Finite Group Databasebeta

← C43×#25152 #24945169

Subgroups — C43×#25152 #24945169

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#463C211yesmaximal, characteristic, complemented
2C2×C43×#450C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic
4C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
5C43×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2036C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2012C211yesmaximal, characteristic, complemented
11C43×#1970C211yesmaximal, characteristic, complemented
12C43×#1923C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1879C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic, complemented
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×Q8×C43C2211yescharacteristic, complemented
25C2×C4×D4×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C22×C22⋊C4×C43—21no—
28C43×#463—24no—
29C43×#450—24no—
30C43×#447—24no—
31C4×SD16×C43—24no—
32C2×#107×C43C2211yescharacteristic, complemented
33C2×#106×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C2×#103×C43C2211yescharacteristic, complemented
36C2×#103×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic, complemented
42C2×#102×C43C2211yescharacteristic, complemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C4×C8×C43C2211yescharacteristic, complemented
46C43×#396—21no—
47C43×#394—21no—
48C43×#390—21no—
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic, complemented
52C43×#389C2211yescharacteristic, complemented
53C43×#388—21no—
54C43×#386—21no—
55C43×#386—21no—
56C43×#380C2211yescharacteristic
57C43×#379—21no—
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—22no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—41no—
72C22×D4×C43—41no—
73C22×D4×C43C2311yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43C2311yescharacteristic
79C2×SD16×C43—22no—
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—41no—
84C2×SD16×C43D414yescomplemented
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—41no—
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#124×C43—22no—
96#124×C43—41no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—41no—
99#121×C43—22no—
100#121×C43—41no—
101C4×Q8×C43—22no—
102C4×Q8×C43—41no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—41no—
106C4×D4×C43—41no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
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×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—44no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#107×C43—41no—
134#106×C43—22no—
135C4⋊C8×C43—22no—
136#103×C43—22no—
137#103×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—41no—
143#102×C43D414yes—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—22no—
146C4×C8×C43—22no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—24no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43C2×D411yescharacteristic
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C2×D412yes—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
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—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—44no—
187C2×D4×C43—44no—
188C2×D4×C43—44no—
189C2×D4×C43—44no—
190C2×D4×C43—42no—
191C2×D4×C43—81no—
192C2×D4×C43C2×D412yes—
193C2×D4×C43C2×D412yes—
194C2×D4×C43#4112yes—
195C2×D4×C43#4112yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
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—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43—81no—
212C22×C4×C43—81no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219SD16×C43—28no—
220SD16×C43—44no—
221D8×C43—44no—
222D8×C43—44no—
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—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43C2×D412yes—
234C2×C8×C43C2×D412yes—
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—42no—
243C4⋊C4×C43—42no—
244C4⋊C4×C43—81no—
245C4⋊C4×C43C2×D412yes—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—81no—
259C22⋊C4×C43—81no—
260C22⋊C4×C43—81no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—42no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—48no—
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—84no—
296C23×C43—84no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43—84no—
300C23×C43#13512yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—41no—
305Q8×C43—41no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—84no—
