Finite Group Databasebeta

← C41×#24468 #23800669

Subgroups — C41×#24468 #23800669

Order 10496.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3488C211yesmaximal, characteristic, complemented
2C41×#3055C211yesmaximal, characteristic, complemented
3C2×C41×#453C211yesmaximal, characteristic, complemented
4C41×#3006C211yesmaximal, characteristic, complemented
5C2×C41×#421C211yesmaximal, characteristic, complemented
6C41×#2619C211yesmaximal, characteristic, complemented
7C41×#2040C211yesmaximal, characteristic, complemented
8C41×#2037C211yesmaximal, characteristic, complemented
9C41×#2006C211yesmaximal, characteristic, complemented
10C41×#2002C211yesmaximal, characteristic, complemented
11C41×#1900C211yesmaximal, characteristic, complemented
12C41×#1897C211yesmaximal, characteristic, complemented
13C41×#1883C211yesmaximal, characteristic, complemented
14C41×#1860C211yesmaximal, characteristic, complemented
15C41×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C41C2211yescharacteristic, complemented
21C22×M16×C41C2211yescharacteristic, complemented
22C41×#550—21no—
23C41×#548—21no—
24C41×#546—21no—
25C41×#546—22no—
26D42×C41—22no—
27D42×C41—21no—
28C41×#537—21no—
29C41×#537C2211yescharacteristic
30C41×#535—21no—
31C41×#535C2211yescharacteristic
32C2×#127×C41C2211yescharacteristic, complemented
33C41×#525—21no—
34C41×#525C2211yescharacteristic
35C2×#121×C41—21no—
36C2×#121×C41C2211yescharacteristic
37C2×#121×C41C2211yescharacteristic, complemented
38C41×#520C2211yescharacteristic
39C2×#117×C41C2211yescharacteristic, complemented
40C41×#469—21no—
41C41×#468—21no—
42C41×#466—21no—
43C41×#465—21no—
44C41×#453—24no—
45C41×#449—21no—
46C41×#449—21no—
47C41×#448—21no—
48C41×#447—21no—
49C41×#428C2211yescharacteristic, complemented
50C41×#421—24no—
51C2×#104×C41C2211yescharacteristic
52C2×#104×C41C2211yescharacteristic
53C2×#104×C41C2211yescharacteristic, complemented
54C2×#104×C41C2211yescharacteristic, complemented
55C2×#104×C41C2211yescharacteristic, complemented
56C2×#104×C41C2211yescharacteristic, complemented
57C41×#418C2211yescharacteristic, complemented
58C41×#417C2211yescharacteristic
59C41×#417C2211yescharacteristic, complemented
60C41×#417C2211yescharacteristic, complemented
61C2×#100×C41C2211yescharacteristic, complemented
62C2×#100×C41C2211yescharacteristic, complemented
63C41×#407C2211yescharacteristic, complemented
64C41×#394—22no—
65C41×#392—22no—
66C41×#390C2211yescharacteristic, complemented
67C41×#390C2211yescharacteristic, complemented
68C41×#382C2211yescharacteristic, complemented
69C41×#343C2211yescharacteristic, complemented
70C41×#343C2211yescharacteristic, complemented
71C41×#339C2211yescharacteristic, complemented
72C41×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C41—22no—
74H(5,𝔽2)×C41—22no—
75H(5,𝔽2)×C41—41no—
76H(5,𝔽2)×C41—41no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—22no—
82C2×#41×C41—22no—
83C2×#41×C41—41no—
84C2×#41×C41—41no—
85C2×#41×C41D411yescharacteristic, complemented
86C2×#41×C41D411yescharacteristic, complemented
