Finite Group Databasebeta

← C43×#25188 #24945205

Subgroups — C43×#25188 #24945205

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3062C211yesmaximal, characteristic, complemented
2C43×#3045C211yesmaximal, characteristic, complemented
3C2×C43×#453C211yesmaximal, characteristic, complemented
4C43×#3012C211yesmaximal, characteristic, complemented
5C2×C43×#443C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2039C211yesmaximal, characteristic, complemented
10C43×#2002C211yesmaximal, characteristic, complemented
11C43×#1957C211yesmaximal, characteristic, complemented
12C43×#1937C211yesmaximal, characteristic, complemented
13C43×#1907C211yesmaximal, characteristic, complemented
14C43×#1907C211yesmaximal, characteristic, complemented
15C43×#1859C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×#135×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic
22C2×#131×C43C2211yescharacteristic, complemented
23C43×#537C2211yescharacteristic
24C43×#535C2211yescharacteristic, complemented
25C2×#127×C43C2211yescharacteristic
26C43×#520C2211yescharacteristic
27C43×#469—21no—
28C43×#468—21no—
29C43×#466—21no—
30C43×#465—21no—
31C43×#464—21no—
32C43×#463—21no—
33C43×#460—21no—
34C43×#459—21no—
35C43×#453—24no—
36C43×#452—21no—
37C43×#450—21no—
38C43×#449—21no—
39C43×#447—21no—
40C43×#443—24no—
41C2×#108×C43C2211yescharacteristic, complemented
42C43×#428C2211yescharacteristic, complemented
43C43×#424C2211yescharacteristic, complemented
44C2×#104×C43C2211yescharacteristic
45C2×#104×C43C2211yescharacteristic
46C2×#104×C43C2211yescharacteristic, complemented
47C43×#418—21no—
48C43×#418C2211yescharacteristic
49C43×#417—21no—
50C43×#417C2211yescharacteristic
51C43×#417C2211yescharacteristic
52C43×#417C2211yescharacteristic, complemented
53C43×#416—21no—
54C43×#416C2211yescharacteristic
55C2×#102×C43—21no—
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#100×C43C2211yescharacteristic
61C2×#100×C43C2211yescharacteristic, complemented
62C43×#408C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic, complemented
64C43×#384C2211yescharacteristic, complemented
65C43×#343C2211yescharacteristic, complemented
66C43×#343C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
69H(5,𝔽2)×C43—22no—
70H(5,𝔽2)×C43—22no—
71H(5,𝔽2)×C43—22no—
72H(5,𝔽2)×C43—41no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43C2311yescharacteristic
76C2×#41×C43C2311yescharacteristic
77C2×#41×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—41no—
81C22×D4×C43—41no—
82C22×D4×C43C2311yescharacteristic
83C22×D4×C43C2311yescharacteristic
84AGL(1,ℤ/8)×C43—22no—
85AGL(1,ℤ/8)×C43—22no—
86AGL(1,ℤ/8)×C43—22no—
87AGL(1,ℤ/8)×C43—22no—
88AGL(1,ℤ/8)×C43—41no—
89AGL(1,ℤ/8)×C43—41no—
90#135×C43—22no—
91#135×C43—22no—
92C2×Q16×C43D411yescharacteristic, complemented
93C2×SD16×C43—21no—
94C2×SD16×C43—21no—
95C2×SD16×C43—21no—
96C2×SD16×C43D411yescharacteristic, complemented
97C2×SD16×C43D411yescharacteristic, complemented
98C2×D8×C43—21no—
99C2×D8×C43—21no—
100C2×D8×C43—21no—
101C2×D8×C43D411yescharacteristic, complemented
102#131×C43—22no—
103#131×C43—22no—
104#131×C43—41no—
105#131×C43—41no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43C2311yescharacteristic
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#127×C43—21no—
117#127×C43—22no—
118#127×C43—22no—
119#124×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—41no—
127#120×C43—41no—
128C4×Q8×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—41no—
131#117×C43—21no—
132#117×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—41no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#108×C43—22no—
139#107×C43—21no—
140#106×C43—21no—
141C4⋊C8×C43—21no—
142C4⋊C8×C43—21no—
143#104×C43—22no—
144#104×C43—22no—
145#104×C43D414yescomplemented
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43D411yescharacteristic, complemented
150#103×C43D411yescharacteristic, complemented
