Finite Group Databasebeta

← C41×#33553 #23809754

Subgroups — C41×#33553 #23809754

Order 10496.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3537C211yesmaximal, characteristic, complemented
2C41×#3027C211yesmaximal, characteristic, complemented
3C41×#3025C211yesmaximal, characteristic, complemented
4C41×#3021C211yesmaximal, characteristic, complemented
5C41×#2200C214yesmaximal, complemented
6C41×#2196C214yesmaximal, complemented
7C41×#2128C211yesmaximal, characteristic, complemented
8C41×#2122C211yesmaximal, characteristic, complemented
9C41×#2120C211yesmaximal, characteristic, complemented
10C41×#585C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C41—21no—
12C41×#560—21no—
13C41×#560C2212yescomplemented
14C41×#553—21no—
15C41×#553—21no—
16D42×C41—21no—
17D42×C41—21no—
18D42×C41—21no—
19D42×C41C2212yescomplemented
20C41×#540—21no—
21C41×#538—22no—
22C41×#535—21no—
23C41×#535C2211yescharacteristic
24C41×#535C2211yescharacteristic
25C41×#534—22no—
26C41×#525—21no—
27C41×#525C2211yescharacteristic
28C2×#121×C41—21no—
29C41×#458—21no—
30C41×#458C2212yescomplemented
31C41×B(4,𝔽2)—21no—
32C41×B(4,𝔽2)—22no—
33C41×B(4,𝔽2)C2212yescomplemented
34C41×B(4,𝔽2)C2214yescomplemented
35C41×#454—22no—
36C41×#453C2214yescomplemented
37C41×#421—21no—
38C41×#413C2211yescharacteristic, complemented
39C41×#410—21no—
40C41×#410—21no—
41C41×#410C2211yescharacteristic, complemented
42C41×#410C2211yescharacteristic, complemented
43C41×#353C2214yescomplemented
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—42no—
57C2×#41×C41C2311yescharacteristic
58C22×D4×C41—21no—
59C22×D4×C41—22no—
60C22×D4×C41—22no—
61C22×D4×C41—22no—
62C22×D4×C41D411yescharacteristic, complemented
63C22×D4×C41D411yescharacteristic, complemented
64C23×C4×C41D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C41—24no—
66AGL(1,ℤ/8)×C41—42no—
67C2×SD16×C41—41no—
68C2×D8×C41—41no—
69C2×M16×C41—21no—
70#127×C41—21no—
71#127×C41—21no—
72#127×C41—41no—
73#127×C41C2312yes—
74#126×C41—22no—
75#126×C41—22no—
76#125×C41—21no—
77#124×C41—21no—
78#124×C41—41no—
79#124×C41D412yescomplemented
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—22no—
85#123×C41D411yescharacteristic, complemented
86#123×C41C2311yescharacteristic
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—41no—
89#121×C41—22no—
90#121×C41—21no—
91#121×C41—21no—
92#121×C41—22no—
93#121×C41—22no—
94#121×C41—21no—
95#121×C41—22no—
96#121×C41—21no—
97#121×C41—21no—
98#121×C41—22no—
99#121×C41—21no—
100#121×C41—21no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—42no—
105#121×C41—41no—
106#120×C41—22no—
107#120×C41—22no—
108#120×C41—22no—
109#120×C41—21no—
110#120×C41—21no—
111#120×C41—22no—
112#120×C41—22no—
113#120×C41—24no—
114#120×C41D411yescharacteristic, complemented
115#120×C41D412yescomplemented
116#120×C41C2311yescharacteristic
117#120×C41C2312yes—
118C4×D4×C41—22no—
119C4×D4×C41—21no—
120C4×D4×C41—21no—
121C4×D4×C41—21no—
122C4×D4×C41—21no—
123C4×D4×C41—22no—
124C4×D4×C41—42no—
125#117×C41—21no—
126#117×C41—21no—
127#117×C41D411yescharacteristic, complemented
128#117×C41D411yescharacteristic, complemented
129#117×C41D411yescharacteristic, complemented
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—24no—
138#99×C41—22no—
139#99×C41—22no—
140#99×C41C2312yes—
141#99×C41C2312yes—
142C24×C41—22no—
143C24×C41—21no—
