Finite Group Databasebeta

← C41×#33560 #23809761

Subgroups — C41×#33560 #23809761

Order 10496.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3551C211yesmaximal, characteristic, complemented
2C41×#3028C211yesmaximal, characteristic, complemented
3C41×#3027C211yesmaximal, characteristic, complemented
4C41×#3018C211yesmaximal, characteristic, complemented
5C41×#2200C214yesmaximal, complemented
6C41×#2197C214yesmaximal, complemented
7C41×#2126C211yesmaximal, characteristic, complemented
8C41×#2123C211yesmaximal, characteristic, complemented
9C41×#2122C211yesmaximal, characteristic, complemented
10C41×#585C2211yescharacteristic
11C41×#575—21no—
12C41×#563—21no—
13C41×#560C2212yescomplemented
14C41×#555—21no—
15C41×#553—21no—
16C41×#552—21no—
17C41×#551C2212yescomplemented
18C41×#548—21no—
19C41×#546—21no—
20C41×#540—22no—
21C41×#538—22no—
22C41×#537—21no—
23C41×#536—21no—
24C41×#536C2211yescharacteristic
25C41×#535—21no—
26C41×#535C2211yescharacteristic
27C41×#532C2211yescharacteristic
28C41×#529—21no—
29C41×#458—22no—
30C41×#458C2214yes—
31C41×B(4,𝔽2)—22no—
32C41×B(4,𝔽2)C2214yes—
33C41×#456—21no—
34C41×#455C2212yes—
35C41×#454—21no—
36C41×#453C2212yes—
37C2×#104×C41—21no—
38C41×#413C2211yescharacteristic
39C41×#410—21no—
40C41×#410—21no—
41C41×#410C2211yescharacteristic
42C41×#410C2211yescharacteristic
43C41×#354C2212yescomplemented
44C41×#353C2212yescomplemented
45C41×#352C2214yescomplemented
46C41×AΣL(1,𝔽16)C2214yescomplemented
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—21no—
57C2×#41×C41—42no—
58C2×#41×C41D411yescharacteristic, complemented
59C2×#41×C41C2311yescharacteristic
60C22×Q8×C41D411yescharacteristic, complemented
61C22×D4×C41D411yescharacteristic
62#137×C41—22no—
63#137×C41—41no—
64AGL(1,ℤ/8)×C41—22no—
65AGL(1,ℤ/8)×C41—41no—
66#135×C41—42no—
67C2×M16×C41—21no—
68C4⋊Q8×C41—21no—
69C4⋊Q8×C41—41no—
70C4⋊Q8×C41D411yescharacteristic, complemented
71#127×C41—21no—
72#127×C41—41no—
73#127×C41C2311yescharacteristic
74#126×C41—22no—
75#126×C41—22no—
76#126×C41—22no—
77#125×C41—21no—
78#125×C41—22no—
79#124×C41—21no—
80#124×C41—22no—
81#124×C41—21no—
82#124×C41—21no—
83#124×C41—41no—
84#124×C41—41no—
85#124×C41D411yescharacteristic, complemented
86#124×C41C2311yescharacteristic
87#123×C41—22no—
88#123×C41—22no—
89#123×C41—22no—
90#123×C41—22no—
91#123×C41—24no—
92#123×C41D412yescomplemented
93#123×C41C2312yes—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—21no—
99C22⋊Q8×C41—42no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—21no—
103#121×C41—22no—
104#121×C41—21no—
105#121×C41—21no—
106#121×C41—22no—
107#121×C41—21no—
108#121×C41—21no—
109#121×C41—22no—
110#121×C41—22no—
111#121×C41—42no—
112#120×C41—22no—
113#120×C41—24no—
114#120×C41D412yes—
115#120×C41C2312yes—
116C4×Q8×C41—21no—
117C4×D4×C41—22no—
118C4×D4×C41—21no—
119C4×D4×C41—22no—
120C4×D4×C41—21no—
121C4×D4×C41—21no—
122C4×D4×C41—22no—
123#117×C41—22no—
124#117×C41—22no—
125#117×C41—21no—
126#117×C41—21no—
127#117×C41D411yescharacteristic
128#117×C41D411yescharacteristic, complemented
129C2×C4⋊C4×C41—21no—
130C2×C22⋊C4×C41—22no—
131C2×C42×C41D411yescharacteristic, complemented
132#104×C41—22no—
133#104×C41—22no—
134#101×C41—21no—
135#100×C41C2312yes—
