Finite Group Databasebeta

← C41×#24467 #23800668

Subgroups — C41×#24467 #23800668

Order 10496.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3488C211yesmaximal, characteristic
2C41×#3056C211yesmaximal, characteristic, complemented
3C2×C41×#455C211yesmaximal, characteristic, complemented
4C41×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C41C211yesmaximal, characteristic, complemented
6C41×#2850C211yesmaximal, characteristic, complemented
7C41×#2040C211yesmaximal, characteristic, complemented
8C41×#2037C211yesmaximal, characteristic, complemented
9C41×#2007C211yesmaximal, characteristic, complemented
10C41×#2004C211yesmaximal, characteristic, complemented
11C41×#1900C211yesmaximal, characteristic, complemented
12C41×#1896C211yesmaximal, characteristic, complemented
13C41×#1882C211yesmaximal, characteristic, complemented
14C41×#1860C211yesmaximal, characteristic, complemented
15C41×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C2×#137×C41C2211yescharacteristic
19C2×#137×C41C2211yescharacteristic, complemented
20C2×#137×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×#124×C41C2211yescharacteristic, complemented
33C41×#525—21no—
34C41×#525C2211yescharacteristic
35C2×C22⋊Q8×C41C2211yescharacteristic, complemented
36C2×#121×C41—21no—
37C2×#121×C41C2211yescharacteristic
38C41×#520C2211yescharacteristic
39C22×C42×C41C2211yescharacteristic, complemented
40C41×#470—21no—
41C41×#468—21no—
42C41×#467—21no—
43C41×#465—21no—
44C41×#455—24no—
45C41×#452—21no—
46C41×#452—21no—
47C41×#451—21no—
48C41×#450—21no—
49C41×#428C2211yescharacteristic, complemented
50C2×#104×C41—24no—
51C2×#104×C41C2211yescharacteristic
52C2×#104×C41C2211yescharacteristic
53C2×#104×C41C2211yescharacteristic, complemented
54C2×#104×C41C2211yescharacteristic, complemented
55C2×#104×C41C2211yescharacteristic, complemented
56C2×#104×C41C2211yescharacteristic, complemented
57C41×#419C2211yescharacteristic, complemented
58C41×#417C2211yescharacteristic
59C41×#417C2211yescharacteristic, complemented
60C41×#417C2211yescharacteristic, complemented
61C2×#100×C41C2211yescharacteristic, complemented
62C2×#100×C41C2211yescharacteristic, complemented
63C41×#407C2211yescharacteristic, complemented
64C41×#391C2211yescharacteristic, complemented
65C41×#390C2211yescharacteristic, complemented
66C41×#388—22no—
67C41×#386—22no—
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
86C2×#41×C41D411yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C2×#41×C41C2311yescharacteristic
90C22×Q8×C41D411yescharacteristic
91C22×Q8×C41C2311yescharacteristic
92C22×D4×C41—21no—
93C22×D4×C41—22no—
94C22×D4×C41—22no—
95C22×D4×C41—21no—
96C22×D4×C41—21no—
97C22×D4×C41D411yescharacteristic
98C22×D4×C41D412yes—
99C22×D4×C41C2311yescharacteristic
100C23×C4×C41—21no—
101C23×C4×C41—21no—
102C23×C4×C41C2311yescharacteristic
103#137×C41—22no—
104#137×C41—22no—
105#137×C41—22no—
106#137×C41—41no—
107#137×C41—41no—
108#137×C41—41no—
109C2×Q16×C41—21no—
110C2×Q16×C41—21no—
111C2×Q16×C41—21no—
112C2×SD16×C41—21no—
113C2×SD16×C41—21no—
114C2×SD16×C41—21no—
115C2×M16×C41—21no—
116C2×M16×C41—22no—
117C2×M16×C41—41no—
118C2×M16×C41C2311yescharacteristic
119C2×M16×C41C2311yescharacteristic
120C2×M16×C41C2311yescharacteristic
121C2×M16×C41C2311yescharacteristic
122C22×C8×C41—21no—