87C2×#41×C41C2311yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C2×#41×C41C2311yescharacteristic
90C22×Q8×C41D411yescharacteristic, complemented
91C22×D4×C41—21no—
92C22×D4×C41—22no—
93C22×D4×C41—22no—
94C22×D4×C41—21no—
95C22×D4×C41—21no—
96C22×D4×C41—21no—
97C22×D4×C41—22no—
98C22×D4×C41D412yes—
99C22×D4×C41D411yescharacteristic, complemented
100C22×D4×C41C2311yescharacteristic
101C22×D4×C41C2311yescharacteristic
102C23×C4×C41—21no—
103C23×C4×C41C2311yescharacteristic
104AGL(1,ℤ/8)×C41—22no—
105AGL(1,ℤ/8)×C41—22no—
106AGL(1,ℤ/8)×C41—22no—
107AGL(1,ℤ/8)×C41—41no—
108AGL(1,ℤ/8)×C41—41no—
109AGL(1,ℤ/8)×C41—41no—
110C2×SD16×C41—21no—
111C2×SD16×C41—21no—
112C2×SD16×C41—21no—
113C2×D8×C41—21no—
114C2×D8×C41—21no—
115C2×D8×C41—21no—
116C2×M16×C41—21no—
117C2×M16×C41—22no—
118C2×M16×C41—41no—
119C2×M16×C41C2311yescharacteristic
120C2×M16×C41C2311yescharacteristic
121C2×M16×C41C2311yescharacteristic
122C2×M16×C41C2311yescharacteristic
123C22×C8×C41—21no—
124#127×C41—22no—
125#127×C41—21no—
126#127×C41—22no—
127#127×C41—41no—
128#124×C41—22no—
129#124×C41—21no—
130#123×C41—22no—
131#123×C41—21no—
132C22⋊Q8×C41—22no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41D411yescharacteristic, complemented
136C22⋊Q8×C41D411yescharacteristic, complemented
137#121×C41—22no—
138#121×C41—22no—
139#121×C41—22no—
140#121×C41—22no—
141#121×C41—22no—
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—22no—
149#121×C41—21no—
150#121×C41—21no—
151#121×C41—21no—
152#121×C41—21no—
153#121×C41—21no—
154#121×C41—21no—
155#121×C41D411yescharacteristic, complemented
156#121×C41D411yescharacteristic, complemented
157#120×C41—22no—
158#120×C41—22no—
159#120×C41—22no—
160#120×C41—21no—
161#120×C41—22no—
162C4×Q8×C41—21no—
163C4×D4×C41—22no—
164C4×D4×C41—22no—
165C4×D4×C41—21no—
166C4×D4×C41—22no—
167C4×D4×C41—21no—
168C4×D4×C41—21no—
169#117×C41—21no—
170#117×C41—22no—
171#117×C41—41no—
172#117×C41C2311yescharacteristic
173C2×C4⋊C4×C41—21no—
174C2×C4⋊C4×C41—21no—
175C2×C4⋊C4×C41C2311yescharacteristic
176C2×C4⋊C4×C41C2311yescharacteristic
177C2×C22⋊C4×C41—22no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×C41—21no—
180C2×C22⋊C4×C41—22no—
181C2×C22⋊C4×C41—22no—
182C2×C22⋊C4×C41D412yes—
183C2×C42×C41C2311yescharacteristic
184C2×C42×C41C2311yescharacteristic
185#107×C41—21no—
186#106×C41—21no—
187#104×C41—22no—
188#104×C41—22no—
189#104×C41—22no—
190#104×C41—22no—
191#104×C41—41no—
192#104×C41D414yescomplemented
193#103×C41—21no—
194#103×C41—21no—
195#103×C41—21no—
196#102×C41—21no—
197#102×C41—21no—
198#102×C41—21no—
199#102×C41—21no—
200#102×C41—21no—
201#100×C41—22no—
202#100×C41—41no—
203C22⋊C8×C41—21no—
204C22⋊C8×C41—21no—
205#95×C41—22no—
206C24×C41—22no—
207C24×C41—21no—
208C24×C41—21no—
209C24×C41C2×D412yes—
210C24×C41C2×D411yescharacteristic
211#41×C41—21no—
212#41×C41—21no—
213#41×C41—22no—
214#41×C41—22no—
215#41×C41—21no—
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—42no—
224#41×C41—42no—
225#41×C41—41no—
226#41×C41—41no—
227#41×C41—42no—