136#99×C41—21no—
137#99×C41—21no—
138#99×C41—24no—
139#99×C41—24no—
140#99×C41C2312yes—
141#99×C41C2312yes—
142C24×C41C2×D412yes—
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—41no—
156#41×C41—41no—
157#41×C41—42no—
158#41×C41—41no—
159#41×C41—41no—
160#41×C41—41no—
161#41×C41—81no—
162#41×C41—81no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41—21no—
167C2×Q8×C41—21no—
168C2×Q8×C41—41no—
169C2×Q8×C41—41no—
170C2×Q8×C41—42no—
171C2×Q8×C41C2×D411yescharacteristic
172C2×Q8×C41C2×D411yescharacteristic
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—22no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
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—21no—
186C2×D4×C41—21no—
187C2×D4×C41—41no—
188C2×D4×C41—41no—
189C2×D4×C41—42no—
190C2×D4×C41—42no—
191C2×D4×C41—42no—
192C2×D4×C41—41no—
193C2×D4×C41—44no—
194C2×D4×C41C2×D411yescharacteristic
195C2×D4×C41C2×D411yescharacteristic
196C2×D4×C41C2×D411yescharacteristic
197C2×D4×C41C2411yescharacteristic
198C22×C4×C41—22no—
199C22×C4×C41—22no—
200C22×C4×C41—22no—
201C22×C4×C41—22no—
202C22×C4×C41—22no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—41no—
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D412yes—
210Q16×C41—42no—
211SD16×C41—42no—
212SD16×C41—42no—
213D8×C41—42no—
214M16×C41—22no—
215M16×C41—41no—
216C2×C8×C41—41no—
217C4⋊C4×C41—22no—
218C4⋊C4×C41—22no—
219C4⋊C4×C41—22no—
220C4⋊C4×C41—22no—
221C4⋊C4×C41—22no—
222C4⋊C4×C41—22no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—22no—
228C4⋊C4×C41—41no—
229C4⋊C4×C41—41no—
230C4⋊C4×C41—44no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—21no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—21no—
240C22⋊C4×C41—21no—
241C22⋊C4×C41—21no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—44no—
247C22⋊C4×C41—44no—
248C22⋊C4×C41C2×D412yes—
249C22⋊C4×C41C2×D412yes—
250C42×C41—22no—
251C42×C41—21no—
252C42×C41—21no—
253C42×C41—21no—
254C42×C41—41no—
255C42×C41—41no—
256C42×C41C2×D411yescharacteristic
257C42×C41C2×D411yescharacteristic
258C23×C41—22no—
259C23×C41—22no—
260C23×C41—22no—
261C23×C41—21no—
262C23×C41—41no—
263C23×C41—42no—
264C23×C41—82no—
265C23×C41#12011yescharacteristic
266C23×C41C22×D411yescharacteristic
267C23×C41C22×D411yescharacteristic
268Q8×C41—22no—
269Q8×C41—41no—
270Q8×C41—41no—
271Q8×C41—41no—
272Q8×C41—41no—
273Q8×C41—41no—
274Q8×C41—41no—
275Q8×C41—41no—
276Q8×C41—81no—
277D4×C41—22no—
278D4×C41—41no—
279D4×C41—41no—
280D4×C41—41no—
281D4×C41—41no—
282D4×C41—41no—
283D4×C41—41no—
284D4×C41—42no—
285D4×C41—42no—
286D4×C41—42no—
287D4×C41—42no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—81no—
292D4×C41—81no—
293D4×C41—82no—
294D4×C41—82no—
295D4×C41—82no—
296D4×C41—81no—
297D4×C41—81no—
298D4×C41—82no—
299D4×C41—164no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—22no—
307C2×C4×C41—22no—
308C2×C4×C41—21no—
309C2×C4×C41—22no—
310C2×C4×C41—21no—
311C2×C4×C41—22no—
312C2×C4×C41—22no—
313C2×C4×C41—21no—
314C2×C4×C41—42no—
315C2×C4×C41—42no—
316C2×C4×C41—42no—
317C2×C4×C41—41no—
318C2×C4×C41—42no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—42no—
322C2×C4×C41—42no—
323C2×C4×C41—42no—
324C2×C4×C41—82no—
325C2×C4×C41—81no—
326C2×C4×C41—82no—