123#127×C41—22no—
124#127×C41—21no—
125#124×C41—22no—
126#124×C41—21no—
127#124×C41—22no—
128#124×C41—41no—
129#123×C41—22no—
130#123×C41—21no—
131C22⋊Q8×C41—22no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41—21no—
136C22⋊Q8×C41—21no—
137C22⋊Q8×C41—21no—
138C22⋊Q8×C41D411yescharacteristic
139C22⋊Q8×C41D411yescharacteristic
140#121×C41—22no—
141#121×C41—22no—
142#121×C41—22no—
143#121×C41—22no—
144#121×C41—22no—
145#121×C41—21no—
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—21no—
151#121×C41—22no—
152#121×C41—21no—
153#121×C41—21no—
154#121×C41D411yescharacteristic
155#121×C41D411yescharacteristic
156#120×C41—22no—
157#120×C41—22no—
158#120×C41—22no—
159#120×C41—21no—
160#120×C41—22no—
161C4×Q8×C41—21no—
162C4×D4×C41—22no—
163C4×D4×C41—22no—
164C4×D4×C41—21no—
165C4×D4×C41—22no—
166C4×D4×C41—21no—
167C4×D4×C41—21no—
168#117×C41—21no—
169#117×C41C2311yescharacteristic
170C2×C4⋊C4×C41—21no—
171C2×C4⋊C4×C41—21no—
172C2×C4⋊C4×C41C2311yescharacteristic
173C2×C4⋊C4×C41C2311yescharacteristic
174C2×C22⋊C4×C41—22no—
175C2×C22⋊C4×C41—21no—
176C2×C22⋊C4×C41—22no—
177C2×C22⋊C4×C41—22no—
178C2×C22⋊C4×C41D412yes—
179C2×C42×C41—22no—
180C2×C42×C41—21no—
181C2×C42×C41—41no—
182C2×C42×C41C2311yescharacteristic
183C2×C42×C41C2311yescharacteristic
184#107×C41—21no—
185#106×C41—21no—
186#104×C41—22no—
187#104×C41—22no—
188#104×C41—22no—
189#104×C41—22no—
190#104×C41—41no—
191#104×C41D414yescomplemented
192#103×C41—21no—
193#103×C41—21no—
194#103×C41—21no—
195#103×C41—21no—
196#103×C41—21no—
197#102×C41—21no—
198#102×C41—21no—
199#102×C41—21no—
200#100×C41—22no—
201#100×C41—41no—
202C22⋊C8×C41—21no—
203C22⋊C8×C41—21no—
204#95×C41—22no—
205#95×C41—22no—
206C24×C41—22no—
207C24×C41—21no—
208C24×C41C2×D411yescharacteristic
209C24×C41C2×D412yes—
210#41×C41—21no—
211#41×C41—21no—
212#41×C41—22no—
213#41×C41—22no—
214#41×C41—21no—
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—42no—
223#41×C41—42no—
224#41×C41—41no—
225#41×C41—41no—
226#41×C41—42no—
227#41×C41—42no—
228#41×C41—42no—
229#41×C41—42no—
230#41×C41—42no—
231#41×C41—42no—
232#41×C41C2×D412yes—
233#41×C41#4112yes—
234C2×Q8×C41—21no—
235C2×Q8×C41—22no—
236C2×Q8×C41—21no—
237C2×Q8×C41—21no—
238C2×Q8×C41—21no—
239C2×Q8×C41—21no—
240C2×Q8×C41—21no—
241C2×Q8×C41—21no—
242C2×Q8×C41—41no—
243C2×Q8×C41C2×D411yescharacteristic
244C2×Q8×C41C2×D411yescharacteristic
245C2×Q8×C41C2×D411yescharacteristic
246C2×D4×C41—21no—
247C2×D4×C41—22no—
248C2×D4×C41—22no—
249C2×D4×C41—22no—
250C2×D4×C41—22no—
251C2×D4×C41—21no—
252C2×D4×C41—21no—
253C2×D4×C41—21no—
254C2×D4×C41—21no—
255C2×D4×C41—21no—
256C2×D4×C41—22no—
257C2×D4×C41—22no—
258C2×D4×C41—22no—
259C2×D4×C41—21no—
260C2×D4×C41—22no—
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—41no—
269C2×D4×C41—42no—
270C2×D4×C41—42no—
271C2×D4×C41—42no—
272C2×D4×C41—42no—
273C2×D4×C41—44no—
274C2×D4×C41—44no—
275C2×D4×C41—42no—
276C2×D4×C41—42no—
277C2×D4×C41—44no—
278C2×D4×C41—84no—
279C2×D4×C41C2×D411yescharacteristic
280C2×D4×C41C2×D411yescharacteristic
281C2×D4×C41C2×D411yescharacteristic
282C22×C4×C41—21no—
283C22×C4×C41—21no—
284C22×C4×C41—21no—
285C22×C4×C41—21no—
286C22×C4×C41—21no—
287C22×C4×C41—22no—
288C22×C4×C41—21no—
289C22×C4×C41—21no—
290C22×C4×C41—21no—
291C22×C4×C41—22no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—21no—
