Finite Group Databasebeta

← C43×#33551 #24953568

Subgroups — C43×#33551 #24953568

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3532C211yesmaximal, characteristic, complemented
2C43×#3026C211yesmaximal, characteristic, complemented
3C2×C43×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C43×#3019C211yesmaximal, characteristic, complemented
5C43×#2200C212yesmaximal, complemented
6C43×#2199C212yesmaximal, complemented
7C43×#2197C212yesmaximal, complemented
8C43×#2196C212yesmaximal, complemented
9C43×#2127C211yesmaximal, characteristic, complemented
10C43×#2121C211yesmaximal, characteristic, complemented
11C2×C43×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
13C43×#575—21no—
14C43×H(3,𝔽4)C2211yescharacteristic, complemented
15C43×#560—21no—
16C43×#560C2211yescharacteristic, complemented
17C43×#551—21no—
18C43×#551C2211yescharacteristic, complemented
19C43×#546—21no—
20C43×#546—21no—
21C43×#546—21no—
22D42×C43—21no—
23D42×C43C2211yescharacteristic, complemented
24C43×#538—21no—
25C43×#538—21no—
26C43×#538—21no—
27C43×#535—21no—
28C43×#535C2211yescharacteristic
29C43×#534—21no—
30C43×#534—21no—
31C43×#534C2211yescharacteristic
32C2×#120×C43—21no—
33C2×#120×C43—21no—
34C2×#120×C43C2211yescharacteristic
35C43×#458—21no—
36C43×#458C2212yescomplemented
37C43×B(4,𝔽2)—21no—
38C43×B(4,𝔽2)—21no—
39C43×B(4,𝔽2)—21no—
40C43×B(4,𝔽2)C2212yes—
41C43×B(4,𝔽2)C2212yescomplemented
42C43×B(4,𝔽2)C2212yescomplemented
43C43×#455—21no—
44C43×#455C2212yescomplemented
45C43×#453—21no—
46C43×#453C2212yescomplemented
47C43×#421—21no—
48C2×#100×C43C2211yescharacteristic, complemented
49C2×#99×C43—21no—
50C2×#99×C43—21no—
51C2×#99×C43C2211yescharacteristic, complemented
52C2×#99×C43C2211yescharacteristic, complemented
53C43×#354C2212yescomplemented
54C43×#353C2212yescomplemented
55C43×#352C2212yescomplemented
56C43×AΣL(1,𝔽16)C2212yescomplemented
57C43×AΣL(1,𝔽16)C2212yescomplemented
58C43×AΣL(1,𝔽16)C2212yescomplemented
59C25×C43D411yescharacteristic, complemented
60H(5,𝔽2)×C43—21no—
61H(5,𝔽2)×C43—21no—
62H(5,𝔽2)×C43—21no—
63H(5,𝔽2)×C43—42no—
64H(5,𝔽2)×C43C2312yes—
65C2×#41×C43—21no—
66C2×#41×C43—21no—
67C2×#41×C43—41no—
68C2×#41×C43D411yescharacteristic, complemented
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—41no—
77C22×D4×C43—41no—
78C22×D4×C43D411yescharacteristic, complemented
79C22×D4×C43C2311yescharacteristic
80#137×C43—22no—
81#137×C43—41no—
82AGL(1,ℤ/8)×C43—22no—
83AGL(1,ℤ/8)×C43—41no—
84#135×C43—42no—
85C2×M16×C43—21no—
86#127×C43—21no—
87#127×C43D411yescharacteristic, complemented
88#127×C43C2311yescharacteristic
89#126×C43—21no—
90#126×C43—21no—
91#126×C43—21no—
92#126×C43—21no—
93#124×C43—21no—
94#124×C43—21no—
95#124×C43—21no—
96#124×C43—21no—
97#124×C43—21no—
98#124×C43D411yescharacteristic, complemented
99#124×C43C2311yescharacteristic
100#123×C43—21no—
101#123×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108#123×C43—22no—
109#123×C43—41no—
110#123×C43D411yescharacteristic, complemented
111#123×C43C2311yescharacteristic
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43—21no—
114C22⋊Q8×C43—21no—
115#121×C43—21no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—42no—
131#120×C43—21no—
132#120×C43—21no—
133#120×C43—21no—
134#120×C43—21no—
135#120×C43—21no—
136#120×C43—21no—
137#120×C43—21no—
138#120×C43—21no—
139#120×C43—21no—
140#120×C43—21no—
141#120×C43—21no—
142#120×C43—21no—
143#120×C43—21no—
144#120×C43—21no—
145#120×C43—22no—
146#120×C43—22no—
147#120×C43—22no—
148#120×C43—42no—
149#120×C43—41no—
150#120×C43D411yescharacteristic, complemented
