Finite Group Databasebeta

← C43×#25549 #24945566

Subgroups — C43×#25549 #24945566

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic, complemented
2C2×C43×#481C211yesmaximal, characteristic, complemented
3C2×C43×#469C211yesmaximal, characteristic, complemented
4C43×#2414C211yesmaximal, characteristic, complemented
5C43×#2058C211yesmaximal, characteristic, complemented
6C43×#2034C211yesmaximal, characteristic, complemented
7C43×#2023C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1879C211yesmaximal, characteristic, complemented
10C43×#1875C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1864C211yesmaximal, characteristic, complemented
14C43×#1853C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C43—21no—
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C43×#547—24no—
20C43×#547—24no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×#123×C43—21no—
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43—21no—
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#481—24no—
35C43×#469—24no—
36C2×#106×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×#106×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#394—21no—
49C43×#392—21no—
50C43×#390—21no—
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#388—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—28no—
64C2×#41×C43—44no—
65C2×#41×C43—44no—
66C22×Q8×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—41no—
82C2×M16×C43—22no—
83C2×M16×C43—22no—
84C2×M16×C43—41no—
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C4⋊Q8×C43—22no—
90C4⋊Q8×C43—22no—
91#123×C43—28no—
92#123×C43—28no—
93C22⋊Q8×C43—28no—
94#121×C43—22no—
95#121×C43—22no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—41no—
101#121×C43D414yescomplemented
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106#117×C43—22no—
107#117×C43—41no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D414yescomplemented
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#106×C43—22no—
137#106×C43—22no—
138#106×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43—41no—
145C22⋊C8×C43—22no—
146C22⋊C8×C43—22no—
147C22⋊C8×C43—41no—
148#95×C43—21no—
149#95×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43C2×D411yescharacteristic
153C24×C43C2×D411yescharacteristic
154#41×C43—432no—
155C2×Q8×C43—24no—
156C2×Q8×C43—42no—
157C2×Q8×C43—42no—
158C2×D4×C43—24no—
159C2×D4×C43—22no—
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—24no—
163C2×D4×C43—22no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—81no—
182C2×D4×C43—81no—
183C2×D4×C43—81no—
184C2×D4×C43C2×D412yes—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—24no—
190C22×C4×C43—24no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—24no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—42no—
205C22×C4×C43—42no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217D8×C43—44no—
218M16×C43—44no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43#4112yescomplemented
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—22no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—81no—
244C4⋊C4×C43C2×D412yes—
245C4⋊C4×C43C2×D412yes—
246C4⋊C4×C43C2×D412yes—
247C4⋊C4×C43#4112yescomplemented
248C22⋊C4×C43—24no—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—81no—
258C22⋊C4×C43—81no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—42no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
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#12012yes—
289C23×C43AGL(1,ℤ/8)12yes—
290C23×C43C22×D411yescharacteristic
291Q8×C43—48no—
292D4×C43—28no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—48no—
296D4×C43—48no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—84no—
304D4×C43—84no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—48no—
324C2×C4×C43—48no—
325C2×C4×C43—48no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43#12012yes—
345C2×C4×C43AGL(1,ℤ/8)12yes—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C2×C4×C432−1+411yescharacteristic
352C8×C43—22no—
353C8×C43—41no—
354C8×C43—41no—
355C8×C43—41no—
356#25549C4311yesmaximal, characteristic, direct product factor, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43C2×#12011yescharacteristic
386C22×C43#54611yescharacteristic
387C22×C43#54711yescharacteristic
388C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C43#57711yescharacteristic
391C22×C43#57711yescharacteristic
392C4×C43—22no—
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43—41no—
399C4×C43—42no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43#53211yescharacteristic
403C4×C43#53711yescharacteristic
404C4×C43#54611yescharacteristic
405C4×C43#54711yescharacteristic
406C2×#547C2×C4311yescharacteristic, complemented
407C2×#481C2×C4311yescharacteristic, complemented
408C2×#469C2×C4311yescharacteristic, complemented
409#2414C2×C4311yescharacteristic, complemented
410#2058C2×C4311yescharacteristic, complemented
411#2034C2×C4311yescharacteristic, complemented
412#2023C2×C4311yescharacteristic, complemented
413#1999C2×C4311yescharacteristic, complemented
414#1879C2×C4311yescharacteristic, complemented
415#1875C2×C4311yescharacteristic, complemented
416#1874C2×C4311yescharacteristic, complemented
417#1870C2×C4311yescharacteristic, complemented
418#1864C2×C4311yescharacteristic, complemented
419#1853C2×C4311yescharacteristic, complemented
420#1736C2×C4311yescharacteristic, complemented
421C2×C43—42no—
422C2×C43—42no—
423C2×C43—82no—
424C2×C43—161no—
425C2×C43#243011yescharacteristic
426C2×C43#300311yescharacteristic