295C22×C4×C41—21no—
296C22×C4×C41—21no—
297C22×C4×C41—21no—
298C22×C4×C41—42no—
299C22×C4×C41—42no—
300C22×C4×C41—42no—
301C22×C4×C41—42no—
302C22×C4×C41—42no—
303C22×C4×C41C2×D411yescharacteristic
304C22×C4×C41C2×D411yescharacteristic
305C22×C4×C41C2×D411yescharacteristic
306C22×C4×C41C2×D411yescharacteristic
307C22×C4×C41C2×D411yescharacteristic
308C22×C4×C41C2×D412yes—
309C22×C4×C41C2411yescharacteristic
310Q16×C41—42no—
311Q16×C41—42no—
312Q16×C41—42no—
313SD16×C41—42no—
314SD16×C41—42no—
315SD16×C41—42no—
316M16×C41—21no—
317M16×C41—21no—
318M16×C41—21no—
319M16×C41—21no—
320M16×C41—21no—
321M16×C41—21no—
322M16×C41—21no—
323M16×C41—42no—
324M16×C41C2×D412yescomplemented
325C2×C8×C41—21no—
326C2×C8×C41—21no—
327C2×C8×C41—21no—
328C2×C8×C41—21no—
329C2×C8×C41—42no—
330C4⋊C4×C41—22no—
331C4⋊C4×C41—22no—
332C4⋊C4×C41—21no—
333C4⋊C4×C41—21no—
334C4⋊C4×C41—21no—
335C4⋊C4×C41—21no—
336C4⋊C4×C41—21no—
337C4⋊C4×C41—21no—
338C4⋊C4×C41—41no—
339C4⋊C4×C41—41no—
340C4⋊C4×C41C2×D411yescharacteristic
341C4⋊C4×C41C2×D411yescharacteristic
342C22⋊C4×C41—22no—
343C22⋊C4×C41—22no—
344C22⋊C4×C41—22no—
345C22⋊C4×C41—22no—
346C22⋊C4×C41—22no—
347C22⋊C4×C41—21no—
348C22⋊C4×C41—21no—
349C22⋊C4×C41—21no—
350C22⋊C4×C41—21no—
351C22⋊C4×C41—22no—
352C22⋊C4×C41—22no—
353C22⋊C4×C41—21no—
354C22⋊C4×C41—44no—
355C22⋊C4×C41—44no—
356C22⋊C4×C41—41no—
357C22⋊C4×C41—41no—
358C42×C41—22no—
359C42×C41—21no—
360C42×C41—21no—
361C42×C41—21no—
362C42×C41—21no—
363C42×C41—42no—
364C42×C41C2×D412yescomplemented
365C23×C41—21no—
366C23×C41—21no—
367C23×C41—21no—
368C23×C41—22no—
369C23×C41—22no—
370C23×C41—21no—
371C23×C41—21no—
372C23×C41—22no—
373C23×C41—22no—
374C23×C41—41no—
375C23×C41—42no—
376C23×C41—44no—
377C23×C41—42no—
378C23×C41—42no—
379C23×C41—42no—
380C23×C41—81no—
381C23×C41—82no—
382C23×C41—82no—
383C23×C41#12011yescharacteristic
384C23×C41#12011yescharacteristic
385C23×C41C22×D411yescharacteristic
386Q8×C41—21no—
387Q8×C41—21no—
388Q8×C41—21no—
389Q8×C41—21no—
390Q8×C41—21no—
391Q8×C41—42no—
392Q8×C41—41no—
393Q8×C41—41no—
394Q8×C41—41no—
395Q8×C41—41no—
396Q8×C41#12112yes—
397D4×C41—22no—
398D4×C41—22no—
399D4×C41—21no—
400D4×C41—21no—
401D4×C41—21no—
402D4×C41—21no—
403D4×C41—21no—
404D4×C41—42no—
405D4×C41—42no—
406D4×C41—44no—
407D4×C41—42no—
408D4×C41—44no—
409D4×C41—41no—
410D4×C41—41no—
411D4×C41—41no—
412D4×C41—41no—
413D4×C41—44no—
414D4×C41—42no—
415D4×C41—41no—
416D4×C41—41no—
417D4×C41—41no—
418D4×C41—41no—
419D4×C41—81no—
420D4×C41—82no—
421D4×C41—82no—
422D4×C41—82no—
423D4×C41—82no—
424D4×C41#12112yes—
425C2×C4×C41—21no—
426C2×C4×C41—21no—
427C2×C4×C41—21no—
428C2×C4×C41—21no—
429C2×C4×C41—21no—
430C2×C4×C41—21no—
431C2×C4×C41—21no—
432C2×C4×C41—21no—
433C2×C4×C41—21no—
434C2×C4×C41—22no—
435C2×C4×C41—21no—
436C2×C4×C41—21no—
437C2×C4×C41—22no—
438C2×C4×C41—22no—
439C2×C4×C41—21no—
440C2×C4×C41—22no—
441C2×C4×C41—21no—
442C2×C4×C41—21no—
443C2×C4×C41—21no—
444C2×C4×C41—22no—
445C2×C4×C41—42no—
446C2×C4×C41—42no—
447C2×C4×C41—42no—
448C2×C4×C41—44no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—48no—
453C2×C4×C41—41no—
454C2×C4×C41—41no—
455C2×C4×C41—41no—
456C2×C4×C41—41no—
457C2×C4×C41—41no—
458C2×C4×C41—42no—
459C2×C4×C41—42no—
460C2×C4×C41—41no—
461C2×C4×C41—41no—
462C2×C4×C41—41no—
463C2×C4×C41—41no—
