Finite Group Databasebeta

← C41×#24017 #23800218

Subgroups — C41×#24017 #23800218

Order 10496.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#537C211yesmaximal, characteristic
2C2×C41×#485C211yesmaximal, characteristic, complemented
3C2×C41×#482C211yesmaximal, characteristic, complemented
4C41×#2311C211yesmaximal, characteristic, complemented
5C41×#2036C211yesmaximal, characteristic, complemented
6C41×#2035C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1874C211yesmaximal, characteristic, complemented
10C41×#1872C211yesmaximal, characteristic, complemented
11C41×#1853C211yesmaximal, characteristic, complemented
12C41×#1852C211yesmaximal, characteristic, complemented
13C41×#1788C211yesmaximal, characteristic, complemented
14C41×#1788C211yesmaximal, characteristic, complemented
15C41×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C41×#537—24no—
19C41×#537—24no—
20C2×C22⋊Q8×C41—21no—
21C2×C22⋊Q8×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41—21no—
24C2×#121×C41—21no—
25C2×#121×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×#117×C41C2211yescharacteristic
29C22×C4⋊C4×C41C2211yescharacteristic
30C22×C4⋊C4×C41C2211yescharacteristic
31C41×#485—24no—
32C41×#482—24no—
33C2×#107×C41C2211yescharacteristic
34C2×#107×C41C2211yescharacteristic
35C2×#106×C41C2211yescharacteristic
36C2×#106×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
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×#391—21no—
52C41×#390—21no—
53C41×#386—21no—
54C41×#386—21no—
55C41×#380C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C41×#380C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C2×#41×C41—22no—
64C2×#41×C41—22no—
65C2×#41×C41—22no—
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—22no—
69C2×#41×C41—22no—
70C2×#41×C41—22no—
71C2×#41×C41—41no—
72C2×#41×C41—41no—
73C2×#41×C41—41no—
74C2×#41×C41—41no—
75C22×Q8×C41D411yescharacteristic
76C22×Q8×C41C2311yescharacteristic
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41D411yescharacteristic
81C22×D4×C41D411yescharacteristic
82C22×D4×C41D411yescharacteristic
83C22×D4×C41C2311yescharacteristic
84C23×C4×C41—21no—
85C23×C4×C41—21no—
86C23×C4×C41—21no—
87C23×C4×C41C2311yescharacteristic
88C23×C4×C41C2311yescharacteristic
89C23×C4×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91C22×C8×C41C2311yescharacteristic
92C22×C8×C41C2311yescharacteristic
93C22×C8×C41C2311yescharacteristic
94C22⋊Q8×C41—28no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—22no—
98C22⋊Q8×C41D414yes—
99#121×C41—28no—
100#121×C41—28no—
101#121×C41—28no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—22no—
105#121×C41D414yes—
106#117×C41—22no—
107#117×C41—22no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—22no—
112C2×C4⋊C4×C41—22no—
113C2×C4⋊C4×C41—21no—
114C2×C4⋊C4×C41—41no—
115C2×C4⋊C4×C41—41no—
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
119C2×C4⋊C4×C41C2311yescharacteristic
120C2×C4⋊C4×C41C2311yescharacteristic
121C2×C4⋊C4×C41C2311yescharacteristic
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×C22⋊C4×C41—21no—
130C2×C22⋊C4×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—21no—
155C24×C41C2×D411yescharacteristic
156C24×C41C2×D411yescharacteristic
157C24×C41C2×D411yescharacteristic
158#41×C41—44no—
159#41×C41—44no—
160#41×C41—44no—
161#41×C41—44no—
162#41×C41—44no—
163#41×C41—44no—
164#41×C41—44no—
165#41×C41—44no—
166C2×Q8×C41—22no—
167C2×Q8×C41—22no—
168C2×Q8×C41—21no—
169C2×Q8×C41—21no—
170C2×Q8×C41—21no—
