Finite Group Databasebeta

← C41×#24405 #23800606

Subgroups — C41×#24405 #23800606

Order 10496.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3484C211yesmaximal, characteristic
2C2×C41×#458C211yesmaximal, characteristic, complemented
3C22×#99×C41C211yesmaximal, characteristic, complemented
4C41×#2412C212yesmaximal, complemented
5C41×#2405C211yesmaximal, characteristic, complemented
6C41×#2044C212yesmaximal, complemented
7C41×#2022C212yesmaximal, complemented
8C41×#1898C212yesmaximal, complemented
9C41×#1890C211yesmaximal, characteristic, complemented
10C41×#1867C211yesmaximal, characteristic, complemented
11C41×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C41C2211yescharacteristic
13C23×D4×C41C2211yescharacteristic
14C41×#546—22no—
15C41×#546—22no—
16D42×C41—22no—
17D42×C41—22no—
18C41×#535—21no—
19C41×#534—21no—
20C41×#534C2212yes—
21C41×#525—21no—
22C2×#123×C41C2211yescharacteristic
23C2×#123×C41C2212yescomplemented
24C2×#123×C41C2211yescharacteristic, complemented
25C2×#120×C41—21no—
26C2×#120×C41C2212yes—
27C41×#518C2211yescharacteristic
28C22×C22⋊C4×C41C2211yescharacteristic, complemented
29C22×C22⋊C4×C41C2212yescomplemented
30C41×#458—24no—
31C2×#99×C41—24no—
32C2×#99×C41C2211yescharacteristic
33C2×#99×C41C2211yescharacteristic
34C2×#99×C41C2212yescomplemented
35C2×#99×C41C2212yescomplemented
36C2×#99×C41C2212yescomplemented
37C41×#397—22no—
38C41×#394—21no—
39C41×#394—21no—
40C41×#394—22no—
41C41×#386—22no—
42C41×#386C2211yescharacteristic
43C41×#386C2211yescharacteristic, complemented
44C41×#386C2212yescomplemented
45C41×#385—21no—
46C41×#385C2212yescomplemented
47C41×#381C2212yescomplemented
48C41×#380—22no—
49C41×#379—21no—
50C41×#379C2211yescharacteristic, complemented
51C41×#342C2212yescomplemented
52C41×#342C2212yescomplemented
53C25×C41D411yescharacteristic
54C25×C41C2311yescharacteristic
55H(5,𝔽2)×C41—22no—
56H(5,𝔽2)×C41—22no—
57H(5,𝔽2)×C41—42no—
58C2×#41×C41—21no—
59C2×#41×C41—22no—
60C22×D4×C41—21no—
61C22×D4×C41—22no—
62C22×D4×C41—22no—
63C22×D4×C41—22no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—22no—
67C22×D4×C41—22no—
68C22×D4×C41—42no—
69C22×D4×C41D411yescharacteristic
70C22×D4×C41D411yescharacteristic
71C22×D4×C41D412yes—
72C22×D4×C41D412yes—
73C22×D4×C41C2312yes—
74C22×D4×C41C2311yescharacteristic
75C22×D4×C41C2311yescharacteristic
76C23×C4×C41—22no—
77C23×C4×C41D411yescharacteristic
78C23×C4×C41C2311yescharacteristic
79C23×C4×C41C2311yescharacteristic
80#127×C41—22no—
81#124×C41—22no—
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—22no—
86#123×C41—22no—
87#123×C41—24no—
88#123×C41—42no—
89#123×C41—42no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—21no—
92#121×C41—21no—
93#121×C41—21no—
94#121×C41—22no—
95#121×C41—22no—
96#121×C41—22no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#120×C41—22no—
101#120×C41—22no—
102#120×C41—22no—
103#120×C41—22no—
104#120×C41—22no—
105#120×C41—22no—
106#120×C41—22no—
107#120×C41—22no—
108#120×C41—22no—
109C4×D4×C41—22no—
110C4×D4×C41—22no—
111C4×D4×C41—22no—
112C4×D4×C41—22no—