464C2×C4×C41—82no—
465C2×C4×C41#12011yescharacteristic
466C2×C4×C41#12011yescharacteristic
467C2×C4×C41C22×D411yescharacteristic
468C2×C4×C41C22×D411yescharacteristic
469C2×C4×C41C22×D411yescharacteristic
470C2×C4×C41C2×#4111yescharacteristic
471C2×C4×C41H(5,𝔽2)11yescharacteristic
472C2×C4×C41H(5,𝔽2)11yescharacteristic
473C8×C41—22no—
474C8×C41—41no—
475C8×C41—41no—
476C8×C41—41no—
477#24467C4111yesmaximal, characteristic, direct product factor, Sylow
478C22×C41—21no—
479C22×C41—21no—
480C22×C41—21no—
481C22×C41—21no—
482C22×C41—21no—
483C22×C41—22no—
484C22×C41—21no—
485C22×C41—21no—
486C22×C41—42no—
487C22×C41—42no—
488C22×C41—41no—
489C22×C41—41no—
490C22×C41—41no—
491C22×C41—41no—
492C22×C41—42no—
493C22×C41—42no—
494C22×C41—41no—
495C22×C41—41no—
496C22×C41—41no—
497C22×C41—42no—
498C22×C41—41no—
499C22×C41—84no—
500C22×C41—82no—
501C22×C41—82no—
502C22×C41—164no—
503C22×C41#45512yescomplemented
504C22×C41C2×#12011yescharacteristic
505C22×C41D4211yescharacteristic
506C22×C41#54611yescharacteristic
507C4×C41—21no—
508C4×C41—21no—
509C4×C41—22no—
510C4×C41—42no—
511C4×C41—42no—
512C4×C41—41no—
513C4×C41—41no—
514C4×C41—42no—
515C4×C41—41no—
516C4×C41—41no—
517C4×C41—81no—
518C4×C41—81no—
519C4×C41C2×#12111yescharacteristic
520C4×C41#53411yescharacteristic
521C4×C41D4211yescharacteristic
522C4×C41#54611yescharacteristic
523#3488C2×C4111yescharacteristic
524#3056C2×C4111yescharacteristic, complemented
525C2×#455C2×C4111yescharacteristic, complemented
526#3007C2×C4111yescharacteristic, complemented
527C22×#104C2×C4111yescharacteristic, complemented
528#2850C2×C4111yescharacteristic, complemented
529#2040C2×C4111yescharacteristic, complemented
530#2037C2×C4111yescharacteristic, complemented
531#2007C2×C4111yescharacteristic, complemented
532#2004C2×C4111yescharacteristic, complemented
533#1900C2×C4111yescharacteristic, complemented
534#1896C2×C4111yescharacteristic, complemented
535#1882C2×C4111yescharacteristic, complemented
536#1860C2×C4111yescharacteristic, complemented
537#1792C2×C4111yescharacteristic, complemented
538C2×C41—21no—
539C2×C41—21no—
540C2×C41—22no—
541C2×C41—41no—
542C2×C41—42no—
543C2×C41—81no—
544C2×C41—82no—
545C2×C41—81no—
546C2×C41#241011yescharacteristic
547C2×C41C2×#45511yescharacteristic
548C2×C41#301811yescharacteristic
549C2×H(5,𝔽2)C22×C4111yescharacteristic
550C22×#41C22×C4111yescharacteristic
551C2×#137C22×C4111yescharacteristic
552C2×#137C22×C4111yescharacteristic, complemented
553C2×#137C22×C4111yescharacteristic, complemented
554C22×M16C22×C4111yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C4111yescharacteristic
563#535—21no—
564#535C22×C4111yescharacteristic
565C2×#124C22×C4111yescharacteristic, complemented
566#525—21no—
567#525C22×C4111yescharacteristic
568C2×C22⋊Q8C22×C4111yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C4111yescharacteristic
571#520C22×C4111yescharacteristic
572C22×C42C22×C4111yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C4111yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C4111yescharacteristic
585C2×#104C22×C4111yescharacteristic
586C2×#104C22×C4111yescharacteristic, complemented
587C2×#104C22×C4111yescharacteristic, complemented
588C2×#104C22×C4111yescharacteristic, complemented
589C2×#104C22×C4111yescharacteristic, complemented
