Finite Group Databasebeta

← C41×#33556 #23809757

Subgroups — C41×#33556 #23809757

Order 10496.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3540C211yesmaximal, characteristic, complemented
2C41×#3028C211yesmaximal, characteristic, complemented
3C41×#3025C211yesmaximal, characteristic, complemented
4C41×#3021C211yesmaximal, characteristic, complemented
5C41×#2200C214yesmaximal, complemented
6C41×#2198C214yesmaximal, complemented
7C41×#2128C211yesmaximal, characteristic, complemented
8C41×#2123C211yesmaximal, characteristic, complemented
9C41×#2120C211yesmaximal, characteristic, complemented
10C41×#585C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C41—21no—
12C41×H(3,𝔽4)—21no—
13C41×#560C2212yescomplemented
14C41×#559C2212yescomplemented
15C41×#556—21no—
16C41×#555—21no—
17C41×#551—21no—
18C41×#548—21no—
19C41×#546—21no—
20C41×#542—22no—
21C41×#542—21no—
22C41×#538—22no—
23C41×#536—21no—
24C41×#536C2211yescharacteristic
25C41×#535C2211yescharacteristic
26C41×#525—21no—
27C41×#525—21no—
28C41×#525C2211yescharacteristic
29C41×#458—21no—
30C41×#458—22no—
31C41×#458C2212yescomplemented
32C41×#458C2214yescomplemented
33C41×B(4,𝔽2)—21no—
34C41×B(4,𝔽2)C2212yescomplemented
35C41×#454—22no—
36C41×#453C2214yes—
37C41×#421—21no—
38C41×#413C2211yescharacteristic
39C41×#410—21no—
40C41×#410—21no—
41C41×#410C2211yescharacteristic
42C41×#410C2211yescharacteristic
43C41×#353C2214yescomplemented
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—21no—
57C2×#41×C41—42no—
58C2×#41×C41C2311yescharacteristic
59C22×Q8×C41D411yescharacteristic, complemented
60C22×D4×C41D411yescharacteristic, complemented
61C23×C4×C41D411yescharacteristic
62AGL(1,ℤ/8)×C41—24no—
63AGL(1,ℤ/8)×C41—42no—
64C2×SD16×C41—41no—
65C2×D8×C41—41no—
66C2×M16×C41—21no—
67C4⋊Q8×C41—21no—
68C4⋊Q8×C41—21no—
69C4⋊Q8×C41—41no—
70#127×C41C2312yes—
71#126×C41—22no—
72#126×C41—22no—
73#126×C41—22no—
74#124×C41—22no—
75#124×C41—21no—
76#124×C41—22no—
77#124×C41—22no—
78#124×C41—21no—
79#124×C41—22no—
80#124×C41—22no—
81#124×C41—41no—
82#124×C41D412yescomplemented
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—22no—
86#123×C41—22no—
87#123×C41—24no—
88#123×C41D411yescharacteristic
89#123×C41D412yescomplemented
90#123×C41C2311yescharacteristic
91#123×C41C2312yes—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—42no—
99C22⋊Q8×C41—41no—
100#121×C41—21no—
101#121×C41—21no—
102#121×C41—22no—
103#121×C41—21no—
104#121×C41—21no—
105#121×C41—22no—
106#121×C41—22no—
107#121×C41—41no—
108#120×C41—22no—
109#120×C41—22no—
110#120×C41—21no—
111#120×C41—21no—
112#120×C41—22no—
113#120×C41D411yescharacteristic
114#120×C41C2311yescharacteristic
115C4×Q8×C41—21no—
116C4×Q8×C41—22no—
117C4×D4×C41—22no—
118C4×D4×C41—21no—
119C4×D4×C41—22no—
120C4×D4×C41—21no—
121C4×D4×C41—21no—
122C4×D4×C41—22no—
123C4×D4×C41—42no—
124#117×C41—21no—
125#117×C41—22no—
126#117×C41—21no—
127#117×C41—21no—
128#117×C41D411yescharacteristic
129#117×C41D411yescharacteristic, complemented
130#117×C41D411yescharacteristic, complemented
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×C41—21no—
143C24×C41C2×D411yescharacteristic
144#41×C41—22no—
145#41×C41—22no—
146#41×C41—41no—
147#41×C41—41no—
148#41×C41—42no—
149#41×C41—41no—
150#41×C41—41no—
151#41×C41—41no—
152#41×C41—41no—
153#41×C41—41no—
154#41×C41—42no—
155#41×C41—42no—
156#41×C41—42no—
157#41×C41—41no—
158#41×C41—41no—
159#41×C41—41no—
160#41×C41—81no—
161#41×C41—81no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—22no—
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×D4×C41—21no—
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—22no—
176C2×D4×C41—22no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—21no—
180C2×D4×C41—22no—
181C2×D4×C41—22no—
182C2×D4×C41—21no—
183C2×D4×C41—21no—
184C2×D4×C41—41no—
185C2×D4×C41—41no—