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#102×C43—21no—
159#102×C43—21no—
160#102×C43—21no—
161#102×C43—21no—
162#102×C43—21no—
163#102×C43—21no—
164#102×C43D411yescharacteristic, complemented
165#102×C43D411yescharacteristic, complemented
166#100×C43—22no—
167#100×C43—41no—
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170C4×C8×C43—22no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—41no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—24no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—42no—
186#41×C43—42no—
187#41×C43—42no—
188#41×C43C2×D412yes—
189#41×C43#4112yes—
190C2×Q8×C43C2×D411yescharacteristic
191C2×Q8×C43C2×D411yescharacteristic
192C2×Q8×C43C2×D411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
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—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—41no—
209C2×D4×C43—41no—
210C2×D4×C43—41no—
211C2×D4×C43—44no—
212C2×D4×C43—41no—
213C2×D4×C43—41no—
214C2×D4×C43—44no—
215C2×D4×C43—42no—
216C2×D4×C43—42no—
217C2×D4×C43—44no—
218C2×D4×C43—42no—
219C2×D4×C43—82no—
220C2×D4×C43—82no—
221C2×D4×C43C2×D411yescharacteristic
222C2×D4×C43C2×D411yescharacteristic
223C2×D4×C43C2×D411yescharacteristic
224C2×D4×C43#4112yes—
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—41no—
232C22×C4×C43—41no—
233C22×C4×C43C2411yescharacteristic
234Q16×C43—22no—
235SD16×C43—22no—
236SD16×C43—22no—
237SD16×C43—42no—
238SD16×C43—42no—
239SD16×C43—42no—
240D8×C43—22no—
241D8×C43—42no—
242D8×C43—42no—
243D8×C43—42no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—42no—
252M16×C43—42no—
253M16×C43C2×D412yes—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—42no—
263C2×C8×C43—42no—
264C2×C8×C43C2×D411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C2×C8×C43C2×D411yescharacteristic
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—41no—
273C4⋊C4×C43—41no—
274C4⋊C4×C43—82no—
275C4⋊C4×C43C2×D411yescharacteristic
276C4⋊C4×C43C2×D411yescharacteristic
277C22⋊C4×C43—21no—
278C22⋊C4×C43—41no—
279C22⋊C4×C43—41no—
280C22⋊C4×C43—41no—
281C22⋊C4×C43—41no—
282C22⋊C4×C43—41no—
283C42×C43—21no—
284C42×C43—21no—
285C42×C43—41no—
286C42×C43C2×D412yes—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—22no—
291C23×C43—44no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—81no—
298C23×C43—81no—
299C23×C43—81no—
300C23×C43—81no—
301C23×C43—161no—
302C23×C43—161no—
303C23×C43H(5,𝔽2)11yescharacteristic
304Q8×C43—21no—
305Q8×C43—21no—
306Q8×C43—21no—
307Q8×C43—21no—
308Q8×C43—21no—
309Q8×C43#12112yes—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—21no—
313D4×C43—21no—
314D4×C43—22no—
315D4×C43—21no—
316D4×C43—21no—
317D4×C43—21no—
318D4×C43—22no—
319D4×C43—44no—
320D4×C43—44no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—88no—
332D4×C43—161no—
333D4×C43—161no—
334D4×C43—161no—
335D4×C43#12112yes—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—44no—
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—81no—
354C2×C4×C43—81no—
355C2×C4×C43—161no—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C8×C43—21no—
363C8×C43—21no—
364C8×C43—21no—
365C8×C43—21no—
366C8×C43—22no—
367C8×C43—41no—
368C8×C43—41no—
369C8×C43—41no—
370#25188C4311yesmaximal, characteristic, direct product factor, Sylow
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—22no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—82no—
384C22×C43—82no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—161no—
391C22×C43—161no—
392C22×C43—164no—
393C22×C43#53811yescharacteristic
394C22×C43D4211yescharacteristic
395C22×C43#54611yescharacteristic
396C4×C43—24no—
397C4×C43—22no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—81no—
403C4×C43—81no—
404C4×C43C2×#12111yescharacteristic
405C4×C43#52511yescharacteristic
406C4×C43D4211yescharacteristic
407C4×C43#54611yescharacteristic
408#3062C2×C4311yescharacteristic, complemented
409#3045C2×C4311yescharacteristic, complemented