228#41×C41—42no—
229#41×C41—42no—
230#41×C41—42no—
231#41×C41—42no—
232#41×C41—42no—
233#41×C41C2×D412yes—
234#41×C41#4112yes—
235C2×Q8×C41—21no—
236C2×Q8×C41—22no—
237C2×Q8×C41—41no—
238C2×Q8×C41C2×D411yescharacteristic
239C2×Q8×C41C2×D411yescharacteristic
240C2×Q8×C41C2×D411yescharacteristic
241C2×D4×C41—21no—
242C2×D4×C41—22no—
243C2×D4×C41—22no—
244C2×D4×C41—22no—
245C2×D4×C41—22no—
246C2×D4×C41—21no—
247C2×D4×C41—21no—
248C2×D4×C41—21no—
249C2×D4×C41—21no—
250C2×D4×C41—21no—
251C2×D4×C41—22no—
252C2×D4×C41—22no—
253C2×D4×C41—22no—
254C2×D4×C41—21no—
255C2×D4×C41—22no—
256C2×D4×C41—21no—
257C2×D4×C41—21no—
258C2×D4×C41—21no—
259C2×D4×C41—21no—
260C2×D4×C41—21no—
261C2×D4×C41—21no—
262C2×D4×C41—21no—
263C2×D4×C41—21no—
264C2×D4×C41—21no—
265C2×D4×C41—21no—
266C2×D4×C41—21no—
267C2×D4×C41—21no—
268C2×D4×C41—21no—
269C2×D4×C41—41no—
270C2×D4×C41—42no—
271C2×D4×C41—42no—
272C2×D4×C41—44no—
273C2×D4×C41—42no—
274C2×D4×C41—42no—
275C2×D4×C41—44no—
276C2×D4×C41—44no—
277C2×D4×C41—42no—
278C2×D4×C41—42no—
279C2×D4×C41—41no—
280C2×D4×C41—41no—
281C2×D4×C41—82no—
282C2×D4×C41—82no—
283C2×D4×C41—82no—
284C2×D4×C41—82no—
285C2×D4×C41—84no—
286C2×D4×C41C2×D411yescharacteristic
287C2×D4×C41C2×D411yescharacteristic
288C2×D4×C41C2×D411yescharacteristic
289C22×C4×C41—21no—
290C22×C4×C41—21no—
291C22×C4×C41—21no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—22no—
295C22×C4×C41—21no—
296C22×C4×C41—21no—
297C22×C4×C41—22no—
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—42no—
305C22×C4×C41—42no—
306C22×C4×C41C2×D411yescharacteristic
307C22×C4×C41C2×D411yescharacteristic
308C22×C4×C41C2×D411yescharacteristic
309C22×C4×C41C2×D411yescharacteristic
310C22×C4×C41C2×D411yescharacteristic
311C22×C4×C41C2×D412yes—
312C22×C4×C41C2411yescharacteristic
313SD16×C41—42no—
314SD16×C41—42no—
315SD16×C41—42no—
316D8×C41—42no—
317D8×C41—42no—
318D8×C41—42no—
319M16×C41—21no—
320M16×C41—21no—
321M16×C41—21no—
322M16×C41—21no—
323M16×C41—21no—
324M16×C41—21no—
325M16×C41—21no—
326M16×C41—42no—
327M16×C41C2×D412yescomplemented
328C2×C8×C41—21no—
329C2×C8×C41—21no—
330C2×C8×C41—21no—
331C2×C8×C41—21no—
332C2×C8×C41—42no—
333C4⋊C4×C41—22no—
334C4⋊C4×C41—22no—
335C4⋊C4×C41—21no—
336C4⋊C4×C41—21no—
337C4⋊C4×C41—21no—
338C4⋊C4×C41—21no—
339C4⋊C4×C41—21no—
340C4⋊C4×C41—21no—
341C4⋊C4×C41—42no—
342C4⋊C4×C41C2×D411yescharacteristic
343C4⋊C4×C41C2×D411yescharacteristic
344C22⋊C4×C41—22no—
345C22⋊C4×C41—22no—
346C22⋊C4×C41—22no—
347C22⋊C4×C41—22no—
348C22⋊C4×C41—22no—
349C22⋊C4×C41—21no—
350C22⋊C4×C41—21no—
351C22⋊C4×C41—21no—
352C22⋊C4×C41—21no—
353C22⋊C4×C41—22no—
354C22⋊C4×C41—22no—
355C22⋊C4×C41—21no—
356C22⋊C4×C41—42no—
357C22⋊C4×C41—41no—
358C22⋊C4×C41—41no—
359C22⋊C4×C41—82no—
360C22⋊C4×C41—82no—
361C42×C41—22no—
362C42×C41—21no—
363C42×C41—21no—
364C42×C41—21no—
365C42×C41—21no—
366C42×C41C2×D412yescomplemented
367C23×C41—21no—
368C23×C41—21no—
369C23×C41—21no—
370C23×C41—22no—
371C23×C41—21no—
372C23×C41—21no—
373C23×C41—22no—
374C23×C41—22no—
375C23×C41—41no—
376C23×C41—41no—
