Finite Group Databasebeta

← C41×#33552 #23809753

Subgroups — C41×#33552 #23809753

Order 10496.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3533C211yesmaximal, characteristic, complemented
2C41×#3026C211yesmaximal, characteristic, complemented
3C2×C41×#458C211yesmaximal, characteristic, complemented
4C41×#3019C211yesmaximal, characteristic, complemented
5C41×#2201C212yesmaximal, complemented
6C41×#2200C212yesmaximal, complemented
7C41×#2198C212yesmaximal, complemented
8C41×#2197C212yesmaximal, complemented
9C41×#2127C211yesmaximal, characteristic, complemented
10C41×#2121C211yesmaximal, characteristic, complemented
11C2×C41×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C41C2211yescharacteristic
13C41×#575—21no—
14C41×#563C2211yescharacteristic, complemented
15C41×#562—21no—
16C41×#560C2211yescharacteristic, complemented
17C41×#559C2211yescharacteristic, complemented
18C41×#553—21no—
19C41×#552—21no—
20C41×#551—21no—
21C41×#551C2211yescharacteristic, complemented
22C41×#547—21no—
23C41×#546—21no—
24C41×#542—21no—
25C41×#540—21no—
26C41×#539—21no—
27C41×#538—21no—
28C41×#538—21no—
29C41×#535C2211yescharacteristic
30C41×#534—21no—
31C41×#534C2211yescharacteristic
32C41×#525—21no—
33C2×#123×C41—21no—
34C2×#123×C41C2211yescharacteristic
35C41×#458—21no—
36C41×#458—21no—
37C41×#458—21no—
38C41×#458C2212yes—
39C41×#458C2212yes—
40C41×#458C2212yes—
41C41×B(4,𝔽2)—21no—
42C41×B(4,𝔽2)C2212yes—
43C41×#455—21no—
44C41×#455C2212yes—
45C41×#453—21no—
46C41×#453C2212yes—
47C41×#421—21no—
48C2×#100×C41C2211yescharacteristic
49C2×#99×C41—21no—
50C2×#99×C41—21no—
51C2×#99×C41C2211yescharacteristic
52C2×#99×C41C2211yescharacteristic
53C41×#354C2212yescomplemented
54C41×#353C2212yescomplemented
55C41×#352C2212yescomplemented
56C41×#352C2212yescomplemented
57C41×#352C2212yescomplemented
58C41×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C41—21no—
60H(5,𝔽2)×C41—21no—
61H(5,𝔽2)×C41—21no—
62H(5,𝔽2)×C41—42no—
63H(5,𝔽2)×C41C2312yes—
64C2×#41×C41—21no—
65C2×#41×C41—21no—
66C2×#41×C41—41no—
67C2×#41×C41D411yescharacteristic, complemented
68C22×D4×C41—21no—
69C22×D4×C41—21no—
70C22×D4×C41—41no—
71C22×D4×C41D411yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C23×C4×C41D411yescharacteristic, complemented
74#137×C41—22no—
75#137×C41—41no—
76AGL(1,ℤ/8)×C41—22no—
77AGL(1,ℤ/8)×C41—41no—
78#135×C41—42no—
79C2×M16×C41—21no—
80C4⋊Q8×C41—21no—
81#127×C41D411yescharacteristic, complemented
82#127×C41C2311yescharacteristic
83#126×C41—21no—
84#126×C41—21no—
85#126×C41—21no—
86#126×C41—21no—
87#126×C41—21no—
88#126×C41—21no—
89#125×C41—21no—
90#125×C41—21no—
91#125×C41—21no—
92#124×C41—21no—
93#124×C41—21no—
94#124×C41—21no—
95#124×C41—21no—
96#124×C41D411yescharacteristic, complemented
97#124×C41C2311yescharacteristic
98#123×C41—21no—
99#123×C41—21no—
100#123×C41—21no—
101#123×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×C41—21no—
107#123×C41—21no—
108#123×C41—21no—
109#123×C41—21no—
110#123×C41—22no—
111#123×C41—22no—
112#123×C41—22no—
113#123×C41—41no—
114#123×C41—42no—
115#123×C41D411yescharacteristic
116#123×C41D411yescharacteristic, complemented