410C2×#453C2×C4311yescharacteristic, complemented
411#3012C2×C4311yescharacteristic, complemented
412C2×#443C2×C4311yescharacteristic, complemented
413#2897C2×C4311yescharacteristic, complemented
414#2063C2×C4311yescharacteristic, complemented
415#2051C2×C4311yescharacteristic, complemented
416#2039C2×C4311yescharacteristic, complemented
417#2002C2×C4311yescharacteristic, complemented
418#1957C2×C4311yescharacteristic, complemented
419#1937C2×C4311yescharacteristic, complemented
420#1907C2×C4311yescharacteristic, complemented
421#1907C2×C4311yescharacteristic, complemented
422#1859C2×C4311yescharacteristic, complemented
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—42no—
426C2×C43—81no—
427C2×C43—81no—
428C2×C43—82no—
429C2×C43—161no—
430C2×C43#242411yescharacteristic
431C2×C43#329111yescharacteristic
432C2×C43#329211yescharacteristic
433C2×H(5,𝔽2)C22×C4311yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
437C2×#135C22×C4311yescharacteristic
438C2×#131C22×C4311yescharacteristic
439C2×#131C22×C4311yescharacteristic, complemented
440#537C22×C4311yescharacteristic
441#535C22×C4311yescharacteristic, complemented
442C2×#127C22×C4311yescharacteristic
443#520C22×C4311yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#443—24no—
458C2×#108C22×C4311yescharacteristic, complemented
459#428C22×C4311yescharacteristic, complemented
460#424C22×C4311yescharacteristic, complemented
461C2×#104C22×C4311yescharacteristic
462C2×#104C22×C4311yescharacteristic
463C2×#104C22×C4311yescharacteristic, complemented
464#418—21no—
465#418C22×C4311yescharacteristic
466#417—21no—
467#417C22×C4311yescharacteristic
468#417C22×C4311yescharacteristic
469#417C22×C4311yescharacteristic, complemented
470#416—21no—
471#416C22×C4311yescharacteristic
472C2×#102—21no—
473C2×#102C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic, complemented
476C2×#102C22×C4311yescharacteristic, complemented
477C2×#100C22×C4311yescharacteristic
478C2×#100C22×C4311yescharacteristic, complemented
479#408C22×C4311yescharacteristic
480C2×C4×C8C22×C4311yescharacteristic, complemented
481#384C22×C4311yescharacteristic, complemented
482#343C22×C4311yescharacteristic, complemented
483#343C22×C4311yescharacteristic, complemented
484#341C22×C4311yescharacteristic, complemented
485#339C22×C4311yescharacteristic, complemented
486C43#2518811yescharacteristic, direct product factor, Sylow
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C4311yescharacteristic
494C2×#41C23×C4311yescharacteristic
495C2×#41C23×C4311yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C4311yescharacteristic
501C22×D4C23×C4311yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C4311yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C4311yescharacteristic, complemented
515C2×SD16D4×C4311yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C4311yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C4311yescharacteristic
527C2×M16C23×C4311yescharacteristic
528C2×M16C23×C4311yescharacteristic
529C2×M16C23×C4311yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C4311yescharacteristic
533C22×C8C23×C4311yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C4311yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C4311yescharacteristic
554C2×C4⋊C4C23×C4311yescharacteristic
555C2×C42C23×C4311yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C4314yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C4311yescharacteristic, complemented
568#103D4×C4311yescharacteristic, complemented
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102D4×C4311yescharacteristic, complemented
583#102D4×C4311yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C4312yes—
607#41#41×C4312yes—
608C2×Q8C2×D4×C4311yescharacteristic
609C2×Q8C2×D4×C4311yescharacteristic
610C2×Q8C2×D4×C4311yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
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—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C4311yescharacteristic
