Finite Group Databasebeta

← C41×#24140 #23800341

Subgroups — C41×#24140 #23800341

Order 10496.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic, complemented
2C41×#2848C211yesmaximal, characteristic, complemented
3C41×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C41C211yesmaximal, characteristic, complemented
5C41×#2044C212yesmaximal, complemented
6C41×#2021C212yesmaximal, complemented
7C41×#1996C211yesmaximal, characteristic, complemented
8C41×#1964C211yesmaximal, characteristic, complemented
9C41×#1889C212yesmaximal, complemented
10C41×#1867C212yesmaximal, complemented
11C41×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C41C2211yescharacteristic
13C41×#553—21no—
14C41×#553—22no—
15C41×#552—21no—
16C41×#551—22no—
17C41×#548—21no—
18C41×#546—21no—
19C41×#539—21no—
20C41×#538—21no—
21C41×#534C2212yes—
22C41×#529—21no—
23C41×#525—21no—
24C2×C22⋊Q8×C41—21no—
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41—21no—
27C2×#121×C41C2211yescharacteristic
28C2×#120×C41C2211yescharacteristic
29C2×#120×C41C2212yes—
30C41×#518C2212yes—
31C2×C4×D4×C41—21no—
32C2×C4×D4×C41C2211yescharacteristic
33C2×#99×C41C2212yes—
34C2×#99×C41C2212yes—
35C2×#99×C41C2212yes—
36C41×#386—21no—
37C41×#386—22no—
38C41×#386C2211yescharacteristic
39C41×#386C2212yes—
40C41×#385—21no—
41C41×#385—22no—
42C41×#385C2211yescharacteristic
43C41×#385C2212yes—
44C41×#380—21no—
45C41×#380—21no—
46C41×#380C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#379C2212yes—
49C41×#379C2211yescharacteristic
50C4×C22⋊C4×C41—21no—
51C4×C22⋊C4×C41C2211yescharacteristic
52C41×#342C2212yes—
53C41×#342C2212yes—
54C41×#342C2212yes—
55C25×C41C2311yescharacteristic
56C2×#41×C41—21no—
57C22×Q8×C41D411yescharacteristic, complemented
58C22×D4×C41—21no—
59C22×D4×C41—22no—
60C22×D4×C41D411yescharacteristic, complemented
61C22×D4×C41C2311yescharacteristic
62C22×D4×C41C2312yes—
63C23×C4×C41—21no—
64C23×C4×C41—21no—
65C23×C4×C41—21no—
66C23×C4×C41—21no—
67C23×C4×C41—21no—
68C23×C4×C41—21no—
69C23×C4×C41—44no—
70C23×C4×C41D411yescharacteristic, complemented
71C23×C4×C41C2311yescharacteristic
72C23×C4×C41C2311yescharacteristic
73#126×C41—22no—
74#126×C41—22no—
75#126×C41—22no—
76#125×C41—21no—
77#125×C41—22no—
78#124×C41—21no—
79#124×C41—22no—
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—22no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—21no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—44no—
92#121×C41—21no—
93#121×C41—22no—
94#121×C41—21no—
95#121×C41—21no—
96#121×C41—21no—
97#121×C41—21no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—44no—
101#120×C41—22no—
102#120×C41—22no—
103#120×C41—22no—
104#120×C41—22no—
105#120×C41—24no—
106#120×C41—42no—
107C4×Q8×C41—21no—
108C4×D4×C41—22no—
109C4×D4×C41—21no—
110C4×D4×C41—21no—
111C4×D4×C41—21no—
112C4×D4×C41—21no—
113C4×D4×C41—21no—
114C4×D4×C41—22no—
115C4×D4×C41—22no—
116C4×D4×C41—22no—
117C4×D4×C41—22no—
118C4×D4×C41—44no—
119#117×C41—21no—
120#117×C41—22no—
121#117×C41—22no—
122C2×C4⋊C4×C41—21no—
123C2×C4⋊C4×C41—21no—
124C2×C4⋊C4×C41—21no—
125C2×C4⋊C4×C41—22no—
126C2×C4⋊C4×C41D411yescharacteristic, complemented
127C2×C4⋊C4×C41D411yescharacteristic, complemented
