Finite Group Databasebeta

← C41×#24008 #23800209

Subgroups — C41×#24008 #23800209

Order 10496.

1448 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#525C211yesmaximal, characteristic
2C2×C41×#485C211yesmaximal, characteristic, complemented
3C2×C41×#482C211yesmaximal, characteristic, complemented
4C41×#2280C211yesmaximal, characteristic, complemented
5C41×#2036C211yesmaximal, characteristic, complemented
6C41×#2035C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1875C211yesmaximal, characteristic, complemented
10C41×#1873C211yesmaximal, characteristic, complemented
11C41×#1854C211yesmaximal, characteristic, complemented
12C41×#1854C211yesmaximal, characteristic, complemented
13C41×#1788C211yesmaximal, characteristic, complemented
14C41×#1788C211yesmaximal, characteristic, complemented
15C41×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C24×C4×C41C2211yescharacteristic
18C41×#525—24no—
19C41×#525—24no—
20C2×#123×C41—21no—
21C2×C22⋊Q8×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×#120×C41—21no—
26C2×C4×D4×C41—21no—
27C2×C4×D4×C41—21no—
28C2×#117×C41C2211yescharacteristic
29C2×#117×C41C2211yescharacteristic
30C2×#117×C41C2211yescharacteristic
31C41×#485—24no—
32C41×#482—24no—
33C2×#107×C41C2211yescharacteristic, complemented
34C2×#107×C41C2211yescharacteristic, complemented
35C2×#106×C41C2211yescharacteristic, complemented
36C2×#106×C41C2211yescharacteristic, complemented
37C2×#103×C41C2211yescharacteristic, complemented
38C2×#103×C41C2211yescharacteristic, complemented
39C2×#103×C41C2211yescharacteristic, complemented
40C2×#103×C41C2211yescharacteristic, complemented
41C2×#102×C41C2211yescharacteristic, complemented
42C2×#102×C41C2211yescharacteristic, complemented
43C2×#102×C41C2211yescharacteristic, complemented
44C2×#102×C41C2211yescharacteristic, complemented
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C2×C22⋊C8×C41C2211yescharacteristic
49C2×C22⋊C8×C41C2211yescharacteristic
50C2×C22⋊C8×C41C2211yescharacteristic
51C41×#381—21no—
52C41×#380C2211yescharacteristic
53C41×#380C2211yescharacteristic
54C41×#380C2211yescharacteristic
55C41×#380C2211yescharacteristic
56C41×#379—21no—
57C4×C22⋊C4×C41—21no—
58C4×C22⋊C4×C41—21no—
59C41×#340C2211yescharacteristic, complemented
60C41×#340C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C25×C41D411yescharacteristic
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—21no—
74C22×D4×C41C2311yescharacteristic
75C23×C4×C41—21no—
76C23×C4×C41—22no—
77C23×C4×C41—22no—
78C23×C4×C41—22no—
79C23×C4×C41—22no—
80C23×C4×C41—41no—
81C23×C4×C41—41no—
82C23×C4×C41D411yescharacteristic
83C23×C4×C41D411yescharacteristic
84C23×C4×C41D411yescharacteristic
85C23×C4×C41C2311yescharacteristic
86C23×C4×C41C2311yescharacteristic
87C23×C4×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91C22×C8×C41C2311yescharacteristic
92#123×C41—28no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41D414yes—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41D414yes—
101#120×C41—28no—
102C4×D4×C41—28no—
103C4×D4×C41—28no—
104#117×C41—22no—
105#117×C41—22no—
106#117×C41—22no—
107#117×C41—22no—
108#117×C41—41no—
109#117×C41—41no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C42×C41—21no—
130C2×C42×C41—21no—
131C2×C42×C41—21no—
132#107×C41—22no—
133#107×C41—22no—
134#106×C41—22no—
135#106×C41—22no—
136#103×C41—22no—
137#103×C41—22no—
138#103×C41—41no—
139#103×C41—41no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—41no—
143#102×C41—41no—
144C22⋊C8×C41—22no—
145C22⋊C8×C41—22no—
146C22⋊C8×C41—22no—
147C22⋊C8×C41—22no—
148C22⋊C8×C41—41no—
149C22⋊C8×C41—41no—
150#95×C41—21no—
151#95×C41—21no—
152#95×C41—21no—
153#95×C41—21no—
154C24×C41—22no—
155C24×C41—22no—
156C24×C41—22no—
157C24×C41—21no—
158C24×C41—41no—
159C24×C41—41no—
160C24×C41—41no—
161C24×C41—41no—
162C24×C41C2×D411yescharacteristic
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—24no—
178C2×D4×C41—21no—
