Finite Group Databasebeta

← C41×#25890 #23802091

Subgroups — C41×#25890 #23802091

Order 10496.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#546C211yesmaximal, characteristic
2C2×C41×#488C211yesmaximal, characteristic, complemented
3C2×C41×#478C211yesmaximal, characteristic, complemented
4C41×#2562C211yesmaximal, characteristic, complemented
5C41×#2036C211yesmaximal, characteristic, complemented
6C41×#2035C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1983C211yesmaximal, characteristic, complemented
10C41×#1954C211yesmaximal, characteristic, complemented
11C41×#1788C211yesmaximal, characteristic, complemented
12C41×#1788C211yesmaximal, characteristic, complemented
13C41×#1786C211yesmaximal, characteristic, complemented
14C41×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C41C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C41×#546—24no—
19C41×#546—24no—
20C2×#125×C41C2211yescharacteristic, complemented
21C2×#124×C41C2211yescharacteristic
22C2×#123×C41—21no—
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×#121×C41—21no—
25C2×#121×C41C2211yescharacteristic
26C2×#120×C41—21no—
27C2×C4×D4×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C22×C22⋊C4×C41—21no—
30C41×#488—24no—
31C41×#478—24no—
32C2×#107×C41C2211yescharacteristic, complemented
33C2×#106×C41C2211yescharacteristic, complemented
34C2×C4⋊C8×C41C2211yescharacteristic, complemented
35C2×#103×C41C2211yescharacteristic, complemented
36C2×#103×C41C2211yescharacteristic, complemented
37C2×#103×C41C2211yescharacteristic, complemented
38C2×#103×C41C2211yescharacteristic, complemented
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C2×C22⋊C8×C41C2211yescharacteristic
49C2×C22⋊C8×C41C2211yescharacteristic, complemented
50C2×C22⋊C8×C41C2211yescharacteristic, complemented
51C2×C4×C8×C41C2211yescharacteristic, complemented
52C41×#400—21no—
53C41×#394—21no—
54C41×#388—21no—
55C41×#388—21no—
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C41×#380C2211yescharacteristic, complemented
59C41×#380C2211yescharacteristic, complemented
60C4×C4⋊C4×C41C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C25×C41—21no—
64C2×#41×C41—22no—
65C2×#41×C41—22no—
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—41no—
69C2×#41×C41—41no—
70C22×Q8×C41C2311yescharacteristic
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—22no—
74C22×D4×C41—22no—
75C22×D4×C41—22no—
76C22×D4×C41—22no—
77C22×D4×C41—21no—
78C22×D4×C41—41no—
79C22×D4×C41—41no—
80C22×D4×C41D411yescharacteristic
81C22×D4×C41C2311yescharacteristic
82C22×D4×C41C2311yescharacteristic
83C23×C4×C41—21no—
84C23×C4×C41—21no—
85C23×C4×C41C2311yescharacteristic
86C23×C4×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91#125×C41—22no—
92#125×C41—22no—
93#124×C41—22no—
94#124×C41D414yes—
95#123×C41—28no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—22no—
98#121×C41—28no—
99#121×C41—22no—
100#121×C41—22no—
101#120×C41—28no—
102C4×D4×C41—22no—
103C4×D4×C41—22no—
104C4×D4×C41—22no—
105C4×D4×C41D414yes—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41D411yescharacteristic
110C2×C4⋊C4×C41C2311yescharacteristic