171C2×Q8×C41—21no—
172C2×Q8×C41—21no—
173C2×Q8×C41—41no—
174C2×Q8×C41C2×D412yes—
175C2×D4×C41—24no—
176C2×D4×C41—22no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—22no—
180C2×D4×C41—24no—
181C2×D4×C41—24no—
182C2×D4×C41—22no—
183C2×D4×C41—22no—
184C2×D4×C41—21no—
185C2×D4×C41—21no—
186C2×D4×C41—21no—
187C2×D4×C41—21no—
188C2×D4×C41—21no—
189C2×D4×C41—41no—
190C2×D4×C41—41no—
191C2×D4×C41—41no—
192C2×D4×C41—42no—
193C2×D4×C41—42no—
194C2×D4×C41—81no—
195C2×D4×C41—81no—
196C2×D4×C41—81no—
197C2×D4×C41—81no—
198C2×D4×C41C2×D412yes—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—24no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—24no—
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—21no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—42no—
223C22×C4×C41—42no—
224C22×C4×C41—42no—
225C22×C4×C41—81no—
226C22×C4×C41—81no—
227C22×C4×C41—81no—
228C22×C4×C41—81no—
229C22×C4×C41C2×D411yescharacteristic
230C22×C4×C41C2×D411yescharacteristic
231C22×C4×C41C2×D412yes—
232C22×C4×C41C2×D412yes—
233C22×C4×C41C2×D411yescharacteristic
234C22×C4×C41#4112yes—
235C22×C4×C41#4112yes—
236C22×C4×C41C2411yescharacteristic
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—
247C2×C8×C41—21no—
248C2×C8×C41—21no—
249C4⋊C4×C41—24no—
250C4⋊C4×C41—24no—
251C4⋊C4×C41—24no—
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×C41—21no—
260C4⋊C4×C41—21no—
261C4⋊C4×C41—21no—
262C4⋊C4×C41—42no—
263C4⋊C4×C41C2×D412yes—
264C4⋊C4×C41C2×D412yes—
265C22⋊C4×C41—24no—
266C22⋊C4×C41—24no—
267C22⋊C4×C41—24no—
268C22⋊C4×C41—24no—
269C22⋊C4×C41—42no—
270C22⋊C4×C41—81no—
271C22⋊C4×C41—81no—
272C22⋊C4×C41—81no—
273C22⋊C4×C41—81no—
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—22no—
289C23×C41—21no—
290C23×C41—21no—
291C23×C41—21no—
292C23×C41—21no—
293C23×C41—21no—
294C23×C41—21no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41—41no—
299C23×C41—41no—
300C23×C41—41no—
301C23×C41#12012yes—
302C23×C41#12312yes—
303C23×C41C22×D411yescharacteristic
304Q8×C41—22no—
305Q8×C41—22no—
306Q8×C41—44no—
307Q8×C41—41no—
308Q8×C41—41no—
309D4×C41—22no—
310D4×C41—22no—
311D4×C41—44no—
312D4×C41—44no—
313D4×C41—44no—
314D4×C41—48no—
315D4×C41—41no—
316D4×C41—41no—
317D4×C41—84no—
318D4×C41—84no—
319C2×C4×C41—21no—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—22no—
324C2×C4×C41—22no—
325C2×C4×C41—22no—
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—21no—
335C2×C4×C41—21no—
336C2×C4×C41—21no—
337C2×C4×C41—48no—
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—84no—
361C2×C4×C41—84no—
362C2×C4×C41#12012yes—
363C2×C4×C41#12312yes—
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#24017C4111yesmaximal, characteristic, direct product factor, Sylow
375C22×C41—22no—
376C22×C41—22no—
377C22×C41—22no—
378C22×C41—22no—
379C22×C41—22no—
380C22×C41—22no—
381C22×C41—41no—
382C22×C41—41no—
383C22×C41—41no—
384C22×C41—41no—
385C22×C41—41no—
386C22×C41—41no—
387C22×C41—41no—
388C22×C41—41no—
389C22×C41—41no—
390C22×C41—41no—
391C22×C41—42no—
392C22×C41—41no—
393C22×C41—41no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—42no—
397C22×C41—41no—
398C22×C41—42no—
399C22×C41—81no—
400C22×C41—81no—
401C22×C41—81no—
402C22×C41—81no—
403C22×C41C2×#12011yescharacteristic
404C22×C41C2×#12311yescharacteristic
405C22×C41#53411yescharacteristic
406C22×C41#57611yescharacteristic
407C22×C41#57711yescharacteristic
408C22×C41#57711yescharacteristic
409C22×C41#57811yescharacteristic
410C4×C41—22no—
411C4×C41—22no—