186C2×D4×C41—42no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41—41no—
190C2×D4×C41—42no—
191C2×D4×C41C2×D411yescharacteristic
192C2×D4×C41C2×D411yescharacteristic
193C2×D4×C41C2×D412yes—
194C2×D4×C41C2411yescharacteristic
195C22×C4×C41—22no—
196C22×C4×C41—22no—
197C22×C4×C41—22no—
198C22×C4×C41—22no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—41no—
202C22×C4×C41—41no—
203C22×C4×C41—41no—
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D412yes—
209SD16×C41—44no—
210D8×C41—44no—
211M16×C41—22no—
212M16×C41—41no—
213C2×C8×C41—41no—
214C4⋊C4×C41—22no—
215C4⋊C4×C41—22no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—22no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—22no—
224C4⋊C4×C41—41no—
225C4⋊C4×C41—41no—
226C4⋊C4×C41—42no—
227C4⋊C4×C41—44no—
228C22⋊C4×C41—22no—
229C22⋊C4×C41—22no—
230C22⋊C4×C41—22no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—21no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—21no—
237C22⋊C4×C41—21no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—22no—
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—22no—
259C23×C41—22no—
260C23×C41—21no—
261C23×C41—22no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—81no—
265C23×C41—81no—
266C23×C41—82no—
267C23×C41#12011yescharacteristic
268C23×C41C22×D411yescharacteristic
269C23×C41C22×D411yescharacteristic
270Q8×C41—22no—
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—42no—
284D4×C41—41no—
285D4×C41—41no—
286D4×C41—42no—
287D4×C41—42no—
288D4×C41—42no—
289D4×C41—42no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—81no—
294D4×C41—82no—
295D4×C41—82no—
296D4×C41—82no—
297D4×C41—81no—
298D4×C41—82no—
299D4×C41—84no—
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—22no—
311C2×C4×C41—21no—
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—41no—
322C2×C4×C41—42no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
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#33556C4111yesmaximal, 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—42no—
341C22×C41—41no—
342C22×C41—41no—
343C22×C41—42no—
344C22×C41—42no—
345C22×C41—42no—
346C22×C41—41no—
347C22×C41—42no—
348C22×C41—82no—
349C22×C41—82no—
350C22×C41—81no—
351C22×C41—161no—
352C22×C41—162no—
353C22×C41C2×#12011yescharacteristic
354C4×C41—21no—
355C4×C41—21no—
356C4×C41—21no—
357C4×C41—41no—
358C4×C41—42no—
359C4×C41—42no—
360C4×C41—41no—
361C4×C41—42no—
362C4×C41—41no—
363C4×C41—42no—
364C4×C41—82no—
365C4×C41—82no—
366C4×C41B(4,𝔽2)11yescharacteristic
367C4×C41B(4,𝔽2)11yescharacteristic
368#3540C2×C4111yescharacteristic, complemented
369#3028C2×C4111yescharacteristic, complemented
370#3025C2×C4111yescharacteristic, complemented
371#3021C2×C4111yescharacteristic, complemented
372#2200C2×C4114yescomplemented
373#2198C2×C4114yescomplemented
374#2128C2×C4111yescharacteristic, complemented
375#2123C2×C4111yescharacteristic, complemented
376#2120C2×C4111yescharacteristic, complemented
377C2×C41—21no—
378C2×C41—41no—
379C2×C41—41no—
380C2×C41—41no—
381C2×C41—81no—
382C2×C41—82no—
383C2×C41—82no—
384C2×C41C2×B(4,𝔽2)11yescharacteristic
385#585C22×C4111yescharacteristic
386C2×AGL(1,ℤ/8)—21no—
387H(3,𝔽4)—21no—
388#560C22×C4112yescomplemented
389#559C22×C4112yescomplemented
390#556—21no—
391#555—21no—
392#551—21no—
393#548—21no—
394#546—21no—
395#542—22no—
396#542—21no—
397#538—22no—
398#536—21no—
399#536C22×C4111yescharacteristic
400#535C22×C4111yescharacteristic
401#525—21no—
402#525—21no—
403#525C22×C4111yescharacteristic
404#458—21no—
405#458—22no—
406#458C22×C4112yescomplemented
407#458C22×C4114yescomplemented
408B(4,𝔽2)—21no—
409B(4,𝔽2)C22×C4112yescomplemented
410#454—22no—
411#453C22×C4114yes—
412#421—21no—
413#413C22×C4111yescharacteristic
414#410—21no—
415#410—21no—
416#410C22×C4111yescharacteristic
417#410C22×C4111yescharacteristic
