Finite Group Databasebeta

← C43×#24454 #24944471

Subgroups — C43×#24454 #24944471

Order 11008.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic, complemented
2C2×C43×#468C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C43×#449C211yesmaximal, characteristic, complemented
5C2×C43×#417C211yesmaximal, characteristic, complemented
6C43×#2416C211yesmaximal, characteristic, complemented
7C43×#2043C211yesmaximal, characteristic, complemented
8C43×#2036C211yesmaximal, characteristic, complemented
9C43×#2013C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1872C211yesmaximal, characteristic, complemented
13C43×#1870C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C22×M16×C43C2211yescharacteristic
22C43×#547—24no—
23C43×#547—24no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×#123×C43—21no—
26C2×#123×C43—21no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊Q8×C43C2211yescharacteristic
29C2×#121×C43—21no—
30C2×#121×C43—21no—
31C2×#121×C43C2211yescharacteristic
32C2×#121×C43C2211yescharacteristic
33C2×C4×D4×C43C2211yescharacteristic
34C2×C4×D4×C43C2211yescharacteristic
35C22×C4⋊C4×C43—21no—
36C22×C4⋊C4×C43C2211yescharacteristic
37C43×#468—24no—
38C43×#449—24no—
39C43×#449—24no—
40C2×#107×C43C2211yescharacteristic
41C43×#417—24no—
42C2×#103×C43C2211yescharacteristic
43C2×#103×C43C2211yescharacteristic
44C2×#103×C43C2211yescharacteristic
45C2×#103×C43C2211yescharacteristic
46C2×#103×C43C2211yescharacteristic
47C2×#103×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C2×#102×C43C2211yescharacteristic
50C2×#102×C43C2211yescharacteristic
51C2×#102×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C43×#396—21no—
56C43×#394—21no—
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#386—21no—
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C43×#336C2211yescharacteristic
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—22no—
72C2×#41×C43—41no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C2×#41×C43—41no—
76C2×#41×C43D414yescomplemented
77C22×Q8×C43C2311yescharacteristic
78C22×Q8×C43C2311yescharacteristic
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43D411yescharacteristic
84C22×D4×C43C2311yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×SD16×C43—22no—
93C2×SD16×C43—22no—
94C2×SD16×C43—22no—
95C2×SD16×C43—41no—
96C2×SD16×C43—41no—
97C2×SD16×C43—41no—
98C2×D8×C43—22no—
99C2×D8×C43—22no—
100C2×D8×C43—22no—
101C2×M16×C43—22no—
102C2×M16×C43—22no—
103C2×M16×C43—41no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4⋊Q8×C43—22no—
109C4⋊Q8×C43—22no—
110#123×C43—28no—
111#123×C43—28no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43D414yescomplemented
116#121×C43—28no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—41no—
121#121×C43—44no—
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C2×C4⋊C4×C43—28no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—41no—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151#107×C43—22no—
152#103×C43—22no—
153#103×C43—22no—
154#103×C43—22no—
155#103×C43—22no—
156#103×C43—22no—
157#103×C43—41no—
158#102×C43—22no—
159#102×C43—22no—
160#102×C43—22no—
161#102×C43D414yescomplemented
162C22⋊C8×C43—22no—
163C22⋊C8×C43—22no—
164C22⋊C8×C43—41no—
165#95×C43—21no—
166#95×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43C2×D411yescharacteristic
170C24×C43C2×D411yescharacteristic
171#41×C43—28no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178#41×C43—44no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43C2×D412yes—
190C2×Q8×C43C2×D412yes—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—24no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—41no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—81no—
215C2×D4×C43C2×D412yes—
216C2×D4×C43C2×D412yes—
217C2×D4×C43#4112yes—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—24no—
223C22×C4×C43—24no—
224C22×C4×C43—24no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—42no—
238C22×C4×C43—42no—
239C22×C4×C43—42no—
240C22×C4×C43—42no—
241C22×C4×C43—42no—
242C22×C4×C43—42no—
243C22×C4×C43—42no—
244C22×C4×C43—42no—
245C22×C4×C43—81no—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253SD16×C43—44no—
254SD16×C43—44no—
255D8×C43—44no—
256M16×C43—44no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43C2×D412yes—
269C4⋊C4×C43—24no—
270C4⋊C4×C43—24no—
271C4⋊C4×C43—24no—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—24no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—42no—
281C4⋊C4×C43—42no—
282C4⋊C4×C43C2×D412yes—
283C4⋊C4×C43C2×D412yes—
284C22⋊C4×C43—24no—
285C22⋊C4×C43—24no—
286C22⋊C4×C43—22no—