412C4×C41—41no—
413C4×C41—42no—
414C4×C41—42no—
415C4×C41—42no—
416C4×C41—81no—
417C4×C41—81no—
418C4×C41—81no—
419C4×C41—81no—
420C4×C41#54611yescharacteristic
421C4×C41#54611yescharacteristic
422C4×C41#54611yescharacteristic
423C4×C41#54611yescharacteristic
424C2×#537C2×C4111yescharacteristic
425C2×#485C2×C4111yescharacteristic, complemented
426C2×#482C2×C4111yescharacteristic, complemented
427#2311C2×C4111yescharacteristic, complemented
428#2036C2×C4111yescharacteristic, complemented
429#2035C2×C4111yescharacteristic, complemented
430#2034C2×C4111yescharacteristic, complemented
431#2033C2×C4111yescharacteristic, complemented
432#1874C2×C4111yescharacteristic, complemented
433#1872C2×C4111yescharacteristic, complemented
434#1853C2×C4111yescharacteristic, complemented
435#1852C2×C4111yescharacteristic, complemented
436#1788C2×C4111yescharacteristic, complemented
437#1788C2×C4111yescharacteristic, complemented
438#1780C2×C4111yescharacteristic, complemented
439C2×C41—42no—
440C2×C41—42no—
441C2×C41—81no—
442C2×C41—82no—
443C2×C41#240511yescharacteristic
444C2×C41#301211yescharacteristic
445C2×C41#301311yescharacteristic
446C2×C41#309811yescharacteristic
447C2×C41#309911yescharacteristic
448C2×C41#319811yescharacteristic
449C2×C41#320111yescharacteristic
450C22×#41C22×C4111yescharacteristic
451C22×#41C22×C4111yescharacteristic
452#537—24no—
453#537—24no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8C22×C4111yescharacteristic
456C2×C22⋊Q8C22×C4111yescharacteristic
457C2×#121—21no—
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C22×C4111yescharacteristic
461C2×#121C22×C4111yescharacteristic
462C2×#117C22×C4111yescharacteristic
463C22×C4⋊C4C22×C4111yescharacteristic
464C22×C4⋊C4C22×C4111yescharacteristic
465#485—24no—
466#482—24no—
467C2×#107C22×C4111yescharacteristic
468C2×#107C22×C4111yescharacteristic
469C2×#106C22×C4111yescharacteristic
470C2×#106C22×C4111yescharacteristic
471C2×#103C22×C4111yescharacteristic
472C2×#103C22×C4111yescharacteristic
473C2×#103C22×C4111yescharacteristic
474C2×#103C22×C4111yescharacteristic
475C2×#102C22×C4111yescharacteristic
476C2×#102C22×C4111yescharacteristic
477C2×#102C22×C4111yescharacteristic
478C2×#102C22×C4111yescharacteristic
479C2×C22⋊C8C22×C4111yescharacteristic
480C2×C22⋊C8C22×C4111yescharacteristic
481C2×C22⋊C8C22×C4111yescharacteristic
482C2×C22⋊C8C22×C4111yescharacteristic
483C2×C22⋊C8C22×C4111yescharacteristic
484C2×C22⋊C8C22×C4111yescharacteristic
485#391—21no—
486#390—21no—
487#386—21no—
488#386—21no—
489#380C22×C4111yescharacteristic
490#380C22×C4111yescharacteristic
491#380C22×C4111yescharacteristic
492#380C22×C4111yescharacteristic
493#340C22×C4111yescharacteristic
494#340C22×C4111yescharacteristic
495#340C22×C4111yescharacteristic
496#340C22×C4111yescharacteristic
497C41#2401711yescharacteristic, direct product factor, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C4111yescharacteristic
511C22×Q8C23×C4111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C4111yescharacteristic
516C22×D4D4×C4111yescharacteristic
517C22×D4D4×C4111yescharacteristic
518C22×D4C23×C4111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C4111yescharacteristic
523C23×C4C23×C4111yescharacteristic
524C23×C4C23×C4111yescharacteristic
525C22×C8C23×C4111yescharacteristic
526C22×C8C23×C4111yescharacteristic
527C22×C8C23×C4111yescharacteristic
528C22×C8C23×C4111yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C4114yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C4114yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C4111yescharacteristic
