Finite Group Databasebeta

← C43×#23894 #24943911

Subgroups — C43×#23894 #24943911

Order 11008.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3586C211yesmaximal, characteristic, complemented
2C43×#3585C211yesmaximal, characteristic, complemented
3C43×#3020C211yesmaximal, characteristic, complemented
4C43×#3019C211yesmaximal, characteristic, complemented
5C43×#3010C211yesmaximal, characteristic, complemented
6C43×#3009C211yesmaximal, characteristic, complemented
7C43×#2019C211yesmaximal, characteristic, complemented
8C43×#2017C211yesmaximal, characteristic, complemented
9C43×#2009C211yesmaximal, characteristic, complemented
10C43×#2008C211yesmaximal, characteristic, complemented
11C43×#1903C211yesmaximal, characteristic, complemented
12C43×#1902C211yesmaximal, characteristic, complemented
13C43×#1881C211yesmaximal, characteristic, complemented
14C43×#1881C211yesmaximal, characteristic, complemented
15C43×#1794C211yesmaximal, characteristic, complemented
16C43×#585C2211yescharacteristic
17C2×2−1+4×C43C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C43C2211yescharacteristic
19C43×#578—22no—
20C43×#578—22no—
21C43×#577—22no—
22C43×#577—22no—
23C43×#577—22no—
24C43×#577—22no—
25C43×#576—22no—
26C43×#576—22no—
27C43×#575—22no—
28C43×#575—22no—
29C43×#575C2211yescharacteristic
30C43×#575C2211yescharacteristic
31C43×#575C2211yescharacteristic
32C43×#575C2211yescharacteristic, complemented
33C43×#575C2211yescharacteristic, complemented
34C2×#137×C43—22no—
35C2×#137×C43C2211yescharacteristic
36C2×#137×C43C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C43—22no—
38C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
40C22×SD16×C43C2211yescharacteristic, complemented
41C43×#568C2211yescharacteristic
42C43×#568C2211yescharacteristic, complemented
43C43×#536C2211yescharacteristic, complemented
44C43×#535C2211yescharacteristic, complemented
45C43×#456—22no—
46C43×#455—22no—
47C43×#454—22no—
48C43×#453—22no—
49C43×#452—22no—
50C43×#450—22no—
51C43×#449—22no—
52C43×#448—22no—
53C43×#421C2211yescharacteristic
54C43×#421C2211yescharacteristic, complemented
55C43×#421C2211yescharacteristic, complemented
56C43×#421C2211yescharacteristic, complemented
57C43×#419C2211yescharacteristic, complemented
58C43×#418C2211yescharacteristic, complemented
59C43×#416C2211yescharacteristic
60C43×#416C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C2×#100×C43C2211yescharacteristic, complemented
63C43×#410C2211yescharacteristic, complemented
64C43×#408C2211yescharacteristic, complemented
65C43×#408C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic, complemented
67C43×#344C2211yescharacteristic, complemented
68C43×#344C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#338C2211yescharacteristic, complemented
712−1+4×C43—22no—
722−1+4×C43—21no—
732−1+4×C43—22no—
742−1+4×C43—21no—
752−1+4×C43—22no—
762−1+4×C43—41no—
772−1+4×C43D412yescomplemented
78H(5,𝔽2)×C43—22no—
79H(5,𝔽2)×C43—21no—
80H(5,𝔽2)×C43—22no—
81H(5,𝔽2)×C43—21no—
82H(5,𝔽2)×C43—22no—
83H(5,𝔽2)×C43—41no—
84H(5,𝔽2)×C43—41no—
85H(5,𝔽2)×C43D412yescomplemented
86C2×#41×C43—22no—
87C2×#41×C43—22no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—21no—
92C2×#41×C43—41no—
93C2×#41×C43—41no—