287C22⋊C4×C43—24no—
288C22⋊C4×C43—22no—
289C22⋊C4×C43—42no—
290C22⋊C4×C43—42no—
291C22⋊C4×C43—42no—
292C22⋊C4×C43—42no—
293C22⋊C4×C43—81no—
294C42×C43—21no—
295C42×C43—21no—
296C23×C43—22no—
297C23×C43—21no—
298C23×C43—22no—
299C23×C43—21no—
300C23×C43—22no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43#12012yes—
324C23×C43C22×D411yescharacteristic
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—41no—
330Q8×C43—41no—
331Q8×C43—41no—
332Q8×C43—41no—
333D4×C43—22no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—44no—
337D4×C43—48no—
338D4×C43—48no—
339D4×C43—41no—
340D4×C43—41no—
341D4×C43—41no—
342D4×C43—41no—
343D4×C43—84no—
344D4×C43—84no—
345D4×C43#12114yescomplemented
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—48no—
365C2×C4×C43—48no—
366C2×C4×C43—48no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—84no—
386C2×C4×C43#12012yes—
387C2×C4×C43AGL(1,ℤ/8)12yes—
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C2×#4111yescharacteristic
392C2×C4×C43H(5,𝔽2)11yescharacteristic
393C2×C4×C43H(5,𝔽2)11yescharacteristic
394C8×C43—22no—
395C8×C43—41no—
396C8×C43—41no—
397C8×C43—41no—
398#24454C4311yesmaximal, characteristic, direct product factor, Sylow
399C22×C43—24no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—42no—
411C22×C43—41no—
412C22×C43—42no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43—81no—
424C22×C43—81no—
425C22×C43—81no—
426C22×C43—81no—
427C22×C43C2×#12011yescharacteristic
428C22×C43D4211yescharacteristic
429C22×C43#54611yescharacteristic
430C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C43#57511yescharacteristic
432C22×C43#57711yescharacteristic
433C22×C43#57811yescharacteristic
434C4×C43—22no—
435C4×C43—22no—
436C4×C43—41no—
437C4×C43—42no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—41no—
441C4×C43—42no—
442C4×C43—81no—
443C4×C43—81no—
444C4×C43C2×#12111yescharacteristic
445C4×C43#53411yescharacteristic
446C4×C43D4211yescharacteristic
447C4×C43#54611yescharacteristic
448C2×#547C2×C4311yescharacteristic, complemented
449C2×#468C2×C4311yescharacteristic, complemented
450C2×#449C2×C4311yescharacteristic, complemented
451C2×#449C2×C4311yescharacteristic, complemented
452C2×#417C2×C4311yescharacteristic, complemented
453#2416C2×C4311yescharacteristic, complemented
454#2043C2×C4311yescharacteristic, complemented
455#2036C2×C4311yescharacteristic, complemented
456#2013C2×C4311yescharacteristic, complemented
457#2000C2×C4311yescharacteristic, complemented
458#1879C2×C4311yescharacteristic, complemented
459#1872C2×C4311yescharacteristic, complemented
460#1870C2×C4311yescharacteristic, complemented
461#1862C2×C4311yescharacteristic, complemented
462#1788C2×C4311yescharacteristic, complemented
463C2×C43—42no—
464C2×C43—44no—
465C2×C43—81no—
466C2×C43—161no—
467C2×C43#241011yescharacteristic
468C2×C43#300611yescharacteristic
469C2×C43#301311yescharacteristic
470C2×C43#326911yescharacteristic
471C2×C43#327211yescharacteristic
472C2×C43#330711yescharacteristic
473C2×C43#333011yescharacteristic
474C22×#41C22×C4311yescharacteristic
475C22×#41C22×C4311yescharacteristic
476C22×SD16C22×C4311yescharacteristic
477C22×SD16C22×C4311yescharacteristic
478C22×D8C22×C4311yescharacteristic
479C22×M16C22×C4311yescharacteristic
480#547—24no—
481#547—24no—
482C2×C4⋊Q8C22×C4311yescharacteristic
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C22×C4311yescharacteristic
486C2×C22⋊Q8C22×C4311yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C4311yescharacteristic
490C2×#121C22×C4311yescharacteristic
491C2×C4×D4C22×C4311yescharacteristic
492C2×C4×D4C22×C4311yescharacteristic
493C22×C4⋊C4—21no—
494C22×C4⋊C4C22×C4311yescharacteristic
495#468—24no—
496#449—24no—
497#449—24no—
498C2×#107C22×C4311yescharacteristic
499#417—24no—
500C2×#103C22×C4311yescharacteristic
501C2×#103C22×C4311yescharacteristic
502C2×#103C22×C4311yescharacteristic
503C2×#103C22×C4311yescharacteristic
504C2×#103C22×C4311yescharacteristic
505C2×#103C22×C4311yescharacteristic
506C2×#102C22×C4311yescharacteristic
507C2×#102C22×C4311yescharacteristic
508C2×#102C22×C4311yescharacteristic
509C2×#102C22×C4311yescharacteristic
510C2×C22⋊C8C22×C4311yescharacteristic
511C2×C22⋊C8C22×C4311yescharacteristic
512C2×C22⋊C8C22×C4311yescharacteristic
513#396—21no—
514#394—21no—
515#390C22×C4311yescharacteristic
516#389C22×C4311yescharacteristic
517#386—21no—
518#380C22×C4311yescharacteristic
519#340C22×C4311yescharacteristic
520#340C22×C4311yescharacteristic
521#336C22×C4311yescharacteristic
522#336C22×C4311yescharacteristic
523C43#2445411yescharacteristic, direct product factor, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C4314yescomplemented
