Finite Group Databasebeta

← C43×#28587 #24948604

Subgroups — C43×#28587 #24948604

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#465C211yesmaximal, characteristic, complemented
3C43×#2619C211yesmaximal, characteristic
4C43×#2323C211yesmaximal, characteristic, complemented
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2074C211yesmaximal, characteristic, complemented
7C43×#2041C211yesmaximal, characteristic, complemented
8C43×#2014C211yesmaximal, characteristic, complemented
9C43×#1926C211yesmaximal, characteristic, complemented
10C43×#1925C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1880C211yesmaximal, characteristic, complemented
15C43×#1729C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×#127×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×Q8×C43C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C43×#468—24no—
27C43×#465—24no—
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C43×#394—21no—
39C43×#394—21no—
40C43×#392—21no—
41C43×#392—21no—
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#389—21no—
46C43×#389C2211yescharacteristic
47C43×#388—21no—
48C43×#388—21no—
49C43×#387—21no—
50C43×#382C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×SD16×C43—22no—
70C2×SD16×C43—22no—
71C2×SD16×C43—22no—
72C2×SD16×C43—22no—
73C2×SD16×C43—41no—
74C2×SD16×C43—41no—
75C2×M16×C43—22no—
76C2×M16×C43—22no—
77C2×M16×C43—41no—
78C22×C8×C43—22no—
79C22×C8×C43—22no—
80C22×C8×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#127×C43—41no—
86#127×C43—41no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43D414yescomplemented
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93C4×Q8×C43—41no—
94C4×Q8×C43—41no—
95#117×C43—41no—
96#117×C43—41no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#106×C43—22no—
123#103×C43—22no—
124#103×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—41no—
130#102×C43—41no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D412yes—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43—81no—
168C2×D4×C43—81no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43C2×D412yes—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43#4112yes—
188C22×C4×C43C2411yescharacteristic
189SD16×C43—44no—
190SD16×C43—44no—
191M16×C43—44no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—44no—
203C2×C8×C43#4112yes—
204C2×C8×C43#4112yes—
205C4⋊C4×C43—24no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—41no—
216C4⋊C4×C43—41no—
217C4⋊C4×C43—42no—
218C4⋊C4×C43—81no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—24no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
228C22⋊C4×C43—81no—
229C22⋊C4×C43—81no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C42×C43—21no—
234C42×C43—42no—
235C42×C43—81no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43#12112yes—
257C23×C43C22×D411yescharacteristic
258Q8×C43—22no—
259Q8×C43—22no—
260Q8×C43—41no—
261Q8×C43—41no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271D4×C43—84no—
272D4×C43—84no—
273D4×C43—84no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43#12112yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C8×C43—22no—
318C8×C43—22no—
319C8×C43—41no—
320C8×C43—41no—
321#28587C4311yesmaximal, characteristic, direct product factor, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C2×#12111yescharacteristic
344C22×C43#53211yescharacteristic
345C22×C43#53411yescharacteristic
346C22×C43#57611yescharacteristic
347C22×C43#57711yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C4×C43—22no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43#54611yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55311yescharacteristic
364C4×C43#55311yescharacteristic
365C2×#468C2×C4311yescharacteristic, complemented
366C2×#465C2×C4311yescharacteristic, complemented
367#2619C2×C4311yescharacteristic
368#2323C2×C4311yescharacteristic, complemented
369#2085C2×C4311yescharacteristic, complemented
370#2074C2×C4311yescharacteristic, complemented
371#2041C2×C4311yescharacteristic, complemented
372#2014C2×C4311yescharacteristic, complemented
373#1926C2×C4311yescharacteristic, complemented
374#1925C2×C4311yescharacteristic, complemented
375#1895C2×C4311yescharacteristic, complemented
376#1893C2×C4311yescharacteristic, complemented
377#1880C2×C4311yescharacteristic, complemented
378#1880C2×C4311yescharacteristic, complemented
379#1729C2×C4311yescharacteristic, complemented
380C2×C43—42no—
381C2×C43—161no—
382C2×C43—161no—
383C2×C43#254311yescharacteristic
384C2×C43#304311yescharacteristic
385C2×C43#304511yescharacteristic
386C2×C43#317411yescharacteristic
387C2×C43#317911yescharacteristic
388C2×C43#319811yescharacteristic
389C2×C43#320011yescharacteristic
390C22×SD16C22×C4311yescharacteristic
391C22×SD16C22×C4311yescharacteristic
392C22×M16C22×C4311yescharacteristic
393C23×C8C22×C4311yescharacteristic
394C2×#127C22×C4311yescharacteristic
395C2×C22⋊Q8C22×C4311yescharacteristic
396C2×#121C22×C4311yescharacteristic
397C2×#121C22×C4311yescharacteristic
398C2×C4×Q8C22×C4311yescharacteristic
399C2×#117C22×C4311yescharacteristic
400#468—24no—
401#465—24no—
402C2×#107C22×C4311yescharacteristic
403C2×#106C22×C4311yescharacteristic
404C2×#103C22×C4311yescharacteristic
405C2×#103C22×C4311yescharacteristic
406C2×#102C22×C4311yescharacteristic
