Finite Group Databasebeta

← C43×#25080 #24945097

Subgroups — C43×#25080 #24945097

Order 11008.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#465C211yesmaximal, characteristic, complemented
2C2×C43×#460C211yesmaximal, characteristic, complemented
3C2×C43×#450C211yesmaximal, characteristic, complemented
4C22×#102×C43C211yesmaximal, characteristic, complemented
5C43×#2433C211yesmaximal, characteristic
6C43×#2360C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2041C211yesmaximal, characteristic, complemented
10C43×#2014C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1926C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1874C211yesmaximal, characteristic, complemented
15C43×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic, complemented
20C23×C8×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
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#465—24no—
30C43×#460—24no—
31C43×#450—24no—
32C2×#106×C43C2211yescharacteristic, complemented
33C2×C4⋊C8×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C2×#103×C43C2211yescharacteristic, complemented
36C2×#102×C43—24no—
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×#389—21no—
53C43×#389C2211yescharacteristic, complemented
54C43×#387—21no—
55C43×#385—21no—
56C4×C4⋊C4×C43C2211yescharacteristic, complemented
57C4×C22⋊C4×C43—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—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×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—22no—
85C2×SD16×C43—22no—
86C2×SD16×C43—22no—
87C2×SD16×C43—22no—
88C2×SD16×C43—41no—
89C2×SD16×C43—41no—
90C2×SD16×C43—41no—
91C22×C8×C43—22no—
92C22×C8×C43—22no—
93C22×C8×C43—41no—
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98#127×C43—22no—
99#127×C43—22no—
100#127×C43—41no—
101#127×C43—41no—
102C22⋊Q8×C43—22no—
103C22⋊Q8×C43D414yescomplemented
104#121×C43—22no—
105#121×C43—22no—
106#120×C43—44no—
107#120×C43—44no—
108C4×Q8×C43—22no—
109C4×Q8×C43—41no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—41no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#106×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—44no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
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×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43—81no—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43#4112yes—
228C22×C4×C43C2411yescharacteristic
229SD16×C43—44no—
230SD16×C43—44no—
231SD16×C43—44no—
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×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—44no—
244C2×C8×C43C2×D412yes—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—42no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43—81no—
255C4⋊C4×C43C2×D412yes—
256C4⋊C4×C43C2×D412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—42no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43SD1614yescomplemented
265C42×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269C42×C43—42no—
270C42×C43—81no—
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×C43C2×SD1612yes—
305C23×C43AGL(1,ℤ/8)12yes—
306C23×C43C22×D411yescharacteristic
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—41no—
310Q8×C43—41no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—48no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—84no—
325D4×C43—84no—
326D4×C43—84no—
327D4×C43—84no—
328D4×C43—84no—
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—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
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—41no—
359C2×C4×C43—41no—
360C2×C4×C43—84no—
361C2×C4×C43#12112yes—
362C2×C4×C43C2×SD1612yes—
363C2×C4×C43C2×SD1612yes—
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C2×#4111yescharacteristic
367C2×C4×C43C2×#4111yescharacteristic
368C2×C4×C43H(5,𝔽2)11yescharacteristic
369C2×C4×C43H(5,𝔽2)11yescharacteristic
370C8×C43—22no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374#25080C4311yesmaximal, characteristic, direct product factor, Sylow
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—816no—
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×C43—81no—
402C22×C43—81no—
403C22×C43#46014yescomplemented
404C22×C43C2×#12111yescharacteristic
