Finite Group Databasebeta

← C41×#33554 #23809755

Subgroups — C41×#33554 #23809755

Order 10496.

1112 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3538C211yesmaximal, characteristic, complemented
2C41×#3028C211yesmaximal, characteristic, complemented
3C41×#3025C211yesmaximal, characteristic
4C41×#3022C211yesmaximal, characteristic, complemented
5C41×#2201C214yesmaximal, complemented
6C41×#2197C214yesmaximal, complemented
7C41×#2129C211yesmaximal, characteristic, complemented
8C41×#2123C211yesmaximal, characteristic, complemented
9C41×#2120C211yesmaximal, characteristic, complemented
10C41×#585C2211yescharacteristic
11C2×#137×C41—21no—
12C41×#563—21no—
13C41×#563C2212yescomplemented
14C41×#552—21no—
15C41×#552—21no—
16C41×#551—21no—
17C41×#551C2212yescomplemented
18D4×Q8×C41—21no—
19D4×Q8×C41—21no—
20C41×#544—22no—
21C41×#541—21no—
22C41×#539—22no—
23C41×#536—21no—
24C41×#536C2211yescharacteristic
25C41×#536C2211yescharacteristic
26C41×#525—21no—
27C41×#525C2211yescharacteristic
28C2×C22⋊Q8×C41—21no—
29C41×#458—21no—
30C41×#458—22no—
31C41×#458C2214yes—
32C41×#458C2212yes—
33C41×B(4,𝔽2)—21no—
34C41×B(4,𝔽2)C2212yes—
35C41×#456—22no—
36C41×#455C2214yes—
37C41×#421—21no—
38C41×#413C2211yescharacteristic
39C41×#410—21no—
40C41×#410—21no—
41C41×#410C2211yescharacteristic
42C41×#410C2211yescharacteristic
43C41×#354C2214yescomplemented
44C41×#352C2212yescomplemented
45C41×#352C2214yescomplemented
46C41×AΣL(1,𝔽16)C2212yescomplemented
472−1+4×C41—21no—
482−1+4×C41—41no—
49H(5,𝔽2)×C41—21no—
50H(5,𝔽2)×C41—21no—
51H(5,𝔽2)×C41—41no—
52H(5,𝔽2)×C41C2312yes—
53C2×#41×C41—21no—
54C2×#41×C41—21no—
55C2×#41×C41—21no—
56C2×#41×C41—42no—
57C2×#41×C41C2311yescharacteristic
58C22×Q8×C41—21no—
59C22×Q8×C41D411yescharacteristic, complemented
60C22×Q8×C41D411yescharacteristic, complemented
61C23×C4×C41D411yescharacteristic
62#137×C41—24no—
63#137×C41—42no—
64C2×Q16×C41—41no—
65C2×SD16×C41—41no—
66C2×M16×C41—21no—
67C4⋊Q8×C41—21no—
68C4⋊Q8×C41—22no—
69C4⋊Q8×C41—21no—
70C4⋊Q8×C41—22no—
71C4⋊Q8×C41—41no—
72C4⋊Q8×C41D412yescomplemented
73#126×C41—22no—
74#126×C41—22no—
75#126×C41—22no—
76#126×C41—22no—
77#125×C41—22no—
78#125×C41—22no—
79#125×C41—21no—
80#125×C41—22no—
81#125×C41—22no—
82#124×C41—21no—
83#124×C41—41no—
84#124×C41C2312yes—
85#123×C41—22no—
86#123×C41—21no—
87#123×C41—21no—
88#123×C41—22no—
89#123×C41—22no—
90#123×C41—24no—
91#123×C41D411yescharacteristic
92#123×C41D412yescomplemented
93#123×C41C2311yescharacteristic
94#123×C41C2312yes—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—22no—
99C22⋊Q8×C41—22no—
100C22⋊Q8×C41—21no—
101C22⋊Q8×C41—22no—
102C22⋊Q8×C41—21no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41—22no—
105C22⋊Q8×C41—21no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—22no—
108C22⋊Q8×C41—42no—
109C22⋊Q8×C41—41no—
110#121×C41—21no—
111#121×C41—41no—
112#120×C41—22no—
113#120×C41D411yescharacteristic
114#120×C41C2311yescharacteristic
115C4×Q8×C41—21no—
116C4×Q8×C41—21no—
117C4×D4×C41—22no—
118C4×D4×C41—21no—
119C4×D4×C41—21no—
120C4×D4×C41—22no—
121C4×D4×C41—42no—
122#117×C41—22no—
123#117×C41—22no—
124#117×C41—21no—
125#117×C41—21no—
126#117×C41D411yescharacteristic
127#117×C41D411yescharacteristic, complemented
128#117×C41D411yescharacteristic, complemented
129C2×C4⋊C4×C41—22no—
130C2×C4⋊C4×C41—21no—
131C2×C22⋊C4×C41—22no—
132#104×C41—24no—
133#101×C41—21no—
134#100×C41C2312yes—
135#99×C41—21no—
136#99×C41—21no—
137#99×C41—22no—
138#99×C41—22no—
139#99×C41—24no—
140#99×C41C2312yes—
141#99×C41C2312yes—
142C24×C41C2×D411yescharacteristic