590#419C22×C4111yescharacteristic, complemented
591#417C22×C4111yescharacteristic
592#417C22×C4111yescharacteristic, complemented
593#417C22×C4111yescharacteristic, complemented
594C2×#100C22×C4111yescharacteristic, complemented
595C2×#100C22×C4111yescharacteristic, complemented
596#407C22×C4111yescharacteristic, complemented
597#391C22×C4111yescharacteristic, complemented
598#390C22×C4111yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C4111yescharacteristic, complemented
602#343C22×C4111yescharacteristic, complemented
603#343C22×C4111yescharacteristic, complemented
604#339C22×C4111yescharacteristic, complemented
605#339C22×C4111yescharacteristic, complemented
606C41#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C4111yescharacteristic
620C2×#41D4×C4111yescharacteristic
621C2×#41C23×C4111yescharacteristic
622C2×#41C23×C4111yescharacteristic
623C2×#41C23×C4111yescharacteristic
624C22×Q8D4×C4111yescharacteristic
625C22×Q8C23×C4111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C4111yescharacteristic
632C22×D4D4×C4112yes—
633C22×D4C23×C4111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C4111yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C4111yescharacteristic
653C2×M16C23×C4111yescharacteristic
654C2×M16C23×C4111yescharacteristic
655C2×M16C23×C4111yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C4111yescharacteristic
673C22⋊Q8D4×C4111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C4111yescharacteristic
689#121D4×C4111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C4111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C4111yescharacteristic
707C2×C4⋊C4C23×C4111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C4112yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C4111yescharacteristic
717C2×C42C23×C4111yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C4114yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C4111yescharacteristic
743C24C2×D4×C4112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C4112yes—
767#41#41×C4112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C4111yescharacteristic
778C2×Q8C2×D4×C4111yescharacteristic
779C2×Q8C2×D4×C4111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C4111yescharacteristic
814C2×D4C2×D4×C4111yescharacteristic
815C2×D4C2×D4×C4111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C4111yescharacteristic
838C22×C4C2×D4×C4111yescharacteristic
839C22×C4C2×D4×C4111yescharacteristic
840C22×C4C2×D4×C4111yescharacteristic
841C22×C4C2×D4×C4111yescharacteristic
842C22×C4C2×D4×C4112yes—
843C22×C4C24×C4111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C4112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C4111yescharacteristic
875C4⋊C4C2×D4×C4111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C4112yescomplemented
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C4111yescharacteristic
918C23#120×C4111yescharacteristic
919C23C22×D4×C4111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C4112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C4112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C4111yescharacteristic
1000C2×C4#120×C4111yescharacteristic
1001C2×C4C22×D4×C4111yescharacteristic
1002C2×C4C22×D4×C4111yescharacteristic
1003C2×C4C22×D4×C4111yescharacteristic
1004C2×C4C2×#41×C4111yescharacteristic
