Finite Group Databasebeta

← C43×#24468 #24944485

Subgroups — C43×#24468 #24944485

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3488C211yesmaximal, characteristic, complemented
2C43×#3055C211yesmaximal, characteristic, complemented
3C2×C43×#453C211yesmaximal, characteristic, complemented
4C43×#3006C211yesmaximal, characteristic, complemented
5C2×C43×#421C211yesmaximal, characteristic, complemented
6C43×#2619C211yesmaximal, characteristic, complemented
7C43×#2040C211yesmaximal, characteristic, complemented
8C43×#2037C211yesmaximal, characteristic, complemented
9C43×#2006C211yesmaximal, characteristic, complemented
10C43×#2002C211yesmaximal, characteristic, complemented
11C43×#1900C211yesmaximal, characteristic, complemented
12C43×#1897C211yesmaximal, characteristic, complemented
13C43×#1883C211yesmaximal, characteristic, complemented
14C43×#1860C211yesmaximal, characteristic, complemented
15C43×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
21C22×M16×C43C2211yescharacteristic, complemented
22C43×#550—21no—
23C43×#548—21no—
24C43×#546—21no—
25C43×#546—22no—
26D42×C43—22no—
27D42×C43—21no—
28C43×#537—21no—
29C43×#537C2211yescharacteristic
30C43×#535—21no—
31C43×#535C2211yescharacteristic
32C2×#127×C43C2211yescharacteristic, complemented
33C43×#525—21no—
34C43×#525C2211yescharacteristic
35C2×#121×C43—21no—
36C2×#121×C43C2211yescharacteristic
37C2×#121×C43C2211yescharacteristic, complemented
38C43×#520C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic, complemented
40C43×#469—21no—
41C43×#468—21no—
42C43×#466—21no—
43C43×#465—21no—
44C43×#453—24no—
45C43×#449—21no—
46C43×#449—21no—
47C43×#448—21no—
48C43×#447—21no—
49C43×#428C2211yescharacteristic, complemented
50C43×#421—24no—
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic, complemented
54C2×#104×C43C2211yescharacteristic, complemented
55C2×#104×C43C2211yescharacteristic, complemented
56C2×#104×C43C2211yescharacteristic, complemented
57C43×#418C2211yescharacteristic, complemented
58C43×#417C2211yescharacteristic
59C43×#417C2211yescharacteristic, complemented
60C43×#417C2211yescharacteristic, complemented
61C2×#100×C43C2211yescharacteristic, complemented
62C2×#100×C43C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic, complemented
64C43×#394—22no—
65C43×#392—22no—
66C43×#390C2211yescharacteristic, complemented
67C43×#390C2211yescharacteristic, complemented
68C43×#382C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C43×#343C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72C43×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C43—22no—
74H(5,𝔽2)×C43—22no—
75H(5,𝔽2)×C43—41no—
76H(5,𝔽2)×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—22no—
82C2×#41×C43—22no—
83C2×#41×C43—41no—
84C2×#41×C43—41no—
85C2×#41×C43D411yescharacteristic, complemented
86C2×#41×C43D411yescharacteristic, complemented
87C2×#41×C43C2311yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C2×#41×C43C2311yescharacteristic
90C22×Q8×C43D411yescharacteristic, complemented
91C22×D4×C43—21no—
92C22×D4×C43—22no—
93C22×D4×C43—22no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—22no—
98C22×D4×C43D412yes—
99C22×D4×C43D411yescharacteristic, complemented
100C22×D4×C43C2311yescharacteristic
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43C2311yescharacteristic
104AGL(1,ℤ/8)×C43—22no—
105AGL(1,ℤ/8)×C43—22no—
106AGL(1,ℤ/8)×C43—22no—
107AGL(1,ℤ/8)×C43—41no—
108AGL(1,ℤ/8)×C43—41no—