94C2×#41×C43C2311yescharacteristic
95C2×#41×C43C2311yescharacteristic
96C2×#41×C43C2311yescharacteristic
97C2×#41×C43C2311yescharacteristic
98C2×#41×C43C2311yescharacteristic
99C22×Q8×C43—21no—
100C22×Q8×C43—21no—
101C22×Q8×C43C2311yescharacteristic
102C22×D4×C43—21no—
103C22×D4×C43—21no—
104C22×D4×C43—41no—
105C22×D4×C43C2311yescharacteristic
106#137×C43—24no—
107#137×C43—24no—
108#137×C43—24no—
109#137×C43—24no—
110#137×C43—22no—
111#137×C43—22no—
112#137×C43—21no—
113#137×C43—22no—
114#137×C43—21no—
115#137×C43—21no—
116#137×C43—21no—
117#137×C43—21no—
118#137×C43—21no—
119#137×C43—21no—
120#137×C43—21no—
121#137×C43—22no—
122#137×C43D412yes—
123#137×C43D412yescomplemented
124AGL(1,ℤ/8)×C43—24no—
125AGL(1,ℤ/8)×C43—24no—
126AGL(1,ℤ/8)×C43—24no—
127AGL(1,ℤ/8)×C43—24no—
128AGL(1,ℤ/8)×C43—22no—
129AGL(1,ℤ/8)×C43—22no—
130AGL(1,ℤ/8)×C43—21no—
131AGL(1,ℤ/8)×C43—22no—
132AGL(1,ℤ/8)×C43—21no—
133AGL(1,ℤ/8)×C43—21no—
134AGL(1,ℤ/8)×C43—21no—
135AGL(1,ℤ/8)×C43—21no—
136AGL(1,ℤ/8)×C43—21no—
137AGL(1,ℤ/8)×C43—21no—
138AGL(1,ℤ/8)×C43—21no—
139AGL(1,ℤ/8)×C43—22no—
140AGL(1,ℤ/8)×C43D412yes—
141AGL(1,ℤ/8)×C43D412yescomplemented
142#135×C43—24no—
143#135×C43—24no—
144#135×C43—24no—
145#135×C43—24no—
146#135×C43—22no—
147#135×C43—22no—
148#135×C43—22no—
149#135×C43—22no—
150#135×C43—41no—
151C2×Q16×C43—24no—
152C2×Q16×C43—21no—
153C2×Q16×C43D412yescomplemented
154C2×SD16×C43—24no—
155C2×SD16×C43—24no—
156C2×SD16×C43—21no—
157C2×SD16×C43—21no—
158C2×SD16×C43—22no—
159C2×SD16×C43—22no—
160C2×SD16×C43—41no—
161C2×SD16×C43D412yes—
162C2×SD16×C43D412yescomplemented
163C2×D8×C43—24no—
164C2×D8×C43—21no—
165C2×D8×C43D412yes—
166#131×C43—22no—
167#131×C43—22no—
168#131×C43—22no—
169#131×C43—22no—
170C2×M16×C43—22no—
171C2×M16×C43—22no—
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C2×M16×C43C2311yescharacteristic
176C2×M16×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178C4⋊Q8×C43—21no—
179#127×C43—21no—
180#124×C43—21no—
181#124×C43—21no—
182#123×C43—41no—
183C22⋊Q8×C43—22no—
184#121×C43—22no—
185#120×C43—41no—
186#117×C43C2311yescharacteristic
187#117×C43C2311yescharacteristic
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—22no—
191#104×C43—22no—
192#103×C43—21no—
193#103×C43—21no—
194#103×C43—22no—
195#102×C43—21no—
196#102×C43—21no—
197#102×C43—22no—
198#101×C43—22no—
199#100×C43—22no—
200#99×C43—41no—
201C22⋊C8×C43—22no—
202C22⋊C8×C43—22no—
203C22⋊C8×C43—41no—
204C24×C43—21no—
205C24×C43—41no—
206#41×C43—21no—
207#41×C43—21no—
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—24no—
211#41×C43—24no—
212#41×C43—22no—
213#41×C43—22no—
214#41×C43—22no—
215#41×C43—22no—
216#41×C43—21no—
217#41×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—21no—
222#41×C43—21no—
223#41×C43—21no—
224#41×C43—21no—
225#41×C43—21no—
226#41×C43—21no—
227#41×C43—21no—
228#41×C43—42no—
229#41×C43—42no—
230#41×C43—42no—
231#41×C43—42no—
232#41×C43—42no—
233#41×C43—44no—
234#41×C43—42no—
235#41×C43—42no—
236#41×C43—42no—
237#41×C43—41no—
238#41×C43—41no—
239#41×C43—44no—
240#41×C43—42no—
241#41×C43—42no—
242#41×C43C2×D412yes—
243#41×C43C2×D412yes—
244#41×C43C2×D412yes—
245#41×C43C2×D412yes—
246C2×Q8×C43—21no—
247C2×Q8×C43—24no—
248C2×Q8×C43—22no—