552C2×C4⋊C4C23×C4111yescharacteristic
553C2×C4⋊C4C23×C4111yescharacteristic
554C2×C4⋊C4C23×C4111yescharacteristic
555C2×C4⋊C4C23×C4111yescharacteristic
556C2×C4⋊C4C23×C4111yescharacteristic
557C2×C22⋊C4—21no—
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×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C4111yescharacteristic
591C24C2×D4×C4111yescharacteristic
592C24C2×D4×C4111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C4112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C4112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
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—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C4111yescharacteristic
665C22×C4C2×D4×C4111yescharacteristic
666C22×C4C2×D4×C4112yes—
667C22×C4C2×D4×C4112yes—
668C22×C4C2×D4×C4111yescharacteristic
669C22×C4#41×C4112yes—
670C22×C4#41×C4112yes—
671C22×C4C24×C4111yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
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—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
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—42no—
698C4⋊C4C2×D4×C4112yes—
699C4⋊C4C2×D4×C4112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C4112yes—
737C23#123×C4112yes—
738C23C22×D4×C4111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
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—84no—
796C2×C4—84no—
797C2×C4#120×C4112yes—
798C2×C4#123×C4112yes—
799C2×C4C22×D4×C4111yescharacteristic
800C2×C4C22×D4×C4111yescharacteristic
801C2×C4C2×#41×C4111yescharacteristic
802C2×C4C2×#41×C4111yescharacteristic
803C2×C4H(5,𝔽2)×C4111yescharacteristic
804C2×C4H(5,𝔽2)×C4111yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C4111yescharacteristic
838C22C2×#123×C4111yescharacteristic
839C22C41×#53411yescharacteristic
840C22C41×#57611yescharacteristic
841C22C41×#57711yescharacteristic
842C22C41×#57711yescharacteristic
843C22C41×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C41×#54611yescharacteristic
855C4C41×#54611yescharacteristic
856C4C41×#54611yescharacteristic
857C4C41×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C41×#240511yescharacteristic
863C2C41×#301211yescharacteristic
864C2C41×#301311yescharacteristic
865C2C41×#309811yescharacteristic
866C2C41×#309911yescharacteristic
867C2C41×#319811yescharacteristic
868C2C41×#320111yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C22×#41×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×#2311C2semidirect
5. C41×#2036C2semidirect
6. C41×#2035C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1874C2semidirect
10. C41×#1872C2semidirect
11. C41×#1853C2semidirect
12. C41×#1852C2semidirect
13. C41×#1788C2semidirect
14. C41×#1788C2semidirect
15. C41×#1780C2semidirect
374. #24017C41direct (N × H)
425. C2×#485C2×C41semidirect
426. C2×#482C2×C41semidirect
427. #2311C2×C41semidirect
428. #2036C2×C41semidirect
429. #2035C2×C41semidirect
430. #2034C2×C41semidirect
431. #2033C2×C41semidirect
432. #1874C2×C41semidirect
433. #1872C2×C41semidirect
434. #1853C2×C41semidirect
435. #1852C2×C41semidirect
436. #1788C2×C41semidirect
437. #1788C2×C41semidirect
438. #1780C2×C41semidirect
497. C41#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5372
C2×C41×#4852
C2×C41×#4822
C41×#23112
C41×#20362
C41×#20352
C41×#20342
C41×#20332
C41×#18742
C41×#18722
C41×#18532
C41×#18522
C41×#17882
C41×#17802
#2401741