407C2×#102C22×C4311yescharacteristic
408C2×#102C22×C4311yescharacteristic
409C2×#102C22×C4311yescharacteristic
410C2×#102C22×C4311yescharacteristic
411C2×#102C22×C4311yescharacteristic
412#394—21no—
413#394—21no—
414#392—21no—
415#392—21no—
416#391C22×C4311yescharacteristic
417#390C22×C4311yescharacteristic
418#390C22×C4311yescharacteristic
419#389—21no—
420#389C22×C4311yescharacteristic
421#388—21no—
422#388—21no—
423#387—21no—
424#382C22×C4311yescharacteristic
425#380C22×C4311yescharacteristic
426C4×C4⋊C4C22×C4311yescharacteristic
427#340C22×C4311yescharacteristic
428#340C22×C4311yescharacteristic
429#340C22×C4311yescharacteristic
430#340C22×C4311yescharacteristic
431#336C22×C4311yescharacteristic
432#336C22×C4311yescharacteristic
433#336C22×C4311yescharacteristic
434#336C22×C4311yescharacteristic
435C43#2858711yescharacteristic, direct product factor, Sylow
436C22×Q8C23×C4311yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C23×C4311yescharacteristic
442C22×D4C23×C4311yescharacteristic
443C23×C4C23×C4311yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8—41no—
456C22×C8C23×C4311yescharacteristic
457C22×C8C23×C4311yescharacteristic
458C22×C8C23×C4311yescharacteristic
459C22×C8C23×C4311yescharacteristic
460#127—41no—
461#127—41no—
462C22⋊Q8—22no—
463C22⋊Q8D4×C4314yescomplemented
464#121—22no—
465#121—22no—
466#121—22no—
467#121—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470#117—41no—
471#117—41no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4D4×C4311yescharacteristic
476C2×C4⋊C4D4×C4311yescharacteristic
477C2×C4⋊C4C23×C4311yescharacteristic
478C2×C4⋊C4C23×C4311yescharacteristic
479C2×C4⋊C4C23×C4311yescharacteristic
480C2×C4⋊C4C23×C4311yescharacteristic
481C2×C4⋊C4C23×C4311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C4311yescharacteristic
491C2×C22⋊C4D4×C4311yescharacteristic
492C2×C42—21no—
493C2×C42—21no—
494C2×C42C23×C4311yescharacteristic
495C2×C42C23×C4311yescharacteristic
496#107—22no—
497#106—22no—
498#103—22no—
499#103—22no—
500#102—22no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505#102—41no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513C24—21no—
514C24—21no—
515C24C2×D4×C4311yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8C2×D4×C4312yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C4311yescharacteristic
557C22×C4C2×D4×C4311yescharacteristic
558C22×C4C2×D4×C4311yescharacteristic
559C22×C4C2×D4×C4311yescharacteristic
560C22×C4C2×D4×C4311yescharacteristic
561C22×C4C2×D4×C4312yes—
562C22×C4#41×C4312yes—
563C22×C4C24×C4311yescharacteristic
564SD16—44no—
565SD16—44no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8#41×C4312yes—
579C2×C8#41×C4312yes—
580C4⋊C4—24no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—42no—
593C4⋊C4—81no—
594C4⋊C4C2×D4×C4312yes—
595C22⋊C4—24no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—42no—
610C42—81no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23#121×C4312yes—
632C23C22×D4×C4311yescharacteristic
633Q8—22no—
634Q8—22no—
635Q8—41no—
636Q8—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—84no—
647D4—84no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4#121×C4312yes—
686C2×C4C22×D4×C4311yescharacteristic
687C2×C4C2×#41×C4311yescharacteristic
688C2×C4C2×#41×C4311yescharacteristic
689C2×C4C2×#41×C4311yescharacteristic
690C2×C4H(5,𝔽2)×C4311yescharacteristic
691C2×C4H(5,𝔽2)×C4311yescharacteristic
692C8—22no—
693C8—22no—
694C8—41no—
695C8—41no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#121×C4311yescharacteristic
718C22C43×#53211yescharacteristic
719C22C43×#53411yescharacteristic
720C22C43×#57611yescharacteristic
721C22C43×#57711yescharacteristic
722C22C43×#57711yescharacteristic
723C22C43×#57711yescharacteristic
724C4—22no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4C43×#54611yescharacteristic
736C4C43×#54611yescharacteristic
737C4C43×#55311yescharacteristic
738C4C43×#55311yescharacteristic
739C2—42no—
740C2—161no—
741C2—161no—
742C2C43×#254311yescharacteristic
743C2C43×#304311yescharacteristic
744C2C43×#304511yescharacteristic
745C2C43×#317411yescharacteristic
746C2C43×#317911yescharacteristic
747C2C43×#319811yescharacteristic
748C2C43×#320011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2619C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#465C2semidirect
4. C43×#2323C2semidirect
5. C43×#2085C2semidirect
6. C43×#2074C2semidirect
7. C43×#2041C2semidirect
8. C43×#2014C2semidirect
9. C43×#1926C2semidirect
10. C43×#1925C2semidirect
11. C43×#1895C2semidirect
12. C43×#1893C2semidirect
13. C43×#1880C2semidirect
14. C43×#1880C2semidirect
15. C43×#1729C2semidirect
88. C22⋊Q8×C43D4semidirect
321. #28587C43direct (N × H)
365. C2×#468C2×C43semidirect
366. C2×#465C2×C43semidirect
368. #2323C2×C43semidirect
369. #2085C2×C43semidirect
370. #2074C2×C43semidirect
371. #2041C2×C43semidirect
372. #2014C2×C43semidirect
373. #1926C2×C43semidirect
374. #1925C2×C43semidirect
375. #1895C2×C43semidirect
376. #1893C2×C43semidirect
377. #1880C2×C43semidirect
378. #1880C2×C43semidirect
379. #1729C2×C43semidirect
435. C43#28587direct (N × H)
463. C22⋊Q8D4×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×#4652
C43×#26192
C43×#23232
C43×#20852
C43×#20742
C43×#20412
C43×#20142
C43×#19262
C43×#19252
C43×#18952
C43×#18932
C43×#18802
C43×#17292
#2858743