249C2×Q8×C43—22no—
250C2×Q8×C43—21no—
251C2×Q8×C43—21no—
252C2×Q8×C43—21no—
253C2×Q8×C43—21no—
254C2×Q8×C43—41no—
255C2×Q8×C43—42no—
256C2×Q8×C43—42no—
257C2×Q8×C43—41no—
258C2×Q8×C43—42no—
259C2×Q8×C43C2×D412yes—
260C2×Q8×C43C2×D411yescharacteristic
261C2×Q8×C43C2×D411yescharacteristic
262C2×Q8×C43C2×D411yescharacteristic
263C2×Q8×C43C2×D411yescharacteristic
264C2×Q8×C43C2×D411yescharacteristic
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—21no—
268C2×D4×C43—21no—
269C2×D4×C43—21no—
270C2×D4×C43—21no—
271C2×D4×C43—24no—
272C2×D4×C43—22no—
273C2×D4×C43—22no—
274C2×D4×C43—21no—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—41no—
279C2×D4×C43—42no—
280C2×D4×C43—41no—
281C2×D4×C43—41no—
282C2×D4×C43—42no—
283C2×D4×C43—44no—
284C2×D4×C43—42no—
285C2×D4×C43—42no—
286C2×D4×C43—42no—
287C2×D4×C43—42no—
288C2×D4×C43—41no—
289C2×D4×C43—44no—
290C2×D4×C43—42no—
291C2×D4×C43C2×D412yes—
292C2×D4×C43C2×D411yescharacteristic
293C2×D4×C43C2×D411yescharacteristic
294C2×D4×C43C2×D411yescharacteristic
295C2×D4×C43C2×D411yescharacteristic
296C2×D4×C43C2×D411yescharacteristic
297C22×C4×C43—21no—
298C22×C4×C43—21no—
299C22×C4×C43—21no—
300C22×C4×C43—21no—
301C22×C4×C43—21no—
302C22×C4×C43—21no—
303C22×C4×C43—41no—
304C22×C4×C43—41no—
305C22×C4×C43—41no—
306C22×C4×C43—42no—
307C22×C4×C43C2411yescharacteristic
308Q16×C43—24no—
309Q16×C43—22no—
310Q16×C43—22no—
311Q16×C43—22no—
312Q16×C43—24no—
313Q16×C43—22no—
314Q16×C43—41no—
315SD16×C43—24no—
316SD16×C43—22no—
317SD16×C43—24no—
318SD16×C43—22no—
319SD16×C43—22no—
320SD16×C43—22no—
321SD16×C43—22no—
322SD16×C43—24no—
323SD16×C43—22no—
324SD16×C43—22no—
325SD16×C43—24no—
326SD16×C43—22no—
327SD16×C43—44no—
328SD16×C43—41no—
329SD16×C43—41no—
330D8×C43—24no—
331D8×C43—22no—
332D8×C43—22no—
333D8×C43—22no—
334D8×C43—24no—
335D8×C43—22no—
336D8×C43—41no—
337M16×C43—24no—
338M16×C43—24no—
339M16×C43—21no—
340M16×C43—21no—
341M16×C43—21no—
342M16×C43—21no—
343M16×C43—21no—
344M16×C43—21no—
345M16×C43—21no—
346M16×C43—21no—
347M16×C43C2×D412yes—
348M16×C43C2×D412yes—
349C2×C8×C43—24no—
350C2×C8×C43—24no—
351C2×C8×C43—21no—
352C2×C8×C43—21no—
353C2×C8×C43—21no—
354C2×C8×C43—21no—
355C2×C8×C43—21no—
356C2×C8×C43—21no—
357C2×C8×C43C2×D412yes—
358C2×C8×C43C2×D412yes—
359C4⋊C4×C43—21no—
360C4⋊C4×C43—21no—
361C4⋊C4×C43—42no—
362C22⋊C4×C43—21no—
363C22⋊C4×C43—21no—
364C22⋊C4×C43—42no—
365C22⋊C4×C43—42no—
366C42×C43—21no—
367C42×C43—21no—
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—21no—
371C23×C43—21no—
372C23×C43—21no—
373C23×C43—22no—
374C23×C43—42no—
375C23×C43—44no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—161no—
379C23×C43—162no—
380C23×C43H(5,𝔽2)11yescharacteristic
381Q8×C43—21no—
382Q8×C43—21no—
383Q8×C43—21no—
384Q8×C43—21no—
385Q8×C43—22no—
386Q8×C43—21no—
387Q8×C43—21no—
388Q8×C43—22no—
389Q8×C43—21no—
390Q8×C43—21no—
391Q8×C43—42no—
392Q8×C43—44no—
393Q8×C43—41no—
394Q8×C43—41no—
395Q8×C43#12012yes—
396Q8×C43#12012yes—
397D4×C43—22no—
398D4×C43—22no—
399D4×C43—22no—
400D4×C43—22no—
401D4×C43—21no—
402D4×C43—21no—
403D4×C43—22no—
404D4×C43—21no—
405D4×C43—21no—
406D4×C43—21no—
407D4×C43—21no—
408D4×C43—21no—
409D4×C43—21no—
410D4×C43—22no—
411D4×C43—42no—
412D4×C43—42no—
413D4×C43—44no—