128C2×C4⋊C4×C41D411yescharacteristic, complemented
129C2×C4⋊C4×C41D412yescomplemented
130C2×C22⋊C4×C41—22no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—22no—
134C2×C22⋊C4×C41—21no—
135C2×C22⋊C4×C41—22no—
136C2×C22⋊C4×C41—22no—
137C2×C22⋊C4×C41—21no—
138C2×C22⋊C4×C41—22no—
139C2×C22⋊C4×C41D411yescharacteristic, complemented
140C2×C22⋊C4×C41D412yescomplemented
141C2×C22⋊C4×C41C2312yes—
142C2×C22⋊C4×C41C2311yescharacteristic
143C2×C22⋊C4×C41C2312yes—
144C2×C22⋊C4×C41C2311yescharacteristic
145C2×C22⋊C4×C41C2312yes—
146C2×C22⋊C4×C41C2311yescharacteristic
147C2×C42×C41—21no—
148C2×C42×C41D411yescharacteristic, complemented
149#99×C41—24no—
150#99×C41—42no—
151#99×C41—42no—
152#95×C41—21no—
153#95×C41—21no—
154#95×C41—21no—
155#95×C41—22no—
156#95×C41—22no—
157#95×C41—21no—
158#95×C41—21no—
159C24×C41—21no—
160C24×C41—21no—
161C24×C41—21no—
162C24×C41—21no—
163C24×C41—21no—
164C24×C41—21no—
165C24×C41—42no—
166C24×C41—42no—
167C24×C41C2×D412yes—
168C24×C41C2×D411yescharacteristic
169C24×C41#4112yescomplemented
170C24×C41C2411yescharacteristic
171#41×C41—82no—
172C2×Q8×C41—21no—
173C2×Q8×C41—21no—
174C2×Q8×C41—42no—
175C2×D4×C41—24no—
176C2×D4×C41—21no—
177C2×D4×C41—22no—
178C2×D4×C41—21no—
179C2×D4×C41—22no—
180C2×D4×C41—22no—
181C2×D4×C41—21no—
182C2×D4×C41—21no—
183C2×D4×C41—22no—
184C2×D4×C41—21no—
185C2×D4×C41—22no—
186C2×D4×C41—21no—
187C2×D4×C41—22no—
188C2×D4×C41—22no—
189C2×D4×C41—22no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
192C2×D4×C41—42no—
193C2×D4×C41—42no—
194C2×D4×C41—42no—
195C2×D4×C41—44no—
196C2×D4×C41—44no—
197C2×D4×C41—44no—
198C22×C4×C41—24no—
199C22×C4×C41—24no—
200C22×C4×C41—24no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—22no—
206C22×C4×C41—22no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—22no—
211C22×C4×C41—22no—
212C22×C4×C41—42no—
213C22×C4×C41—42no—
214C22×C4×C41—42no—
215C22×C4×C41—42no—
216C22×C4×C41—42no—
217C22×C4×C41—42no—
218C22×C4×C41—42no—
219C22×C4×C41—42no—
220C22×C4×C41—42no—
221C22×C4×C41—42no—
222C22×C4×C41—42no—
223C22×C4×C41—42no—
224C22×C4×C41—41no—
225C22×C4×C41—41no—
226C22×C4×C41—41no—
227C22×C4×C41—41no—
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41C2×D412yes—
230C22×C4×C41C2×D411yescharacteristic
231C22×C4×C41C2×D411yescharacteristic
232C22×C4×C41C2×D411yescharacteristic
233C22×C4×C41C2×D411yescharacteristic
234C22×C4×C41C2×D412yes—
235C22×C4×C41C2×D411yescharacteristic
236C22×C4×C41C2×D412yes—
237C22×C4×C41C2×D411yescharacteristic
238C22×C4×C41C2×D411yescharacteristic
239C22×C4×C41C2×D411yescharacteristic
240C4⋊C4×C41—22no—
241C4⋊C4×C41—22no—
242C4⋊C4×C41—22no—
243C4⋊C4×C41—22no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41—22no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—21no—
250C4⋊C4×C41—22no—
251C4⋊C4×C41—21no—
252C4⋊C4×C41—42no—
253C4⋊C4×C41—42no—
254C4⋊C4×C41—42no—
255C4⋊C4×C41—44no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—24no—
259C22⋊C4×C41—22no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—22no—
262C22⋊C4×C41—22no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—22no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—22no—
267C22⋊C4×C41—21no—
