Finite Group Databasebeta

← C41×#33555 #23809756

Subgroups — C41×#33555 #23809756

Order 10496.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3540C211yesmaximal, characteristic, complemented
2C41×#3027C211yesmaximal, characteristic, complemented
3C41×#3025C211yesmaximal, characteristic, complemented
4C41×#3022C211yesmaximal, characteristic, complemented
5C41×#2199C214yesmaximal, complemented
6C41×#2197C214yesmaximal, complemented
7C41×#2129C211yesmaximal, characteristic, complemented
8C41×#2122C211yesmaximal, characteristic, complemented
9C41×#2120C211yesmaximal, characteristic, complemented
10C41×#585C2211yescharacteristic
11C2×#137×C41—21no—
12C41×H(3,𝔽4)C2212yescomplemented
13C41×#560—21no—
14C41×#559—21no—
15C41×#556—21no—
16C41×#555—21no—
17C41×#551C2212yescomplemented
18C41×#548—21no—
19C41×#546—21no—
20C41×#542—22no—
21C41×#542—21no—
22C41×#538—22no—
23C41×#536C2211yescharacteristic
24C41×#535—21no—
25C41×#535C2211yescharacteristic
26C41×#525—21no—
27C41×#525—21no—
28C41×#525C2211yescharacteristic
29C41×#458—21no—
30C41×#458C2212yes—
31C41×B(4,𝔽2)—21no—
32C41×B(4,𝔽2)—22no—
33C41×B(4,𝔽2)C2214yes—
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×AΣL(1,𝔽16)C2212yescomplemented
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×C41C2311yescharacteristic
59C22×Q8×C41D411yescharacteristic, complemented
60C22×D4×C41D411yescharacteristic, complemented
61C23×C4×C41D411yescharacteristic, complemented
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×C41D412yescomplemented
69#127×C41—21no—
70#127×C41—41no—
71#126×C41—22no—
72#126×C41—22no—
73#126×C41—22no—
74#124×C41—22no—
75#124×C41—21no—
76#124×C41—21no—
77#124×C41—22no—
78#124×C41—22no—
79#124×C41—22no—
80#124×C41—22no—
81#124×C41—41no—
82#124×C41C2312yes—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41—21no—
86#123×C41—21no—
87#123×C41—22no—
88#123×C41—22no—
89#123×C41D411yescharacteristic, complemented
90#123×C41C2311yescharacteristic
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41—41no—
98#121×C41—21no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—21no—
103#121×C41—21no—
104#121×C41—21no—
105#121×C41—42no—
106#121×C41—41no—
107#120×C41—22no—
108#120×C41—22no—
109#120×C41—22no—
110#120×C41—24no—
111#120×C41D411yescharacteristic, complemented
112#120×C41D412yescomplemented
113#120×C41C2311yescharacteristic
114#120×C41C2312yes—
115C4×Q8×C41—21no—
116C4×Q8×C41—22no—
117C4×D4×C41—22no—
118C4×D4×C41—22no—
119C4×D4×C41—21no—
120C4×D4×C41—22no—
121C4×D4×C41—21no—
122C4×D4×C41—21no—
123C4×D4×C41—42no—
124#117×C41—21no—
125#117×C41—22no—
126#117×C41—21no—
127#117×C41—21no—
128#117×C41D411yescharacteristic, complemented
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—24no—
138#99×C41—22no—
139#99×C41—22no—
140#99×C41C2312yes—
141#99×C41C2312yes—
142C24×C41C2×D412yes—
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—41no—
168C2×Q8×C41—41no—
169C2×Q8×C41—42no—
170C2×Q8×C41C2×D412yes—
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—21no—
182C2×D4×C41—22no—
183C2×D4×C41—21no—
184C2×D4×C41—21no—
185C2×D4×C41—41no—
186C2×D4×C41—41no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41—42no—
190C2×D4×C41—41no—
191C2×D4×C41—42no—
192C2×D4×C41—44no—
193C2×D4×C41C2×D411yescharacteristic
194C2×D4×C41C2×D411yescharacteristic
195C2×D4×C41C2411yescharacteristic
196C22×C4×C41—22no—
197C22×C4×C41—22no—
198C22×C4×C41—22no—
199C22×C4×C41—22no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—41no—
204C22×C4×C41—41no—
205C22×C4×C41—41no—
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210Q16×C41—44no—
211SD16×C41—44no—
212M16×C41—22no—
213M16×C41—41no—
214C2×C8×C41—41no—
215C4⋊C4×C41—22no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—22no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—22no—
221C4⋊C4×C41—22no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—41no—
226C4⋊C4×C41—41no—
227C4⋊C4×C41—42no—
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—21no—