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C22⋊C4×C41—28no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41D411yescharacteristic
126C2×C22⋊C4×C41D411yescharacteristic
127C2×C42×C41—21no—
128C2×C42×C41C2311yescharacteristic
129#107×C41—22no—
130#106×C41—22no—
131C4⋊C8×C41—22no—
132#103×C41—22no—
133#103×C41—22no—
134#103×C41—41no—
135#103×C41—41no—
136#102×C41—22no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—41no—
143#102×C41—41no—
144C22⋊C8×C41—41no—
145C22⋊C8×C41—41no—
146C22⋊C8×C41—41no—
147C22⋊C8×C41—41no—
148C4×C8×C41—22no—
149#95×C41—21no—
150#95×C41—21no—
151#95×C41—21no—
152#95×C41—21no—
153#95×C41—21no—
154C24×C41—21no—
155C24×C41—24no—
156C24×C41—21no—
157C24×C41—42no—
158C24×C41—42no—
159C24×C41—42no—
160C24×C41—42no—
161C24×C41—81no—
162C24×C41—81no—
163C24×C41C2×D411yescharacteristic
164C24×C41C2×D411yescharacteristic
165#41×C41—44no—
166#41×C41—44no—
167#41×C41—44no—
168#41×C41—44no—
169C2×Q8×C41—21no—
170C2×Q8×C41—21no—
171C2×Q8×C41—21no—
172C2×Q8×C41—21no—
173C2×Q8×C41—21no—
174C2×Q8×C41C2×D412yes—
175C2×D4×C41—24no—
176C2×D4×C41—24no—
177C2×D4×C41—22no—
178C2×D4×C41—24no—
179C2×D4×C41—22no—
180C2×D4×C41—21no—
181C2×D4×C41—21no—
182C2×D4×C41—21no—
183C2×D4×C41—21no—
184C2×D4×C41—21no—
185C2×D4×C41—21no—
186C2×D4×C41—21no—
187C2×D4×C41—21no—
188C2×D4×C41—41no—
189C2×D4×C41—42no—
190C2×D4×C41—42no—
191C2×D4×C41—44no—
192C2×D4×C41—44no—
193C2×D4×C41—44no—
194C2×D4×C41—42no—
195C2×D4×C41—42no—
196C2×D4×C41—44no—
197C2×D4×C41—81no—
198C2×D4×C41—81no—
199C2×D4×C41C2×D412yes—
200C2×D4×C41C2×D412yes—
201C2×D4×C41#4112yes—
202C2×D4×C41#4112yes—
203C22×C4×C41—24no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—24no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—42no—
224C22×C4×C41—42no—
225C22×C4×C41—81no—
226C22×C4×C41—81no—
227C22×C4×C41C2×D411yescharacteristic
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41C2×D411yescharacteristic
230C22×C4×C41C2×D411yescharacteristic
231C22×C4×C41C2411yescharacteristic
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41—21no—
236C2×C8×C41—21no—
237C2×C8×C41—21no—
238C2×C8×C41—21no—
239C2×C8×C41—21no—
240C2×C8×C41—21no—
241C2×C8×C41—21no—
242C2×C8×C41—21no—
243C2×C8×C41—21no—
244C4⋊C4×C41—24no—
245C4⋊C4×C41—22no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—21no—
250C4⋊C4×C41—21no—
251C4⋊C4×C41—21no—
252C4⋊C4×C41—21no—
253C4⋊C4×C41—21no—
254C4⋊C4×C41—21no—
255C4⋊C4×C41—42no—
256C4⋊C4×C41—42no—
257C4⋊C4×C41C2×D412yes—
258C22⋊C4×C41—24no—
259C22⋊C4×C41—24no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—24no—
262C22⋊C4×C41—24no—
263C22⋊C4×C41—24no—
264C22⋊C4×C41—22no—
265C22⋊C4×C41—42no—
266C22⋊C4×C41—42no—
267C22⋊C4×C41—81no—
268C22⋊C4×C41—81no—
269C42×C41—81no—
270C42×C41C2×D412yes—
271C42×C41C2×D412yes—
272C23×C41—21no—
273C23×C41—22no—
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—22no—
277C23×C41—22no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—21no—
281C23×C41—22no—
282C23×C41—21no—
283C23×C41—21no—
284C23×C41—21no—
285C23×C41—21no—
286C23×C41—21no—
287C23×C41—21no—
288C23×C41—21no—
289C23×C41—48no—
290C23×C41—48no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41—41no—
299C23×C41—41no—
300C23×C41—41no—
301C23×C41—84no—
302C23×C41—84no—
303C23×C41—84no—