418#353C22×C4114yescomplemented
419#352C22×C4112yescomplemented
420#352C22×C4114yescomplemented
421AΣL(1,𝔽16)C22×C4112yescomplemented
422C41#3355611yescharacteristic, direct product factor, Sylow
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C4112yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C4111yescharacteristic
435C22×Q8D4×C4111yescharacteristic, complemented
436C22×D4D4×C4111yescharacteristic, complemented
437C23×C4D4×C4111yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C4112yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C4112yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C4111yescharacteristic
465#123D4×C4112yescomplemented
466#123C23×C4111yescharacteristic
467#123C23×C4112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C4111yescharacteristic
490#120C23×C4111yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C4111yescharacteristic
505#117D4×C4111yescharacteristic, complemented
506#117D4×C4111yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C4112yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C4112yes—
517#99C23×C4112yes—
518C24—21no—
519C24C2×D4×C4111yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C4111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C4111yescharacteristic
568C2×D4C2×D4×C4111yescharacteristic
569C2×D4C2×D4×C4112yes—
570C2×D4C24×C4111yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C4111yescharacteristic
581C22×C4C2×D4×C4111yescharacteristic
582C22×C4C2×D4×C4111yescharacteristic
583C22×C4C2×D4×C4111yescharacteristic
584C22×C4C2×D4×C4112yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C4111yescharacteristic
625C22⋊C4C2×D4×C4111yescharacteristic
626C22⋊C4C2×D4×C4112yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C4112yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C4111yescharacteristic
644C23C22×D4×C4111yescharacteristic
645C23C22×D4×C4111yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C4111yescharacteristic
705C2×C4#120×C4111yescharacteristic
706C2×C4#120×C4111yescharacteristic
707C2×C4C22×D4×C4111yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C4111yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C41×B(4,𝔽2)11yescharacteristic
742C4C41×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×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×#3540C2semidirect
2. C41×#3028C2semidirect
3. C41×#3025C2semidirect
4. C41×#3021C2semidirect
5. C41×#2200C2semidirect
6. C41×#2198C2semidirect
7. C41×#2128C2semidirect
8. C41×#2123C2semidirect
9. C41×#2120C2semidirect
13. C41×#560C22semidirect
14. C41×#559C22semidirect
31. C41×#458C22semidirect
32. C41×#458C22semidirect
34. C41×B(4,𝔽2)C22semidirect
43. C41×#353C22semidirect
44. C41×#352C22semidirect
45. C41×#352C22semidirect
46. C41×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C41D4semidirect
60. C22×D4×C41D4semidirect
82. #124×C41D4semidirect
89. #123×C41D4semidirect
129. #117×C41D4semidirect
130. #117×C41D4semidirect
333. #33556C41direct (N × H)
368. #3540C2×C41semidirect
369. #3028C2×C41semidirect
370. #3025C2×C41semidirect
371. #3021C2×C41semidirect
372. #2200C2×C41semidirect
373. #2198C2×C41semidirect
374. #2128C2×C41semidirect
375. #2123C2×C41semidirect
376. #2120C2×C41semidirect
388. #560C22×C41semidirect
389. #559C22×C41semidirect
406. #458C22×C41semidirect
407. #458C22×C41semidirect
409. B(4,𝔽2)C22×C41semidirect
418. #353C22×C41semidirect
419. #352C22×C41semidirect
420. #352C22×C41semidirect
421. AΣL(1,𝔽16)C22×C41semidirect
422. C41#33556direct (N × H)
435. C22×Q8D4×C41semidirect
436. C22×D4D4×C41semidirect
458. #124D4×C41semidirect
465. #123D4×C41semidirect
505. #117D4×C41semidirect
506. #117D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35402
C41×#30282
C41×#30252
C41×#30212
C41×#22002
C41×#21982
C41×#21282
C41×#21232
C41×#21202
#3355641