179C2×D4×C41—21no—
180C2×D4×C41—21no—
181C2×D4×C41—21no—
182C2×D4×C41—21no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—42no—
186C2×D4×C41—42no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41C2×D412yes—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—24no—
199C22×C4×C41—22no—
200C22×C4×C41—22no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—22no—
205C22×C4×C41—22no—
206C22×C4×C41—22no—
207C22×C4×C41—22no—
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—41no—
219C22×C4×C41—41no—
220C22×C4×C41—41no—
221C22×C4×C41—44no—
222C22×C4×C41—44no—
223C22×C4×C41—44no—
224C22×C4×C41—44no—
225C22×C4×C41—42no—
226C22×C4×C41—42no—
227C22×C4×C41C2×D411yescharacteristic
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41C2×D412yes—
230C22×C4×C41C2×D412yes—
231C22×C4×C41C2×D411yescharacteristic
232C22×C4×C41#4112yes—
233C22×C4×C41#4112yes—
234C22×C4×C41C2411yescharacteristic
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—
244C2×C8×C41—21no—
245C2×C8×C41—21no—
246C2×C8×C41—21no—
247C4⋊C4×C41—24no—
248C4⋊C4×C41—24no—
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—21no—
256C4⋊C4×C41—21no—
257C4⋊C4×C41—21no—
258C4⋊C4×C41—21no—
259C4⋊C4×C41C2×D412yes—
260C4⋊C4×C41C2×D412yes—
261C22⋊C4×C41—24no—
262C22⋊C4×C41—24no—
263C22⋊C4×C41—24no—
264C22⋊C4×C41—24no—
265C22⋊C4×C41—24no—
266C22⋊C4×C41—42no—
267C22⋊C4×C41—42no—
268C22⋊C4×C41—42no—
269C22⋊C4×C41—42no—
270C22⋊C4×C41—42no—
271C22⋊C4×C41—42no—
272C42×C41—24no—
273C42×C41—42no—
274C42×C41—42no—
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—21no—
281C23×C41—21no—
282C23×C41—21no—
283C23×C41—21no—
284C23×C41—21no—
285C23×C41—21no—
286C23×C41—21no—
287C23×C41—21no—
288C23×C41—21no—
289C23×C41—21no—
290C23×C41—21no—
291C23×C41—21no—
292C23×C41—21no—
293C23×C41—22no—
294C23×C41—44no—
295C23×C41—44no—
296C23×C41—44no—
297C23×C41—44no—
298C23×C41—44no—
299C23×C41—44no—
300C23×C41—44no—
301C23×C41—41no—
302C23×C41—41no—
303C23×C41—41no—
304C23×C41—41no—
305C23×C41—41no—
306C23×C41—41no—
307C23×C41#12012yes—
308C23×C41#12312yes—
309C23×C41#13512yes—
310C23×C41C22×D411yescharacteristic
311Q8×C41—22no—
312Q8×C41—22no—
313Q8×C41—41no—
314Q8×C41—41no—
315D4×C41—22no—
316D4×C41—22no—
317D4×C41—48no—
318D4×C41—48no—
319D4×C41—48no—
320D4×C41—41no—
321D4×C41—41no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—22no—
327C2×C4×C41—22no—
328C2×C4×C41—22no—
329C2×C4×C41—22no—
330C2×C4×C41—22no—
331C2×C4×C41—22no—
332C2×C4×C41—22no—
333C2×C4×C41—22no—
334C2×C4×C41—22no—
335C2×C4×C41—22no—
336C2×C4×C41—21no—
337C2×C4×C41—22no—
338C2×C4×C41—21no—
339C2×C4×C41—21no—
340C2×C4×C41—44no—
341C2×C4×C41—44no—
342C2×C4×C41—44no—
343C2×C4×C41—48no—
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—41no—
362C2×C4×C41—41no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—41no—
366C2×C4×C41#12012yes—
367C2×C4×C41#12312yes—
368C2×C4×C41C22×D411yescharacteristic
369C2×C4×C41C22×D411yescharacteristic
370C2×C4×C41C2×#4111yescharacteristic
371C2×C4×C41C2×#4111yescharacteristic
372C2×C4×C41H(5,𝔽2)11yescharacteristic
373C2×C4×C41H(5,𝔽2)11yescharacteristic
374C8×C41—41no—
375C8×C41—41no—
376C8×C41—41no—
377C8×C41—41no—
378#24008C4111yesmaximal, characteristic, direct product factor, Sylow
379C22×C41—22no—
380C22×C41—22no—
381C22×C41—22no—
382C22×C41—22no—
383C22×C41—22no—
384C22×C41—22no—
385C22×C41—22no—
386C22×C41—22no—
387C22×C41—22no—
388C22×C41—416no—
389C22×C41—41no—
390C22×C41—41no—
391C22×C41—41no—
392C22×C41—41no—
393C22×C41—41no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—41no—
399C22×C41—41no—
400C22×C41—41no—
401C22×C41—42no—
402C22×C41—42no—
403C22×C41—42no—
404C22×C41—81no—
405C22×C41—81no—
406C22×C41—81no—
407C22×C41—81no—
408C22×C41C2×#12011yescharacteristic
409C22×C41C2×#12311yescharacteristic
410C22×C41#53411yescharacteristic
411C22×C41C2×#13511yescharacteristic
412C22×C41#57511yescharacteristic
413C22×C41#57511yescharacteristic