117#123×C41D411yescharacteristic, complemented
118#123×C41C2311yescharacteristic
119#123×C41C2311yescharacteristic
120#123×C41C2311yescharacteristic
121C22⋊Q8×C41—21no—
122C22⋊Q8×C41—21no—
123C22⋊Q8×C41—21no—
124C22⋊Q8×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129#121×C41—21no—
130#121×C41—21no—
131#121×C41—21no—
132#121×C41—21no—
133#121×C41—21no—
134#121×C41—21no—
135#121×C41—21no—
136#121×C41—21no—
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41—21no—
141#121×C41—42no—
142#120×C41—21no—
143#120×C41—21no—
144#120×C41—21no—
145#120×C41—21no—
146#120×C41—22no—
147#120×C41—41no—
148#120×C41D411yescharacteristic
149#120×C41C2311yescharacteristic
150C4×Q8×C41—21no—
151C4×D4×C41—21no—
152C4×D4×C41—21no—
153C4×D4×C41—21no—
154C4×D4×C41—21no—
155C4×D4×C41—21no—
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160#117×C41—21no—
161#117×C41—21no—
162#117×C41—21no—
163#117×C41D411yescharacteristic, complemented
164C2×C4⋊C4×C41—21no—
165C2×C4⋊C4×C41—21no—
166C2×C4⋊C4×C41—41no—
167C2×C22⋊C4×C41—21no—
168C2×C22⋊C4×C41—21no—
169C2×C22⋊C4×C41—21no—
170C2×C22⋊C4×C41—21no—
171C2×C22⋊C4×C41—41no—
172C2×C22⋊C4×C41D411yescharacteristic
173C2×C22⋊C4×C41D411yescharacteristic, complemented
174#104×C41—22no—
175#104×C41—22no—
176#100×C41—21no—
177#100×C41C2312yes—
178#99×C41—21no—
179#99×C41—21no—
180#99×C41—22no—
181#99×C41—22no—
182#99×C41—22no—
183#99×C41—22no—
184#99×C41C2312yes—
185#99×C41C2312yes—
186C24×C41—21no—
187C24×C41—21no—
188C24×C41C2×D411yescharacteristic
189C24×C41C2×D411yescharacteristic
190C24×C41C2×D411yescharacteristic
191#41×C41—22no—
192#41×C41—22no—
193#41×C41—42no—
194#41×C41—41no—
195#41×C41—42no—
196#41×C41—42no—
197#41×C41—41no—
198#41×C41—41no—
199#41×C41—42no—
200#41×C41—41no—
201#41×C41—81no—
202#41×C41—81no—
203C2×Q8×C41—21no—
204C2×Q8×C41—21no—
205C2×Q8×C41—21no—
206C2×Q8×C41C2×D411yescharacteristic
207C2×D4×C41—21no—
208C2×D4×C41—22no—
209C2×D4×C41—22no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—22no—
213C2×D4×C41—22no—
214C2×D4×C41—21no—
215C2×D4×C41—21no—
216C2×D4×C41—21no—
217C2×D4×C41—21no—
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—41no—
224C2×D4×C41—41no—
225C2×D4×C41—42no—
226C2×D4×C41—42no—
227C2×D4×C41—41no—
228C2×D4×C41—41no—
229C2×D4×C41—41no—
230C2×D4×C41—41no—
231C2×D4×C41—42no—
232C2×D4×C41—42no—
233C2×D4×C41—41no—
234C2×D4×C41—41no—
235C2×D4×C41—41no—
236C2×D4×C41—41no—
237C2×D4×C41—41no—
238C2×D4×C41—42no—
239C2×D4×C41C2×D411yescharacteristic
240C2×D4×C41C2×D411yescharacteristic
241C2×D4×C41C2×D411yescharacteristic
242C2×D4×C41C2×D411yescharacteristic
243C2×D4×C41C2411yescharacteristic
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—41no—
256C22×C4×C41—41no—
257C22×C4×C41—41no—
258C22×C4×C41—41no—
259C22×C4×C41—41no—
260C22×C4×C41C2×D411yescharacteristic
261C22×C4×C41C2×D411yescharacteristic
262C22×C4×C41C2×D411yescharacteristic
263C22×C4×C41C2×D411yescharacteristic
264Q16×C41—42no—
265SD16×C41—42no—
266SD16×C41—42no—
267D8×C41—42no—
268M16×C41—22no—
269M16×C41—41no—
270C2×C8×C41—41no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—21no—
289C4⋊C4×C41—21no—