377C23×C41—42no—
378C23×C41—42no—
379C23×C41—44no—
380C23×C41—42no—
381C23×C41—42no—
382C23×C41—42no—
383C23×C41—42no—
384C23×C41—41no—
385C23×C41—41no—
386C23×C41—41no—
387C23×C41—81no—
388C23×C41—82no—
389C23×C41—82no—
390C23×C41#12011yescharacteristic
391C23×C41#12011yescharacteristic
392C23×C41C22×D411yescharacteristic
393Q8×C41—21no—
394Q8×C41—21no—
395Q8×C41—21no—
396Q8×C41—21no—
397Q8×C41—21no—
398Q8×C41—42no—
399Q8×C41#12112yes—
400D4×C41—22no—
401D4×C41—22no—
402D4×C41—21no—
403D4×C41—21no—
404D4×C41—21no—
405D4×C41—21no—
406D4×C41—21no—
407D4×C41—42no—
408D4×C41—42no—
409D4×C41—44no—
410D4×C41—42no—
411D4×C41—44no—
412D4×C41—44no—
413D4×C41—42no—
414D4×C41—41no—
415D4×C41—41no—
416D4×C41—41no—
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—41no—
426D4×C41—81no—
427D4×C41—82no—
428D4×C41—82no—
429D4×C41—82no—
430D4×C41—82no—
431D4×C41—88no—
432D4×C41—82no—
433D4×C41—82no—
434D4×C41#12112yes—
435C2×C4×C41—21no—
436C2×C4×C41—21no—
437C2×C4×C41—21no—
438C2×C4×C41—21no—
439C2×C4×C41—21no—
440C2×C4×C41—21no—
441C2×C4×C41—21no—
442C2×C4×C41—21no—
443C2×C4×C41—21no—
444C2×C4×C41—22no—
445C2×C4×C41—21no—
446C2×C4×C41—21no—
447C2×C4×C41—22no—
448C2×C4×C41—21no—
449C2×C4×C41—22no—
450C2×C4×C41—21no—
451C2×C4×C41—21no—
452C2×C4×C41—21no—
453C2×C4×C41—22no—
454C2×C4×C41—42no—
455C2×C4×C41—42no—
456C2×C4×C41—42no—
457C2×C4×C41—44no—
458C2×C4×C41—41no—
459C2×C4×C41—41no—
460C2×C4×C41—41no—
461C2×C4×C41—41no—
462C2×C4×C41—41no—
463C2×C4×C41—41no—
464C2×C4×C41—42no—
465C2×C4×C41—41no—
466C2×C4×C41—41no—
467C2×C4×C41—42no—
468C2×C4×C41—41no—
469C2×C4×C41—41no—
470C2×C4×C41—82no—
471C2×C4×C41#12011yescharacteristic
472C2×C4×C41#12011yescharacteristic
473C2×C4×C41C22×D411yescharacteristic
474C2×C4×C41C22×D411yescharacteristic
475C2×C4×C41C22×D411yescharacteristic
476C2×C4×C41C2×#4111yescharacteristic
477C2×C4×C41H(5,𝔽2)11yescharacteristic
478C2×C4×C41H(5,𝔽2)11yescharacteristic
479C8×C41—22no—
480C8×C41—41no—
481C8×C41—41no—
482C8×C41—41no—
483#24468C4111yesmaximal, characteristic, direct product factor, Sylow
484C22×C41—21no—
485C22×C41—21no—
486C22×C41—21no—
487C22×C41—21no—
488C22×C41—22no—
489C22×C41—21no—
490C22×C41—21no—
491C22×C41—21no—
492C22×C41—21no—
493C22×C41—41no—
494C22×C41—41no—
495C22×C41—41no—
496C22×C41—41no—
497C22×C41—42no—
498C22×C41—42no—
499C22×C41—41no—
500C22×C41—41no—
501C22×C41—41no—
502C22×C41—42no—
503C22×C41—41no—
504C22×C41—81no—
505C22×C41—81no—
506C22×C41—82no—
507C22×C41—82no—
508C22×C41—82no—
509C22×C41—82no—
510C22×C41—84no—
511C22×C41—81no—
512C22×C41—81no—
513C22×C41—81no—
514C22×C41—164no—
515C22×C41C2×#12011yescharacteristic
516C22×C41D4211yescharacteristic
517C22×C41#54611yescharacteristic
518C4×C41—21no—
519C4×C41—21no—
520C4×C41—22no—
521C4×C41—42no—
522C4×C41—41no—
523C4×C41—41no—
524C4×C41—42no—
525C4×C41—41no—
526C4×C41—41no—
527C4×C41—81no—
528C4×C41—81no—
529C4×C41C2×#12111yescharacteristic
530C4×C41#53411yescharacteristic
531C4×C41D4211yescharacteristic
532C4×C41#54611yescharacteristic
533#3488C2×C4111yescharacteristic, complemented