113#117×C41—21no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41—21no—
117C2×C4⋊C4×C41—22no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—24no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—22no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—22no—
126C2×C22⋊C4×C41—22no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—22no—
130C2×C22⋊C4×C41—21no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—21no—
134C2×C22⋊C4×C41—22no—
135C2×C22⋊C4×C41—42no—
136C2×C22⋊C4×C41D412yes—
137C2×C22⋊C4×C41D412yes—
138C2×C22⋊C4×C41C2312yes—
139C2×C22⋊C4×C41C2311yescharacteristic
140C2×C22⋊C4×C41C2311yescharacteristic
141C2×C22⋊C4×C41C2312yes—
142C2×C22⋊C4×C41C2312yes—
143#99×C41—22no—
144#99×C41—24no—
145#99×C41—24no—
146#99×C41—42no—
147#99×C41D414yescomplemented
148#95×C41—22no—
149#95×C41—22no—
150#95×C41—22no—
151#95×C41—21no—
152#95×C41—21no—
153#95×C41—22no—
154C24×C41—21no—
155C24×C41—21no—
156C24×C41—22no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41—22no—
161C24×C41—41no—
162C24×C41—42no—
163C24×C41—42no—
164C24×C41—81no—
165C24×C41—81no—
166C24×C41C2×D411yescharacteristic
167C24×C41C2×D412yes—
168C24×C41C2×D411yescharacteristic
169C24×C41C2×D412yes—
170C24×C41C2×D412yes—
171C24×C41C2×D411yescharacteristic
172C24×C41C2×D411yescharacteristic
173C24×C41C2411yescharacteristic
174#41×C41—44no—
175#41×C41—44no—
176#41×C41—42no—
177#41×C41—42no—
178C2×Q8×C41—21no—
179C2×D4×C41—22no—
180C2×D4×C41—22no—
181C2×D4×C41—22no—
182C2×D4×C41—21no—
183C2×D4×C41—22no—
184C2×D4×C41—22no—
185C2×D4×C41—22no—
186C2×D4×C41—22no—
187C2×D4×C41—22no—
188C2×D4×C41—21no—
189C2×D4×C41—22no—
190C2×D4×C41—22no—
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—21no—
194C2×D4×C41—22no—
195C2×D4×C41—22no—
196C2×D4×C41—22no—
197C2×D4×C41—22no—
198C2×D4×C41—22no—
199C2×D4×C41—22no—
200C2×D4×C41—22no—
201C2×D4×C41—22no—
202C2×D4×C41—22no—
203C2×D4×C41—41no—
204C2×D4×C41—41no—
205C2×D4×C41—44no—
206C2×D4×C41—44no—
207C2×D4×C41—44no—
208C2×D4×C41—44no—
209C2×D4×C41—44no—
210C2×D4×C41—44no—
211C2×D4×C41—42no—
212C2×D4×C41—42no—
213C2×D4×C41—44no—
214C2×D4×C41—82no—
215C2×D4×C41—82no—
216C2×D4×C41—82no—
217C2×D4×C41C2×D412yes—
218C2×D4×C41#4112yes—
219C22×C4×C41—21no—
220C22×C4×C41—22no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—22no—
224C22×C4×C41—21no—
225C22×C4×C41—21no—
226C22×C4×C41—22no—
227C22×C4×C41—22no—
228C22×C4×C41—21no—
229C22×C4×C41—22no—
230C22×C4×C41—22no—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—22no—
237C22×C4×C41—41no—
238C22×C4×C41—44no—
239C22×C4×C41—44no—
240C22×C4×C41—81no—
241C22×C4×C41—82no—
242C22×C4×C41C2×D412yes—
243C22×C4×C41C2×D411yescharacteristic
244C22×C4×C41C2×D411yescharacteristic
245C22×C4×C41C2×D412yes—
246C22×C4×C41C2×D412yes—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—22no—
250C4⋊C4×C41—22no—
251C4⋊C4×C41—44no—
252C4⋊C4×C41—42no—
253C4⋊C4×C41—42no—
254C4⋊C4×C41—82no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—22no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—22no—
262C22⋊C4×C41—22no—
263C22⋊C4×C41—22no—
264C22⋊C4×C41—22no—
265C22⋊C4×C41—22no—