109AGL(1,ℤ/8)×C43—41no—
110C2×SD16×C43—21no—
111C2×SD16×C43—21no—
112C2×SD16×C43—21no—
113C2×D8×C43—21no—
114C2×D8×C43—21no—
115C2×D8×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—22no—
118C2×M16×C43—41no—
119C2×M16×C43C2311yescharacteristic
120C2×M16×C43C2311yescharacteristic
121C2×M16×C43C2311yescharacteristic
122C2×M16×C43C2311yescharacteristic
123C22×C8×C43—21no—
124#127×C43—22no—
125#127×C43—21no—
126#127×C43—22no—
127#127×C43—41no—
128#124×C43—22no—
129#124×C43—21no—
130#123×C43—22no—
131#123×C43—21no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43D411yescharacteristic, complemented
136C22⋊Q8×C43D411yescharacteristic, complemented
137#121×C43—22no—
138#121×C43—22no—
139#121×C43—22no—
140#121×C43—22no—
141#121×C43—22no—
142#121×C43—21no—
143#121×C43—21no—
144#121×C43—21no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—22no—
149#121×C43—21no—
150#121×C43—21no—
151#121×C43—21no—
152#121×C43—21no—
153#121×C43—21no—
154#121×C43—21no—
155#121×C43D411yescharacteristic, complemented
156#121×C43D411yescharacteristic, complemented
157#120×C43—22no—
158#120×C43—22no—
159#120×C43—22no—
160#120×C43—21no—
161#120×C43—22no—
162C4×Q8×C43—21no—
163C4×D4×C43—22no—
164C4×D4×C43—22no—
165C4×D4×C43—21no—
166C4×D4×C43—22no—
167C4×D4×C43—21no—
168C4×D4×C43—21no—
169#117×C43—21no—
170#117×C43—22no—
171#117×C43—41no—
172#117×C43C2311yescharacteristic
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—22no—
181C2×C22⋊C4×C43—22no—
182C2×C22⋊C4×C43D412yes—
183C2×C42×C43C2311yescharacteristic
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—22no—
191#104×C43—41no—
192#104×C43D414yescomplemented
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#102×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199#102×C43—21no—
200#102×C43—21no—
201#100×C43—22no—
202#100×C43—41no—
203C22⋊C8×C43—21no—
204C22⋊C8×C43—21no—
205#95×C43—22no—
206C24×C43—22no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43C2×D412yes—
210C24×C43C2×D411yescharacteristic
211#41×C43—21no—
212#41×C43—21no—
213#41×C43—22no—
214#41×C43—22no—
215#41×C43—21no—
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—42no—
224#41×C43—42no—
225#41×C43—41no—
226#41×C43—41no—
227#41×C43—42no—
228#41×C43—42no—
229#41×C43—42no—
230#41×C43—42no—
231#41×C43—42no—
232#41×C43—42no—
233#41×C43C2×D412yes—
234#41×C43#4112yes—
235C2×Q8×C43—21no—
236C2×Q8×C43—22no—
237C2×Q8×C43—41no—
238C2×Q8×C43C2×D411yescharacteristic
239C2×Q8×C43C2×D411yescharacteristic
240C2×Q8×C43C2×D411yescharacteristic
241C2×D4×C43—22no—
242C2×D4×C43—22no—
243C2×D4×C43—22no—
244C2×D4×C43—22no—
245C2×D4×C43—22no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43—21no—
250C2×D4×C43—21no—
251C2×D4×C43—21no—
252C2×D4×C43—21no—
253C2×D4×C43—22no—
254C2×D4×C43—21no—
255C2×D4×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—21no—
258C2×D4×C43—22no—
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—22no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—21no—
268C2×D4×C43—21no—
269C2×D4×C43—44no—
270C2×D4×C43—42no—
271C2×D4×C43—42no—
272C2×D4×C43—44no—
273C2×D4×C43—44no—
274C2×D4×C43—41no—
275C2×D4×C43—42no—
276C2×D4×C43—42no—
277C2×D4×C43—42no—
278C2×D4×C43—42no—
279C2×D4×C43—41no—
280C2×D4×C43—41no—
281C2×D4×C43—82no—
282C2×D4×C43—82no—
283C2×D4×C43—82no—
284C2×D4×C43—82no—
285C2×D4×C43—84no—
286C2×D4×C43C2×D411yescharacteristic
287C2×D4×C43C2×D411yescharacteristic
288C2×D4×C43C2×D411yescharacteristic