144C24×C41C2×D411yescharacteristic
145C24×C41C2×D412yes—
146#41×C41—22no—
147#41×C41—22no—
148#41×C41—41no—
149#41×C41—41no—
150#41×C41—42no—
151#41×C41—41no—
152#41×C41—41no—
153#41×C41—41no—
154#41×C41—41no—
155#41×C41—41no—
156#41×C41—42no—
157#41×C41—42no—
158#41×C41—42no—
159#41×C41—41no—
160#41×C41—41no—
161#41×C41—41no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—42no—
166C2×Q8×C41C2×D411yescharacteristic
167C2×D4×C41—21no—
168C2×D4×C41—22no—
169C2×D4×C41—22no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—22no—
174C2×D4×C41—22no—
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—22no—
182C2×D4×C41—22no—
183C2×D4×C41—21no—
184C2×D4×C41—21no—
185C2×D4×C41—21no—
186C2×D4×C41—41no—
187C2×D4×C41—41no—
188C2×D4×C41—41no—
189C2×D4×C41—41no—
190C2×D4×C41—42no—
191C2×D4×C41—42no—
192C2×D4×C41—42no—
193C2×D4×C41—41no—
194C2×D4×C41—42no—
195C2×D4×C41—44no—
196C2×D4×C41—81no—
197C2×D4×C41—81no—
198C2×D4×C41—84no—
199C2×D4×C41—84no—
200C2×D4×C41—84no—
201C2×D4×C41C2×D411yescharacteristic
202C2×D4×C41C2×D411yescharacteristic
203C2×D4×C41C2×D412yes—
204C2×D4×C41C2411yescharacteristic
205C22×C4×C41—22no—
206C22×C4×C41—22no—
207C22×C4×C41—22no—
208C22×C4×C41—22no—
209C22×C4×C41—22no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—41no—
213C22×C4×C41—41no—
214C22×C4×C41—41no—
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219SD16×C41—44no—
220D8×C41—44no—
221M16×C41—22no—
222M16×C41—41no—
223C2×C8×C41—41no—
224C4⋊C4×C41—22no—
225C4⋊C4×C41—22no—
226C4⋊C4×C41—22no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—41no—
233C4⋊C4×C41—41no—
234C4⋊C4×C41—42no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
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—21no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—21no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—44no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41C2×D412yes—
254C22⋊C4×C41C2×D411yescharacteristic
255C22⋊C4×C41C2×D411yescharacteristic
256C42×C41—21no—
257C42×C41—21no—
258C42×C41—41no—
259C42×C41—41no—
260C42×C41C2×D412yes—
261C23×C41—21no—
262C23×C41—22no—
263C23×C41—22no—
264C23×C41—22no—
265C23×C41—22no—
266C23×C41—41no—
267C23×C41—42no—
268C23×C41—41no—
269C23×C41—44no—
270C23×C41—42no—
271C23×C41—81no—
272C23×C41—82no—
273C23×C41—82no—
274C23×C41—82no—
275C23×C41—82no—
276C23×C41#12011yescharacteristic
277C23×C41C22×D411yescharacteristic
278C23×C41C22×D411yescharacteristic
279Q8×C41—22no—
280Q8×C41—41no—
281Q8×C41—41no—
282Q8×C41—41no—
283Q8×C41—41no—
284D4×C41—22no—
285D4×C41—41no—
286D4×C41—41no—
287D4×C41—41no—
288D4×C41—42no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—42no—
292D4×C41—42no—
293D4×C41—42no—
294D4×C41—42no—
295D4×C41—44no—
296D4×C41—44no—
297D4×C41—42no—
298D4×C41—42no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—41no—
304D4×C41—81no—
305D4×C41—82no—
306D4×C41—82no—
307D4×C41—82no—
308D4×C41—82no—
309D4×C41—82no—
310D4×C41—82no—
311D4×C41—82no—
312D4×C41—84no—
313D4×C41—164no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—22no—
321C2×C4×C41—22no—
322C2×C4×C41—22no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—22no—
326C2×C4×C41—21no—
327C2×C4×C41—42no—
328C2×C4×C41—42no—
329C2×C4×C41—42no—
330C2×C4×C41—41no—
331C2×C4×C41—42no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—42no—
336C2×C4×C41—42no—