319D4×C43#12114yes—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
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—41no—
345C2×C4×C43—41no—
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—84no—
354C2×C4×C43—84no—
355C2×C4×C43AGL(1,ℤ/8)12yes—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C8×C43—22no—
363C8×C43—22no—
364C8×C43—41no—
365C8×C43—41no—
366#25152C4311yesmaximal, characteristic, direct product factor, Sylow
367C22×C43—22no—
368C22×C43—24no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—816no—
385C22×C43—81no—
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#52511yescharacteristic
397C22×C43D4211yescharacteristic
398C22×C43D4211yescharacteristic
399C22×C43C2×#13511yescharacteristic
400C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C43#57611yescharacteristic
402C22×C43#57711yescharacteristic
403C4×C43—22no—
404C4×C43—41no—
405C4×C43—42no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—81no—
411C4×C43—81no—
412C4×C43—81no—
413C4×C43C2×#12111yescharacteristic
414C4×C43#53811yescharacteristic
415C4×C43#54611yescharacteristic
416C4×C43#54611yescharacteristic
417C2×#463C2×C4311yescharacteristic, complemented
418C2×#450C2×C4311yescharacteristic, complemented
419C2×#447C2×C4311yescharacteristic
420C2×C4×SD16C2×C4311yescharacteristic, complemented
421#2426C2×C4311yescharacteristic, complemented
422D4×C22⋊C4C2×C4311yescharacteristic, complemented
423#2065C2×C4311yescharacteristic, complemented
424#2036C2×C4311yescharacteristic, complemented
425#2034C2×C4311yescharacteristic, complemented
426#2012C2×C4311yescharacteristic, complemented
427#1970C2×C4311yescharacteristic, complemented
428#1923C2×C4311yescharacteristic, complemented
429#1880C2×C4311yescharacteristic, complemented
430#1879C2×C4311yescharacteristic, complemented
431#1862C2×C4311yescharacteristic, complemented
432C2×C43—42no—
433C2×C43—44no—
434C2×C43—82no—
435C2×C43—161no—
436C2×C43#242411yescharacteristic
437C2×C43#310511yescharacteristic
438C2×C43#311811yescharacteristic
439C2×C43#326511yescharacteristic
440C2×C43#327411yescharacteristic
441C2×C43#328011yescharacteristic
442C2×C43#328211yescharacteristic
443C23×D4C22×C4311yescharacteristic
444C22×SD16C22×C4311yescharacteristic
445C22×SD16C22×C4311yescharacteristic
446C22×D8C22×C4311yescharacteristic
447C22×D8C22×C4311yescharacteristic
448C2×#124C22×C4311yescharacteristic, complemented
449C2×C22⋊Q8C22×C4311yescharacteristic
450C2×#121C22×C4311yescharacteristic
451C2×C4×Q8C22×C4311yescharacteristic, complemented
452C2×C4×D4C22×C4311yescharacteristic
453C2×C4×D4C22×C4311yescharacteristic
454C22×C22⋊C4—21no—
455#463—24no—
456#450—24no—
457#447—24no—
458C4×SD16—24no—
459C2×#107C22×C4311yescharacteristic, complemented
460C2×#106C22×C4311yescharacteristic, complemented
461C2×C4⋊C8C22×C4311yescharacteristic, complemented
462C2×#103C22×C4311yescharacteristic, complemented
463C2×#103C22×C4311yescharacteristic, complemented
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic, complemented
469C2×#102C22×C4311yescharacteristic, complemented
470C2×C22⋊C8C22×C4311yescharacteristic
471C2×C22⋊C8C22×C4311yescharacteristic
472C2×C4×C8C22×C4311yescharacteristic, complemented
473#396—21no—
474#394—21no—
475#390—21no—
476#390C22×C4311yescharacteristic
477#390C22×C4311yescharacteristic
478#390C22×C4311yescharacteristic, complemented
479#389C22×C4311yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#386—21no—
483#380C22×C4311yescharacteristic
484#379—21no—
485C4×C22⋊C4C22×C4311yescharacteristic
486#340C22×C4311yescharacteristic, complemented
487#340C22×C4311yescharacteristic, complemented
488#336C22×C4311yescharacteristic, complemented
489#336C22×C4311yescharacteristic, complemented
490C43#2515211yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C4311yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C4311yescharacteristic
502C22×D4C23×C4311yescharacteristic
503C22×D4C23×C4311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C4311yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C4314yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C4311yescharacteristic
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522C22×C8C23×C4311yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C4⋊C4C23×C4311yescharacteristic
541C2×C4⋊C4C23×C4311yescharacteristic
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⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C4311yescharacteristic