640C2×D4C2×D4×C4311yescharacteristic
641C2×D4C2×D4×C4311yescharacteristic
642C2×D4#41×C4312yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C4311yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C4312yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C4311yescharacteristic
683C2×C8C2×D4×C4311yescharacteristic
684C2×C8C2×D4×C4311yescharacteristic
685C2×C8C2×D4×C4311yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C4311yescharacteristic
694C4⋊C4C2×D4×C4311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C4312yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C4311yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C4312yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C4312yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C4311yescharacteristic
775C2×C4C22×D4×C4311yescharacteristic
776C2×C4C22×D4×C4311yescharacteristic
777C2×C4C2×#41×C4311yescharacteristic
778C2×C4C2×#41×C4311yescharacteristic
779C2×C4H(5,𝔽2)×C4311yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22C43×#53811yescharacteristic
811C22D42×C4311yescharacteristic
812C22C43×#54611yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C4311yescharacteristic
822C4C43×#52511yescharacteristic
823C4D42×C4311yescharacteristic
824C4C43×#54611yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2C43×#242411yescharacteristic
833C2C43×#329111yescharacteristic
834C2C43×#329211yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3062C2semidirect
2. C43×#3045C2semidirect
3. C2×C43×#453C2semidirect
4. C43×#3012C2semidirect
5. C2×C43×#443C2semidirect
6. C43×#2897C2semidirect
7. C43×#2063C2semidirect
8. C43×#2051C2semidirect
9. C43×#2039C2semidirect
10. C43×#2002C2semidirect
11. C43×#1957C2semidirect
12. C43×#1937C2semidirect
13. C43×#1907C2semidirect
14. C43×#1907C2semidirect
15. C43×#1859C2semidirect
22. C2×#131×C43C22semidirect
24. C43×#535C22semidirect
41. C2×#108×C43C22semidirect
42. C43×#428C22semidirect
43. C43×#424C22semidirect
46. C2×#104×C43C22semidirect
52. C43×#417C22semidirect
58. C2×#102×C43C22semidirect
59. C2×#102×C43C22semidirect
61. C2×#100×C43C22semidirect
63. C2×C4×C8×C43C22semidirect
64. C43×#384C22semidirect
65. C43×#343C22semidirect
66. C43×#343C22semidirect
67. C43×#341C22semidirect
68. C43×#339C22semidirect
92. C2×Q16×C43D4semidirect
96. C2×SD16×C43D4semidirect
97. C2×SD16×C43D4semidirect
101. C2×D8×C43D4semidirect
145. #104×C43D4semidirect
149. #103×C43D4semidirect
150. #103×C43D4semidirect
164. #102×C43D4semidirect
165. #102×C43D4semidirect
370. #25188C43direct (N × H)
408. #3062C2×C43semidirect
409. #3045C2×C43semidirect
410. C2×#453C2×C43semidirect
411. #3012C2×C43semidirect
412. C2×#443C2×C43semidirect
413. #2897C2×C43semidirect
414. #2063C2×C43semidirect
415. #2051C2×C43semidirect
416. #2039C2×C43semidirect
417. #2002C2×C43semidirect
418. #1957C2×C43semidirect
419. #1937C2×C43semidirect
420. #1907C2×C43semidirect
421. #1907C2×C43semidirect
422. #1859C2×C43semidirect
439. C2×#131C22×C43semidirect
441. #535C22×C43semidirect
458. C2×#108C22×C43semidirect
459. #428C22×C43semidirect
460. #424C22×C43semidirect
463. C2×#104C22×C43semidirect
469. #417C22×C43semidirect
475. C2×#102C22×C43semidirect
476. C2×#102C22×C43semidirect
478. C2×#100C22×C43semidirect
480. C2×C4×C8C22×C43semidirect
481. #384C22×C43semidirect
482. #343C22×C43semidirect
483. #343C22×C43semidirect
484. #341C22×C43semidirect
485. #339C22×C43semidirect
486. C43#25188direct (N × H)
510. C2×Q16D4×C43semidirect
514. C2×SD16D4×C43semidirect
515. C2×SD16D4×C43semidirect
519. C2×D8D4×C43semidirect
563. #104D4×C43semidirect
567. #103D4×C43semidirect
568. #103D4×C43semidirect
582. #102D4×C43semidirect
583. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#30622
C43×#30452
C2×C43×#4532
C43×#30122
C2×C43×#4432
C43×#28972
C43×#20632
C43×#20512
C43×#20392
C43×#20022
C43×#19572
C43×#19372
C43×#19072
C43×#18592
#2518843