescharacteristic, complemented
467#1795C2×C4111yescharacteristic, complemented
468C2×C41—21no—
469C2×C41—21no—
470C2×C41—21no—
471C2×C41—42no—
472C2×C41—81no—
473C2×C41—81no—
474C2×C41—82no—
475C2×C41—81no—
476C2×C41#240811yescharacteristic
477C2×2−1+4C22×C4111yescharacteristic
478C2×H(5,𝔽2)C22×C4111yescharacteristic
479#577—22no—
480#577—22no—
481#577—22no—
482#577—22no—
483#575C22×C4111yescharacteristic
484#575C22×C4111yescharacteristic
485#575C22×C4111yescharacteristic, complemented
486C2×#137—21no—
487C2×#137C22×C4111yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
490C2×#135—21no—
491C2×#135C22×C4111yescharacteristic
492C22×SD16—21no—
493C22×SD16C22×C4111yescharacteristic
494C2×#131C22×C4111yescharacteristic
495C2×#131C22×C4111yescharacteristic, complemented
496#536C22×C4111yescharacteristic, complemented
497#535C22×C4111yescharacteristic
498#473—21no—
499#472—21no—
500#471—21no—
501#471—21no—
502#468—22no—
503#465—22no—
504#456—22no—
505#455—22no—
506#454—22no—
507#453—22no—
508#444—22no—
509#443—22no—
510#430C22×C4111yescharacteristic, complemented
511C2×#108C22×C4111yescharacteristic, complemented
512#427C22×C4111yescharacteristic, complemented
513#421C22×C4111yescharacteristic
514#421C22×C4111yescharacteristic
515#421C22×C4111yescharacteristic
516#421C22×C4111yescharacteristic
517#421C22×C4111yescharacteristic, complemented
518#421C22×C4111yescharacteristic, complemented
519#419C22×C4111yescharacteristic, complemented
520#419C22×C4111yescharacteristic, complemented
521#418C22×C4111yescharacteristic
522#418C22×C4111yescharacteristic
523#413C22×C4111yescharacteristic
524#413C22×C4111yescharacteristic, complemented
525C2×#101C22×C4111yescharacteristic, complemented
526C2×#100C22×C4111yescharacteristic
527#410C22×C4111yescharacteristic
528#410C22×C4111yescharacteristic, complemented
529#405C22×C4111yescharacteristic, complemented
530#344C22×C4111yescharacteristic, complemented
531#344C22×C4111yescharacteristic, complemented
532C41#2429511yescharacteristic, direct product factor, Sylow
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C4111yescharacteristic
547C2×#41C23×C4111yescharacteristic
548C2×#41C23×C4111yescharacteristic
549C2×#41C23×C4111yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C4111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C4111yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C4112yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C4112yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C4111yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C4112yes—
597C2×SD16D4×C4112yes—
598C2×SD16D4×C4111yescharacteristic, complemented
599C2×SD16D4×C4111yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C4111yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C4112yescomplemented
609#131D4×C4112yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C4111yescharacteristic
613C2×M16C23×C4111yescharacteristic
614C2×M16C23×C4111yescharacteristic
615C2×M16C23×C4111yescharacteristic
616C2×M16C23×C4111yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C4111yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C4111yescharacteristic
629#117C23×C4111yescharacteristic
630#117C23×C4111yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C4112yes—
683#41C2×D4×C4112yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C4111yescharacteristic
695C2×Q8C2×D4×C4111yescharacteristic
696C2×Q8C2×D4×C4112yes—
697C2×Q8C2×D4×C4111yescharacteristic
698C2×Q8#41×C4111yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C4111yescharacteristic
719C2×D4C2×D4×C4111yescharacteristic
720C2×D4C2×D4×C4112yes—
721C2×D4C2×D4×C4111yescharacteristic