151#120×C43D411yescharacteristic, complemented
152#120×C43D411yescharacteristic, complemented
153#120×C43C2311yescharacteristic
154#120×C43C2311yescharacteristic
155#120×C43C2311yescharacteristic
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161C4×D4×C43—21no—
162#117×C43—21no—
163#117×C43D411yescharacteristic, complemented
164C2×C22⋊C4×C43—21no—
165C2×C22⋊C4×C43—21no—
166C2×C22⋊C4×C43—21no—
167C2×C22⋊C4×C43—21no—
168C2×C22⋊C4×C43—21no—
169C2×C22⋊C4×C43—21no—
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—41no—
172C2×C22⋊C4×C43D411yescharacteristic, complemented
173C2×C22⋊C4×C43D411yescharacteristic, complemented
174#104×C43—22no—
175#104×C43—22no—
176#100×C43—21no—
177#100×C43C2312yes—
178#99×C43—21no—
179#99×C43—21no—
180#99×C43—22no—
181#99×C43—22no—
182#99×C43—22no—
183#99×C43—22no—
184#99×C43C2312yes—
185#99×C43C2312yes—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—41no—
192C24×C43—41no—
193C24×C43—82no—
194C24×C43C2×D411yescharacteristic
195C24×C43C2×D411yescharacteristic
196C24×C43C2×D411yescharacteristic
197C24×C43C2×D411yescharacteristic
198C24×C43C2×D411yescharacteristic, complemented
199#41×C43—22no—
200#41×C43—22no—
201#41×C43—42no—
202#41×C43—41no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—41no—
206#41×C43—41no—
207#41×C43—42no—
208#41×C43—41no—
209#41×C43—82no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43C2×D411yescharacteristic, complemented
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—22no—
216C2×D4×C43—22no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—22no—
231C2×D4×C43—22no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—41no—
239C2×D4×C43—41no—
240C2×D4×C43—42no—
241C2×D4×C43—41no—
242C2×D4×C43—41no—
243C2×D4×C43—41no—
244C2×D4×C43—41no—
245C2×D4×C43—42no—
246C2×D4×C43—42no—
247C2×D4×C43—41no—
248C2×D4×C43—41no—
249C2×D4×C43—42no—
250C2×D4×C43—42no—
251C2×D4×C43—42no—
252C2×D4×C43—42no—
253C2×D4×C43—41no—
254C2×D4×C43—41no—
255C2×D4×C43—41no—
256C2×D4×C43—82no—
257C2×D4×C43—82no—
258C2×D4×C43—82no—
259C2×D4×C43—82no—
260C2×D4×C43—81no—
261C2×D4×C43—81no—
262C2×D4×C43—84no—
263C2×D4×C43C2×D411yescharacteristic
264C2×D4×C43C2×D411yescharacteristic
265C2×D4×C43C2×D411yescharacteristic
266C2×D4×C43C2×D411yescharacteristic, complemented
267C2×D4×C43C2411yescharacteristic
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43—21no—
271C22×C4×C43—21no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—41no—
279C22×C4×C43—41no—
280C22×C4×C43—41no—
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic, complemented
283Q16×C43—42no—
284SD16×C43—42no—
285SD16×C43—42no—
286D8×C43—42no—
287M16×C43—22no—
288M16×C43—41no—
289C2×C8×C43—41no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—21no—
298C4⋊C4×C43—21no—
299C4⋊C4×C43—42no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—21no—
321C22⋊C4×C43—21no—
322C22⋊C4×C43—21no—
323C22⋊C4×C43—21no—
324C22⋊C4×C43—21no—
325C22⋊C4×C43—22no—
326C22⋊C4×C43—22no—
327C22⋊C4×C43—41no—
328C22⋊C4×C43—41no—
329C22⋊C4×C43—42no—
330C22⋊C4×C43—42no—
331C22⋊C4×C43—42no—
332C22⋊C4×C43—42no—
333C22⋊C4×C43C2×D411yescharacteristic
334C22⋊C4×C43C2×D411yescharacteristic
335C22⋊C4×C43C2×D411yescharacteristic, complemented
336C22⋊C4×C43C2×D411yescharacteristic, complemented
337C42×C43—21no—
338C42×C43—21no—
339C42×C43C2×D411yescharacteristic, complemented
340C42×C43C2×D411yescharacteristic, complemented
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—21no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43—21no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—42no—
354C23×C43—42no—