534#3055C2×C4111yescharacteristic, complemented
535C2×#453C2×C4111yescharacteristic, complemented
536#3006C2×C4111yescharacteristic, complemented
537C2×#421C2×C4111yescharacteristic, complemented
538#2619C2×C4111yescharacteristic, complemented
539#2040C2×C4111yescharacteristic, complemented
540#2037C2×C4111yescharacteristic, complemented
541#2006C2×C4111yescharacteristic, complemented
542#2002C2×C4111yescharacteristic, complemented
543#1900C2×C4111yescharacteristic, complemented
544#1897C2×C4111yescharacteristic, complemented
545#1883C2×C4111yescharacteristic, complemented
546#1860C2×C4111yescharacteristic, complemented
547#1792C2×C4111yescharacteristic, complemented
548C2×C41—21no—
549C2×C41—21no—
550C2×C41—41no—
551C2×C41—41no—
552C2×C41—42no—
553C2×C41—81no—
554C2×C41—82no—
555C2×C41—81no—
556C2×C41—161no—
557C2×C41#241011yescharacteristic
558C2×C41#301911yescharacteristic
559C2×C41#302111yescharacteristic
560C2×H(5,𝔽2)C22×C4111yescharacteristic
561C22×#41C22×C4111yescharacteristic
562C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
563C2×AGL(1,ℤ/8)C22×C4111yescharacteristic, complemented
564C2×AGL(1,ℤ/8)C22×C4111yescharacteristic, complemented
565C22×M16C22×C4111yescharacteristic, complemented
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C22×C4111yescharacteristic
574#535—21no—
575#535C22×C4111yescharacteristic
576C2×#127C22×C4111yescharacteristic, complemented
577#525—21no—
578#525C22×C4111yescharacteristic
579C2×#121—21no—
580C2×#121C22×C4111yescharacteristic
581C2×#121C22×C4111yescharacteristic, complemented
582#520C22×C4111yescharacteristic
583C2×#117C22×C4111yescharacteristic, complemented
584#469—21no—
585#468—21no—
586#466—21no—
587#465—21no—
588#453—24no—
589#449—21no—
590#449—21no—
591#448—21no—
592#447—21no—
593#428C22×C4111yescharacteristic, complemented
594#421—24no—
595C2×#104C22×C4111yescharacteristic
596C2×#104C22×C4111yescharacteristic
597C2×#104C22×C4111yescharacteristic, complemented
598C2×#104C22×C4111yescharacteristic, complemented
599C2×#104C22×C4111yescharacteristic, complemented
600C2×#104C22×C4111yescharacteristic, complemented
601#418C22×C4111yescharacteristic, complemented
602#417C22×C4111yescharacteristic
603#417C22×C4111yescharacteristic, complemented
604#417C22×C4111yescharacteristic, complemented
605C2×#100C22×C4111yescharacteristic, complemented
606C2×#100C22×C4111yescharacteristic, complemented
607#407C22×C4111yescharacteristic, complemented
608#394—22no—
609#392—22no—
610#390C22×C4111yescharacteristic, complemented
611#390C22×C4111yescharacteristic, complemented
612#382C22×C4111yescharacteristic, complemented
613#343C22×C4111yescharacteristic, complemented
614#343C22×C4111yescharacteristic, complemented
615#339C22×C4111yescharacteristic, complemented
616#339C22×C4111yescharacteristic, complemented
617C41#2446811yescharacteristic, direct product factor, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C4111yescharacteristic, complemented
631C2×#41D4×C4111yescharacteristic, complemented