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—21no—
292C22×C4×C43—21no—
293C22×C4×C43—21no—
294C22×C4×C43—22no—
295C22×C4×C43—22no—
296C22×C4×C43—21no—
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—21no—
304C22×C4×C43—42no—
305C22×C4×C43—42no—
306C22×C4×C43C2×D411yescharacteristic
307C22×C4×C43C2×D411yescharacteristic
308C22×C4×C43C2×D411yescharacteristic
309C22×C4×C43C2×D411yescharacteristic
310C22×C4×C43C2×D411yescharacteristic
311C22×C4×C43C2×D412yes—
312C22×C4×C43C2411yescharacteristic
313SD16×C43—42no—
314SD16×C43—42no—
315SD16×C43—42no—
316D8×C43—42no—
317D8×C43—42no—
318D8×C43—42no—
319M16×C43—21no—
320M16×C43—21no—
321M16×C43—21no—
322M16×C43—21no—
323M16×C43—21no—
324M16×C43—21no—
325M16×C43—21no—
326M16×C43—42no—
327M16×C43C2×D412yescomplemented
328C2×C8×C43—21no—
329C2×C8×C43—21no—
330C2×C8×C43—21no—
331C2×C8×C43—21no—
332C2×C8×C43—42no—
333C4⋊C4×C43—22no—
334C4⋊C4×C43—22no—
335C4⋊C4×C43—21no—
336C4⋊C4×C43—21no—
337C4⋊C4×C43—21no—
338C4⋊C4×C43—21no—
339C4⋊C4×C43—21no—
340C4⋊C4×C43—21no—
341C4⋊C4×C43—42no—
342C4⋊C4×C43C2×D411yescharacteristic
343C4⋊C4×C43C2×D411yescharacteristic
344C22⋊C4×C43—22no—
345C22⋊C4×C43—22no—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—22no—
351C22⋊C4×C43—22no—
352C22⋊C4×C43—21no—
353C22⋊C4×C43—21no—
354C22⋊C4×C43—21no—
355C22⋊C4×C43—21no—
356C22⋊C4×C43—42no—
357C22⋊C4×C43—41no—
358C22⋊C4×C43—41no—
359C22⋊C4×C43—82no—
360C22⋊C4×C43—82no—
361C42×C43—22no—
362C42×C43—21no—
363C42×C43—21no—
364C42×C43—21no—
365C42×C43—21no—
366C42×C43C2×D412yescomplemented
367C23×C43—21no—
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—22no—
371C23×C43—21no—
372C23×C43—21no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—42no—
378C23×C43—42no—
379C23×C43—44no—
380C23×C43—42no—
381C23×C43—42no—
382C23×C43—42no—
383C23×C43—42no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43—81no—
388C23×C43—82no—
389C23×C43—82no—
390C23×C43#12011yescharacteristic
391C23×C43#12011yescharacteristic
392C23×C43C22×D411yescharacteristic
393Q8×C43—21no—
394Q8×C43—21no—
395Q8×C43—21no—
396Q8×C43—21no—
397Q8×C43—21no—
398Q8×C43—42no—
399Q8×C43#12112yes—
400D4×C43—22no—
401D4×C43—22no—
402D4×C43—21no—
403D4×C43—21no—
404D4×C43—21no—
405D4×C43—21no—
406D4×C43—21no—
407D4×C43—42no—
408D4×C43—42no—
409D4×C43—44no—
410D4×C43—42no—
411D4×C43—44no—
412D4×C43—44no—
413D4×C43—42no—
414D4×C43—41no—
415D4×C43—41no—
416D4×C43—41no—
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—41no—
426D4×C43—81no—
427D4×C43—82no—
428D4×C43—82no—
429D4×C43—82no—
430D4×C43—82no—
431D4×C43—88no—
432D4×C43—82no—
433D4×C43—82no—
434D4×C43#12112yes—
435C2×C4×C43—21no—
436C2×C4×C43—21no—
437C2×C4×C43—21no—
438C2×C4×C43—21no—
439C2×C4×C43—21no—
440C2×C4×C43—21no—
441C2×C4×C43—21no—
442C2×C4×C43—21no—
443C2×C4×C43—21no—
444C2×C4×C43—22no—
445C2×C4×C43—21no—
446C2×C4×C43—21no—
447C2×C4×C43—22no—
448C2×C4×C43—21no—
449C2×C4×C43—22no—
450C2×C4×C43—21no—
451C2×C4×C43—21no—
452C2×C4×C43—21no—
453C2×C4×C43—22no—
454C2×C4×C43—42no—
455C2×C4×C43—42no—
456C2×C4×C43—42no—
457C2×C4×C43—44no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—42no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—42no—
468C2×C4×C43—41no—
469C2×C4×C43—41no—
470C2×C4×C43—82no—
471C2×C4×C43#12011yescharacteristic
472C2×C4×C43#12011yescharacteristic
473C2×C4×C43C22×D411yescharacteristic
474C2×C4×C43C22×D411yescharacteristic
475C2×C4×C43C22×D411yescharacteristic