143#41×C41—22no—
144#41×C41—22no—
145#41×C41—41no—
146#41×C41—41no—
147#41×C41—42no—
148#41×C41—41no—
149#41×C41—41no—
150#41×C41—41no—
151#41×C41—41no—
152#41×C41—41no—
153#41×C41—42no—
154#41×C41—42no—
155#41×C41—42no—
156#41×C41—41no—
157#41×C41—41no—
158#41×C41—41no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—22no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41—41no—
167C2×Q8×C41—41no—
168C2×Q8×C41—41no—
169C2×Q8×C41—41no—
170C2×Q8×C41—42no—
171C2×Q8×C41—81no—
172C2×Q8×C41—81no—
173C2×Q8×C41C2×D412yes—
174C2×Q8×C41C2×D411yescharacteristic
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—21no—
179C2×D4×C41—22no—
180C2×D4×C41—22no—
181C2×D4×C41—21no—
182C2×D4×C41—42no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—41no—
186C2×D4×C41—42no—
187C2×D4×C41C2×D411yescharacteristic
188C2×D4×C41C2×D411yescharacteristic
189C2×D4×C41C2411yescharacteristic
190C22×C4×C41—22no—
191C22×C4×C41—22no—
192C22×C4×C41—22no—
193C22×C4×C41—22no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—41no—
198C22×C4×C41—41no—
199C22×C4×C41—41no—
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D412yes—
204C22×C4×C41C2×D411yescharacteristic
205Q16×C41—44no—
206SD16×C41—44no—
207M16×C41—22no—
208M16×C41—41no—
209C2×C8×C41—41no—
210C4⋊C4×C41—22no—
211C4⋊C4×C41—22no—
212C4⋊C4×C41—22no—
213C4⋊C4×C41—22no—
214C4⋊C4×C41—22no—
215C4⋊C4×C41—22no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—22no—
218C4⋊C4×C41—22no—
219C4⋊C4×C41—22no—
220C4⋊C4×C41—22no—
221C4⋊C4×C41—22no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—22no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—41no—
229C4⋊C4×C41—41no—
230C4⋊C4×C41—42no—
231C4⋊C4×C41—44no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—21no—
235C22⋊C4×C41—21no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—21no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—21no—
242C22⋊C4×C41—21no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—44no—
248C22⋊C4×C41C2×D411yescharacteristic
249C22⋊C4×C41C2×D411yescharacteristic
250C22⋊C4×C41C2×D412yes—
251C42×C41—22no—
252C42×C41—22no—
253C42×C41—21no—
254C42×C41—21no—
255C42×C41—41no—
256C42×C41—41no—
257C42×C41C2×D412yes—
258C23×C41—21no—
259C23×C41—22no—
260C23×C41—22no—
261C23×C41—41no—
262C23×C41—42no—
263C23×C41—41no—
264C23×C41#12011yescharacteristic
265C23×C41C22×D411yescharacteristic
266C23×C41C22×D411yescharacteristic
267Q8×C41—22no—
268Q8×C41—41no—
269Q8×C41—42no—
270Q8×C41—41no—
271Q8×C41—41no—
272Q8×C41—41no—
273Q8×C41—41no—
274Q8×C41—41no—
275Q8×C41—41no—
276Q8×C41—41no—
277Q8×C41—81no—
278Q8×C41—82no—
279D4×C41—22no—
280D4×C41—41no—
281D4×C41—41no—
282D4×C41—41no—
283D4×C41—41no—
284D4×C41—41no—
285D4×C41—42no—
286D4×C41—42no—
287D4×C41—42no—
288D4×C41—42no—
289D4×C41—42no—
290D4×C41—42no—
291D4×C41—41no—
292D4×C41—84no—
293C2×C4×C41—21no—
294C2×C4×C41—21no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—21no—
298C2×C4×C41—21no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—22no—
304C2×C4×C41—22no—
305C2×C4×C41—22no—
306C2×C4×C41—22no—
307C2×C4×C41—21no—
308C2×C4×C41—42no—
309C2×C4×C41—42no—
310C2×C4×C41—42no—
311C2×C4×C41—44no—
312C2×C4×C41—41no—
313C2×C4×C41—42no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—42no—
318C2×C4×C41—42no—
319C2×C4×C41—42no—
320C2×C4×C41—81no—
321C2×C4×C41—81no—
322C2×C4×C41—82no—
323C2×C4×C41#12011yescharacteristic
324C2×C4×C41#12011yescharacteristic
325C2×C4×C41#12011yescharacteristic
326C2×C4×C41C22×D411yescharacteristic
327C8×C41—42no—
328#33554C4111yesmaximal, characteristic, direct product factor, Sylow