722C2×D4#41×C4111yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C4111yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C4112yes—
773M16C2×D4×C4112yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C4111yescharacteristic
784C2×C8C2×D4×C4111yescharacteristic
785C2×C8C2×D4×C4111yescharacteristic
786C2×C8C2×D4×C4111yescharacteristic
787C2×C8C2×D4×C4111yescharacteristic
788C2×C8C2×D4×C4111yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C4111yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C4112yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C4112yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C4111yescharacteristic
871C2×C4C22×D4×C4111yescharacteristic
872C2×C4C22×D4×C4111yescharacteristic
873C2×C4C22×D4×C4111yescharacteristic
874C2×C4C2×#41×C4111yescharacteristic
875C2×C4H(5,𝔽2)×C4111yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C4111yescharacteristic
882C8#120×C4111yescharacteristic
883C8#120×C4111yescharacteristic
884C8#120×C4111yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22C41×#53511yescharacteristic
900C22D42×C4111yescharacteristic
901C22C41×#54611yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C4111yescharacteristic
911C4C2×#121×C4111yescharacteristic
912C4D42×C4111yescharacteristic
913C4C41×#54611yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C41×#240811yescharacteristic
subgroupG/H
center, socleC2×C41#2408
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. C2×C41×#577C2semidirect
2. C41×#3067C2semidirect
3. C41×#3057C2semidirect
4. C41×#3020C2semidirect
5. C41×#3019C2semidirect
6. C41×#2955C2semidirect
7. C41×#2049C2semidirect
8. C41×#2048C2semidirect
9. C41×#2009C2semidirect
10. C41×#2008C2semidirect
11. C41×#1977C2semidirect
12. C41×#1976C2semidirect
13. C41×#1814C2semidirect
14. C41×#1796C2semidirect
15. C41×#1795C2semidirect
24. C41×#575C22semidirect
34. C2×#131×C41C22semidirect
35. C41×#536C22semidirect
49. C41×#430C22semidirect
50. C2×#108×C41C22semidirect
51. C41×#427C22semidirect
56. C41×#421C22semidirect
57. C41×#421C22semidirect
58. C41×#419C22semidirect
59. C41×#419C22semidirect
63. C41×#413C22semidirect
64. C2×#101×C41C22semidirect
67. C41×#410C22semidirect
68. C41×#405C22semidirect
69. C41×#344C22semidirect
70. C41×#344C22semidirect
125. C2×Q16×C41D4semidirect
136. C2×SD16×C41D4semidirect
137. C2×SD16×C41D4semidirect
139. C2×D8×C41D4semidirect
146. #131×C41D4semidirect
147. #131×C41D4semidirect
423. #24295C41direct (N × H)
453. C2×#577C2×C41semidirect
454. #3067C2×C41semidirect
455. #3057C2×C41semidirect
456. #3020C2×C41semidirect
457. #3019C2×C41semidirect
458. #2955C2×C41semidirect
459. #2049C2×C41semidirect
460. #2048C2×C41semidirect
461. #2009C2×C41semidirect
462. #2008C2×C41semidirect
463. #1977C2×C41semidirect
464. #1976C2×C41semidirect
465. #1814C2×C41semidirect
466. #1796C2×C41semidirect
467. #1795C2×C41semidirect
485. #575C22×C41semidirect
495. C2×#131C22×C41semidirect
496. #536C22×C41semidirect
510. #430C22×C41semidirect
511. C2×#108C22×C41semidirect
512. #427C22×C41semidirect
517. #421C22×C41semidirect
518. #421C22×C41semidirect
519. #419C22×C41semidirect
520. #419C22×C41semidirect
524. #413C22×C41semidirect
525. C2×#101C22×C41semidirect
528. #410C22×C41semidirect
529. #405C22×C41semidirect
530. #344C22×C41semidirect
531. #344C22×C41semidirect
532. C41#24295direct (N × H)
587. C2×Q16D4×C41semidirect
598. C2×SD16D4×C41semidirect
599. C2×SD16D4×C41semidirect
601. C2×D8D4×C41semidirect
608. #131D4×C41semidirect
609. #131D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5772
C41×#30672
C41×#30572
C41×#30202
C41×#30192
C41×#29552
C41×#20492
C41×#20482
C41×#20092
C41×#20082
C41×#19772
C41×#19762
C41×#18142
C41×#17962
C41×#17952
#2429541