476C2×C4×C43C2×#4111yescharacteristic
477C2×C4×C43H(5,𝔽2)11yescharacteristic
478C2×C4×C43H(5,𝔽2)11yescharacteristic
479C8×C43—22no—
480C8×C43—41no—
481C8×C43—41no—
482C8×C43—41no—
483#24468C4311yesmaximal, characteristic, direct product factor, Sylow
484C22×C43—21no—
485C22×C43—21no—
486C22×C43—21no—
487C22×C43—21no—
488C22×C43—22no—
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—21no—
493C22×C43—41no—
494C22×C43—41no—
495C22×C43—42no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43—41no—
499C22×C43—42no—
500C22×C43—41no—
501C22×C43—42no—
502C22×C43—41no—
503C22×C43—41no—
504C22×C43—81no—
505C22×C43—81no—
506C22×C43—82no—
507C22×C43—82no—
508C22×C43—82no—
509C22×C43—82no—
510C22×C43—84no—
511C22×C43—81no—
512C22×C43—81no—
513C22×C43—81no—
514C22×C43—164no—
515C22×C43C2×#12011yescharacteristic
516C22×C43D4211yescharacteristic
517C22×C43#54611yescharacteristic
518C4×C43—21no—
519C4×C43—21no—
520C4×C43—22no—
521C4×C43—42no—
522C4×C43—41no—
523C4×C43—41no—
524C4×C43—42no—
525C4×C43—41no—
526C4×C43—41no—
527C4×C43—81no—
528C4×C43—81no—
529C4×C43C2×#12111yescharacteristic
530C4×C43#53411yescharacteristic
531C4×C43D4211yescharacteristic
532C4×C43#54611yescharacteristic
533#3488C2×C4311yescharacteristic, complemented
534#3055C2×C4311yescharacteristic, complemented
535C2×#453C2×C4311yescharacteristic, complemented
536#3006C2×C4311yescharacteristic, complemented
537C2×#421C2×C4311yescharacteristic, complemented
538#2619C2×C4311yescharacteristic, complemented
539#2040C2×C4311yescharacteristic, complemented
540#2037C2×C4311yescharacteristic, complemented
541#2006C2×C4311yescharacteristic, complemented
542#2002C2×C4311yescharacteristic, complemented
543#1900C2×C4311yescharacteristic, complemented
544#1897C2×C4311yescharacteristic, complemented
545#1883C2×C4311yescharacteristic, complemented
546#1860C2×C4311yescharacteristic, complemented
547#1792C2×C4311yescharacteristic, complemented
548C2×C43—21no—
549C2×C43—21no—
550C2×C43—41no—
551C2×C43—41no—
552C2×C43—42no—
553C2×C43—81no—
554C2×C43—82no—
555C2×C43—81no—
556C2×C43—161no—
557C2×C43#241011yescharacteristic
558C2×C43#301911yescharacteristic
559C2×C43#302111yescharacteristic
560C2×H(5,𝔽2)C22×C4311yescharacteristic
561C22×#41C22×C4311yescharacteristic
562C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
563C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
564C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
565C22×M16C22×C4311yescharacteristic, complemented
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C22×C4311yescharacteristic
574#535—21no—
575#535C22×C4311yescharacteristic
576C2×#127C22×C4311yescharacteristic, complemented
577#525—21no—
578#525C22×C4311yescharacteristic
579C2×#121—21no—
580C2×#121C22×C4311yescharacteristic
581C2×#121C22×C4311yescharacteristic, complemented
582#520C22×C4311yescharacteristic
583C2×#117C22×C4311yescharacteristic, complemented
584#469—21no—
585#468—21no—
586#466—21no—
587#465—21no—
588#453—24no—
589#449—21no—
590#449—21no—
591#448—21no—
592#447—21no—
593#428C22×C4311yescharacteristic, complemented
594#421—24no—
595C2×#104C22×C4311yescharacteristic
596C2×#104C22×C4311yescharacteristic
597C2×#104C22×C4311yescharacteristic, complemented
598C2×#104C22×C4311yescharacteristic, complemented
599C2×#104C22×C4311yescharacteristic, complemented
600C2×#104C22×C4311yescharacteristic, complemented
601#418C22×C4311yescharacteristic, complemented