414C22×C41#57511yescharacteristic
415C4×C41—22no—
416C4×C41—22no—
417C4×C41—41no—
418C4×C41—42no—
419C4×C41—42no—
420C4×C41—42no—
421C4×C41—81no—
422C4×C41—81no—
423C4×C41—81no—
424C4×C41—81no—
425C4×C41#54611yescharacteristic
426C4×C41#54611yescharacteristic
427C4×C41#54611yescharacteristic
428C4×C41#54611yescharacteristic
429C2×#525C2×C4111yescharacteristic
430C2×#485C2×C4111yescharacteristic, complemented
431C2×#482C2×C4111yescharacteristic, complemented
432#2280C2×C4111yescharacteristic, complemented
433#2036C2×C4111yescharacteristic, complemented
434#2035C2×C4111yescharacteristic, complemented
435#2034C2×C4111yescharacteristic, complemented
436#2033C2×C4111yescharacteristic, complemented
437#1875C2×C4111yescharacteristic, complemented
438#1873C2×C4111yescharacteristic, complemented
439#1854C2×C4111yescharacteristic, complemented
440#1854C2×C4111yescharacteristic, complemented
441#1788C2×C4111yescharacteristic, complemented
442#1788C2×C4111yescharacteristic, complemented
443#1779C2×C4111yescharacteristic, complemented
444C2×C41—42no—
445C2×C41—42no—
446C2×C41—42no—
447C2×C41—82no—
448C2×C41#240511yescharacteristic
449C2×C41#300211yescharacteristic
450C2×C41#300511yescharacteristic
451C2×C41#309111yescharacteristic
452C2×C41#309311yescharacteristic
453C2×C41#319111yescharacteristic
454C2×C41#319711yescharacteristic
455C22×#41C22×C4111yescharacteristic
456C24×C4C22×C4111yescharacteristic
457#525—24no—
458#525—24no—
459C2×#123—21no—
460C2×C22⋊Q8C22×C4111yescharacteristic
461C2×C22⋊Q8C22×C4111yescharacteristic
462C2×#121C22×C4111yescharacteristic
463C2×#121C22×C4111yescharacteristic
464C2×#120—21no—
465C2×C4×D4—21no—
466C2×C4×D4—21no—
467C2×#117C22×C4111yescharacteristic
468C2×#117C22×C4111yescharacteristic
469C2×#117C22×C4111yescharacteristic
470#485—24no—
471#482—24no—
472C2×#107C22×C4111yescharacteristic, complemented
473C2×#107C22×C4111yescharacteristic, complemented
474C2×#106C22×C4111yescharacteristic, complemented
475C2×#106C22×C4111yescharacteristic, complemented
476C2×#103C22×C4111yescharacteristic, complemented
477C2×#103C22×C4111yescharacteristic, complemented
478C2×#103C22×C4111yescharacteristic, complemented
479C2×#103C22×C4111yescharacteristic, complemented
480C2×#102C22×C4111yescharacteristic, complemented
481C2×#102C22×C4111yescharacteristic, complemented
482C2×#102C22×C4111yescharacteristic, complemented
483C2×#102C22×C4111yescharacteristic, complemented
484C2×C22⋊C8C22×C4111yescharacteristic
485C2×C22⋊C8C22×C4111yescharacteristic
486C2×C22⋊C8C22×C4111yescharacteristic
487C2×C22⋊C8C22×C4111yescharacteristic
488C2×C22⋊C8C22×C4111yescharacteristic
489C2×C22⋊C8C22×C4111yescharacteristic
490#381—21no—
491#380C22×C4111yescharacteristic
492#380C22×C4111yescharacteristic
493#380C22×C4111yescharacteristic
494#380C22×C4111yescharacteristic
495#379—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498#340C22×C4111yescharacteristic, complemented
499#340C22×C4111yescharacteristic, complemented
500#340C22×C4111yescharacteristic, complemented
501#340C22×C4111yescharacteristic, complemented
502C41#2400811yescharacteristic, direct product factor, Sylow
503C25D4×C4111yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C4111yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C4111yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C4111yescharacteristic
523C23×C4D4×C4111yescharacteristic
524C23×C4D4×C4111yescharacteristic
525C23×C4C23×C4111yescharacteristic
526C23×C4C23×C4111yescharacteristic
527C23×C4C23×C4111yescharacteristic
528C22×C8C23×C4111yescharacteristic
529C22×C8C23×C4111yescharacteristic
530C22×C8C23×C4111yescharacteristic
531C22×C8C23×C4111yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C4114yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C4114yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C4111yescharacteristic
553C2×C4⋊C4C23×C4111yescharacteristic
554C2×C4⋊C4C23×C4111yescharacteristic