304C23×C41—84no—
305C23×C41—84no—
306C23×C41#13512yes—
307C23×C41C22×D411yescharacteristic
308Q8×C41—22no—
309Q8×C41—22no—
310Q8×C41—41no—
311Q8×C41—41no—
312D4×C41—22no—
313D4×C41—22no—
314D4×C41—22no—
315D4×C41—22no—
316D4×C41—22no—
317D4×C41—44no—
318D4×C41—48no—
319D4×C41—48no—
320D4×C41—41no—
321D4×C41—41no—
322D4×C41—84no—
323D4×C41#12414yes—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—21no—
327C2×C4×C41—21no—
328C2×C4×C41—22no—
329C2×C4×C41—21no—
330C2×C4×C41—22no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
336C2×C4×C41—48no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—41no—
356C2×C4×C41—41no—
357C2×C4×C41—41no—
358C2×C4×C41—41no—
359C2×C4×C41—41no—
360C2×C4×C41—41no—
361C2×C4×C41—84no—
362C2×C4×C41#12012yes—
363C2×C4×C41#12012yes—
364C2×C4×C41C22×D411yescharacteristic
365C2×C4×C41C22×D411yescharacteristic
366C2×C4×C41C2×#4111yescharacteristic
367C2×C4×C41C2×#4111yescharacteristic
368C2×C4×C41H(5,𝔽2)11yescharacteristic
369C2×C4×C41H(5,𝔽2)11yescharacteristic
370C8×C41—41no—
371C8×C41—41no—
372C8×C41—41no—
373C8×C41—41no—
374#25890C4111yesmaximal, characteristic, direct product factor, Sylow
375C22×C41—24no—
376C22×C41—22no—
377C22×C41—22no—
378C22×C41—22no—
379C22×C41—41no—
380C22×C41—42no—
381C22×C41—42no—
382C22×C41—41no—
383C22×C41—42no—
384C22×C41—42no—
385C22×C41—41no—
386C22×C41—42no—
387C22×C41—41no—
388C22×C41—42no—
389C22×C41—41no—
390C22×C41—42no—
391C22×C41—41no—
392C22×C41—42no—
393C22×C41—41no—
394C22×C41—42no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—41no—
399C22×C41—816no—
400C22×C41—81no—
401C22×C41—81no—
402C22×C41—81no—
403C22×C41—81no—
404C22×C41C2×#12011yescharacteristic
405C22×C41#54611yescharacteristic
406C22×C41#54611yescharacteristic
407C22×C41C2×#13511yescharacteristic
408C22×C41#57511yescharacteristic
409C22×C41#57611yescharacteristic
410C22×C41#57711yescharacteristic
411C4×C41—22no—
412C4×C41—22no—
413C4×C41—41no—
414C4×C41—41no—
415C4×C41—42no—
416C4×C41—42no—
417C4×C41—81no—
418C4×C41—81no—
419C4×C41—81no—
420C4×C41—81no—
421C4×C41C2×#12411yescharacteristic
422C4×C41#53511yescharacteristic
423C4×C41#54611yescharacteristic
424C4×C41#54611yescharacteristic
425C2×#546C2×C4111yescharacteristic
426C2×#488C2×C4111yescharacteristic, complemented
427C2×#478C2×C4111yescharacteristic, complemented
428#2562C2×C4111yescharacteristic, complemented
429#2036C2×C4111yescharacteristic, complemented
430#2035C2×C4111yescharacteristic, complemented
431#2034C2×C4111yescharacteristic, complemented
432#2033C2×C4111yescharacteristic, complemented
433#1983C2×C4111yescharacteristic, complemented
434#1954C2×C4111yescharacteristic, complemented
435#1788C2×C4111yescharacteristic, complemented
436#1788C2×C4111yescharacteristic, complemented
437#1786C2×C4111yescharacteristic, complemented
438#1786C2×C4111yescharacteristic, complemented
439C4×#102C2×C4111yescharacteristic, complemented
440C2×C41—42no—
441C2×C41—44no—
442C2×C41—81no—
443C2×C41—82no—
444C2×C41#243511yescharacteristic
445C2×C41#300211yescharacteristic
446C2×C41#301211yescharacteristic
447C2×C41#329611yescharacteristic
448C2×C41#329711yescharacteristic
449C2×C41#332211yescharacteristic
450C2×C41#332311yescharacteristic