268C22⋊C4×C41—22no—
269C22⋊C4×C41—21no—
270C22⋊C4×C41—21no—
271C22⋊C4×C41—22no—
272C22⋊C4×C41—22no—
273C22⋊C4×C41—22no—
274C22⋊C4×C41—21no—
275C22⋊C4×C41—22no—
276C22⋊C4×C41—22no—
277C22⋊C4×C41—21no—
278C22⋊C4×C41—44no—
279C22⋊C4×C41—42no—
280C22⋊C4×C41—44no—
281C22⋊C4×C41—44no—
282C22⋊C4×C41—42no—
283C22⋊C4×C41—42no—
284C22⋊C4×C41—44no—
285C22⋊C4×C41#4112yescomplemented
286C42×C41—22no—
287C42×C41—22no—
288C42×C41—21no—
289C42×C41—21no—
290C42×C41—42no—
291C23×C41—22no—
292C23×C41—22no—
293C23×C41—22no—
294C23×C41—22no—
295C23×C41—22no—
296C23×C41—22no—
297C23×C41—22no—
298C23×C41—22no—
299C23×C41—22no—
300C23×C41—21no—
301C23×C41—22no—
302C23×C41—21no—
303C23×C41—21no—
304C23×C41—22no—
305C23×C41—22no—
306C23×C41—41no—
307C23×C41—44no—
308C23×C41—41no—
309C23×C41—41no—
310C23×C41—41no—
311C23×C41—41no—
312C23×C41—41no—
313C23×C41—41no—
314C23×C41—41no—
315C23×C41—44no—
316C23×C41—44no—
317C23×C41—44no—
318C23×C41—41no—
319C23×C41—41no—
320C23×C41—42no—
321C23×C41—42no—
322C23×C41—41no—
323C23×C41—41no—
324C23×C41—41no—
325C23×C41—41no—
326C23×C41C22×D411yescharacteristic
327C23×C41C22×D411yescharacteristic
328C23×C41C22×D411yescharacteristic
329C23×C41C2×#4111yescharacteristic
330C23×C41C2×#4111yescharacteristic
331C23×C41H(5,𝔽2)11yescharacteristic
332C23×C412−1+411yescharacteristic
333Q8×C41—42no—
334Q8×C41—81no—
335D4×C41—48no—
336D4×C41—42no—
337D4×C41—42no—
338D4×C41—41no—
339D4×C41—41no—
340D4×C41—41no—
341D4×C41—42no—
342D4×C41—42no—
343D4×C41—41no—
344D4×C41—42no—
345D4×C41—81no—
346D4×C41—82no—
347D4×C41—82no—
348D4×C41—88no—
349C2×C4×C41—22no—
350C2×C4×C41—22no—
351C2×C4×C41—22no—
352C2×C4×C41—22no—
353C2×C4×C41—22no—
354C2×C4×C41—22no—
355C2×C4×C41—21no—
356C2×C4×C41—22no—
357C2×C4×C41—21no—
358C2×C4×C41—21no—
359C2×C4×C41—22no—
360C2×C4×C41—22no—
361C2×C4×C41—21no—
362C2×C4×C41—22no—
363C2×C4×C41—21no—
364C2×C4×C41—22no—
365C2×C4×C41—22no—
366C2×C4×C41—41no—
367C2×C4×C41—41no—
368C2×C4×C41—41no—
369C2×C4×C41—44no—
370C2×C4×C41—44no—
371C2×C4×C41—44no—
372C2×C4×C41—41no—
373C2×C4×C41—41no—
374C2×C4×C41—41no—
375C2×C4×C41—41no—
376C2×C4×C41—41no—
377C2×C4×C41—41no—
378C2×C4×C41—44no—
379C2×C4×C41—42no—
380C2×C4×C41—41no—
381C2×C4×C41—42no—
382C2×C4×C41—41no—
383C2×C4×C41—42no—
384C2×C4×C41—41no—
385C2×C4×C41—42no—
386C2×C4×C41—42no—
387C2×C4×C41—42no—
388C2×C4×C41—41no—
389C2×C4×C41—42no—
390C2×C4×C41—41no—
391C2×C4×C41—42no—
392C2×C4×C41—42no—
393C2×C4×C41—81no—
394C2×C4×C41—82no—
395C2×C4×C41—82no—
396C2×C4×C41#12011yescharacteristic
397C2×C4×C41#12011yescharacteristic
398C2×C4×C41#12011yescharacteristic
399C2×C4×C41#12011yescharacteristic
400#24140C4111yesmaximal, characteristic, direct product factor, Sylow
401C22×C41—21no—
402C22×C41—21no—
403C22×C41—21no—
404C22×C41—21no—
405C22×C41—21no—
406C22×C41—21no—
407C22×C41—24no—
408C22×C41—24no—
409C22×C41—24no—
410C22×C41—41no—
411C22×C41—41no—
412C22×C41—41no—
413C22×C41—41no—
414C22×C41—42no—
415C22×C41—42no—
416C22×C41—42no—
417C22×C41—42no—
418C22×C41—42no—
419C22×C41—42no—
420C22×C41—42no—
421C22×C41—42no—
422C22×C41—42no—
423C22×C41—42no—
424C22×C41—42no—
425C22×C41—42no—
426C22×C41—42no—
427C22×C41—41no—
428C22×C41—42no—