355C23×C43—42no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—42no—
359C23×C43—41no—
360C23×C43—44no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—81no—
365C23×C43—81no—
366C23×C43—81no—
367C23×C43—81no—
368C23×C43—81no—
369C23×C43—81no—
370C23×C43—81no—
371C23×C43—81no—
372C23×C43—81no—
373C23×C43—82no—
374C23×C43—82no—
375C23×C43—82no—
376C23×C43—82no—
377C23×C43—161no—
378C23×C43#12011yescharacteristic
379C23×C43#12011yescharacteristic
380C23×C43#12011yescharacteristic
381C23×C43C22×D411yescharacteristic
382C23×C43C22×D411yescharacteristic
383Q8×C43—22no—
384Q8×C43—41no—
385Q8×C43—41no—
386Q8×C43—81no—
387D4×C43—22no—
388D4×C43—41no—
389D4×C43—41no—
390D4×C43—41no—
391D4×C43—41no—
392D4×C43—41no—
393D4×C43—41no—
394D4×C43—42no—
395D4×C43—42no—
396D4×C43—42no—
397D4×C43—42no—
398D4×C43—42no—
399D4×C43—42no—
400D4×C43—42no—
401D4×C43—42no—
402D4×C43—42no—
403D4×C43—42no—
404D4×C43—41no—
405D4×C43—41no—
406D4×C43—41no—
407D4×C43—41no—
408D4×C43—81no—
409D4×C43—81no—
410D4×C43—81no—
411D4×C43—81no—
412D4×C43—81no—
413D4×C43—81no—
414D4×C43—81no—
415D4×C43—81no—
416D4×C43—81no—
417D4×C43—81no—
418D4×C43—81no—
419D4×C43—81no—
420D4×C43—81no—
421D4×C43—81no—
422D4×C43—84no—
423D4×C43—84no—
424D4×C43—162no—
425C2×C4×C43—21no—
426C2×C4×C43—21no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—21no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—21no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—21no—
437C2×C4×C43—42no—
438C2×C4×C43—42no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—42no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—42no—
445C2×C4×C43—42no—
446C2×C4×C43—81no—
447C2×C4×C43—81no—
448C2×C4×C43—81no—
449C2×C4×C43—81no—
450C2×C4×C43—81no—
451C2×C4×C43—81no—
452C2×C4×C43—81no—
453C2×C4×C43—82no—
454C2×C4×C43—161no—
455C2×C4×C43#12011yescharacteristic
456C2×C4×C43C22×D411yescharacteristic
457C8×C43—42no—
458#33551C4311yesmaximal, characteristic, direct product factor, Sylow
459C22×C43—22no—
460C22×C43—21no—
461C22×C43—21no—
462C22×C43—21no—
463C22×C43—21no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—41no—
467C22×C43—41no—
468C22×C43—41no—
469C22×C43—41no—
470C22×C43—42no—
471C22×C43—41no—
472C22×C43—41no—
473C22×C43—41no—
474C22×C43—41no—
475C22×C43—41no—
476C22×C43—41no—
477C22×C43—42no—
478C22×C43—41no—
479C22×C43—42no—
480C22×C43—42no—
481C22×C43—41no—
482C22×C43—41no—
483C22×C43—41no—
484C22×C43—81no—
485C22×C43—81no—
486C22×C43—81no—
487C22×C43—82no—
488C22×C43—82no—
489C22×C43—82no—
490C22×C43—81no—
491C22×C43—84no—
492C22×C43—82no—
493C22×C43—82no—
494C22×C43—81no—
495C22×C43—82no—
496C22×C43—162no—
497C22×C43—161no—
498C22×C43—161no—
499C22×C43B(4,𝔽2)11yescharacteristic
500C22×C43B(4,𝔽2)11yescharacteristic
501C22×C43C2×#12011yescharacteristic
502C4×C43—21no—
503C4×C43—21no—
504C4×C43—41no—
505C4×C43—41no—
506C4×C43—41no—
507C4×C43—41no—
508C4×C43—41no—
509C4×C43—41no—
510C4×C43—42no—
511C4×C43—41no—
512C4×C43—41no—
513C4×C43—82no—
514C4×C43—82no—
515#3532C2×C4311yescharacteristic, complemented
516#3026C2×C4311yescharacteristic, complemented
517C2×B(4,𝔽2)C2×C4311yescharacteristic, complemented
518#3019C2×C4311yescharacteristic, complemented
519#2200C2×C4312yescomplemented
520#2199C2×C4312yescomplemented
521#2197C2×C4312yescomplemented
522#2196C2×C4312yescomplemented
523#2127C2×C4311yescharacteristic, complemented
524#2121C2×C4311yescharacteristic, complemented
525C2×AΣL(1,𝔽16)C2×C4311yescharacteristic, complemented
526C2×C43—21no—
527C2×C43—21no—
528C2×C43—21no—
529C2×C43—41no—
530C2×C43—41no—
531C2×C43—42no—
532C2×C43—41no—
533C2×C43—41no—
534C2×C43—81no—