405C22×C43D4211yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43C22×SD1611yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43#57611yescharacteristic
410C22×C43#57711yescharacteristic
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—42no—
415C4×C43—41no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43—41no—
419C4×C43—81no—
420C4×C43—81no—
421C4×C43#52511yescharacteristic
422C4×C43#53811yescharacteristic
423C4×C43D4211yescharacteristic
424C4×C43#54611yescharacteristic
425C2×#465C2×C4311yescharacteristic, complemented
426C2×#460C2×C4311yescharacteristic, complemented
427C2×#450C2×C4311yescharacteristic, complemented
428C22×#102C2×C4311yescharacteristic, complemented
429#2433C2×C4311yescharacteristic
430#2360C2×C4311yescharacteristic, complemented
431#2065C2×C4311yescharacteristic, complemented
432#2055C2×C4311yescharacteristic, complemented
433#2041C2×C4311yescharacteristic, complemented
434#2014C2×C4311yescharacteristic, complemented
435#1982C2×C4311yescharacteristic, complemented
436#1926C2×C4311yescharacteristic, complemented
437#1880C2×C4311yescharacteristic, complemented
438#1874C2×C4311yescharacteristic, complemented
439#1850C2×C4311yescharacteristic, complemented
440C2×C43—24no—
441C2×C43—82no—
442C2×C43—82no—
443C2×C43—161no—
444C2×C43#242411yescharacteristic
445C2×C43C2×#46011yescharacteristic
446C2×C43#304511yescharacteristic
447C2×C43#326411yescharacteristic
448C2×C43D4×SD1611yescharacteristic
449C2×C43#329511yescharacteristic
450C2×C43#331011yescharacteristic
451C23×D4C22×C4311yescharacteristic
452C22×SD16C22×C4311yescharacteristic
453C22×SD16C22×C4311yescharacteristic
454C22×SD16C22×C4311yescharacteristic, complemented
455C23×C8C22×C4311yescharacteristic
456C2×#127C22×C4311yescharacteristic
457C2×#127C22×C4311yescharacteristic
458C2×C22⋊Q8C22×C4311yescharacteristic
459C2×#121C22×C4311yescharacteristic
460C2×#120—21no—
461C2×#120—21no—
462C2×C4×Q8C22×C4311yescharacteristic, complemented
463C22×C4⋊C4C22×C4311yescharacteristic
464#465—24no—
465#460—24no—
466#450—24no—
467C2×#106C22×C4311yescharacteristic, complemented
468C2×C4⋊C8C22×C4311yescharacteristic, complemented
469C2×C4⋊C8C22×C4311yescharacteristic, complemented
470C2×#103C22×C4311yescharacteristic, complemented
471C2×#102—24no—
472C2×#102C22×C4311yescharacteristic
473C2×#102C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic
476C2×#102C22×C4311yescharacteristic
477C2×#102C22×C4311yescharacteristic
478C2×#102C22×C4311yescharacteristic, complemented
479C2×#102C22×C4311yescharacteristic, complemented
480C2×#102C22×C4311yescharacteristic, complemented
481C2×C22⋊C8C22×C4311yescharacteristic
482#392—21no—
483#392—21no—
484#391C22×C4311yescharacteristic, complemented
485#390C22×C4311yescharacteristic
486#390C22×C4311yescharacteristic
487#389—21no—
488#389C22×C4311yescharacteristic, complemented
489#387—21no—
490#385—21no—
491C4×C4⋊C4C22×C4311yescharacteristic, complemented
492C4×C22⋊C4—21no—
493C4×C22⋊C4C22×C4311yescharacteristic
494#340C22×C4311yescharacteristic, complemented
495#340C22×C4311yescharacteristic, complemented
496#336C22×C4311yescharacteristic, complemented
497#336C22×C4311yescharacteristic, complemented
498C43#2508011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C22×Q8C23×C4311yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C4311yescharacteristic
514C22×D4C23×C4311yescharacteristic
515C22×D4C23×C4311yescharacteristic
516C23×C4—21no—
517C23×C4C23×C4311yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C4311yescharacteristic
531C22×C8C23×C4311yescharacteristic
532C22×C8C23×C4311yescharacteristic
533C22×C8C23×C4311yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C4314yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C4⋊C4C23×C4311yescharacteristic
554C2×C4⋊C4C23×C4311yescharacteristic
555C2×C4⋊C4C23×C4311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C4311yescharacteristic
563C2×C22⋊C4D4×C4311yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C4311yescharacteristic
567C2×C42C23×C4311yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C4314yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C4311yescharacteristic
587#95D4×C4311yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C4311yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C4312yes—