290C4⋊C4×C41—42no—
291C4⋊C4×C41—42no—
292C4⋊C4×C41—42no—
293C22⋊C4×C41—21no—
294C22⋊C4×C41—21no—
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—21no—
305C22⋊C4×C41—21no—
306C22⋊C4×C41—21no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—22no—
317C22⋊C4×C41—22no—
318C22⋊C4×C41—42no—
319C22⋊C4×C41—41no—
320C22⋊C4×C41—41no—
321C22⋊C4×C41—42no—
322C22⋊C4×C41—42no—
323C22⋊C4×C41—42no—
324C22⋊C4×C41C2×D411yescharacteristic
325C22⋊C4×C41C2×D411yescharacteristic
326C22⋊C4×C41C2×D411yescharacteristic
327C22⋊C4×C41C2×D411yescharacteristic
328C42×C41—21no—
329C42×C41—21no—
330C42×C41—21no—
331C42×C41—21no—
332C42×C41C2×D411yescharacteristic
333C42×C41C2×D411yescharacteristic
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—22no—
339C23×C41—22no—
340C23×C41—21no—
341C23×C41—21no—
342C23×C41—41no—
343C23×C41—41no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—81no—
347C23×C41—81no—
348C23×C41—81no—
349C23×C41—82no—
350C23×C41—161no—
351C23×C41#12011yescharacteristic
352C23×C41#12011yescharacteristic
353C23×C41#12011yescharacteristic
354C23×C41C22×D411yescharacteristic
355C23×C41C22×D411yescharacteristic
356Q8×C41—22no—
357Q8×C41—41no—
358Q8×C41—41no—
359Q8×C41—81no—
360Q8×C41—81no—
361D4×C41—22no—
362D4×C41—41no—
363D4×C41—41no—
364D4×C41—41no—
365D4×C41—41no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—42no—
369D4×C41—42no—
370D4×C41—42no—
371D4×C41—42no—
372D4×C41—42no—
373D4×C41—42no—
374D4×C41—41no—
375D4×C41—41no—
376D4×C41—41no—
377D4×C41—41no—
378D4×C41—81no—
379D4×C41—81no—
380D4×C41—81no—
381D4×C41—81no—
382D4×C41—81no—
383D4×C41—81no—
384D4×C41—81no—
385D4×C41—81no—
386D4×C41—81no—
387D4×C41—162no—
388C2×C4×C41—21no—
389C2×C4×C41—21no—
390C2×C4×C41—22no—
391C2×C4×C41—22no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—21no—
396C2×C4×C41—21no—
397C2×C4×C41—21no—
398C2×C4×C41—21no—
399C2×C4×C41—21no—
400C2×C4×C41—21no—
401C2×C4×C41—21no—
402C2×C4×C41—42no—
403C2×C4×C41—42no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41—41no—
409C2×C4×C41—41no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—42no—
413C2×C4×C41—42no—
414C2×C4×C41—81no—
415C2×C4×C41—81no—
416C2×C4×C41—81no—
417C2×C4×C41—81no—
418C2×C4×C41—81no—
419C2×C4×C41—81no—
420C2×C4×C41—81no—
421C2×C4×C41—81no—
422C2×C4×C41—82no—
423C2×C4×C41—161no—
424C2×C4×C41#12011yescharacteristic
425C2×C4×C41C22×D411yescharacteristic
426C8×C41—42no—
427#33552C4111yesmaximal, characteristic, direct product factor, Sylow
428C22×C41—21no—
429C22×C41—21no—
430C22×C41—21no—
431C22×C41—21no—
432C22×C41—41no—
433C22×C41—41no—
434C22×C41—41no—
435C22×C41—41no—
436C22×C41—41no—
437C22×C41—42no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—42no—
443C22×C41—41no—
444C22×C41—41no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41—82no—
449C22×C41—82no—
450C22×C41—82no—
451C22×C41—82no—
452C22×C41—161no—
453C22×C41—161no—
454C22×C41B(4,𝔽2)11yescharacteristic
455C22×C41B(4,𝔽2)11yescharacteristic
456C22×C41C2×#12011yescharacteristic
457C4×C41—21no—
458C4×C41—21no—
459C4×C41—41no—
460C4×C41—41no—
461C4×C41—41no—
462C4×C41—41no—
463C4×C41—41no—
