Finite Group Databasebeta

← C43×#29744 #24949761

Subgroups — C43×#29744 #24949761

Order 11008.

1168 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#407C211yesmaximal, characteristic, complemented
3C43×#2848C211yesmaximal, characteristic, complemented
4C43×#2847C211yesmaximal, characteristic
5C43×#2076C211yesmaximal, characteristic, complemented
6C43×#2075C211yesmaximal, characteristic, complemented
7C43×#2036C211yesmaximal, characteristic, complemented
8C43×#2035C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2033C211yesmaximal, characteristic, complemented
11C43×#2000C211yesmaximal, characteristic, complemented
12C43×#2000C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1894C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic, complemented
18C22×M16×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C2×C22⋊Q8×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#120×C43—21no—
27C43×#468—24no—
28C2×#107×C43C2211yescharacteristic, complemented
29C2×#107×C43C2211yescharacteristic, complemented
30C2×#106×C43C2211yescharacteristic, complemented
31C2×#103×C43C2211yescharacteristic, complemented
32C2×#103×C43C2211yescharacteristic, complemented
33C2×#103×C43C2211yescharacteristic, complemented
34C2×#102×C43C2211yescharacteristic, complemented
35C2×#102×C43C2211yescharacteristic, complemented
36C2×#102×C43C2211yescharacteristic, complemented
37C43×#407—24no—
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×C22⋊C8×C43C2211yescharacteristic
41C2×C22⋊C8×C43C2211yescharacteristic
42C43×#386—21no—
43C43×#386—21no—
44C43×#386—21no—
45C43×#385—21no—
46C43×#385—21no—
47C43×#385—21no—
48C43×#380C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#380C2211yescharacteristic
54C43×#379—21no—
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C25×C43D411yescharacteristic
62C22×Q8×C43C2311yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2311yescharacteristic
67C23×C4×C43—22no—
68C23×C4×C43—22no—
69C23×C4×C43—41no—
70C23×C4×C43—41no—
71C23×C4×C43—41no—
72C23×C4×C43—41no—
73C23×C4×C43D411yescharacteristic
74C23×C4×C43D411yescharacteristic
75C23×C4×C43D411yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C2×SD16×C43—22no—
80C2×SD16×C43—41no—
81C2×SD16×C43—41no—
82C2×M16×C43—22no—
83C2×M16×C43—41no—
84C2×M16×C43—41no—
85C2×M16×C43—41no—
86C2×M16×C43—41no—
87C2×M16×C43D414yescomplemented
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—41no—
95C22⋊Q8×C43—41no—
96C22⋊Q8×C43—41no—
97C22⋊Q8×C43—41no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—41no—
101#121×C43—41no—
102#121×C43—41no—
103#121×C43—41no—
104#120×C43—44no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
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—
126#107×C43—22no—
127#107×C43—41no—
128#106×C43—41no—
129#103×C43—22no—
130#103×C43—41no—
131#103×C43—41no—
132#102×C43—22no—
133#102×C43—41no—
134#102×C43—41no—
135C22⋊C8×C43—22no—
136C22⋊C8×C43—22no—
137C22⋊C8×C43—22no—
138C22⋊C8×C43—22no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144#95×C43—21no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—21no—
149C24×C43—41no—
150C24×C43—41no—
151C24×C43—41no—
152C24×C43—41no—
153C24×C43C2×D411yescharacteristic
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—22no—
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—41no—
204C22×C4×C43—41no—
205C22×C4×C43—41no—
206C22×C4×C43—41no—
207C22×C4×C43—41no—
208C22×C4×C43—41no—
209C22×C4×C43—44no—
210C22×C4×C43—44no—
211C22×C4×C43—44no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43#4112yes—
218C22×C4×C43C2411yescharacteristic
219SD16×C43—44no—
220M16×C43—44no—
221M16×C43—44no—
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—21no—
231C2×C8×C43—21no—
232C2×C8×C43C2×D412yes—
233C2×C8×C43C2×D412yes—
234C4⋊C4×C43—21no—
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—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43—42no—
248C4⋊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—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C23×C43—21no—
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—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—44no—
280C23×C43—44no—
281C23×C43—44no—
282C23×C43—44no—
283C23×C43—44no—
284C23×C43—44no—
285C23×C43—44no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43#12112yes—
294C23×C43AGL(1,ℤ/8)12yes—
295C23×C43#13712yes—
296C23×C43C22×D411yescharacteristic
297Q8×C43—41no—
298Q8×C43—41no—
299Q8×C43—41no—
300Q8×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—84no—
306D4×C43—84no—