337C2×C4×C41—81no—
338C2×C4×C41—82no—
339C2×C4×C41—82no—
340C2×C4×C41—82no—
341C2×C4×C41#12011yescharacteristic
342C2×C4×C41#12011yescharacteristic
343C2×C4×C41#12011yescharacteristic
344C2×C4×C41C22×D411yescharacteristic
345C8×C41—42no—
346#33553C4111yesmaximal, characteristic, direct product factor, Sylow
347C22×C41—22no—
348C22×C41—21no—
349C22×C41—21no—
350C22×C41—21no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—42no—
356C22×C41—42no—
357C22×C41—42no—
358C22×C41—42no—
359C22×C41—42no—
360C22×C41—41no—
361C22×C41—42no—
362C22×C41—42no—
363C22×C41—42no—
364C22×C41—81no—
365C22×C41—82no—
366C22×C41—82no—
367C22×C41—84no—
368C22×C41—161no—
369C22×C41—164no—
370C22×C41—162no—
371C22×C41C2×#12011yescharacteristic
372C4×C41—21no—
373C4×C41—21no—
374C4×C41—21no—
375C4×C41—42no—
376C4×C41—41no—
377C4×C41—41no—
378C4×C41—42no—
379C4×C41—42no—
380C4×C41—41no—
381C4×C41—82no—
382C4×C41—82no—
383C4×C41B(4,𝔽2)11yescharacteristic
384C4×C41B(4,𝔽2)11yescharacteristic
385#3537C2×C4111yescharacteristic, complemented
386#3027C2×C4111yescharacteristic, complemented
387#3025C2×C4111yescharacteristic, complemented
388#3021C2×C4111yescharacteristic, complemented
389#2200C2×C4114yescomplemented
390#2196C2×C4114yescomplemented
391#2128C2×C4111yescharacteristic, complemented
392#2122C2×C4111yescharacteristic, complemented
393#2120C2×C4111yescharacteristic, complemented
394C2×C41—21no—
395C2×C41—41no—
396C2×C41—41no—
397C2×C41—42no—
398C2×C41—41no—
399C2×C41—82no—
400C2×C41—82no—
401C2×C41—82no—
402C2×C41C2×B(4,𝔽2)11yescharacteristic
403#585C22×C4111yescharacteristic, complemented
404C2×AGL(1,ℤ/8)—21no—
405#560—21no—
406#560C22×C4112yescomplemented
407#553—21no—
408#553—21no—
409D42—21no—
410D42—21no—
411D42—21no—
412D42C22×C4112yescomplemented
413#540—21no—
414#538—22no—
415#535—21no—
416#535C22×C4111yescharacteristic
417#535C22×C4111yescharacteristic
418#534—22no—
419#525—21no—
420#525C22×C4111yescharacteristic
421C2×#121—21no—
422#458—21no—
423#458C22×C4112yescomplemented
424B(4,𝔽2)—21no—
425B(4,𝔽2)—22no—
426B(4,𝔽2)C22×C4112yescomplemented
427B(4,𝔽2)C22×C4114yescomplemented
428#454—22no—
429#453C22×C4114yescomplemented
430#421—21no—
431#413C22×C4111yescharacteristic, complemented
432#410—21no—
433#410—21no—
434#410C22×C4111yescharacteristic, complemented
435#410C22×C4111yescharacteristic, complemented
436#353C22×C4114yescomplemented
437#352C22×C4112yescomplemented
438AΣL(1,𝔽16)C22×C4112yescomplemented
439AΣL(1,𝔽16)C22×C4114yescomplemented
440C41#3355311yescharacteristic, direct product factor, Sylow
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C4112yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C4111yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C4111yescharacteristic, complemented
457C22×D4D4×C4111yescharacteristic, complemented
458C23×C4D4×C4111yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C4112yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C4112yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C4111yescharacteristic, complemented
480#123C23×C4111yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C4111yescharacteristic, complemented
509#120D4×C4112yescomplemented
510#120C23×C4111yescharacteristic
511#120C23×C4112yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C4111yescharacteristic, complemented