464C4×C41—41no—
465C4×C41—42no—
466C4×C41—41no—
467C4×C41—41no—
468C4×C41—41no—
469C4×C41—41no—
470C4×C41—82no—
471C4×C41—82no—
472#3533C2×C4111yescharacteristic, complemented
473#3026C2×C4111yescharacteristic, complemented
474C2×#458C2×C4111yescharacteristic, complemented
475#3019C2×C4111yescharacteristic, complemented
476#2201C2×C4112yescomplemented
477#2200C2×C4112yescomplemented
478#2198C2×C4112yescomplemented
479#2197C2×C4112yescomplemented
480#2127C2×C4111yescharacteristic, complemented
481#2121C2×C4111yescharacteristic, complemented
482C2×#352C2×C4111yescharacteristic, complemented
483C2×C41—21no—
484C2×C41—21no—
485C2×C41—21no—
486C2×C41—41no—
487C2×C41—41no—
488C2×C41—41no—
489C2×C41—41no—
490C2×C41—81no—
491C2×C41—81no—
492C2×C41—82no—
493C2×C41C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C4111yescharacteristic
495#575—21no—
496#563C22×C4111yescharacteristic, complemented
497#562—21no—
498#560C22×C4111yescharacteristic, complemented
499#559C22×C4111yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C4111yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C4111yescharacteristic
512#534—21no—
513#534C22×C4111yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C4111yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C4112yes—
521#458C22×C4112yes—
522#458C22×C4112yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C4112yes—
525#455—21no—
526#455C22×C4112yes—
527#453—21no—
528#453C22×C4112yes—
529#421—21no—
530C2×#100C22×C4111yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C4111yescharacteristic
534C2×#99C22×C4111yescharacteristic
535#354C22×C4112yescomplemented
536#353C22×C4112yescomplemented
537#352C22×C4112yescomplemented
538#352C22×C4112yescomplemented
539#352C22×C4112yescomplemented
540AΣL(1,𝔽16)C22×C4112yescomplemented
541C41#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C4112yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C4111yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C4111yescharacteristic
555C22×D4C23×C4111yescharacteristic
556C23×C4D4×C4111yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C4111yescharacteristic, complemented
565#127C23×C4111yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C4111yescharacteristic, complemented
580#124C23×C4111yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C4111yescharacteristic
599#123D4×C4111yescharacteristic, complemented
600#123D4×C4111yescharacteristic, complemented
601#123C23×C4111yescharacteristic
602#123C23×C4111yescharacteristic
603#123C23×C4111yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C4111yescharacteristic
632#120C23×C4111yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C4111yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C4111yescharacteristic
656C2×C22⋊C4D4×C4111yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C4112yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C4112yes—
668#99C23×C4112yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C4111yescharacteristic
672C24C2×D4×C4111yescharacteristic
673C24C2×D4×C4111yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C4111yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C4111yescharacteristic