535C2×C43—81no—
536C2×C43—81no—
537C2×C43—82no—
538C2×C43C2×B(4,𝔽2)11yescharacteristic
539C2×H(5,𝔽2)C22×C4311yescharacteristic, complemented
540#575—21no—
541H(3,𝔽4)C22×C4311yescharacteristic, complemented
542#560—21no—
543#560C22×C4311yescharacteristic, complemented
544#551—21no—
545#551C22×C4311yescharacteristic, complemented
546#546—21no—
547#546—21no—
548#546—21no—
549D42—21no—
550D42C22×C4311yescharacteristic, complemented
551#538—21no—
552#538—21no—
553#538—21no—
554#535—21no—
555#535C22×C4311yescharacteristic
556#534—21no—
557#534—21no—
558#534C22×C4311yescharacteristic
559C2×#120—21no—
560C2×#120—21no—
561C2×#120C22×C4311yescharacteristic
562#458—21no—
563#458C22×C4312yescomplemented
564B(4,𝔽2)—21no—
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)C22×C4312yes—
568B(4,𝔽2)C22×C4312yescomplemented
569B(4,𝔽2)C22×C4312yescomplemented
570#455—21no—
571#455C22×C4312yescomplemented
572#453—21no—
573#453C22×C4312yescomplemented
574#421—21no—
575C2×#100C22×C4311yescharacteristic, complemented
576C2×#99—21no—
577C2×#99—21no—
578C2×#99C22×C4311yescharacteristic, complemented
579C2×#99C22×C4311yescharacteristic, complemented
580#354C22×C4312yescomplemented
581#353C22×C4312yescomplemented
582#352C22×C4312yescomplemented
583AΣL(1,𝔽16)C22×C4312yescomplemented
584AΣL(1,𝔽16)C22×C4312yescomplemented
585AΣL(1,𝔽16)C22×C4312yescomplemented
586C43#3355111yescharacteristic, direct product factor, Sylow
587C25D4×C4311yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C4312yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C4311yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C4311yescharacteristic, complemented
607C22×D4C23×C4311yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C4311yescharacteristic, complemented
616#127C23×C4311yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C4311yescharacteristic, complemented
627#124C23×C4311yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C4311yescharacteristic, complemented
639#123C23×C4311yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C4311yescharacteristic, complemented
679#120D4×C4311yescharacteristic, complemented
680#120D4×C4311yescharacteristic, complemented
681#120C23×C4311yescharacteristic
682#120C23×C4311yescharacteristic
683#120C23×C4311yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C4311yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C4311yescharacteristic, complemented
701C2×C22⋊C4D4×C4311yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C4312yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C4312yes—
713#99C23×C4312yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C4311yescharacteristic
723C24C2×D4×C4311yescharacteristic
724C24C2×D4×C4311yescharacteristic
725C24C2×D4×C4311yescharacteristic
726C24C2×D4×C4311yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C4311yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C4311yescharacteristic
792C2×D4C2×D4×C4311yescharacteristic
793C2×D4C2×D4×C4311yescharacteristic
794C2×D4C2×D4×C4311yescharacteristic, complemented
795C2×D4C24×C4311yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C4311yescharacteristic
810C22×C4C2×D4×C4311yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C4311yescharacteristic
862C22⋊C4C2×D4×C4311yescharacteristic
863C22⋊C4C2×D4×C4311yescharacteristic, complemented
864C22⋊C4C2×D4×C4311yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C4311yescharacteristic, complemented
868C42C2×D4×C4311yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C4311yescharacteristic
907C23#120×C4311yescharacteristic
908C23#120×C4311yescharacteristic