414D4×C43—42no—
415D4×C43—44no—
416D4×C43—44no—
417D4×C43—41no—
418D4×C43—41no—
419D4×C43—41no—
420D4×C43—41no—
421D4×C43—41no—
422D4×C43—41no—
423D4×C43—41no—
424D4×C43—41no—
425D4×C43—162no—
426D4×C43#12012yes—
427D4×C43#12012yes—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—22no—
437C2×C4×C43—21no—
438C2×C4×C43—42no—
439C2×C4×C43—42no—
440C2×C4×C43—42no—
441C2×C4×C43—44no—
442C2×C4×C43—44no—
443C2×C4×C43—44no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43C22×D411yescharacteristic
455C2×C4×C43C22×D411yescharacteristic
456C2×C4×C43C22×D411yescharacteristic
457C2×C4×C43C22×D411yescharacteristic
458C2×C4×C43C22×D411yescharacteristic
459C2×C4×C43H(5,𝔽2)11yescharacteristic
460C8×C43—22no—
461C8×C43—22no—
462C8×C43—22no—
463C8×C43—22no—
464C8×C43—41no—
465C8×C43—41no—
466#23894C4311yesmaximal, characteristic, direct product factor, Sylow
467C22×C43—22no—
468C22×C43—22no—
469C22×C43—41no—
470C22×C43—42no—
471C22×C43—42no—
472C22×C43—41no—
473C22×C43—42no—
474C22×C43—41no—
475C22×C43—41no—
476C22×C43—81no—
477C22×C43—81no—
478C22×C43—81no—
479C22×C43—82no—
480C22×C43—82no—
481C22×C43—161no—
482C22×C43—162no—
483C22×C43—164no—
484C22×C43#53411yescharacteristic
485C22×C43D4211yescharacteristic
486C22×C43D4211yescharacteristic
487C4×C43—22no—
488C4×C43—22no—
489C4×C43—41no—
490C4×C43—41no—
491C4×C43—41no—
492C4×C43—42no—
493C4×C43—81no—
494C4×C43—81no—
495C4×C43C2×#12011yescharacteristic
496C4×C43C2×#12011yescharacteristic
497C4×C43D4211yescharacteristic
498C4×C43D4211yescharacteristic
499#3586C2×C4311yescharacteristic, complemented
500#3585C2×C4311yescharacteristic, complemented
501#3020C2×C4311yescharacteristic, complemented
502#3019C2×C4311yescharacteristic, complemented
503#3010C2×C4311yescharacteristic, complemented
504#3009C2×C4311yescharacteristic, complemented
505#2019C2×C4311yescharacteristic, complemented
506#2017C2×C4311yescharacteristic, complemented
507#2009C2×C4311yescharacteristic, complemented
508#2008C2×C4311yescharacteristic, complemented
509#1903C2×C4311yescharacteristic, complemented
510#1902C2×C4311yescharacteristic, complemented
511#1881C2×C4311yescharacteristic, complemented
512#1881C2×C4311yescharacteristic, complemented
513#1794C2×C4311yescharacteristic, complemented
514C2×C43—21no—
515C2×C43—21no—
516C2×C43—21no—
517C2×C43—42no—
518C2×C43—42no—
519C2×C43—81no—
520C2×C43—81no—
521C2×C43—82no—
522C2×C43—81no—
523C2×C43#240311yescharacteristic
524#585C22×C4311yescharacteristic
525C2×2−1+4C22×C4311yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C4311yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C4311yescharacteristic
538#575C22×C4311yescharacteristic
539#575C22×C4311yescharacteristic
540#575C22×C4311yescharacteristic, complemented
541#575C22×C4311yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C4311yescharacteristic
544C2×#137C22×C4311yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
547C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
548C22×SD16C22×C4311yescharacteristic, complemented
549#568C22×C4311yescharacteristic
550#568C22×C4311yescharacteristic, complemented
551#536C22×C4311yescharacteristic, complemented
552#535C22×C4311yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C4311yescharacteristic