236C22⋊C4×C41—21no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—21no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—21no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—44no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41C2×D412yes—
249C22⋊C4×C41C2×D411yescharacteristic
250C22⋊C4×C41C2×D411yescharacteristic
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—22no—
261C23×C41—21no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—42no—
265C23×C41—81no—
266C23×C41—82no—
267C23×C41#12011yescharacteristic
268C23×C41C22×D411yescharacteristic
269C23×C41C22×D411yescharacteristic
270Q8×C41—22no—
271Q8×C41—41no—
272Q8×C41—42no—
273Q8×C41—41no—
274Q8×C41—41no—
275Q8×C41—41no—
276Q8×C41—41no—
277Q8×C41—41no—
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—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—81no—
293D4×C41—81no—
294D4×C41—82no—
295D4×C41—82no—
296D4×C41—82no—
297D4×C41—81no—
298D4×C41—82no—
299D4×C41—84no—
300D4×C41—164no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—22no—
308C2×C4×C41—22no—
309C2×C4×C41—21no—
310C2×C4×C41—22no—
311C2×C4×C41—21no—
312C2×C4×C41—22no—
313C2×C4×C41—22no—
314C2×C4×C41—21no—
315C2×C4×C41—42no—
316C2×C4×C41—42no—
317C2×C4×C41—42no—
318C2×C4×C41—41no—
319C2×C4×C41—42no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
325C2×C4×C41—81no—
326C2×C4×C41—81no—
327C2×C4×C41—82no—
328C2×C4×C41—82no—
329C2×C4×C41#12011yescharacteristic
330C2×C4×C41#12011yescharacteristic
331C2×C4×C41#12011yescharacteristic
332C2×C4×C41C22×D411yescharacteristic
333C8×C41—42no—
334#33555C4111yesmaximal, characteristic, direct product factor, Sylow
335C22×C41—21no—
336C22×C41—21no—
337C22×C41—21no—
338C22×C41—41no—
339C22×C41—41no—
340C22×C41—41no—
341C22×C41—42no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—42no—
345C22×C41—42no—
346C22×C41—42no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—82no—
350C22×C41—82no—
351C22×C41—84no—
352C22×C41—81no—
353C22×C41—161no—
354C22×C41C2×#12011yescharacteristic
355C4×C41—21no—
356C4×C41—21no—
357C4×C41—21no—
358C4×C41—41no—
359C4×C41—42no—
360C4×C41—42no—
361C4×C41—41no—
362C4×C41—42no—
363C4×C41—41no—
364C4×C41—42no—
365C4×C41—82no—
366C4×C41—82no—
367C4×C41B(4,𝔽2)11yescharacteristic
368C4×C41B(4,𝔽2)11yescharacteristic
369#3540C2×C4111yescharacteristic, complemented
370#3027C2×C4111yescharacteristic, complemented
371#3025C2×C4111yescharacteristic, complemented
372#3022C2×C4111yescharacteristic, complemented
373#2199C2×C4114yescomplemented
374#2197C2×C4114yescomplemented
375#2129C2×C4111yescharacteristic, complemented
376#2122C2×C4111yescharacteristic, complemented
377#2120C2×C4111yescharacteristic, complemented
378C2×C41—21no—
379C2×C41—41no—
380C2×C41—41no—
381C2×C41—41no—
382C2×C41—81no—
383C2×C41—82no—
384C2×C41—82no—
385C2×C41C2×B(4,𝔽2)11yescharacteristic
386#585C22×C4111yescharacteristic
387C2×#137—21no—
388H(3,𝔽4)C22×C4112yescomplemented
389#560—21no—
390#559—21no—
391#556—21no—
392#555—21no—
393#551C22×C4112yescomplemented
394#548—21no—
395#546—21no—
396#542—22no—
397#542—21no—
398#538—22no—
399#536C22×C4111yescharacteristic
400#535—21no—
401#535C22×C4111yescharacteristic
402#525—21no—
403#525—21no—
404#525C22×C4111yescharacteristic
405#458—21no—
406#458C22×C4112yes—
407B(4,𝔽2)—21no—
408B(4,𝔽2)—22no—
409B(4,𝔽2)C22×C4114yes—
410B(4,𝔽2)C22×C4112yes—
411#456—22no—
412#455C22×C4114yes—
413#421—21no—
414#413C22×C4111yescharacteristic
415#410—21no—
416#410—21no—
417#410C22×C4111yescharacteristic
418#410C22×C4111yescharacteristic
419#354C22×C4114yescomplemented
420#352C22×C4112yescomplemented
421AΣL(1,𝔽16)C22×C4112yescomplemented
422AΣL(1,𝔽16)C22×C4114yescomplemented
423C41#3355511yescharacteristic, direct product factor, Sylow
4242−1+4—21no—
4252−1+4—41no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)C23×C4112yes—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—42no—
435C2×#41C23×C4111yescharacteristic
436C22×Q8D4×C4111yescharacteristic, complemented