723C2×D4C2×D4×C4111yescharacteristic
724C2×D4C2×D4×C4111yescharacteristic
725C2×D4C2×D4×C4111yescharacteristic
726C2×D4C24×C4111yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C4111yescharacteristic
744C22×C4C2×D4×C4111yescharacteristic
745C22×C4C2×D4×C4111yescharacteristic
746C22×C4C2×D4×C4111yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C4111yescharacteristic
808C22⋊C4C2×D4×C4111yescharacteristic
809C22⋊C4C2×D4×C4111yescharacteristic
810C22⋊C4C2×D4×C4111yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C4111yescharacteristic
816C42C2×D4×C4111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C4111yescharacteristic
835C23#120×C4111yescharacteristic
836C23#120×C4111yescharacteristic
837C23C22×D4×C4111yescharacteristic
838C23C22×D4×C4111yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—41no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C4111yescharacteristic
908C2×C4C22×D4×C4111yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C41×B(4,𝔽2)11yescharacteristic
937C22C41×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C4111yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×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 ◁ C23×C41 ◁ C22×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3533C2semidirect
2. C41×#3026C2semidirect
3. C2×C41×#458C2semidirect
4. C41×#3019C2semidirect
5. C41×#2201C2semidirect
6. C41×#2200C2semidirect
7. C41×#2198C2semidirect
8. C41×#2197C2semidirect
9. C41×#2127C2semidirect
10. C41×#2121C2semidirect
11. C2×C41×#352C2semidirect
14. C41×#563C22semidirect
16. C41×#560C22semidirect
17. C41×#559C22semidirect
21. C41×#551C22semidirect
53. C41×#354C22semidirect
54. C41×#353C22semidirect
55. C41×#352C22semidirect
56. C41×#352C22semidirect
57. C41×#352C22semidirect
58. C41×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C41D4semidirect
73. C23×C4×C41D4semidirect
81. #127×C41D4semidirect
96. #124×C41D4semidirect
116. #123×C41D4semidirect
117. #123×C41D4semidirect
163. #117×C41D4semidirect
173. C2×C22⋊C4×C41D4semidirect
427. #33552C41direct (N × H)
472. #3533C2×C41semidirect
473. #3026C2×C41semidirect
474. C2×#458C2×C41semidirect
475. #3019C2×C41semidirect
476. #2201C2×C41semidirect
477. #2200C2×C41semidirect
478. #2198C2×C41semidirect
479. #2197C2×C41semidirect
480. #2127C2×C41semidirect
481. #2121C2×C41semidirect
482. C2×#352C2×C41semidirect
496. #563C22×C41semidirect
498. #560C22×C41semidirect
499. #559C22×C41semidirect
503. #551C22×C41semidirect
535. #354C22×C41semidirect
536. #353C22×C41semidirect
537. #352C22×C41semidirect
538. #352C22×C41semidirect
539. #352C22×C41semidirect
540. AΣL(1,𝔽16)C22×C41semidirect
541. C41#33552direct (N × H)
550. C2×#41D4×C41semidirect
556. C23×C4D4×C41semidirect
564. #127D4×C41semidirect
579. #124D4×C41semidirect
599. #123D4×C41semidirect
600. #123D4×C41semidirect
646. #117D4×C41semidirect
656. C2×C22⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35332
C41×#30262
C2×C41×#4582
C41×#30192
C41×#22012
C41×#22002
C41×#21982
C41×#21972
C41×#21272
C41×#21212
C2×C41×#3522
#3355241