536C22×Q8C23×C4311yescharacteristic
537C22×Q8C23×C4311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C4311yescharacteristic
543C22×D4C23×C4311yescharacteristic
544C22×D4C23×C4311yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C4311yescharacteristic
550C23×C4C23×C4311yescharacteristic
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C4311yescharacteristic
564C22×C8C23×C4311yescharacteristic
565C22×C8C23×C4311yescharacteristic
566C22×C8C23×C4311yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#123—28no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8D4×C4314yescomplemented
575#121—28no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—44no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4D4×C4311yescharacteristic
595C2×C4⋊C4C23×C4311yescharacteristic
596C2×C4⋊C4C23×C4311yescharacteristic
597C2×C4⋊C4C23×C4311yescharacteristic
598C2×C4⋊C4C23×C4311yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4D4×C4311yescharacteristic
608C2×C22⋊C4D4×C4311yescharacteristic
609C2×C42C23×C4311yescharacteristic
610#107—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102D4×C4314yescomplemented
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—21no—
628C24C2×D4×C4311yescharacteristic
629C24C2×D4×C4311yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C4312yes—
649C2×Q8C2×D4×C4312yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—81no—
674C2×D4C2×D4×C4312yes—
675C2×D4C2×D4×C4312yes—
676C2×D4#41×C4312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C4311yescharacteristic
706C22×C4C2×D4×C4311yescharacteristic
707C22×C4C2×D4×C4311yescharacteristic
708C22×C4C2×D4×C4312yes—
709C22×C4C2×D4×C4312yes—
710C22×C4C2×D4×C4311yescharacteristic
711C22×C4C24×C4311yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C4312yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4C2×D4×C4312yes—
742C4⋊C4C2×D4×C4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C42—21no—
754C42—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#120×C4312yes—
783C23C22×D4×C4311yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804D4#121×C4314yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C4312yes—
846C2×C4AGL(1,ℤ/8)×C4312yes—
847C2×C4C22×D4×C4311yescharacteristic
848C2×C4C22×D4×C4311yescharacteristic
849C2×C4C22×D4×C4311yescharacteristic
850C2×C4C2×#41×C4311yescharacteristic
851C2×C4H(5,𝔽2)×C4311yescharacteristic
852C2×C4H(5,𝔽2)×C4311yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C4311yescharacteristic
886C22D42×C4311yescharacteristic
887C22C43×#54611yescharacteristic
888C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
889C22C43×#57511yescharacteristic
890C22C43×#57711yescharacteristic
891C22C43×#57811yescharacteristic
892C4—22no—
893C4—22no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—42no—
900C4—81no—
901C4—81no—
902C4C2×#121×C4311yescharacteristic
903C4C43×#53411yescharacteristic
904C4D42×C4311yescharacteristic
905C4C43×#54611yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—161no—
910C2C43×#241011yescharacteristic
911C2C43×#300611yescharacteristic
912C2C43×#301311yescharacteristic
913C2C43×#326911yescharacteristic
914C2C43×#327211yescharacteristic
915C2C43×#330711yescharacteristic
916C2C43×#333011yescharacteristic
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×#468C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C43×#449C2semidirect
5. C2×C43×#417C2semidirect
6. C43×#2416C2semidirect
7. C43×#2043C2semidirect
8. C43×#2036C2semidirect
9. C43×#2013C2semidirect
10. C43×#2000C2semidirect
11. C43×#1879C2semidirect
12. C43×#1872C2semidirect
13. C43×#1870C2semidirect
14. C43×#1862C2semidirect
15. C43×#1788C2semidirect
76. C2×#41×C43D4semidirect
115. C22⋊Q8×C43D4semidirect
161. #102×C43D4semidirect
345. D4×C43#121semidirect
398. #24454C43direct (N × H)
448. C2×#547C2×C43semidirect
449. C2×#468C2×C43semidirect
450. C2×#449C2×C43semidirect
451. C2×#449C2×C43semidirect
452. C2×#417C2×C43semidirect
453. #2416C2×C43semidirect
454. #2043C2×C43semidirect
455. #2036C2×C43semidirect
456. #2013C2×C43semidirect
457. #2000C2×C43semidirect
458. #1879C2×C43semidirect
459. #1872C2×C43semidirect
460. #1870C2×C43semidirect
461. #1862C2×C43semidirect
462. #1788C2×C43semidirect
523. C43#24454direct (N × H)
535. C2×#41D4×C43semidirect
574. C22⋊Q8D4×C43semidirect
620. #102D4×C43semidirect
804. D4#121×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×#4682
C2×C43×#4492
C2×C43×#4172
C43×#24162
C43×#20432
C43×#20362
C43×#20132
C43×#20002
C43×#18792
C43×#18722
C43×#18702
C43×#18622
C43×#17882
#2445443