451C22×#41C22×C4111yescharacteristic
452C23×D4C22×C4111yescharacteristic
453#546—24no—
454#546—24no—
455C2×#125C22×C4111yescharacteristic, complemented
456C2×#124C22×C4111yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C22×C4111yescharacteristic
459C2×#121—21no—
460C2×#121C22×C4111yescharacteristic
461C2×#120—21no—
462C2×C4×D4C22×C4111yescharacteristic
463C2×C4×D4C22×C4111yescharacteristic
464C22×C22⋊C4—21no—
465#488—24no—
466#478—24no—
467C2×#107C22×C4111yescharacteristic, complemented
468C2×#106C22×C4111yescharacteristic, complemented
469C2×C4⋊C8C22×C4111yescharacteristic, complemented
470C2×#103C22×C4111yescharacteristic, complemented
471C2×#103C22×C4111yescharacteristic, complemented
472C2×#103C22×C4111yescharacteristic, complemented
473C2×#103C22×C4111yescharacteristic, complemented
474C2×#102C22×C4111yescharacteristic
475C2×#102C22×C4111yescharacteristic
476C2×#102C22×C4111yescharacteristic
477C2×#102C22×C4111yescharacteristic
478C2×#102C22×C4111yescharacteristic
479C2×#102C22×C4111yescharacteristic
480C2×#102C22×C4111yescharacteristic
481C2×#102C22×C4111yescharacteristic
482C2×C22⋊C8C22×C4111yescharacteristic
483C2×C22⋊C8C22×C4111yescharacteristic
484C2×C22⋊C8C22×C4111yescharacteristic, complemented
485C2×C22⋊C8C22×C4111yescharacteristic, complemented
486C2×C4×C8C22×C4111yescharacteristic, complemented
487#400—21no—
488#394—21no—
489#388—21no—
490#388—21no—
491#380C22×C4111yescharacteristic
492#380C22×C4111yescharacteristic
493#380C22×C4111yescharacteristic, complemented
494#380C22×C4111yescharacteristic, complemented
495C4×C4⋊C4C22×C4111yescharacteristic, complemented
496#340C22×C4111yescharacteristic, complemented
497#340C22×C4111yescharacteristic, complemented
498C41#2589011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C4111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C4111yescharacteristic
517C22×D4C23×C4111yescharacteristic
518C22×D4C23×C4111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C4111yescharacteristic
522C23×C4C23×C4111yescharacteristic
523C22×C8C23×C4111yescharacteristic
524C22×C8C23×C4111yescharacteristic
525C22×C8C23×C4111yescharacteristic
526C22×C8C23×C4111yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C4114yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C4114yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C4111yescharacteristic
546C2×C4⋊C4C23×C4111yescharacteristic
547C2×C4⋊C4C23×C4111yescharacteristic
548C2×C4⋊C4C23×C4111yescharacteristic
549C2×C4⋊C4C23×C4111yescharacteristic
550C2×C4⋊C4C23×C4111yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C4111yescharacteristic
562C2×C22⋊C4D4×C4111yescharacteristic
563C2×C42—21no—
564C2×C42C23×C4111yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C4111yescharacteristic
600C24C2×D4×C4111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C4112yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C4112yes—
636C2×D4C2×D4×C4112yes—
637C2×D4#41×C4112yes—
638C2×D4#41×C4112yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C4111yescharacteristic
664C22×C4C2×D4×C4111yescharacteristic
665C22×C4C2×D4×C4111yescharacteristic
666C22×C4C2×D4×C4111yescharacteristic