427C2×C43#301011yescharacteristic
428C2×C43#330611yescharacteristic
429C2×C43#333211yescharacteristic
430C2×C43#334511yescharacteristic
431C2×C43#335411yescharacteristic
432C22×#41—21no—
433C22×D8C22×C4311yescharacteristic
434C22×M16C22×C4311yescharacteristic
435#547—24no—
436#547—24no—
437C2×C4⋊Q8C22×C4311yescharacteristic
438C2×#123—21no—
439C2×#123—21no—
440C2×C22⋊Q8—21no—
441C2×#121C22×C4311yescharacteristic
442C2×#121C22×C4311yescharacteristic
443C2×#121C22×C4311yescharacteristic
444C2×#121C22×C4311yescharacteristic
445C2×C4×D4C22×C4311yescharacteristic
446C2×C4×D4C22×C4311yescharacteristic
447C2×#117C22×C4311yescharacteristic
448C22×C4⋊C4C22×C4311yescharacteristic
449C22×C4⋊C4C22×C4311yescharacteristic
450#481—24no—
451#469—24no—
452C2×#106C22×C4311yescharacteristic
453C2×#106C22×C4311yescharacteristic
454C2×#106C22×C4311yescharacteristic
455C2×#102C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×#102C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×C22⋊C8C22×C4311yescharacteristic
462C2×C22⋊C8C22×C4311yescharacteristic
463C2×C22⋊C8C22×C4311yescharacteristic
464#394—21no—
465#392—21no—
466#390—21no—
467#390C22×C4311yescharacteristic
468#389C22×C4311yescharacteristic
469#388—21no—
470#380C22×C4311yescharacteristic
471#340C22×C4311yescharacteristic
472#340C22×C4311yescharacteristic
473#340C22×C4311yescharacteristic
474#340C22×C4311yescharacteristic
475#340C22×C4311yescharacteristic
476#340C22×C4311yescharacteristic
477#336C22×C4311yescharacteristic
478#336C22×C4311yescharacteristic
479C43#2554911yescharacteristic, direct product factor, Sylow
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4311yescharacteristic
489C22×D4C23×C4311yescharacteristic
490C22×D4C23×C4311yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C4311yescharacteristic
495C23×C4C23×C4311yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C4311yescharacteristic
503C22×C8C23×C4311yescharacteristic
504C22×C8C23×C4311yescharacteristic
505C22×C8C23×C4311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C4314yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C4311yescharacteristic
533C2×C4⋊C4D4×C4314yescomplemented
534C2×C4⋊C4C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C4⋊C4C23×C4311yescharacteristic
537C2×C4⋊C4C23×C4311yescharacteristic
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C4311yescharacteristic
550C2×C22⋊C4D4×C4311yescharacteristic
551C2×C42—21no—
552C2×C42C23×C4311yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C4311yescharacteristic
570C24C2×D4×C4311yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C4311yescharacteristic
628C22×C4C2×D4×C4311yescharacteristic
629C22×C4C2×D4×C4311yescharacteristic
630C22×C4C2×D4×C4312yes—
631C22×C4C2×D4×C4312yes—
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C24×C4311yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C4312yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C4312yes—
662C4⋊C4C2×D4×C4312yes—
663C4⋊C4C2×D4×C4312yes—
664C4⋊C4#41×C4312yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C4312yes—
706C23AGL(1,ℤ/8)×C4312yes—
707C23C22×D4×C4311yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4#120×C4312yes—
762C2×C4AGL(1,ℤ/8)×C4312yes—
763C2×C4C22×D4×C4311yescharacteristic
764C2×C4C22×D4×C4311yescharacteristic
765C2×C4C2×#41×C4311yescharacteristic
766C2×C4C2×#41×C4311yescharacteristic
767C2×C4H(5,𝔽2)×C4311yescharacteristic
768C2×C42−1+4×C4311yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C4311yescharacteristic
802C22C43×#54611yescharacteristic
803C22C43×#54711yescharacteristic
804C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
805C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
806C22C43×#57711yescharacteristic
807C22C43×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4C43×#53211yescharacteristic
819C4C43×#53711yescharacteristic
820C4C43×#54611yescharacteristic
821C4C43×#54711yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C43×#243011yescharacteristic
827C2C43×#300311yescharacteristic
828C2C43×#301011yescharacteristic
829C2C43×#330611yescharacteristic
830C2C43×#333211yescharacteristic
831C2C43×#334511yescharacteristic
832C2C43×#335411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#547C2semidirect
2. C2×C43×#481C2semidirect
3. C2×C43×#469C2semidirect
4. C43×#2414C2semidirect
5. C43×#2058C2semidirect
6. C43×#2034C2semidirect
7. C43×#2023C2semidirect
8. C43×#1999C2semidirect
9. C43×#1879C2semidirect
10. C43×#1875C2semidirect
11. C43×#1874C2semidirect
12. C43×#1870C2semidirect
13. C43×#1864C2semidirect
14. C43×#1853C2semidirect
15. C43×#1736C2semidirect
101. #121×C43D4semidirect
116. C2×C4⋊C4×C43D4semidirect
230. C2×C8×C43#41semidirect
247. C4⋊C4×C43#41semidirect
356. #25549C43direct (N × H)
406. C2×#547C2×C43semidirect
407. C2×#481C2×C43semidirect
408. C2×#469C2×C43semidirect
409. #2414C2×C43semidirect
410. #2058C2×C43semidirect
411. #2034C2×C43semidirect
412. #2023C2×C43semidirect
413. #1999C2×C43semidirect
414. #1879C2×C43semidirect
415. #1875C2×C43semidirect
416. #1874C2×C43semidirect
417. #1870C2×C43semidirect
418. #1864C2×C43semidirect
419. #1853C2×C43semidirect
420. #1736C2×C43semidirect
479. C43#25549direct (N × H)
518. #121D4×C43semidirect
533. C2×C4⋊C4D4×C43semidirect
647. C2×C8#41×C43semidirect
664. C4⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5472
C2×C43×#4812
C2×C43×#4692
C43×#24142
C43×#20582
C43×#20342
C43×#20232
C43×#19992
C43×#18792
C43×#18752
C43×#18742
C43×#18702
C43×#18642
C43×#18532
C43×#17362
#2554943