1005C2×C4H(5,𝔽2)×C4111yescharacteristic
1006C2×C4H(5,𝔽2)×C4111yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C41×#45512yescomplemented
1037C22C2×#120×C4111yescharacteristic
1038C22D42×C4111yescharacteristic
1039C22C41×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C4111yescharacteristic
1053C4C41×#53411yescharacteristic
1054C4D42×C4111yescharacteristic
1055C4C41×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C41×#241011yescharacteristic
1065C2C2×C41×#45511yescharacteristic
1066C2C41×#301811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3488C2
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
2. C41×#3056C2semidirect
3. C2×C41×#455C2semidirect
4. C41×#3007C2semidirect
5. C22×#104×C41C2semidirect
6. C41×#2850C2semidirect
7. C41×#2040C2semidirect
8. C41×#2037C2semidirect
9. C41×#2007C2semidirect
10. C41×#2004C2semidirect
11. C41×#1900C2semidirect
12. C41×#1896C2semidirect
13. C41×#1882C2semidirect
14. C41×#1860C2semidirect
15. C41×#1792C2semidirect
19. C2×#137×C41C22semidirect
20. C2×#137×C41C22semidirect
21. C22×M16×C41C22semidirect
32. C2×#124×C41C22semidirect
35. C2×C22⋊Q8×C41C22semidirect
39. C22×C42×C41C22semidirect
49. C41×#428C22semidirect
53. C2×#104×C41C22semidirect
54. C2×#104×C41C22semidirect
55. C2×#104×C41C22semidirect
56. C2×#104×C41C22semidirect
57. C41×#419C22semidirect
59. C41×#417C22semidirect
60. C41×#417C22semidirect
61. C2×#100×C41C22semidirect
62. C2×#100×C41C22semidirect
63. C41×#407C22semidirect
64. C41×#391C22semidirect
65. C41×#390C22semidirect
68. C41×#382C22semidirect
69. C41×#343C22semidirect
70. C41×#343C22semidirect
71. C41×#339C22semidirect
72. C41×#339C22semidirect
191. #104×C41D4semidirect
324. M16×C41C2×D4semidirect
364. C42×C41C2×D4semidirect
477. #24467C41direct (N × H)
503. C22×C41#455semidirect
524. #3056C2×C41semidirect
525. C2×#455C2×C41semidirect
526. #3007C2×C41semidirect
527. C22×#104C2×C41semidirect
528. #2850C2×C41semidirect
529. #2040C2×C41semidirect
530. #2037C2×C41semidirect
531. #2007C2×C41semidirect
532. #2004C2×C41semidirect
533. #1900C2×C41semidirect
534. #1896C2×C41semidirect
535. #1882C2×C41semidirect
536. #1860C2×C41semidirect
537. #1792C2×C41semidirect
552. C2×#137C22×C41semidirect
553. C2×#137C22×C41semidirect
554. C22×M16C22×C41semidirect
565. C2×#124C22×C41semidirect
568. C2×C22⋊Q8C22×C41semidirect
572. C22×C42C22×C41semidirect
582. #428C22×C41semidirect
586. C2×#104C22×C41semidirect
587. C2×#104C22×C41semidirect
588. C2×#104C22×C41semidirect
589. C2×#104C22×C41semidirect
590. #419C22×C41semidirect
592. #417C22×C41semidirect
593. #417C22×C41semidirect
594. C2×#100C22×C41semidirect
595. C2×#100C22×C41semidirect
596. #407C22×C41semidirect
597. #391C22×C41semidirect
598. #390C22×C41semidirect
601. #382C22×C41semidirect
602. #343C22×C41semidirect
603. #343C22×C41semidirect
604. #339C22×C41semidirect
605. #339C22×C41semidirect
606. C41#24467direct (N × H)
725. #104D4×C41semidirect
858. M16C2×D4×C41semidirect
898. C42C2×D4×C41semidirect
1036. C22C41×#455semidirect

Maximal subgroups

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

subgroupindex
C41×#34882
C41×#30562
C2×C41×#4552
C41×#30072
C22×#104×C412
C41×#28502
C41×#20402
C41×#20372
C41×#20072
C41×#20042
C41×#19002
C41×#18962
C41×#18822
C41×#18602
C41×#17922
#2446741