327C2×C4×C41—82no—
328C2×C4×C41#12011yescharacteristic
329C2×C4×C41#12011yescharacteristic
330C2×C4×C41#12011yescharacteristic
331C2×C4×C41C22×D411yescharacteristic
332C8×C41—42no—
333#33560C4111yesmaximal, characteristic, direct product factor, Sylow
334C22×C41—21no—
335C22×C41—21no—
336C22×C41—21no—
337C22×C41—41no—
338C22×C41—41no—
339C22×C41—41no—
340C22×C41—41no—
341C22×C41—42no—
342C22×C41—41no—
343C22×C41—42no—
344C22×C41—42no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—82no—
348C22×C41—84no—
349C22×C41—82no—
350C22×C41—161no—
351C22×C41C2×#12011yescharacteristic
352C4×C41—21no—
353C4×C41—21no—
354C4×C41—21no—
355C4×C41—41no—
356C4×C41—42no—
357C4×C41—42no—
358C4×C41—41no—
359C4×C41—42no—
360C4×C41—41no—
361C4×C41—42no—
362C4×C41—82no—
363C4×C41—82no—
364C4×C41B(4,𝔽2)11yescharacteristic
365C4×C41B(4,𝔽2)11yescharacteristic
366#3551C2×C4111yescharacteristic, complemented
367#3028C2×C4111yescharacteristic, complemented
368#3027C2×C4111yescharacteristic, complemented
369#3018C2×C4111yescharacteristic, complemented
370#2200C2×C4114yescomplemented
371#2197C2×C4114yescomplemented
372#2126C2×C4111yescharacteristic, complemented
373#2123C2×C4111yescharacteristic, complemented
374#2122C2×C4111yescharacteristic, complemented
375C2×C41—21no—
376C2×C41—41no—
377C2×C41—41no—
378C2×C41—41no—
379C2×C41—81no—
380C2×C41—82no—
381C2×C41—82no—
382C2×C41C2×B(4,𝔽2)11yescharacteristic
383#585C22×C4111yescharacteristic
384#575—21no—
385#563—21no—
386#560C22×C4112yescomplemented
387#555—21no—
388#553—21no—
389#552—21no—
390#551C22×C4112yescomplemented
391#548—21no—
392#546—21no—
393#540—22no—
394#538—22no—
395#537—21no—
396#536—21no—
397#536C22×C4111yescharacteristic
398#535—21no—
399#535C22×C4111yescharacteristic
400#532C22×C4111yescharacteristic
401#529—21no—
402#458—22no—
403#458C22×C4114yes—
404B(4,𝔽2)—22no—
405B(4,𝔽2)C22×C4114yes—
406#456—21no—
407#455C22×C4112yes—
408#454—21no—
409#453C22×C4112yes—
410C2×#104—21no—
411#413C22×C4111yescharacteristic
412#410—21no—
413#410—21no—
414#410C22×C4111yescharacteristic
415#410C22×C4111yescharacteristic
416#354C22×C4112yescomplemented
417#353C22×C4112yescomplemented
418#352C22×C4114yescomplemented
419AΣL(1,𝔽16)C22×C4114yescomplemented
420C41#3356011yescharacteristic, direct product factor, Sylow
4212−1+4—21no—
4222−1+4—41no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—41no—
426H(5,𝔽2)C23×C4112yes—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—42no—
432C2×#41D4×C4111yescharacteristic, complemented
433C2×#41C23×C4111yescharacteristic
434C22×Q8D4×C4111yescharacteristic, complemented
435C22×D4D4×C4111yescharacteristic
436#137—22no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440#135—42no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—41no—
444C4⋊Q8D4×C4111yescharacteristic, complemented
445#127—21no—
446#127—41no—
447#127C23×C4111yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#124—21no—
456#124—21no—
457#124—41no—
458#124—41no—
459#124D4×C4111yescharacteristic, complemented
460#124C23×C4111yescharacteristic
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—24no—
466#123D4×C4112yescomplemented
467#123C23×C4112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—42no—