329C22×C41—22no—
330C22×C41—21no—
331C22×C41—21no—
332C22×C41—21no—
333C22×C41—41no—
334C22×C41—41no—
335C22×C41—41no—
336C22×C41—41no—
337C22×C41—42no—
338C22×C41—41no—
339C22×C41—42no—
340C22×C41—81no—
341C22×C41—82no—
342C22×C41—82no—
343C22×C41—161no—
344C22×C41C2×#12011yescharacteristic
345C4×C41—21no—
346C4×C41—21no—
347C4×C41—21no—
348C4×C41—42no—
349C4×C41—42no—
350C4×C41—41no—
351C4×C41—41no—
352C4×C41—42no—
353C4×C41—41no—
354C4×C41—42no—
355C4×C41—42no—
356C4×C41—82no—
357C4×C41—82no—
358C4×C41B(4,𝔽2)11yescharacteristic
359C4×C41B(4,𝔽2)11yescharacteristic
360#3538C2×C4111yescharacteristic, complemented
361#3028C2×C4111yescharacteristic, complemented
362#3025C2×C4111yescharacteristic
363#3022C2×C4111yescharacteristic, complemented
364#2201C2×C4114yescomplemented
365#2197C2×C4114yescomplemented
366#2129C2×C4111yescharacteristic, complemented
367#2123C2×C4111yescharacteristic, complemented
368#2120C2×C4111yescharacteristic, complemented
369C2×C41—21no—
370C2×C41—41no—
371C2×C41—41no—
372C2×C41—42no—
373C2×C41—41no—
374C2×C41—82no—
375C2×C41C2×B(4,𝔽2)11yescharacteristic
376#585C22×C4111yescharacteristic
377C2×#137—21no—
378#563—21no—
379#563C22×C4112yescomplemented
380#552—21no—
381#552—21no—
382#551—21no—
383#551C22×C4112yescomplemented
384D4×Q8—21no—
385D4×Q8—21no—
386#544—22no—
387#541—21no—
388#539—22no—
389#536—21no—
390#536C22×C4111yescharacteristic
391#536C22×C4111yescharacteristic
392#525—21no—
393#525C22×C4111yescharacteristic
394C2×C22⋊Q8—21no—
395#458—21no—
396#458—22no—
397#458C22×C4114yes—
398#458C22×C4112yes—
399B(4,𝔽2)—21no—
400B(4,𝔽2)C22×C4112yes—
401#456—22no—
402#455C22×C4114yes—
403#421—21no—
404#413C22×C4111yescharacteristic
405#410—21no—
406#410—21no—
407#410C22×C4111yescharacteristic
408#410C22×C4111yescharacteristic
409#354C22×C4114yescomplemented
410#352C22×C4112yescomplemented
411#352C22×C4114yescomplemented
412AΣL(1,𝔽16)C22×C4112yescomplemented
413C41#3355411yescharacteristic, direct product factor, Sylow
4142−1+4—21no—
4152−1+4—41no—
416H(5,𝔽2)—21no—
417H(5,𝔽2)—21no—
418H(5,𝔽2)—41no—
419H(5,𝔽2)C23×C4112yes—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—42no—
424C2×#41C23×C4111yescharacteristic
425C22×Q8—21no—
426C22×Q8D4×C4111yescharacteristic, complemented
427C22×Q8D4×C4111yescharacteristic, complemented
428C23×C4D4×C4111yescharacteristic
429#137—24no—
430#137—42no—
431C2×Q16—41no—
432C2×SD16—41no—
433C2×M16—21no—
434C4⋊Q8—21no—
435C4⋊Q8—22no—
436C4⋊Q8—21no—
437C4⋊Q8—22no—
438C4⋊Q8—41no—
439C4⋊Q8D4×C4112yescomplemented
440#126—22no—
441#126—22no—
442#126—22no—
443#126—22no—
444#125—22no—
445#125—22no—
446#125—21no—
447#125—22no—
448#125—22no—
449#124—21no—
450#124—41no—
451#124C23×C4112yes—
452#123—22no—
453#123—21no—
454#123—21no—
455#123—22no—
456#123—22no—
457#123—24no—
458#123D4×C4111yescharacteristic
459#123D4×C4112yescomplemented
460#123C23×C4111yescharacteristic
461#123C23×C4112yes—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8—42no—
476C22⋊Q8—41no—
477#121—21no—
478#121—41no—
479#120—22no—
480#120D4×C4111yescharacteristic
481#120C23×C4111yescharacteristic
482C4×Q8—21no—
483C4×Q8—21no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—22no—
488C4×D4—42no—
489#117—22no—
490#117—22no—
491#117—21no—
492#117—21no—
493#117D4×C4111yescharacteristic
494#117D4×C4111yescharacteristic, complemented
495#117D4×C4111yescharacteristic, complemented
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C22⋊C4—22no—
499#104—24no—
500#101—21no—
501#100C23×C4112yes—
502#99—21no—
503#99—21no—