667C22×C4C24×C4111yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C4112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C4112yes—
707C42C2×D4×C4112yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C4112yes—
743C23C22×D4×C4111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C4114yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C4112yes—
799C2×C4#120×C4112yes—
800C2×C4C22×D4×C4111yescharacteristic
801C2×C4C22×D4×C4111yescharacteristic
802C2×C4C2×#41×C4111yescharacteristic
803C2×C4C2×#41×C4111yescharacteristic
804C2×C4H(5,𝔽2)×C4111yescharacteristic
805C2×C4H(5,𝔽2)×C4111yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C4111yescharacteristic
840C22C41×#54611yescharacteristic
841C22C41×#54611yescharacteristic
842C22C2×#135×C4111yescharacteristic
843C22C41×#57511yescharacteristic
844C22C41×#57611yescharacteristic
845C22C41×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C4111yescharacteristic
857C4C41×#53511yescharacteristic
858C4C41×#54611yescharacteristic
859C4C41×#54611yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C41×#243511yescharacteristic
865C2C41×#300211yescharacteristic
866C2C41×#301211yescharacteristic
867C2C41×#329611yescharacteristic
868C2C41×#329711yescharacteristic
869C2C41×#332211yescharacteristic
870C2C41×#332311yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#488C2semidirect
3. C2×C41×#478C2semidirect
4. C41×#2562C2semidirect
5. C41×#2036C2semidirect
6. C41×#2035C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1983C2semidirect
10. C41×#1954C2semidirect
11. C41×#1788C2semidirect
12. C41×#1788C2semidirect
13. C41×#1786C2semidirect
14. C41×#1786C2semidirect
15. C4×#102×C41C2semidirect
20. C2×#125×C41C22semidirect
32. C2×#107×C41C22semidirect
33. C2×#106×C41C22semidirect
34. C2×C4⋊C8×C41C22semidirect
35. C2×#103×C41C22semidirect
36. C2×#103×C41C22semidirect
37. C2×#103×C41C22semidirect
38. C2×#103×C41C22semidirect
49. C2×C22⋊C8×C41C22semidirect
50. C2×C22⋊C8×C41C22semidirect
51. C2×C4×C8×C41C22semidirect
58. C41×#380C22semidirect
59. C41×#380C22semidirect
60. C4×C4⋊C4×C41C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
374. #25890C41direct (N × H)
426. C2×#488C2×C41semidirect
427. C2×#478C2×C41semidirect
428. #2562C2×C41semidirect
429. #2036C2×C41semidirect
430. #2035C2×C41semidirect
431. #2034C2×C41semidirect
432. #2033C2×C41semidirect
433. #1983C2×C41semidirect
434. #1954C2×C41semidirect
435. #1788C2×C41semidirect
436. #1788C2×C41semidirect
437. #1786C2×C41semidirect
438. #1786C2×C41semidirect
439. C4×#102C2×C41semidirect
455. C2×#125C22×C41semidirect
467. C2×#107C22×C41semidirect
468. C2×#106C22×C41semidirect
469. C2×C4⋊C8C22×C41semidirect
470. C2×#103C22×C41semidirect
471. C2×#103C22×C41semidirect
472. C2×#103C22×C41semidirect
473. C2×#103C22×C41semidirect
484. C2×C22⋊C8C22×C41semidirect
485. C2×C22⋊C8C22×C41semidirect
486. C2×C4×C8C22×C41semidirect
493. #380C22×C41semidirect
494. #380C22×C41semidirect
495. C4×C4⋊C4C22×C41semidirect
496. #340C22×C41semidirect
497. #340C22×C41semidirect
498. C41#25890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5462
C2×C41×#4882
C2×C41×#4782
C41×#25622
C41×#20362
C41×#20352
C41×#20342
C41×#20332
C41×#19832
C41×#19542
C41×#17882
C41×#17862
C4×#102×C412
#2589041