429C22×C41—41no—
430C22×C41—42no—
431C22×C41—42no—
432C22×C41—41no—
433C22×C41—82no—
434C22×C41—81no—
435C22×C41—82no—
436C22×C41C2×#12011yescharacteristic
437C22×C41#52511yescharacteristic
438C22×C41#53711yescharacteristic
439C22×C41#54611yescharacteristic
440C22×C41#54711yescharacteristic
441C22×C41#54811yescharacteristic
442C22×C41#55011yescharacteristic
443C4×C41—21no—
444C4×C41—21no—
445C4×C41—21no—
446C4×C41—42no—
447C4×C41—41no—
448C4×C41—42no—
449C4×C41—42no—
450C4×C41—41no—
451C4×C41—42no—
452C4×C41—41no—
453C4×C41—42no—
454C4×C41—82no—
455C4×C41—81no—
456C4×C41—82no—
457C4×C41B(4,𝔽2)12yes—
458#3505C2×C4111yescharacteristic, complemented
459#2848C2×C4111yescharacteristic, complemented
460#2847C2×C4111yescharacteristic, complemented
461C4×#120C2×C4111yescharacteristic, complemented
462#2044C2×C4112yescomplemented
463#2021C2×C4112yescomplemented
464#1996C2×C4111yescharacteristic, complemented
465#1964C2×C4111yescharacteristic, complemented
466#1889C2×C4112yescomplemented
467#1867C2×C4112yescomplemented
468#1799C2×C4111yescharacteristic, complemented
469C2×C41—21no—
470C2×C41—21no—
471C2×C41—21no—
472C2×C41—21no—
473C2×C41—21no—
474C2×C41—21no—
475C2×C41—44no—
476C2×C41—81no—
477C2×C41—82no—
478C2×C41#240711yescharacteristic
479C2×C41C2×B(4,𝔽2)11yescharacteristic
480C2×C41#302511yescharacteristic
481C24×C4C22×C4111yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C4112yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C4111yescharacteristic
495C2×#121—21no—
496C2×#121C22×C4111yescharacteristic
497C2×#120C22×C4111yescharacteristic
498C2×#120C22×C4112yes—
499#518C22×C4112yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C4111yescharacteristic
502C2×#99C22×C4112yes—
503C2×#99C22×C4112yes—
504C2×#99C22×C4112yes—
505#386—22no—
506#386—21no—
507#386C22×C4112yes—
508#386C22×C4111yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C4112yes—
512#385C22×C4111yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C4111yescharacteristic
516#380C22×C4111yescharacteristic
517#379C22×C4112yes—
518#379C22×C4111yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C4111yescharacteristic
521#342C22×C4112yes—
522#342C22×C4112yes—
523#342C22×C4112yes—
524C41#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C4111yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C4111yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C4111yescharacteristic, complemented
531C22×D4C23×C4111yescharacteristic
532C22×D4C23×C4112yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C4111yescharacteristic, complemented
541C23×C4C23×C4111yescharacteristic
542C23×C4C23×C4111yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C4111yescharacteristic, complemented
597C2×C4⋊C4D4×C4111yescharacteristic, complemented
598C2×C4⋊C4D4×C4111yescharacteristic, complemented
599C2×C4⋊C4D4×C4112yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C4111yescharacteristic, complemented
610C2×C22⋊C4D4×C4112yescomplemented
611C2×C22⋊C4C23×C4112yes—
612C2×C22⋊C4C23×C4111yescharacteristic
613C2×C22⋊C4C23×C4112yes—
614C2×C22⋊C4C23×C4111yescharacteristic
615C2×C22⋊C4C23×C4112yes—
616C2×C22⋊C4C23×C4111yescharacteristic
617C2×C42—21no—