632C2×#41C23×C4111yescharacteristic
633C2×#41C23×C4111yescharacteristic
634C2×#41C23×C4111yescharacteristic
635C22×Q8D4×C4111yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C4112yes—
644C22×D4D4×C4111yescharacteristic, complemented
645C22×D4C23×C4111yescharacteristic
646C22×D4C23×C4111yescharacteristic
647C23×C4—21no—
648C23×C4C23×C4111yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C4111yescharacteristic
665C2×M16C23×C4111yescharacteristic
666C2×M16C23×C4111yescharacteristic
667C2×M16C23×C4111yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C4111yescharacteristic, complemented
681C22⋊Q8D4×C4111yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C4111yescharacteristic, complemented
701#121D4×C4111yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C4111yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C4111yescharacteristic
721C2×C4⋊C4C23×C4111yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C4112yes—
728C2×C42C23×C4111yescharacteristic
729C2×C42C23×C4111yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C4114yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C4112yes—
755C24C2×D4×C4111yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C4112yes—
779#41#41×C4112yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C4111yescharacteristic
784C2×Q8C2×D4×C4111yescharacteristic
785C2×Q8C2×D4×C4111yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C4111yescharacteristic
832C2×D4C2×D4×C4111yescharacteristic
833C2×D4C2×D4×C4111yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C4111yescharacteristic
852C22×C4C2×D4×C4111yescharacteristic
853C22×C4C2×D4×C4111yescharacteristic
854C22×C4C2×D4×C4111yescharacteristic
855C22×C4C2×D4×C4111yescharacteristic
856C22×C4C2×D4×C4112yes—
857C22×C4C24×C4111yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C4112yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C4111yescharacteristic
888C4⋊C4C2×D4×C4111yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C4112yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C4111yescharacteristic
936C23#120×C4111yescharacteristic
937C23C22×D4×C4111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C4112yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C4112yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C4111yescharacteristic
1017C2×C4#120×C4111yescharacteristic
1018C2×C4C22×D4×C4111yescharacteristic
1019C2×C4C22×D4×C4111yescharacteristic
1020C2×C4C22×D4×C4111yescharacteristic
1021C2×C4C2×#41×C4111yescharacteristic
1022C2×C4H(5,𝔽2)×C4111yescharacteristic
1023C2×C4H(5,𝔽2)×C4111yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C4111yescharacteristic
1060C22D42×C4111yescharacteristic
1061C22C41×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C4111yescharacteristic
1074C4C41×#53411yescharacteristic
1075C4D42×C4111yescharacteristic
1076C4C41×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C41×#241011yescharacteristic
1087C2C41×#301911yescharacteristic
1088C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3488C2semidirect