307D4×C43—84no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—44no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
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—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#12112yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C8×C43—22no—
360C8×C43—22no—
361C8×C43—41no—
362C8×C43—41no—
363#29744C4311yesmaximal, characteristic, direct product factor, Sylow
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—416no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43C2×#12111yescharacteristic
394C22×C43#53411yescharacteristic
395C22×C43#53411yescharacteristic
396C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C43C2×#13711yescharacteristic
398C22×C43#57511yescharacteristic
399C22×C43#57511yescharacteristic
400C4×C43—22no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43—81no—
404C4×C43—81no—
405C4×C43—81no—
406C4×C43—81no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43—81no—
410C4×C43#53411yescharacteristic
411C4×C43#53511yescharacteristic
412C4×C43#53811yescharacteristic
413C4×C43#53811yescharacteristic
414C2×#468C2×C4311yescharacteristic, complemented
415C2×#407C2×C4311yescharacteristic, complemented
416#2848C2×C4311yescharacteristic, complemented
417#2847C2×C4311yescharacteristic
418#2076C2×C4311yescharacteristic, complemented
419#2075C2×C4311yescharacteristic, complemented
420#2036C2×C4311yescharacteristic, complemented
421#2035C2×C4311yescharacteristic, complemented
422#2034C2×C4311yescharacteristic, complemented
423#2033C2×C4311yescharacteristic, complemented
424#2000C2×C4311yescharacteristic, complemented
425#2000C2×C4311yescharacteristic, complemented
426#1895C2×C4311yescharacteristic, complemented
427#1894C2×C4311yescharacteristic, complemented
428#1809C2×C4311yescharacteristic, complemented
429C2×C43—42no—
430C2×C43—42no—
431C2×C43—42no—
432C2×C43—161no—
433C2×C43#261711yescharacteristic
434C2×C43#305511yescharacteristic
435C2×C43#305611yescharacteristic
436C2×C43#319311yescharacteristic
437C2×C43#319411yescharacteristic
438C2×C43#319611yescharacteristic
439C2×C43#319711yescharacteristic
440C24×C4C22×C4311yescharacteristic
441C22×SD16C22×C4311yescharacteristic, complemented
442C22×M16C22×C4311yescharacteristic
443C22×M16C22×C4311yescharacteristic
444C2×C22⋊Q8C22×C4311yescharacteristic
445C2×C22⋊Q8C22×C4311yescharacteristic
446C2×C22⋊Q8C22×C4311yescharacteristic
447C2×#121C22×C4311yescharacteristic
448C2×#121C22×C4311yescharacteristic
449C2×#121C22×C4311yescharacteristic
450C2×#120—21no—
451#468—24no—
452C2×#107C22×C4311yescharacteristic, complemented
453C2×#107C22×C4311yescharacteristic, complemented
454C2×#106C22×C4311yescharacteristic, complemented
455C2×#103C22×C4311yescharacteristic, complemented
456C2×#103C22×C4311yescharacteristic, complemented
457C2×#103C22×C4311yescharacteristic, complemented
458C2×#102C22×C4311yescharacteristic, complemented
459C2×#102C22×C4311yescharacteristic, complemented
460C2×#102C22×C4311yescharacteristic, complemented
461#407—24no—
462C2×C22⋊C8C22×C4311yescharacteristic
463C2×C22⋊C8C22×C4311yescharacteristic
464C2×C22⋊C8C22×C4311yescharacteristic
465C2×C22⋊C8C22×C4311yescharacteristic
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#385—21no—
471#385—21no—
472#380C22×C4311yescharacteristic
473#380C22×C4311yescharacteristic
474#380C22×C4311yescharacteristic
475#380C22×C4311yescharacteristic
476#380C22×C4311yescharacteristic
477#380C22×C4311yescharacteristic
478#379—21no—
479#340C22×C4311yescharacteristic, complemented
480#340C22×C4311yescharacteristic, complemented
481#340C22×C4311yescharacteristic, complemented
482#340C22×C4311yescharacteristic, complemented
483#340C22×C4311yescharacteristic, complemented
484#340C22×C4311yescharacteristic, complemented
485C43#2974411yescharacteristic, direct product factor, Sylow
486C25D4×C4311yescharacteristic
487C22×Q8C23×C4311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C23×C4311yescharacteristic
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—41no—
497C23×C4—41no—
498C23×C4D4×C4311yescharacteristic
499C23×C4D4×C4311yescharacteristic
500C23×C4D4×C4311yescharacteristic
501C23×C4C23×C4311yescharacteristic
502C23×C4C23×C4311yescharacteristic
503C23×C4C23×C4311yescharacteristic
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16D4×C4314yescomplemented
513C22×C8C23×C4311yescharacteristic
514C22×C8C23×C4311yescharacteristic
515C22×C8C23×C4311yescharacteristic
516C22×C8C23×C4311yescharacteristic
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—41no—