557C2×C22⋊C4D4×C4311yescharacteristic
558C2×C42—21no—
559C2×C42C23×C4311yescharacteristic
560C2×C42C23×C4311yescharacteristic
561#107—41no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C4314yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C4311yescharacteristic
578#95D4×C4311yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C4311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C4312yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
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—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C4312yes—
621C2×D4C2×D4×C4312yes—
622C2×D4#41×C4312yes—
623C2×D4#41×C4312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4311yescharacteristic
643C22×C4C2×D4×C4311yescharacteristic
644C22×C4C2×D4×C4311yescharacteristic
645C22×C4C2×D4×C4311yescharacteristic
646C22×C4C24×C4311yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C4312yes—
662C2×C8C2×D4×C4312yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C4312yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
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—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#135×C4312yes—
729C23C22×D4×C4311yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C4314yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4AGL(1,ℤ/8)×C4312yes—
784C2×C4C22×D4×C4311yescharacteristic
785C2×C4C22×D4×C4311yescharacteristic
786C2×C4C2×#41×C4311yescharacteristic
787C2×C4C2×#41×C4311yescharacteristic
788C2×C4H(5,𝔽2)×C4311yescharacteristic
789C2×C4H(5,𝔽2)×C4311yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C43×#52511yescharacteristic
824C22D42×C4311yescharacteristic
825C22D42×C4311yescharacteristic
826C22C2×#135×C4311yescharacteristic
827C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
828C22C43×#57611yescharacteristic
829C22C43×#57711yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C4311yescharacteristic
841C4C43×#53811yescharacteristic
842C4C43×#54611yescharacteristic
843C4C43×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C43×#242411yescharacteristic
849C2C43×#310511yescharacteristic
850C2C43×#311811yescharacteristic
851C2C43×#326511yescharacteristic
852C2C43×#327411yescharacteristic
853C2C43×#328011yescharacteristic
854C2C43×#328211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
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×#463C2semidirect
2. C2×C43×#450C2semidirect
4. C2×C4×SD16×C43C2semidirect
5. C43×#2426C2semidirect
6. D4×C22⋊C4×C43C2semidirect
7. C43×#2065C2semidirect
8. C43×#2036C2semidirect
9. C43×#2034C2semidirect
10. C43×#2012C2semidirect
11. C43×#1970C2semidirect
12. C43×#1923C2semidirect
13. C43×#1880C2semidirect
14. C43×#1879C2semidirect
15. C43×#1862C2semidirect
21. C2×#124×C43C22semidirect
24. C2×C4×Q8×C43C22semidirect
32. C2×#107×C43C22semidirect
33. C2×#106×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
35. C2×#103×C43C22semidirect
36. C2×#103×C43C22semidirect
41. C2×#102×C43C22semidirect
42. C2×#102×C43C22semidirect
45. C2×C4×C8×C43C22semidirect
51. C43×#390C22semidirect
52. C43×#389C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
84. C2×SD16×C43D4semidirect
366. #25152C43direct (N × H)
417. C2×#463C2×C43semidirect
418. C2×#450C2×C43semidirect
420. C2×C4×SD16C2×C43semidirect
421. #2426C2×C43semidirect
422. D4×C22⋊C4C2×C43semidirect
423. #2065C2×C43semidirect
424. #2036C2×C43semidirect
425. #2034C2×C43semidirect
426. #2012C2×C43semidirect
427. #1970C2×C43semidirect
428. #1923C2×C43semidirect
429. #1880C2×C43semidirect
430. #1879C2×C43semidirect
431. #1862C2×C43semidirect
448. C2×#124C22×C43semidirect
451. C2×C4×Q8C22×C43semidirect
459. C2×#107C22×C43semidirect
460. C2×#106C22×C43semidirect
461. C2×C4⋊C8C22×C43semidirect
462. C2×#103C22×C43semidirect
463. C2×#103C22×C43semidirect
468. C2×#102C22×C43semidirect
469. C2×#102C22×C43semidirect
472. C2×C4×C8C22×C43semidirect
478. #390C22×C43semidirect
479. #389C22×C43semidirect
486. #340C22×C43semidirect
487. #340C22×C43semidirect
488. #336C22×C43semidirect
489. #336C22×C43semidirect
490. C43#25152direct (N × H)
512. C2×SD16D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4632
C2×C43×#4502
C2×C43×#4472
C2×C4×SD16×C432
C43×#24262
D4×C22⋊C4×C432
C43×#20652
C43×#20362
C43×#20342
C43×#20122
C43×#19702
C43×#19232
C43×#18802
C43×#18792
C43×#18622
#2515243