562#421C22×C4311yescharacteristic, complemented
563#421C22×C4311yescharacteristic, complemented
564#421C22×C4311yescharacteristic, complemented
565#419C22×C4311yescharacteristic, complemented
566#418C22×C4311yescharacteristic, complemented
567#416C22×C4311yescharacteristic
568#416C22×C4311yescharacteristic, complemented
569C2×#101C22×C4311yescharacteristic, complemented
570C2×#100C22×C4311yescharacteristic, complemented
571#410C22×C4311yescharacteristic, complemented
572#408C22×C4311yescharacteristic, complemented
573#408C22×C4311yescharacteristic, complemented
574#408C22×C4311yescharacteristic, complemented
575#344C22×C4311yescharacteristic, complemented
576#344C22×C4311yescharacteristic, complemented
577#341C22×C4311yescharacteristic, complemented
578#338C22×C4311yescharacteristic, complemented
579C43#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C4312yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C4312yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C4311yescharacteristic
604C2×#41C23×C4311yescharacteristic
605C2×#41C23×C4311yescharacteristic
606C2×#41C23×C4311yescharacteristic
607C2×#41C23×C4311yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C4311yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C4311yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C4312yes—
632#137D4×C4312yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C4312yes—
650AGL(1,ℤ/8)D4×C4312yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C4312yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C4312yes—
671C2×SD16D4×C4312yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C4312yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C4311yescharacteristic
682C2×M16C23×C4311yescharacteristic
683C2×M16C23×C4311yescharacteristic
684C2×M16C23×C4311yescharacteristic
685C2×M16C23×C4311yescharacteristic
686C22×C8C23×C4311yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C4311yescharacteristic
696#117C23×C4311yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C4312yes—
752#41C2×D4×C4312yes—
753#41C2×D4×C4312yes—
754#41C2×D4×C4312yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C4312yes—
769C2×Q8C2×D4×C4311yescharacteristic
770C2×Q8C2×D4×C4311yescharacteristic
771C2×Q8C2×D4×C4311yescharacteristic
772C2×Q8C2×D4×C4311yescharacteristic
773C2×Q8C2×D4×C4311yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C4312yes—
801C2×D4C2×D4×C4311yescharacteristic
802C2×D4C2×D4×C4311yescharacteristic
803C2×D4C2×D4×C4311yescharacteristic
804C2×D4C2×D4×C4311yescharacteristic
805C2×D4C2×D4×C4311yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C4311yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C4312yes—
857M16C2×D4×C4312yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C4312yes—
867C2×C8C2×D4×C4312yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C4311yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C4312yes—
905Q8#120×C4312yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C4312yes—
936D4#120×C4312yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C4311yescharacteristic
964C2×C4C22×D4×C4311yescharacteristic
965C2×C4C22×D4×C4311yescharacteristic
966C2×C4C22×D4×C4311yescharacteristic