602#417C22×C4311yescharacteristic
603#417C22×C4311yescharacteristic, complemented
604#417C22×C4311yescharacteristic, complemented
605C2×#100C22×C4311yescharacteristic, complemented
606C2×#100C22×C4311yescharacteristic, complemented
607#407C22×C4311yescharacteristic, complemented
608#394—22no—
609#392—22no—
610#390C22×C4311yescharacteristic, complemented
611#390C22×C4311yescharacteristic, complemented
612#382C22×C4311yescharacteristic, complemented
613#343C22×C4311yescharacteristic, complemented
614#343C22×C4311yescharacteristic, complemented
615#339C22×C4311yescharacteristic, complemented
616#339C22×C4311yescharacteristic, complemented
617C43#2446811yescharacteristic, direct product factor, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C4311yescharacteristic, complemented
631C2×#41D4×C4311yescharacteristic, complemented
632C2×#41C23×C4311yescharacteristic
633C2×#41C23×C4311yescharacteristic
634C2×#41C23×C4311yescharacteristic
635C22×Q8D4×C4311yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C4312yes—
644C22×D4D4×C4311yescharacteristic, complemented
645C22×D4C23×C4311yescharacteristic
646C22×D4C23×C4311yescharacteristic
647C23×C4—21no—
648C23×C4C23×C4311yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C4311yescharacteristic
665C2×M16C23×C4311yescharacteristic
666C2×M16C23×C4311yescharacteristic
667C2×M16C23×C4311yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C4311yescharacteristic, complemented
681C22⋊Q8D4×C4311yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C4311yescharacteristic, complemented
701#121D4×C4311yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C4311yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C4311yescharacteristic
721C2×C4⋊C4C23×C4311yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C4312yes—
728C2×C42C23×C4311yescharacteristic
729C2×C42C23×C4311yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C4314yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C4312yes—
755C24C2×D4×C4311yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C4312yes—
779#41#41×C4312yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C4311yescharacteristic
784C2×Q8C2×D4×C4311yescharacteristic
785C2×Q8C2×D4×C4311yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C4311yescharacteristic
832C2×D4C2×D4×C4311yescharacteristic
833C2×D4C2×D4×C4311yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C4311yescharacteristic
852C22×C4C2×D4×C4311yescharacteristic
853C22×C4C2×D4×C4311yescharacteristic
854C22×C4C2×D4×C4311yescharacteristic
855C22×C4C2×D4×C4311yescharacteristic
856C22×C4C2×D4×C4312yes—
857C22×C4C24×C4311yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C4312yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C4311yescharacteristic
888C4⋊C4C2×D4×C4311yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C4312yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C4311yescharacteristic
936C23#120×C4311yescharacteristic
937C23C22×D4×C4311yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C4312yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C4312yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C4311yescharacteristic
1017C2×C4#120×C4311yescharacteristic
1018C2×C4C22×D4×C4311yescharacteristic
1019C2×C4C22×D4×C4311yescharacteristic
1020C2×C4C22×D4×C4311yescharacteristic
1021C2×C4C2×#41×C4311yescharacteristic
1022C2×C4H(5,𝔽2)×C4311yescharacteristic
1023C2×C4H(5,𝔽2)×C4311yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C4311yescharacteristic