909C23C22×D4×C4311yescharacteristic
910C23C22×D4×C4311yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C4311yescharacteristic
984C2×C4C22×D4×C4311yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22C43×B(4,𝔽2)11yescharacteristic
1027C22C43×B(4,𝔽2)11yescharacteristic
1028C22C2×#120×C4311yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C43C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C43
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C23×C43 ◁ C22×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3532C2semidirect
2. C43×#3026C2semidirect
3. C2×C43×B(4,𝔽2)C2semidirect
4. C43×#3019C2semidirect
5. C43×#2200C2semidirect
6. C43×#2199C2semidirect
7. C43×#2197C2semidirect
8. C43×#2196C2semidirect
9. C43×#2127C2semidirect
10. C43×#2121C2semidirect
11. C2×C43×AΣL(1,𝔽16)C2semidirect
12. C2×H(5,𝔽2)×C43C22semidirect
14. C43×H(3,𝔽4)C22semidirect
16. C43×#560C22semidirect
18. C43×#551C22semidirect
23. D42×C43C22semidirect
36. C43×#458C22semidirect
41. C43×B(4,𝔽2)C22semidirect
42. C43×B(4,𝔽2)C22semidirect
44. C43×#455C22semidirect
46. C43×#453C22semidirect
48. C2×#100×C43C22semidirect
51. C2×#99×C43C22semidirect
52. C2×#99×C43C22semidirect
53. C43×#354C22semidirect
54. C43×#353C22semidirect
55. C43×#352C22semidirect
56. C43×AΣL(1,𝔽16)C22semidirect
57. C43×AΣL(1,𝔽16)C22semidirect
58. C43×AΣL(1,𝔽16)C22semidirect
59. C25×C43D4semidirect
68. C2×#41×C43D4semidirect
78. C22×D4×C43D4semidirect
87. #127×C43D4semidirect
98. #124×C43D4semidirect
110. #123×C43D4semidirect
150. #120×C43D4semidirect
151. #120×C43D4semidirect
152. #120×C43D4semidirect
163. #117×C43D4semidirect
172. C2×C22⋊C4×C43D4semidirect
173. C2×C22⋊C4×C43D4semidirect
198. C24×C43C2×D4semidirect
212. C2×Q8×C43C2×D4semidirect
266. C2×D4×C43C2×D4semidirect
282. C22×C4×C43C2×D4semidirect
335. C22⋊C4×C43C2×D4semidirect
336. C22⋊C4×C43C2×D4semidirect
339. C42×C43C2×D4semidirect
340. C42×C43C2×D4semidirect
458. #33551C43direct (N × H)
515. #3532C2×C43semidirect
516. #3026C2×C43semidirect
517. C2×B(4,𝔽2)C2×C43semidirect
518. #3019C2×C43semidirect
519. #2200C2×C43semidirect
520. #2199C2×C43semidirect
521. #2197C2×C43semidirect
522. #2196C2×C43semidirect
523. #2127C2×C43semidirect
524. #2121C2×C43semidirect
525. C2×AΣL(1,𝔽16)C2×C43semidirect
539. C2×H(5,𝔽2)C22×C43semidirect
541. H(3,𝔽4)C22×C43semidirect
543. #560C22×C43semidirect
545. #551C22×C43semidirect
550. D42C22×C43semidirect
563. #458C22×C43semidirect
568. B(4,𝔽2)C22×C43semidirect
569. B(4,𝔽2)C22×C43semidirect
571. #455C22×C43semidirect
573. #453C22×C43semidirect
575. C2×#100C22×C43semidirect
578. C2×#99C22×C43semidirect
579. C2×#99C22×C43semidirect
580. #354C22×C43semidirect
581. #353C22×C43semidirect
582. #352C22×C43semidirect
583. AΣL(1,𝔽16)C22×C43semidirect
584. AΣL(1,𝔽16)C22×C43semidirect
585. AΣL(1,𝔽16)C22×C43semidirect
586. C43#33551direct (N × H)
587. C25D4×C43semidirect
596. C2×#41D4×C43semidirect
606. C22×D4D4×C43semidirect
615. #127D4×C43semidirect
626. #124D4×C43semidirect
638. #123D4×C43semidirect
678. #120D4×C43semidirect
679. #120D4×C43semidirect
680. #120D4×C43semidirect
691. #117D4×C43semidirect
700. C2×C22⋊C4D4×C43semidirect
701. C2×C22⋊C4D4×C43semidirect
726. C24C2×D4×C43semidirect
740. C2×Q8C2×D4×C43semidirect
794. C2×D4C2×D4×C43semidirect
810. C22×C4C2×D4×C43semidirect
863. C22⋊C4C2×D4×C43semidirect
864. C22⋊C4C2×D4×C43semidirect
867. C42C2×D4×C43semidirect
868. C42C2×D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35322
C43×#30262
C2×C43×B(4,𝔽2)2
C43×#30192
C43×#22002
C43×#21992
C43×#21972
C43×#21962
C43×#21272
C43×#21212
C2×C43×AΣL(1,𝔽16)2
#3355143