Finite Group Databasebeta

← C43×#25093 #24945110

Subgroups — C43×#25093 #24945110

Order 11008.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#460C211yesmaximal, characteristic, complemented
3C2×C43×#450C211yesmaximal, characteristic, complemented
4C2×C43×#418C211yesmaximal, characteristic, complemented
5C43×#2433C211yesmaximal, characteristic
6C43×#2362C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2041C211yesmaximal, characteristic, complemented
10C43×#2014C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1925C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1875C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic, complemented
20C22×M16×C43C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C2×#127×C43C2211yescharacteristic
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#120×C43—21no—
26C2×#120×C43—21no—
27C2×C4×Q8×C43C2211yescharacteristic, complemented
28C2×#117×C43C2211yescharacteristic
29C43×#468—24no—
30C43×#460—24no—
31C43×#450—24no—
32C2×#107×C43C2211yescharacteristic, complemented
33C2×C4⋊C8×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C43×#418—24no—
36C2×#103×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic, complemented
44C2×#102×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#392—21no—
48C43×#392—21no—
49C43×#391C2211yescharacteristic, complemented
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic, complemented
53C43×#388—21no—
54C43×#388—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×Q8×C43C2311yescharacteristic
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—21no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—22no—
75C22×D4×C43—41no—
76C22×D4×C43—41no—
77C22×D4×C43C2311yescharacteristic
78C22×D4×C43C2311yescharacteristic
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—22no—
85C2×SD16×C43—22no—
86C2×SD16×C43—22no—
87C2×SD16×C43—41no—
88C2×SD16×C43—41no—
89C2×SD16×C43—41no—
90C2×M16×C43—22no—
91C2×M16×C43—22no—
92C2×M16×C43—41no—
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97#127×C43—22no—
98#127×C43—22no—
99#127×C43—41no—
100#127×C43—41no—
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43D414yescomplemented
103#121×C43—22no—
104#121×C43—22no—
105#120×C43—44no—
106#120×C43—44no—
107C4×Q8×C43—22no—
108C4×Q8×C43—41no—
109#117×C43—22no—
110#117×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133C4⋊C8×C43—22no—
134C4⋊C8×C43—41no—
135#103×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144#102×C43D414yescomplemented
145C22⋊C8×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43D411yescharacteristic
151#95×C43D411yescharacteristic
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—42no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43C2×D412yes—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—28no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—44no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—81no—
204C2×D4×C43—81no—
205C2×D4×C43—81no—
206C2×D4×C43—81no—
207C2×D4×C43C2×D412yes—
208C2×D4×C43#4112yes—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43C2×D412yes—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43#4112yes—
225C22×C4×C43C2411yescharacteristic
226SD16×C43—44no—
227SD16×C43—44no—
228SD16×C43—44no—
229M16×C43—44no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43C2×D412yes—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—42no—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C2×D412yes—
252C4⋊C4×C43C2×D412yes—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—21no—
266C42×C43—42no—
267C42×C43—42no—
268C42×C43—42no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—48no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43—84no—
300C23×C43—84no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43#12112yes—
304C23×C43C22×D411yescharacteristic
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—41no—
308Q8×C43—41no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—48no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—84no—
323D4×C43—84no—
324D4×C43—84no—
325D4×C43—84no—
326D4×C43—84no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43#12112yes—
359C2×C4×C43AGL(1,ℤ/8)12yes—
360C2×C4×C43AGL(1,ℤ/8)12yes—
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×C4×C43H(5,𝔽2)11yescharacteristic
367C8×C43—22no—
368C8×C43—41no—
369C8×C43—41no—
370C8×C43—41no—