1060C22D42×C4311yescharacteristic
1061C22C43×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C4311yescharacteristic
1074C4C43×#53411yescharacteristic
1075C4D42×C4311yescharacteristic
1076C4C43×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C43×#241011yescharacteristic
1087C2C43×#301911yescharacteristic
1088C2C43×#302111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3488C2semidirect
2. C43×#3055C2semidirect
3. C2×C43×#453C2semidirect
4. C43×#3006C2semidirect
5. C2×C43×#421C2semidirect
6. C43×#2619C2semidirect
7. C43×#2040C2semidirect
8. C43×#2037C2semidirect
9. C43×#2006C2semidirect
10. C43×#2002C2semidirect
11. C43×#1900C2semidirect
12. C43×#1897C2semidirect
13. C43×#1883C2semidirect
14. C43×#1860C2semidirect
15. C43×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C43C22semidirect
20. C2×AGL(1,ℤ/8)×C43C22semidirect
21. C22×M16×C43C22semidirect
32. C2×#127×C43C22semidirect
37. C2×#121×C43C22semidirect
39. C2×#117×C43C22semidirect
49. C43×#428C22semidirect
53. C2×#104×C43C22semidirect
54. C2×#104×C43C22semidirect
55. C2×#104×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C43×#418C22semidirect
59. C43×#417C22semidirect
60. C43×#417C22semidirect
61. C2×#100×C43C22semidirect
62. C2×#100×C43C22semidirect
63. C43×#407C22semidirect
66. C43×#390C22semidirect
67. C43×#390C22semidirect
68. C43×#382C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
85. C2×#41×C43D4semidirect
86. C2×#41×C43D4semidirect
90. C22×Q8×C43D4semidirect
99. C22×D4×C43D4semidirect
135. C22⋊Q8×C43D4semidirect
136. C22⋊Q8×C43D4semidirect
155. #121×C43D4semidirect
156. #121×C43D4semidirect
192. #104×C43D4semidirect
327. M16×C43C2×D4semidirect
366. C42×C43C2×D4semidirect
483. #24468C43direct (N × H)
533. #3488C2×C43semidirect
534. #3055C2×C43semidirect
535. C2×#453C2×C43semidirect
536. #3006C2×C43semidirect
537. C2×#421C2×C43semidirect
538. #2619C2×C43semidirect
539. #2040C2×C43semidirect
540. #2037C2×C43semidirect
541. #2006C2×C43semidirect
542. #2002C2×C43semidirect
543. #1900C2×C43semidirect
544. #1897C2×C43semidirect
545. #1883C2×C43semidirect
546. #1860C2×C43semidirect
547. #1792C2×C43semidirect
563. C2×AGL(1,ℤ/8)C22×C43semidirect
564. C2×AGL(1,ℤ/8)C22×C43semidirect
565. C22×M16C22×C43semidirect
576. C2×#127C22×C43semidirect
581. C2×#121C22×C43semidirect
583. C2×#117C22×C43semidirect
593. #428C22×C43semidirect
597. C2×#104C22×C43semidirect
598. C2×#104C22×C43semidirect
599. C2×#104C22×C43semidirect
600. C2×#104C22×C43semidirect
601. #418C22×C43semidirect
603. #417C22×C43semidirect
604. #417C22×C43semidirect
605. C2×#100C22×C43semidirect
606. C2×#100C22×C43semidirect
607. #407C22×C43semidirect
610. #390C22×C43semidirect
611. #390C22×C43semidirect
612. #382C22×C43semidirect
613. #343C22×C43semidirect
614. #343C22×C43semidirect
615. #339C22×C43semidirect
616. #339C22×C43semidirect
617. C43#24468direct (N × H)
630. C2×#41D4×C43semidirect
631. C2×#41D4×C43semidirect
635. C22×Q8D4×C43semidirect
644. C22×D4D4×C43semidirect
680. C22⋊Q8D4×C43semidirect
681. C22⋊Q8D4×C43semidirect
700. #121D4×C43semidirect
701. #121D4×C43semidirect
737. #104D4×C43semidirect
872. M16C2×D4×C43semidirect
911. C42C2×D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34882
C43×#30552
C2×C43×#4532
C43×#30062
C2×C43×#4212
C43×#26192
C43×#20402
C43×#20372
C43×#20062
C43×#20022
C43×#19002
C43×#18972
C43×#18832
C43×#18602
C43×#17922
#2446843