967C2×C4C22×D4×C4311yescharacteristic
968C2×C4H(5,𝔽2)×C4311yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C43×#53411yescharacteristic
993C22D42×C4311yescharacteristic
994C22D42×C4311yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C4311yescharacteristic
1004C4C2×#120×C4311yescharacteristic
1005C4D42×C4311yescharacteristic
1006C4D42×C4311yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C43×#240311yescharacteristic
subgroupG/H
center, socleC2×C43#2403
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3586C2semidirect
2. C43×#3585C2semidirect
3. C43×#3020C2semidirect
4. C43×#3019C2semidirect
5. C43×#3010C2semidirect
6. C43×#3009C2semidirect
7. C43×#2019C2semidirect
8. C43×#2017C2semidirect
9. C43×#2009C2semidirect
10. C43×#2008C2semidirect
11. C43×#1903C2semidirect
12. C43×#1902C2semidirect
13. C43×#1881C2semidirect
14. C43×#1881C2semidirect
15. C43×#1794C2semidirect
17. C2×2−1+4×C43C22semidirect
32. C43×#575C22semidirect
33. C43×#575C22semidirect
36. C2×#137×C43C22semidirect
40. C22×SD16×C43C22semidirect
42. C43×#568C22semidirect
43. C43×#536C22semidirect
44. C43×#535C22semidirect
54. C43×#421C22semidirect
55. C43×#421C22semidirect
56. C43×#421C22semidirect
57. C43×#419C22semidirect
58. C43×#418C22semidirect
60. C43×#416C22semidirect
61. C2×#101×C43C22semidirect
62. C2×#100×C43C22semidirect
63. C43×#410C22semidirect
64. C43×#408C22semidirect
65. C43×#408C22semidirect
66. C43×#408C22semidirect
67. C43×#344C22semidirect
68. C43×#344C22semidirect
69. C43×#341C22semidirect
70. C43×#338C22semidirect
77. 2−1+4×C43D4semidirect
85. H(5,𝔽2)×C43D4semidirect
123. #137×C43D4semidirect
141. AGL(1,ℤ/8)×C43D4semidirect
153. C2×Q16×C43D4semidirect
162. C2×SD16×C43D4semidirect
466. #23894C43direct (N × H)
499. #3586C2×C43semidirect
500. #3585C2×C43semidirect
501. #3020C2×C43semidirect
502. #3019C2×C43semidirect
503. #3010C2×C43semidirect
504. #3009C2×C43semidirect
505. #2019C2×C43semidirect
506. #2017C2×C43semidirect
507. #2009C2×C43semidirect
508. #2008C2×C43semidirect
509. #1903C2×C43semidirect
510. #1902C2×C43semidirect
511. #1881C2×C43semidirect
512. #1881C2×C43semidirect
513. #1794C2×C43semidirect
525. C2×2−1+4C22×C43semidirect
540. #575C22×C43semidirect
541. #575C22×C43semidirect
544. C2×#137C22×C43semidirect
548. C22×SD16C22×C43semidirect
550. #568C22×C43semidirect
551. #536C22×C43semidirect
552. #535C22×C43semidirect
562. #421C22×C43semidirect
563. #421C22×C43semidirect
564. #421C22×C43semidirect
565. #419C22×C43semidirect
566. #418C22×C43semidirect
568. #416C22×C43semidirect
569. C2×#101C22×C43semidirect
570. C2×#100C22×C43semidirect
571. #410C22×C43semidirect
572. #408C22×C43semidirect
573. #408C22×C43semidirect
574. #408C22×C43semidirect
575. #344C22×C43semidirect
576. #344C22×C43semidirect
577. #341C22×C43semidirect
578. #338C22×C43semidirect
579. C43#23894direct (N × H)
586. 2−1+4D4×C43semidirect
594. H(5,𝔽2)D4×C43semidirect
632. #137D4×C43semidirect
650. AGL(1,ℤ/8)D4×C43semidirect
662. C2×Q16D4×C43semidirect
671. C2×SD16D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35862
C43×#35852
C43×#30202
C43×#30192
C43×#30102
C43×#30092
C43×#20192
C43×#20172
C43×#20092
C43×#20082
C43×#19032
C43×#19022
C43×#18812
C43×#17942
#2389443