2. C41×#3055C2semidirect
3. C2×C41×#453C2semidirect
4. C41×#3006C2semidirect
5. C2×C41×#421C2semidirect
6. C41×#2619C2semidirect
7. C41×#2040C2semidirect
8. C41×#2037C2semidirect
9. C41×#2006C2semidirect
10. C41×#2002C2semidirect
11. C41×#1900C2semidirect
12. C41×#1897C2semidirect
13. C41×#1883C2semidirect
14. C41×#1860C2semidirect
15. C41×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C41C22semidirect
20. C2×AGL(1,ℤ/8)×C41C22semidirect
21. C22×M16×C41C22semidirect
32. C2×#127×C41C22semidirect
37. C2×#121×C41C22semidirect
39. C2×#117×C41C22semidirect
49. C41×#428C22semidirect
53. C2×#104×C41C22semidirect
54. C2×#104×C41C22semidirect
55. C2×#104×C41C22semidirect
56. C2×#104×C41C22semidirect
57. C41×#418C22semidirect
59. C41×#417C22semidirect
60. C41×#417C22semidirect
61. C2×#100×C41C22semidirect
62. C2×#100×C41C22semidirect
63. C41×#407C22semidirect
66. C41×#390C22semidirect
67. C41×#390C22semidirect
68. C41×#382C22semidirect
69. C41×#343C22semidirect
70. C41×#343C22semidirect
71. C41×#339C22semidirect
72. C41×#339C22semidirect
85. C2×#41×C41D4semidirect
86. C2×#41×C41D4semidirect
90. C22×Q8×C41D4semidirect
99. C22×D4×C41D4semidirect
135. C22⋊Q8×C41D4semidirect
136. C22⋊Q8×C41D4semidirect
155. #121×C41D4semidirect
156. #121×C41D4semidirect
192. #104×C41D4semidirect
327. M16×C41C2×D4semidirect
366. C42×C41C2×D4semidirect
483. #24468C41direct (N × H)
533. #3488C2×C41semidirect
534. #3055C2×C41semidirect
535. C2×#453C2×C41semidirect
536. #3006C2×C41semidirect
537. C2×#421C2×C41semidirect
538. #2619C2×C41semidirect
539. #2040C2×C41semidirect
540. #2037C2×C41semidirect
541. #2006C2×C41semidirect
542. #2002C2×C41semidirect
543. #1900C2×C41semidirect
544. #1897C2×C41semidirect
545. #1883C2×C41semidirect
546. #1860C2×C41semidirect
547. #1792C2×C41semidirect
563. C2×AGL(1,ℤ/8)C22×C41semidirect
564. C2×AGL(1,ℤ/8)C22×C41semidirect
565. C22×M16C22×C41semidirect
576. C2×#127C22×C41semidirect
581. C2×#121C22×C41semidirect
583. C2×#117C22×C41semidirect
593. #428C22×C41semidirect
597. C2×#104C22×C41semidirect
598. C2×#104C22×C41semidirect
599. C2×#104C22×C41semidirect
600. C2×#104C22×C41semidirect
601. #418C22×C41semidirect
603. #417C22×C41semidirect
604. #417C22×C41semidirect
605. C2×#100C22×C41semidirect
606. C2×#100C22×C41semidirect
607. #407C22×C41semidirect
610. #390C22×C41semidirect
611. #390C22×C41semidirect
612. #382C22×C41semidirect
613. #343C22×C41semidirect
614. #343C22×C41semidirect
615. #339C22×C41semidirect
616. #339C22×C41semidirect
617. C41#24468direct (N × H)
630. C2×#41D4×C41semidirect
631. C2×#41D4×C41semidirect
635. C22×Q8D4×C41semidirect
644. C22×D4D4×C41semidirect
680. C22⋊Q8D4×C41semidirect
681. C22⋊Q8D4×C41semidirect
700. #121D4×C41semidirect
701. #121D4×C41semidirect
737. #104D4×C41semidirect
872. M16C2×D4×C41semidirect
911. C42C2×D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34882
C41×#30552
C2×C41×#4532
C41×#30062
C2×C41×#4212
C41×#26192
C41×#20402
C41×#20372
C41×#20062
C41×#20022
C41×#19002
C41×#18972
C41×#18832
C41×#18602
C41×#17922
#2446841