371#25093C4311yesmaximal, characteristic, direct product factor, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—816no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43C2×#12111yescharacteristic
402C22×C43D4211yescharacteristic
403C22×C43#54611yescharacteristic
404C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C43#57711yescharacteristic
407C22×C43#57711yescharacteristic
408C4×C43—22no—
409C4×C43—22no—
410C4×C43—22no—
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—41no—
416C4×C43—81no—
417C4×C43—81no—
418C4×C43#52511yescharacteristic
419C4×C43#53811yescharacteristic
420C4×C43D4211yescharacteristic
421C4×C43#54611yescharacteristic
422C2×#468C2×C4311yescharacteristic, complemented
423C2×#460C2×C4311yescharacteristic, complemented
424C2×#450C2×C4311yescharacteristic, complemented
425C2×#418C2×C4311yescharacteristic, complemented
426#2433C2×C4311yescharacteristic
427#2362C2×C4311yescharacteristic, complemented
428#2067C2×C4311yescharacteristic, complemented
429#2055C2×C4311yescharacteristic, complemented
430#2041C2×C4311yescharacteristic, complemented
431#2014C2×C4311yescharacteristic, complemented
432#1982C2×C4311yescharacteristic, complemented
433#1925C2×C4311yescharacteristic, complemented
434#1880C2×C4311yescharacteristic, complemented
435#1875C2×C4311yescharacteristic, complemented
436#1851C2×C4311yescharacteristic, complemented
437C2×C43—42no—
438C2×C43—82no—
439C2×C43—82no—
440C2×C43—161no—
441C2×C43#242411yescharacteristic
442C2×C43#303811yescharacteristic
443C2×C43#304311yescharacteristic
444C2×C43#326511yescharacteristic
445C2×C43#327211yescharacteristic
446C2×C43#331011yescharacteristic
447C2×C43#332411yescharacteristic
448C23×D4C22×C4311yescharacteristic
449C22×SD16C22×C4311yescharacteristic
450C22×SD16C22×C4311yescharacteristic
451C22×SD16C22×C4311yescharacteristic, complemented
452C22×M16C22×C4311yescharacteristic
453C2×#127C22×C4311yescharacteristic
454C2×#127C22×C4311yescharacteristic
455C2×C22⋊Q8C22×C4311yescharacteristic
456C2×#121C22×C4311yescharacteristic
457C2×#120—21no—
458C2×#120—21no—
459C2×C4×Q8C22×C4311yescharacteristic, complemented
460C2×#117C22×C4311yescharacteristic
461#468—24no—
462#460—24no—
463#450—24no—
464C2×#107C22×C4311yescharacteristic, complemented
465C2×C4⋊C8C22×C4311yescharacteristic, complemented
466C2×C4⋊C8C22×C4311yescharacteristic, complemented
467#418—24no—
468C2×#103C22×C4311yescharacteristic, complemented
469C2×#102C22×C4311yescharacteristic
470C2×#102C22×C4311yescharacteristic
471C2×#102C22×C4311yescharacteristic
472C2×#102C22×C4311yescharacteristic
473C2×#102C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic, complemented
476C2×#102C22×C4311yescharacteristic, complemented
477C2×#102C22×C4311yescharacteristic, complemented
478C2×C22⋊C8C22×C4311yescharacteristic
479#392—21no—
480#392—21no—
481#391C22×C4311yescharacteristic, complemented
482#390C22×C4311yescharacteristic
483#390C22×C4311yescharacteristic
484#389C22×C4311yescharacteristic, complemented
485#388—21no—
486#388—21no—
487#387—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4C22×C4311yescharacteristic, complemented
490C4×C22⋊C4C22×C4311yescharacteristic
491#340C22×C4311yescharacteristic, complemented
492#340C22×C4311yescharacteristic, complemented
493#336C22×C4311yescharacteristic, complemented
494#336C22×C4311yescharacteristic, complemented
495C43#2509311yescharacteristic, direct product factor, Sylow
496C25—21no—
497C22×Q8C23×C4311yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C4311yescharacteristic
511C22×D4C23×C4311yescharacteristic
512C22×D4C23×C4311yescharacteristic
513C23×C4C23×C4311yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C22×C8C23×C4311yescharacteristic
527C22×C8C23×C4311yescharacteristic
528C22×C8C23×C4311yescharacteristic
529C22×C8C23×C4311yescharacteristic
530#127—22no—
531#127—22no—
532#127—41no—
533#127—41no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C4314yescomplemented
536#121—22no—
537#121—22no—
538#120—44no—
539#120—44no—
540C4×Q8—22no—
541C4×Q8—41no—
542#117—22no—
543#117—41no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4C23×C4311yescharacteristic
548C2×C4⋊C4C23×C4311yescharacteristic
549C2×C4⋊C4C23×C4311yescharacteristic
550C2×C4⋊C4C23×C4311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C4311yescharacteristic
559C2×C22⋊C4D4×C4311yescharacteristic
560C2×C42—21no—
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C4311yescharacteristic