618C2×C42D4×C4111yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C4112yes—
638C24C2×D4×C4111yescharacteristic
639C24#41×C4112yescomplemented
640C24C24×C4111yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C4111yescharacteristic
699C22×C4C2×D4×C4112yes—
700C22×C4C2×D4×C4111yescharacteristic
701C22×C4C2×D4×C4111yescharacteristic
702C22×C4C2×D4×C4111yescharacteristic
703C22×C4C2×D4×C4111yescharacteristic
704C22×C4C2×D4×C4112yes—
705C22×C4C2×D4×C4111yescharacteristic
706C22×C4C2×D4×C4112yes—
707C22×C4C2×D4×C4111yescharacteristic
708C22×C4C2×D4×C4111yescharacteristic
709C22×C4C2×D4×C4111yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C4112yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C4111yescharacteristic
797C23C22×D4×C4111yescharacteristic
798C23C22×D4×C4111yescharacteristic
799C23C2×#41×C4111yescharacteristic
800C23C2×#41×C4111yescharacteristic
801C23H(5,𝔽2)×C4111yescharacteristic
802C232−1+4×C4111yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C4111yescharacteristic
867C2×C4#120×C4111yescharacteristic
868C2×C4#120×C4111yescharacteristic
869C2×C4#120×C4111yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C4111yescharacteristic
906C22C41×#52511yescharacteristic
907C22C41×#53711yescharacteristic
908C22C41×#54611yescharacteristic
909C22C41×#54711yescharacteristic
910C22C41×#54811yescharacteristic
911C22C41×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C41×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C41×#240711yescharacteristic
937C2C2×C41×B(4,𝔽2)11yescharacteristic
938C2C41×#302511yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
LCSG ▷ C24 ▷ 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×#3505C2semidirect
2. C41×#2848C2semidirect
3. C41×#2847C2semidirect
4. C4×#120×C41C2semidirect
5. C41×#2044C2semidirect
6. C41×#2021C2semidirect
7. C41×#1996C2semidirect
8. C41×#1964C2semidirect
9. C41×#1889C2semidirect
10. C41×#1867C2semidirect
11. C41×#1799C2semidirect
57. C22×Q8×C41D4semidirect
60. C22×D4×C41D4semidirect
70. C23×C4×C41D4semidirect
126. C2×C4⋊C4×C41D4semidirect
127. C2×C4⋊C4×C41D4semidirect
128. C2×C4⋊C4×C41D4semidirect
129. C2×C4⋊C4×C41D4semidirect
139. C2×C22⋊C4×C41D4semidirect
140. C2×C22⋊C4×C41D4semidirect
148. C2×C42×C41D4semidirect
169. C24×C41#41semidirect
285. C22⋊C4×C41#41semidirect
400. #24140C41direct (N × H)
458. #3505C2×C41semidirect
459. #2848C2×C41semidirect
460. #2847C2×C41semidirect
461. C4×#120C2×C41semidirect
462. #2044C2×C41semidirect
463. #2021C2×C41semidirect
464. #1996C2×C41semidirect
465. #1964C2×C41semidirect
466. #1889C2×C41semidirect
467. #1867C2×C41semidirect
468. #1799C2×C41semidirect
524. C41#24140direct (N × H)
527. C22×Q8D4×C41semidirect
530. C22×D4D4×C41semidirect
540. C23×C4D4×C41semidirect
596. C2×C4⋊C4D4×C41semidirect
597. C2×C4⋊C4D4×C41semidirect
598. C2×C4⋊C4D4×C41semidirect
599. C2×C4⋊C4D4×C41semidirect
609. C2×C22⋊C4D4×C41semidirect
610. C2×C22⋊C4D4×C41semidirect
618. C2×C42D4×C41semidirect
639. C24#41×C41semidirect
755. C22⋊C4#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35052
C41×#28482
C41×#28472
C4×#120×C412
C41×#20442
C41×#20212
C41×#19962
C41×#19642
C41×#18892
C41×#18672
C41×#17992
#2414041