266C22⋊C4×C41—22no—
267C22⋊C4×C41—22no—
268C22⋊C4×C41—21no—
269C22⋊C4×C41—21no—
270C22⋊C4×C41—22no—
271C22⋊C4×C41—22no—
272C22⋊C4×C41—44no—
273C22⋊C4×C41—44no—
274C22⋊C4×C41—42no—
275C22⋊C4×C41—42no—
276C22⋊C4×C41—41no—
277C22⋊C4×C41—42no—
278C22⋊C4×C41—41no—
279C22⋊C4×C41—42no—
280C22⋊C4×C41—81no—
281C22⋊C4×C41—81no—
282C22⋊C4×C41—81no—
283C22⋊C4×C41—82no—
284C22⋊C4×C41C2×D414yescomplemented
285C42×C41—22no—
286C23×C41—21no—
287C23×C41—21no—
288C23×C41—21no—
289C23×C41—22no—
290C23×C41—22no—
291C23×C41—22no—
292C23×C41—24no—
293C23×C41—21no—
294C23×C41—21no—
295C23×C41—21no—
296C23×C41—22no—
297C23×C41—22no—
298C23×C41—21no—
299C23×C41—22no—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—22no—
303C23×C41—22no—
304C23×C41—42no—
305C23×C41—41no—
306C23×C41—41no—
307C23×C41—41no—
308C23×C41—41no—
309C23×C41—42no—
310C23×C41—42no—
311C23×C41—41no—
312C23×C41—42no—
313C23×C41—42no—
314C23×C41—41no—
315C23×C41—41no—
316C23×C41—41no—
317C23×C41—41no—
318C23×C41—42no—
319C23×C41—42no—
320C23×C41—42no—
321C23×C41—42no—
322C23×C41—42no—
323C23×C41—81no—
324C23×C41—81no—
325C23×C41—82no—
326C23×C41—82no—
327C23×C41—84no—
328C23×C41—81no—
329C23×C41—81no—
330C23×C41—84no—
331C23×C41—84no—
332C23×C41#12011yescharacteristic
333C23×C41#12012yes—
334C23×C41#12011yescharacteristic
335C23×C41#12112yes—
336C23×C41C22×D411yescharacteristic
337C23×C41C22×D412yes—
338C23×C41C22×D411yescharacteristic
339C23×C41C2×#4111yescharacteristic
340C23×C41H(5,𝔽2)12yes—
341Q8×C41—42no—
342D4×C41—24no—
343D4×C41—24no—
344D4×C41—44no—
345D4×C41—42no—
346D4×C41—44no—
347D4×C41—44no—
348D4×C41—44no—
349D4×C41—42no—
350D4×C41—42no—
351D4×C41—42no—
352D4×C41—42no—
353D4×C41—42no—
354D4×C41—42no—
355D4×C41—44no—
356D4×C41—82no—
357D4×C41—82no—
358D4×C41—82no—
359D4×C41—82no—
360C2×C4×C41—21no—
361C2×C4×C41—21no—
362C2×C4×C41—22no—
363C2×C4×C41—22no—
364C2×C4×C41—22no—
365C2×C4×C41—21no—
366C2×C4×C41—21no—
367C2×C4×C41—21no—
368C2×C4×C41—24no—
369C2×C4×C41—22no—
370C2×C4×C41—22no—
371C2×C4×C41—42no—
372C2×C4×C41—42no—
373C2×C4×C41—44no—
374C2×C4×C41—42no—
375C2×C4×C41—42no—
376C2×C4×C41—42no—
377C2×C4×C41—42no—
378C2×C4×C41—42no—
379C2×C4×C41—41no—
380C2×C4×C41—41no—
381C2×C4×C41—41no—
382C2×C4×C41—41no—
383C2×C4×C41—42no—
384C2×C4×C41—42no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—42no—
388C2×C4×C41—42no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—42no—
396C2×C4×C41—42no—
397C2×C4×C41—42no—
398C2×C4×C41—81no—
399C2×C4×C41—81no—
400C2×C4×C41—88no—
401C2×C4×C41#12112yes—
402#24405C4111yesmaximal, characteristic, direct product factor, Sylow
403C22×C41—21no—
404C22×C41—22no—
405C22×C41—21no—
406C22×C41—22no—
407C22×C41—21no—
408C22×C41—21no—
409C22×C41—21no—
410C22×C41—22no—
411C22×C41—22no—
412C22×C41—22no—
413C22×C41—21no—
414C22×C41—21no—
415C22×C41—22no—
416C22×C41—41no—
417C22×C41—41no—
418C22×C41—42no—
419C22×C41—44no—
420C22×C41—44no—
421C22×C41—42no—
422C22×C41—42no—
423C22×C41—42no—
424C22×C41—42no—
425C22×C41—41no—
426C22×C41—41no—
427C22×C41—42no—
428C22×C41—41no—
429C22×C41—42no—
430C22×C41—41no—
431C22×C41—42no—