555C2×C4⋊C4C23×C4111yescharacteristic
556C2×C4⋊C4C23×C4111yescharacteristic
557C2×C4⋊C4C23×C4111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C4111yescharacteristic
603C24C2×D4×C4111yescharacteristic
604C24C2×D4×C4111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C4112yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C4112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C4111yescharacteristic
668C22×C4C2×D4×C4111yescharacteristic
669C22×C4C2×D4×C4112yes—
670C22×C4C2×D4×C4112yes—
671C22×C4C2×D4×C4111yescharacteristic
672C22×C4#41×C4112yes—
673C22×C4#41×C4112yes—
674C22×C4C24×C4111yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C4112yes—
700C4⋊C4C2×D4×C4112yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C4112yes—
748C23#123×C4112yes—
749C23#135×C4112yes—
750C23C22×D4×C4111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
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—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C4112yes—
807C2×C4#123×C4112yes—
808C2×C4C22×D4×C4111yescharacteristic
809C2×C4C22×D4×C4111yescharacteristic
810C2×C4C2×#41×C4111yescharacteristic
811C2×C4C2×#41×C4111yescharacteristic
812C2×C4H(5,𝔽2)×C4111yescharacteristic
813C2×C4H(5,𝔽2)×C4111yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C4111yescharacteristic
848C22C2×#123×C4111yescharacteristic
849C22C41×#53411yescharacteristic
850C22C2×#135×C4111yescharacteristic
851C22C41×#57511yescharacteristic
852C22C41×#57511yescharacteristic
853C22C41×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4C41×#54611yescharacteristic
865C4C41×#54611yescharacteristic
866C4C41×#54611yescharacteristic
867C4C41×#54611yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C41×#240511yescharacteristic
873C2C41×#300211yescharacteristic
874C2C41×#300511yescharacteristic
875C2C41×#309111yescharacteristic
876C2C41×#309311yescharacteristic
877C2C41×#319111yescharacteristic
878C2C41×#319711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C24×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#485C2semidirect
3. C2×C41×#482C2semidirect
4. C41×#2280C2semidirect
5. C41×#2036C2semidirect
6. C41×#2035C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1875C2semidirect
10. C41×#1873C2semidirect
11. C41×#1854C2semidirect
12. C41×#1854C2semidirect
13. C41×#1788C2semidirect
14. C41×#1788C2semidirect
15. C41×#1779C2semidirect
33. C2×#107×C41C22semidirect
34. C2×#107×C41C22semidirect
35. C2×#106×C41C22semidirect
36. C2×#106×C41C22semidirect
37. C2×#103×C41C22semidirect
38. C2×#103×C41C22semidirect
39. C2×#103×C41C22semidirect
40. C2×#103×C41C22semidirect
41. C2×#102×C41C22semidirect
42. C2×#102×C41C22semidirect
43. C2×#102×C41C22semidirect
44. C2×#102×C41C22semidirect
59. C41×#340C22semidirect
60. C41×#340C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
378. #24008C41direct (N × H)
430. C2×#485C2×C41semidirect
431. C2×#482C2×C41semidirect
432. #2280C2×C41semidirect
433. #2036C2×C41semidirect
434. #2035C2×C41semidirect
435. #2034C2×C41semidirect
436. #2033C2×C41semidirect
437. #1875C2×C41semidirect
438. #1873C2×C41semidirect
439. #1854C2×C41semidirect
440. #1854C2×C41semidirect
441. #1788C2×C41semidirect
442. #1788C2×C41semidirect
443. #1779C2×C41semidirect
472. C2×#107C22×C41semidirect
473. C2×#107C22×C41semidirect
474. C2×#106C22×C41semidirect
475. C2×#106C22×C41semidirect
476. C2×#103C22×C41semidirect
477. C2×#103C22×C41semidirect
478. C2×#103C22×C41semidirect
479. C2×#103C22×C41semidirect
480. C2×#102C22×C41semidirect
481. C2×#102C22×C41semidirect
482. C2×#102C22×C41semidirect
483. C2×#102C22×C41semidirect
498. #340C22×C41semidirect
499. #340C22×C41semidirect
500. #340C22×C41semidirect
501. #340C22×C41semidirect
502. C41#24008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5252
C2×C41×#4852
C2×C41×#4822
C41×#22802
C41×#20362
C41×#20352
C41×#20342
C41×#20332
C41×#18752
C41×#18732
C41×#18542
C41×#17882
C41×#17792
#2400841