504#99—22no—
505#99—22no—
506#99—24no—
507#99C23×C4112yes—
508#99C23×C4112yes—
509C24C2×D4×C4111yescharacteristic
510#41—22no—
511#41—22no—
512#41—41no—
513#41—41no—
514#41—42no—
515#41—41no—
516#41—41no—
517#41—41no—
518#41—41no—
519#41—41no—
520#41—42no—
521#41—42no—
522#41—42no—
523#41—41no—
524#41—41no—
525#41—41no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8—81no—
539C2×Q8—81no—
540C2×Q8C2×D4×C4112yes—
541C2×Q8C2×D4×C4111yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4C2×D4×C4111yescharacteristic
555C2×D4C2×D4×C4111yescharacteristic
556C2×D4C24×C4111yescharacteristic
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4C2×D4×C4111yescharacteristic
568C22×C4C2×D4×C4111yescharacteristic
569C22×C4C2×D4×C4111yescharacteristic
570C22×C4C2×D4×C4112yes—
571C22×C4C2×D4×C4111yescharacteristic
572Q16—44no—
573SD16—44no—
574M16—22no—
575M16—41no—
576C2×C8—41no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—42no—
598C4⋊C4—44no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—44no—
615C22⋊C4C2×D4×C4111yescharacteristic
616C22⋊C4C2×D4×C4111yescharacteristic
617C22⋊C4C2×D4×C4112yes—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—41no—
623C42—41no—
624C42C2×D4×C4112yes—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23#120×C4111yescharacteristic
632C23C22×D4×C4111yescharacteristic
633C23C22×D4×C4111yescharacteristic
634Q8—22no—
635Q8—41no—
636Q8—42no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—81no—
645Q8—82no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—41no—
659D4—84no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—82no—
690C2×C4#120×C4111yescharacteristic
691C2×C4#120×C4111yescharacteristic
692C2×C4#120×C4111yescharacteristic
693C2×C4C22×D4×C4111yescharacteristic
694C8—42no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—161no—
710C22C2×#120×C4111yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—42no—
722C4—82no—
723C4—82no—
724C4C41×B(4,𝔽2)11yescharacteristic
725C4C41×B(4,𝔽2)11yescharacteristic
726C2—21no—
727C2—41no—
728C2—41no—
729C2—42no—
730C2—41no—
731C2—82no—
732C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C41C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
prime radicalC41×#3025C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3538C2semidirect
2. C41×#3028C2semidirect
4. C41×#3022C2semidirect
5. C41×#2201C2semidirect
6. C41×#2197C2semidirect
7. C41×#2129C2semidirect
8. C41×#2123C2semidirect
9. C41×#2120C2semidirect
13. C41×#563C22semidirect
17. C41×#551C22semidirect
43. C41×#354C22semidirect
44. C41×#352C22semidirect
45. C41×#352C22semidirect
46. C41×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C41D4semidirect
60. C22×Q8×C41D4semidirect
72. C4⋊Q8×C41D4semidirect
92. #123×C41D4semidirect
127. #117×C41D4semidirect
128. #117×C41D4semidirect
328. #33554C41direct (N × H)
360. #3538C2×C41semidirect
361. #3028C2×C41semidirect
363. #3022C2×C41semidirect
364. #2201C2×C41semidirect
365. #2197C2×C41semidirect
366. #2129C2×C41semidirect
367. #2123C2×C41semidirect
368. #2120C2×C41semidirect
379. #563C22×C41semidirect
383. #551C22×C41semidirect
409. #354C22×C41semidirect
410. #352C22×C41semidirect
411. #352C22×C41semidirect
412. AΣL(1,𝔽16)C22×C41semidirect
413. C41#33554direct (N × H)
426. C22×Q8D4×C41semidirect
427. C22×Q8D4×C41semidirect
439. C4⋊Q8D4×C41semidirect
459. #123D4×C41semidirect
494. #117D4×C41semidirect
495. #117D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35382
C41×#30282
C41×#30252
C41×#30222
C41×#22012
C41×#21972
C41×#21292
C41×#21232
C41×#21202
#3355441