432C22×C41—41no—
433C22×C41—82no—
434C22×C41—81no—
435C22×C41—81no—
436C22×C41—81no—
437C22×C41—82no—
438C22×C41—84no—
439C22×C41—82no—
440C22×C41—82no—
441C22×C41—81no—
442C22×C41—84no—
443C22×C41—162no—
444C22×C41#45812yescomplemented
445C22×C41C2×#12011yescharacteristic
446C22×C41C2×#12111yescharacteristic
447C22×C41#53411yescharacteristic
448C22×C41D4212yes—
449C22×C41#54612yes—
450C4×C41—22no—
451C4×C41—44no—
452C4×C41—41no—
453C4×C41—42no—
454C4×C41—42no—
455C4×C41—42no—
456C4×C41—81no—
457C4×C41—81no—
458C4×C41—82no—
459C4×C41—81no—
460C4×C41—81no—
461#3484C2×C4111yescharacteristic
462C2×#458C2×C4111yescharacteristic, complemented
463C22×#99C2×C4111yescharacteristic, complemented
464#2412C2×C4112yescomplemented
465#2405C2×C4111yescharacteristic, complemented
466#2044C2×C4112yescomplemented
467#2022C2×C4112yescomplemented
468#1898C2×C4112yescomplemented
469#1890C2×C4111yescharacteristic, complemented
470#1867C2×C4111yescharacteristic, complemented
471#1790C2×C4111yescharacteristic, complemented
472C2×C41—22no—
473C2×C41—21no—
474C2×C41—21no—
475C2×C41—22no—
476C2×C41—22no—
477C2×C41—42no—
478C2×C41—41no—
479C2×C41—42no—
480C2×C41—81no—
481C2×C41—82no—
482C2×C41#241011yescharacteristic
483C2×C41C2×#45811yescharacteristic
484C2×C41#302611yescharacteristic
485C2×H(5,𝔽2)C22×C4111yescharacteristic
486C23×D4C22×C4111yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C4112yes—
494#525—21no—
495C2×#123C22×C4111yescharacteristic
496C2×#123C22×C4112yescomplemented
497C2×#123C22×C4111yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C4112yes—
500#518C22×C4111yescharacteristic
501C22×C22⋊C4C22×C4111yescharacteristic, complemented
502C22×C22⋊C4C22×C4112yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C4111yescharacteristic
506C2×#99C22×C4111yescharacteristic
507C2×#99C22×C4112yescomplemented
508C2×#99C22×C4112yescomplemented
509C2×#99C22×C4112yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C4111yescharacteristic
516#386C22×C4111yescharacteristic, complemented
517#386C22×C4112yescomplemented
518#385—21no—
519#385C22×C4112yescomplemented
520#381C22×C4112yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C4111yescharacteristic, complemented
524#342C22×C4112yescomplemented
525#342C22×C4112yescomplemented
526C41#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C4111yescharacteristic
528C25C23×C4111yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C4111yescharacteristic
544C22×D4D4×C4111yescharacteristic
545C22×D4D4×C4112yes—
546C22×D4D4×C4112yes—
547C22×D4C23×C4112yes—
548C22×D4C23×C4111yescharacteristic
549C22×D4C23×C4111yescharacteristic
550C23×C4—22no—
551C23×C4D4×C4111yescharacteristic
552C23×C4C23×C4111yescharacteristic
553C23×C4C23×C4111yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C4112yes—
611C2×C22⋊C4D4×C4112yes—
612C2×C22⋊C4C23×C4112yes—
613C2×C22⋊C4C23×C4111yescharacteristic
614C2×C22⋊C4C23×C4111yescharacteristic
615C2×C22⋊C4C23×C4112yes—
616C2×C22⋊C4C23×C4112yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C4114yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C4111yescharacteristic