520C22⋊Q8—41no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—41no—
528#121—41no—
529#120—44no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4C23×C4311yescharacteristic
534C2×C4⋊C4C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C4⋊C4C23×C4311yescharacteristic
537C2×C4⋊C4C23×C4311yescharacteristic
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C22⋊C4—21no—
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⋊C4—21no—
550C2×C22⋊C4—21no—
551#107—22no—
552#107—41no—
553#106—41no—
554#103—22no—
555#103—41no—
556#103—41no—
557#102—22no—
558#102—41no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—21no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—41no—
578C24C2×D4×C4311yescharacteristic
579C24C2×D4×C4311yescharacteristic
580C24C2×D4×C4311yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
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—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4C2×D4×C4311yescharacteristic
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4312yes—
642C22×C4#41×C4312yes—
643C22×C4C24×C4311yescharacteristic
644SD16—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8C2×D4×C4312yes—
658C2×C8C2×D4×C4312yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
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—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23#121×C4312yes—
719C23AGL(1,ℤ/8)×C4312yes—
720C23#137×C4312yes—
721C23C22×D4×C4311yescharacteristic
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
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—41no—
762C2×C4—41no—
763C2×C4—41no—
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#121×C4312yes—
778C2×C4C22×D4×C4311yescharacteristic
779C2×C4C2×#41×C4311yescharacteristic
780C2×C4H(5,𝔽2)×C4311yescharacteristic
781C2×C4H(5,𝔽2)×C4311yescharacteristic
782C2×C4H(5,𝔽2)×C4311yescharacteristic
783C2×C4H(5,𝔽2)×C4311yescharacteristic
784C8—22no—
785C8—22no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C2×#121×C4311yescharacteristic
818C22C43×#53411yescharacteristic
819C22C43×#53411yescharacteristic
820C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
821C22C2×#137×C4311yescharacteristic
822C22C43×#57511yescharacteristic
823C22C43×#57511yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C43×#53411yescharacteristic
835C4C43×#53511yescharacteristic
836C4C43×#53811yescharacteristic
837C4C43×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—161no—
842C2C43×#261711yescharacteristic
843C2C43×#305511yescharacteristic
844C2C43×#305611yescharacteristic
845C2C43×#319311yescharacteristic
846C2C43×#319411yescharacteristic
847C2C43×#319611yescharacteristic
848C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#407C2semidirect
3. C43×#2848C2semidirect
5. C43×#2076C2semidirect
6. C43×#2075C2semidirect
7. C43×#2036C2semidirect
8. C43×#2035C2semidirect
9. C43×#2034C2semidirect
10. C43×#2033C2semidirect
11. C43×#2000C2semidirect
12. C43×#2000C2semidirect
13. C43×#1895C2semidirect
14. C43×#1894C2semidirect
15. C43×#1809C2semidirect
17. C22×SD16×C43C22semidirect
28. C2×#107×C43C22semidirect
29. C2×#107×C43C22semidirect
30. C2×#106×C43C22semidirect
31. C2×#103×C43C22semidirect
32. C2×#103×C43C22semidirect
33. C2×#103×C43C22semidirect
34. C2×#102×C43C22semidirect
35. C2×#102×C43C22semidirect
36. C2×#102×C43C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
87. C2×M16×C43D4semidirect
363. #29744C43direct (N × H)
414. C2×#468C2×C43semidirect
415. C2×#407C2×C43semidirect
416. #2848C2×C43semidirect
418. #2076C2×C43semidirect
419. #2075C2×C43semidirect
420. #2036C2×C43semidirect
421. #2035C2×C43semidirect
422. #2034C2×C43semidirect
423. #2033C2×C43semidirect
424. #2000C2×C43semidirect
425. #2000C2×C43semidirect
426. #1895C2×C43semidirect
427. #1894C2×C43semidirect
428. #1809C2×C43semidirect
441. C22×SD16C22×C43semidirect
452. C2×#107C22×C43semidirect
453. C2×#107C22×C43semidirect
454. C2×#106C22×C43semidirect
455. C2×#103C22×C43semidirect
456. C2×#103C22×C43semidirect
457. C2×#103C22×C43semidirect
458. C2×#102C22×C43semidirect
459. C2×#102C22×C43semidirect
460. C2×#102C22×C43semidirect
479. #340C22×C43semidirect
480. #340C22×C43semidirect
481. #340C22×C43semidirect
482. #340C22×C43semidirect
483. #340C22×C43semidirect
484. #340C22×C43semidirect
485. C43#29744direct (N × H)
512. C2×M16D4×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×#4072
C43×#28482
C43×#28472
C43×#20762
C43×#20752
C43×#20362
C43×#20352
C43×#20342
C43×#20332
C43×#20002
C43×#18952
C43×#18942
C43×#18092
#2974443