605C2×D4—28no—
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—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
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—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C4312yes—
644C2×D4#41×C4312yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C4311yescharacteristic
658C22×C4C2×D4×C4311yescharacteristic
659C22×C4C2×D4×C4311yescharacteristic
660C22×C4C2×D4×C4312yes—
661C22×C4C2×D4×C4311yescharacteristic
662C22×C4C2×D4×C4311yescharacteristic
663C22×C4#41×C4312yes—
664C22×C4C24×C4311yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C4312yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C4312yes—
692C4⋊C4C2×D4×C4312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C4314yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
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—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C4312yes—
740C23C2×SD16×C4312yes—
741C23AGL(1,ℤ/8)×C4312yes—
742C23C22×D4×C4311yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4#121×C4312yes—
798C2×C4C2×SD16×C4312yes—
799C2×C4C2×SD16×C4312yes—
800C2×C4C22×D4×C4311yescharacteristic
801C2×C4C22×D4×C4311yescharacteristic
802C2×C4C2×#41×C4311yescharacteristic
803C2×C4C2×#41×C4311yescharacteristic
804C2×C4H(5,𝔽2)×C4311yescharacteristic
805C2×C4H(5,𝔽2)×C4311yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22C43×#46014yescomplemented
839C22C2×#121×C4311yescharacteristic
840C22D42×C4311yescharacteristic
841C22C43×#54611yescharacteristic
842C22C22×SD16×C4311yescharacteristic
843C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
844C22C43×#57611yescharacteristic
845C22C43×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C43×#52511yescharacteristic
857C4C43×#53811yescharacteristic
858C4D42×C4311yescharacteristic
859C4C43×#54611yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C43×#242411yescharacteristic
865C2C2×C43×#46011yescharacteristic
866C2C43×#304511yescharacteristic
867C2C43×#326411yescharacteristic
868C2D4×SD16×C4311yescharacteristic
869C2C43×#329511yescharacteristic
870C2C43×#331011yescharacteristic
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×#465C2semidirect
2. C2×C43×#460C2semidirect
3. C2×C43×#450C2semidirect
4. C22×#102×C43C2semidirect
6. C43×#2360C2semidirect
7. C43×#2065C2semidirect
8. C43×#2055C2semidirect
9. C43×#2041C2semidirect
10. C43×#2014C2semidirect
11. C43×#1982C2semidirect
12. C43×#1926C2semidirect
13. C43×#1880C2semidirect
14. C43×#1874C2semidirect
15. C43×#1850C2semidirect
19. C22×SD16×C43C22semidirect
27. C2×C4×Q8×C43C22semidirect
32. C2×#106×C43C22semidirect
33. C2×C4⋊C8×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
35. C2×#103×C43C22semidirect
43. C2×#102×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
49. C43×#391C22semidirect
53. C43×#389C22semidirect
56. C4×C4⋊C4×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
103. C22⋊Q8×C43D4semidirect
144. #102×C43D4semidirect
264. C22⋊C4×C43SD16semidirect
374. #25080C43direct (N × H)
403. C22×C43#460semidirect
425. C2×#465C2×C43semidirect
426. C2×#460C2×C43semidirect
427. C2×#450C2×C43semidirect
428. C22×#102C2×C43semidirect
430. #2360C2×C43semidirect
431. #2065C2×C43semidirect
432. #2055C2×C43semidirect
433. #2041C2×C43semidirect
434. #2014C2×C43semidirect
435. #1982C2×C43semidirect
436. #1926C2×C43semidirect
437. #1880C2×C43semidirect
438. #1874C2×C43semidirect
439. #1850C2×C43semidirect
454. C22×SD16C22×C43semidirect
462. C2×C4×Q8C22×C43semidirect
467. C2×#106C22×C43semidirect
468. C2×C4⋊C8C22×C43semidirect
469. C2×C4⋊C8C22×C43semidirect
470. C2×#103C22×C43semidirect
478. C2×#102C22×C43semidirect
479. C2×#102C22×C43semidirect
480. C2×#102C22×C43semidirect
484. #391C22×C43semidirect
488. #389C22×C43semidirect
491. C4×C4⋊C4C22×C43semidirect
494. #340C22×C43semidirect
495. #340C22×C43semidirect
496. #336C22×C43semidirect
497. #336C22×C43semidirect
498. C43#25080direct (N × H)
539. C22⋊Q8D4×C43semidirect
580. #102D4×C43semidirect
700. C22⋊C4SD16×C43semidirect
838. C22C43×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4652
C2×C43×#4602
C2×C43×#4502
C22×#102×C432
C43×#24332
C43×#23602
C43×#20652
C43×#20552
C43×#20412
C43×#20142
C43×#19822
C43×#19262
C43×#18802
C43×#18742
C43×#18502
#2508043