522#117D4×C4111yescharacteristic, complemented
523#117D4×C4111yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C4112yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C4112yes—
535#99C23×C4112yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C4111yescharacteristic
539C24C2×D4×C4112yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C4111yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C4111yescharacteristic
596C2×D4C2×D4×C4111yescharacteristic
597C2×D4C2×D4×C4112yes—
598C2×D4C24×C4111yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4C2×D4×C4111yescharacteristic
612C22×C4C2×D4×C4111yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C4112yes—
648C22⋊C4C2×D4×C4111yescharacteristic
649C22⋊C4C2×D4×C4111yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C4112yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C4111yescharacteristic
671C23C22×D4×C4111yescharacteristic
672C23C22×D4×C4111yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C4111yescharacteristic
736C2×C4#120×C4111yescharacteristic
737C2×C4#120×C4111yescharacteristic
738C2×C4C22×D4×C4111yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C4111yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C41×B(4,𝔽2)11yescharacteristic
777C4C41×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×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×#3537C2semidirect
2. C41×#3027C2semidirect
3. C41×#3025C2semidirect
4. C41×#3021C2semidirect
5. C41×#2200C2semidirect
6. C41×#2196C2semidirect
7. C41×#2128C2semidirect
8. C41×#2122C2semidirect
9. C41×#2120C2semidirect
10. C41×#585C22semidirect
13. C41×#560C22semidirect
19. D42×C41C22semidirect
30. C41×#458C22semidirect
33. C41×B(4,𝔽2)C22semidirect
34. C41×B(4,𝔽2)C22semidirect
36. C41×#453C22semidirect
38. C41×#413C22semidirect
41. C41×#410C22semidirect
42. C41×#410C22semidirect
43. C41×#353C22semidirect
44. C41×#352C22semidirect
45. C41×AΣL(1,𝔽16)C22semidirect
46. C41×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C41D4semidirect
63. C22×D4×C41D4semidirect
64. C23×C4×C41D4semidirect
79. #124×C41D4semidirect
85. #123×C41D4semidirect
114. #120×C41D4semidirect
115. #120×C41D4semidirect
127. #117×C41D4semidirect
128. #117×C41D4semidirect
129. #117×C41D4semidirect
346. #33553C41direct (N × H)
385. #3537C2×C41semidirect
386. #3027C2×C41semidirect
387. #3025C2×C41semidirect
388. #3021C2×C41semidirect
389. #2200C2×C41semidirect
390. #2196C2×C41semidirect
391. #2128C2×C41semidirect
392. #2122C2×C41semidirect
393. #2120C2×C41semidirect
403. #585C22×C41semidirect
406. #560C22×C41semidirect
412. D42C22×C41semidirect
423. #458C22×C41semidirect
426. B(4,𝔽2)C22×C41semidirect
427. B(4,𝔽2)C22×C41semidirect
429. #453C22×C41semidirect
431. #413C22×C41semidirect
434. #410C22×C41semidirect
435. #410C22×C41semidirect
436. #353C22×C41semidirect
437. #352C22×C41semidirect
438. AΣL(1,𝔽16)C22×C41semidirect
439. AΣL(1,𝔽16)C22×C41semidirect
440. C41#33553direct (N × H)
456. C22×D4D4×C41semidirect
457. C22×D4D4×C41semidirect
458. C23×C4D4×C41semidirect
473. #124D4×C41semidirect
479. #123D4×C41semidirect
508. #120D4×C41semidirect
509. #120D4×C41semidirect
521. #117D4×C41semidirect
522. #117D4×C41semidirect
523. #117D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35372
C41×#30272
C41×#30252
C41×#30212
C41×#22002
C41×#21962
C41×#21282
C41×#21222
C41×#21202
#3355341