641C24C2×D4×C4112yes—
642C24C2×D4×C4111yescharacteristic
643C24C2×D4×C4112yes—
644C24C2×D4×C4112yes—
645C24C2×D4×C4111yescharacteristic
646C24C2×D4×C4111yescharacteristic
647C24C24×C4111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C4112yes—
692C2×D4#41×C4112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C4112yes—
717C22×C4C2×D4×C4111yescharacteristic
718C22×C4C2×D4×C4111yescharacteristic
719C22×C4C2×D4×C4112yes—
720C22×C4C2×D4×C4112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C4114yescomplemented
759C42—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C4111yescharacteristic
807C23#120×C4112yes—
808C23#120×C4111yescharacteristic
809C23#121×C4112yes—
810C23C22×D4×C4111yescharacteristic
811C23C22×D4×C4112yes—
812C23C22×D4×C4111yescharacteristic
813C23C2×#41×C4111yescharacteristic
814C23H(5,𝔽2)×C4112yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C4112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C41×#45812yescomplemented
918C22C2×#120×C4111yescharacteristic
919C22C2×#121×C4111yescharacteristic
920C22C41×#53411yescharacteristic
921C22D42×C4112yes—
922C22C41×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C41×#241011yescharacteristic
945C2C2×C41×#45811yescharacteristic
946C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#458C2semidirect
3. C22×#99×C41C2semidirect
4. C41×#2412C2semidirect
5. C41×#2405C2semidirect
6. C41×#2044C2semidirect
7. C41×#2022C2semidirect
8. C41×#1898C2semidirect
9. C41×#1890C2semidirect
10. C41×#1867C2semidirect
11. C41×#1790C2semidirect
23. C2×#123×C41C22semidirect
24. C2×#123×C41C22semidirect
28. C22×C22⋊C4×C41C22semidirect
29. C22×C22⋊C4×C41C22semidirect
34. C2×#99×C41C22semidirect
35. C2×#99×C41C22semidirect
36. C2×#99×C41C22semidirect
43. C41×#386C22semidirect
44. C41×#386C22semidirect
46. C41×#385C22semidirect
47. C41×#381C22semidirect
50. C41×#379C22semidirect
51. C41×#342C22semidirect
52. C41×#342C22semidirect
147. #99×C41D4semidirect
284. C22⋊C4×C41C2×D4semidirect
402. #24405C41direct (N × H)
444. C22×C41#458semidirect
462. C2×#458C2×C41semidirect
463. C22×#99C2×C41semidirect
464. #2412C2×C41semidirect
465. #2405C2×C41semidirect
466. #2044C2×C41semidirect
467. #2022C2×C41semidirect
468. #1898C2×C41semidirect
469. #1890C2×C41semidirect
470. #1867C2×C41semidirect
471. #1790C2×C41semidirect
496. C2×#123C22×C41semidirect
497. C2×#123C22×C41semidirect
501. C22×C22⋊C4C22×C41semidirect
502. C22×C22⋊C4C22×C41semidirect
507. C2×#99C22×C41semidirect
508. C2×#99C22×C41semidirect
509. C2×#99C22×C41semidirect
516. #386C22×C41semidirect
517. #386C22×C41semidirect
519. #385C22×C41semidirect
520. #381C22×C41semidirect
523. #379C22×C41semidirect
524. #342C22×C41semidirect
525. #342C22×C41semidirect
526. C41#24405direct (N × H)
621. #99D4×C41semidirect
758. C22⋊C4C2×D4×C41semidirect
917. C22C41×#458semidirect

Maximal subgroups

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

subgroupindex
C41×#34842
C2×C41×#4582
C22×#99×C412
C41×#24122
C41×#24052
C41×#20442
C41×#20222
C41×#18982
C41×#18902
C41×#18672
C41×#17902
#2440541