564C2×C42C23×C4311yescharacteristic
565#107—22no—
566C4⋊C8—22no—
567C4⋊C8—41no—
568#103—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102D4×C4314yescomplemented
578C22⋊C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95D4×C4311yescharacteristic
584#95D4×C4311yescharacteristic
585C24—21no—
586C24—21no—
587C24—21no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—81no—
594C24—81no—
595C24C2×D4×C4311yescharacteristic
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C4312yes—
602C2×D4—28no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4C2×D4×C4312yes—
641C2×D4#41×C4312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4C2×D4×C4311yescharacteristic
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4C2×D4×C4311yescharacteristic
654C22×C4C2×D4×C4312yes—
655C22×C4C2×D4×C4311yescharacteristic
656C22×C4C2×D4×C4311yescharacteristic
657C22×C4#41×C4312yes—
658C22×C4C24×C4311yescharacteristic
659SD16—44no—
660SD16—44no—
661SD16—44no—
662M16—44no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8C2×D4×C4312yes—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4C2×D4×C4312yes—
685C4⋊C4C2×D4×C4312yes—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23#121×C4312yes—
737C23C22×D4×C4311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#121×C4312yes—
792C2×C4AGL(1,ℤ/8)×C4312yes—
793C2×C4AGL(1,ℤ/8)×C4312yes—
794C2×C4C22×D4×C4311yescharacteristic
795C2×C4C22×D4×C4311yescharacteristic
796C2×C4C2×#41×C4311yescharacteristic
797C2×C4C2×#41×C4311yescharacteristic
798C2×C4H(5,𝔽2)×C4311yescharacteristic
799C2×C4H(5,𝔽2)×C4311yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22C2×#121×C4311yescharacteristic
834C22D42×C4311yescharacteristic
835C22C43×#54611yescharacteristic
836C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
837C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
838C22C43×#57711yescharacteristic
839C22C43×#57711yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—42no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—81no—
849C4—81no—
850C4C43×#52511yescharacteristic
851C4C43×#53811yescharacteristic
852C4D42×C4311yescharacteristic
853C4C43×#54611yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2C43×#242411yescharacteristic
859C2C43×#303811yescharacteristic
860C2C43×#304311yescharacteristic
861C2C43×#326511yescharacteristic
862C2C43×#327211yescharacteristic
863C2C43×#331011yescharacteristic
864C2C43×#332411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#460C2semidirect
3. C2×C43×#450C2semidirect
4. C2×C43×#418C2semidirect
6. C43×#2362C2semidirect
7. C43×#2067C2semidirect
8. C43×#2055C2semidirect
9. C43×#2041C2semidirect
10. C43×#2014C2semidirect
11. C43×#1982C2semidirect
12. C43×#1925C2semidirect
13. C43×#1880C2semidirect
14. C43×#1875C2semidirect
15. C43×#1851C2semidirect
19. C22×SD16×C43C22semidirect
27. C2×C4×Q8×C43C22semidirect
32. C2×#107×C43C22semidirect
33. C2×C4⋊C8×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
36. C2×#103×C43C22semidirect
43. C2×#102×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
49. C43×#391C22semidirect
52. C43×#389C22semidirect
57. C4×C4⋊C4×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
102. C22⋊Q8×C43D4semidirect
144. #102×C43D4semidirect
371. #25093C43direct (N × H)
422. C2×#468C2×C43semidirect
423. C2×#460C2×C43semidirect
424. C2×#450C2×C43semidirect
425. C2×#418C2×C43semidirect
427. #2362C2×C43semidirect
428. #2067C2×C43semidirect
429. #2055C2×C43semidirect
430. #2041C2×C43semidirect
431. #2014C2×C43semidirect
432. #1982C2×C43semidirect
433. #1925C2×C43semidirect
434. #1880C2×C43semidirect
435. #1875C2×C43semidirect
436. #1851C2×C43semidirect
451. C22×SD16C22×C43semidirect
459. C2×C4×Q8C22×C43semidirect
464. C2×#107C22×C43semidirect
465. C2×C4⋊C8C22×C43semidirect
466. C2×C4⋊C8C22×C43semidirect
468. C2×#103C22×C43semidirect
475. C2×#102C22×C43semidirect
476. C2×#102C22×C43semidirect
477. C2×#102C22×C43semidirect
481. #391C22×C43semidirect
484. #389C22×C43semidirect
489. C4×C4⋊C4C22×C43semidirect
491. #340C22×C43semidirect
492. #340C22×C43semidirect
493. #336C22×C43semidirect
494. #336C22×C43semidirect
495. C43#25093direct (N × H)
535. C22⋊Q8D4×C43semidirect
577. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4602
C2×C43×#4502
C2×C43×#4182
C43×#24332
C43×#23622
C43×#20672
C43×#20552
C43×#20412
C43×#20142
C43×#19822
C43×#19252
C43×#18802
C43×#18752
C43×#18512
#2509343