486#120—22no—
487#120—24no—
488#120D4×C4112yes—
489#120C23×C4112yes—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117D4×C4111yescharacteristic
502#117D4×C4111yescharacteristic, complemented
503C2×C4⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C42D4×C4111yescharacteristic, complemented
506#104—22no—
507#104—22no—
508#101—21no—
509#100C23×C4112yes—
510#99—21no—
511#99—21no—
512#99—24no—
513#99—24no—
514#99C23×C4112yes—
515#99C23×C4112yes—
516C24C2×D4×C4112yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C4111yescharacteristic
546C2×Q8C2×D4×C4111yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C4111yescharacteristic
569C2×D4C2×D4×C4111yescharacteristic
570C2×D4C2×D4×C4111yescharacteristic
571C2×D4C24×C4111yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C4111yescharacteristic
581C22×C4C2×D4×C4111yescharacteristic
582C22×C4C2×D4×C4111yescharacteristic
583C22×C4C2×D4×C4112yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C4112yes—
623C22⋊C4C2×D4×C4112yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C4111yescharacteristic
631C42C2×D4×C4111yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23#120×C4111yescharacteristic
640C23C22×D4×C4111yescharacteristic
641C23C22×D4×C4111yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—82no—
671D4—81no—
672D4—81no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4#120×C4111yescharacteristic
703C2×C4#120×C4111yescharacteristic
704C2×C4#120×C4111yescharacteristic
705C2×C4C22×D4×C4111yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×#120×C4111yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C41×B(4,𝔽2)11yescharacteristic
738C4C41×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C41C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
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×#3551C2semidirect
2. C41×#3028C2semidirect
3. C41×#3027C2semidirect
4. C41×#3018C2semidirect
5. C41×#2200C2semidirect
6. C41×#2197C2semidirect
7. C41×#2126C2semidirect
8. C41×#2123C2semidirect
9. C41×#2122C2semidirect
13. C41×#560C22semidirect
17. C41×#551C22semidirect
43. C41×#354C22semidirect
44. C41×#353C22semidirect
45. C41×#352C22semidirect
46. C41×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C41D4semidirect
60. C22×Q8×C41D4semidirect
70. C4⋊Q8×C41D4semidirect
85. #124×C41D4semidirect
92. #123×C41D4semidirect
128. #117×C41D4semidirect
131. C2×C42×C41D4semidirect
333. #33560C41direct (N × H)
366. #3551C2×C41semidirect
367. #3028C2×C41semidirect
368. #3027C2×C41semidirect
369. #3018C2×C41semidirect
370. #2200C2×C41semidirect
371. #2197C2×C41semidirect
372. #2126C2×C41semidirect
373. #2123C2×C41semidirect
374. #2122C2×C41semidirect
386. #560C22×C41semidirect
390. #551C22×C41semidirect
416. #354C22×C41semidirect
417. #353C22×C41semidirect
418. #352C22×C41semidirect
419. AΣL(1,𝔽16)C22×C41semidirect
420. C41#33560direct (N × H)
432. C2×#41D4×C41semidirect
434. C22×Q8D4×C41semidirect
444. C4⋊Q8D4×C41semidirect
459. #124D4×C41semidirect
466. #123D4×C41semidirect
502. #117D4×C41semidirect
505. C2×C42D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35512
C41×#30282
C41×#30272
C41×#30182
C41×#22002
C41×#21972
C41×#21262
C41×#21232
C41×#21222
#3356041