437C22×D4D4×C4111yescharacteristic, complemented
438C23×C4D4×C4111yescharacteristic, complemented
439#137—24no—
440#137—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×M16—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C4112yescomplemented
446#127—21no—
447#127—41no—
448#126—22no—
449#126—22no—
450#126—22no—
451#124—22no—
452#124—21no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459#124C23×C4112yes—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123D4×C4111yescharacteristic, complemented
467#123C23×C4111yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—41no—
475#121—21no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—42no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—24no—
488#120D4×C4111yescharacteristic, complemented
489#120D4×C4112yescomplemented
490#120C23×C4111yescharacteristic
491#120C23×C4112yes—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—42no—
501#117—21no—
502#117—22no—
503#117—21no—
504#117—21no—
505#117D4×C4111yescharacteristic, complemented
506#117D4×C4111yescharacteristic, complemented
507#117D4×C4111yescharacteristic, complemented
508C2×C22⋊C4—22no—
509#104—24no—
510#101—21no—
511#100C23×C4112yes—
512#99—21no—
513#99—21no—
514#99—24no—
515#99—22no—
516#99—22no—
517#99C23×C4112yes—
518#99C23×C4112yes—
519C24C2×D4×C4112yes—
520C24C2×D4×C4111yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C4112yes—
548C2×Q8C2×D4×C4111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C4111yescharacteristic
571C2×D4C2×D4×C4111yescharacteristic
572C2×D4C24×C4111yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C4111yescharacteristic
584C22×C4C2×D4×C4111yescharacteristic
585C22×C4C2×D4×C4111yescharacteristic
586C22×C4C2×D4×C4111yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C4112yes—
626C22⋊C4C2×D4×C4111yescharacteristic
627C22⋊C4C2×D4×C4111yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C4112yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23#120×C4111yescharacteristic
645C23C22×D4×C4111yescharacteristic
646C23C22×D4×C4111yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C4111yescharacteristic
707C2×C4#120×C4111yescharacteristic
708C2×C4#120×C4111yescharacteristic
709C2×C4C22×D4×C4111yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×#120×C4111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C41×B(4,𝔽2)11yescharacteristic
744C4C41×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3027C2semidirect
3. C41×#3025C2semidirect
4. C41×#3022C2semidirect
5. C41×#2199C2semidirect
6. C41×#2197C2semidirect
7. C41×#2129C2semidirect
8. C41×#2122C2semidirect
9. C41×#2120C2semidirect
12. C41×H(3,𝔽4)C22semidirect
17. C41×#551C22semidirect
43. C41×#354C22semidirect
44. C41×#352C22semidirect
45. C41×AΣL(1,𝔽16)C22semidirect
46. C41×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C41D4semidirect
60. C22×D4×C41D4semidirect
61. C23×C4×C41D4semidirect
68. C4⋊Q8×C41D4semidirect
89. #123×C41D4semidirect
111. #120×C41D4semidirect
112. #120×C41D4semidirect
128. #117×C41D4semidirect
129. #117×C41D4semidirect
130. #117×C41D4semidirect
334. #33555C41direct (N × H)
369. #3540C2×C41semidirect
370. #3027C2×C41semidirect
371. #3025C2×C41semidirect
372. #3022C2×C41semidirect
373. #2199C2×C41semidirect
374. #2197C2×C41semidirect
375. #2129C2×C41semidirect
376. #2122C2×C41semidirect
377. #2120C2×C41semidirect
388. H(3,𝔽4)C22×C41semidirect
393. #551C22×C41semidirect
419. #354C22×C41semidirect
420. #352C22×C41semidirect
421. AΣL(1,𝔽16)C22×C41semidirect
422. AΣL(1,𝔽16)C22×C41semidirect
423. C41#33555direct (N × H)
436. C22×Q8D4×C41semidirect
437. C22×D4D4×C41semidirect
438. C23×C4D4×C41semidirect
445. C4⋊Q8D4×C41semidirect
466. #123D4×C41semidirect
488. #120D4×C41semidirect
489. #120D4×C41semidirect
505. #117D4×C41semidirect
506. #117D4×C41semidirect
507. #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×#30272
C41×#30252
C41×#30222
C41×#21992
C41×#21972
C41×#21292
C41×#21222
C41×#21202
#3355541