Finite Group Databasebeta

← C43×#24457 #24944474

Subgroups — C43×#24457 #24944474

Order 11008.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#577C211yesmaximal, characteristic, complemented
2C2×C43×#471C211yesmaximal, characteristic, complemented
3C43×#3045C211yesmaximal, characteristic, complemented
4C2×C43×#453C211yesmaximal, characteristic, complemented
5C43×#3010C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2051C211yesmaximal, characteristic, complemented
8C43×#2046C211yesmaximal, characteristic, complemented
9C43×#2014C211yesmaximal, characteristic, complemented
10C43×#2002C211yesmaximal, characteristic, complemented
11C43×#1907C211yesmaximal, characteristic, complemented
12C43×#1882C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic, complemented
14C43×#1866C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C2×H(5,𝔽2)×C43C2211yescharacteristic
18C43×#577—24no—
19C43×#577—24no—
20C2×#137×C43—21no—
21C2×#137×C43C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C43—21no—
23C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
26C2×#135×C43—21no—
27C2×#135×C43C2211yescharacteristic
28C22×SD16×C43—21no—
29C22×SD16×C43C2211yescharacteristic
30C22×SD16×C43C2211yescharacteristic, complemented
31C2×#131×C43C2211yescharacteristic
32C2×#131×C43C2211yescharacteristic
33C43×#535C2211yescharacteristic, complemented
34C2×#127×C43C2211yescharacteristic
35C43×#520C2211yescharacteristic
36C43×#471—24no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#460—21no—
40C43×#459—21no—
41C43×#453—24no—
42C43×#449—21no—
43C43×#449—21no—
44C43×#448—21no—
45C43×#448—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C43×#424C2211yescharacteristic, complemented
48C2×#104×C43C2211yescharacteristic
49C2×#104×C43C2211yescharacteristic
50C2×#104×C43C2211yescharacteristic, complemented
51C43×#419C2211yescharacteristic, complemented
52C43×#418—21no—
53C43×#418C2211yescharacteristic
54C43×#417—21no—
55C43×#417C2211yescharacteristic
56C43×#417C2211yescharacteristic, complemented
57C43×#416—21no—
58C43×#416C2211yescharacteristic
59C2×#102×C43—21no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C2×#100×C43C2211yescharacteristic
64C2×#100×C43C2211yescharacteristic, complemented
65C43×#408C2211yescharacteristic, complemented
66C43×#391C2211yescharacteristic, complemented
67C43×#343C2211yescharacteristic, complemented
68C43×#341C2211yescharacteristic, complemented
69C43×#339C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
712−1+4×C43—22no—
722−1+4×C43—22no—
732−1+4×C43—22no—
742−1+4×C43—41no—
75H(5,𝔽2)×C43—22no—
76H(5,𝔽2)×C43—22no—
77H(5,𝔽2)×C43—41no—
78H(5,𝔽2)×C43D414yescomplemented
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43—41no—
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C2×#41×C43C2311yescharacteristic
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43C2311yescharacteristic
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—41no—
93C22×D4×C43—41no—
94C22×D4×C43C2311yescharacteristic
95C22×D4×C43C2311yescharacteristic
96#137×C43—28no—
97#137×C43—22no—
98#137×C43D414yescomplemented
99AGL(1,ℤ/8)×C43—28no—
100AGL(1,ℤ/8)×C43—22no—
101AGL(1,ℤ/8)×C43—22no—
102AGL(1,ℤ/8)×C43—22no—
103AGL(1,ℤ/8)×C43—22no—
104AGL(1,ℤ/8)×C43—22no—
105AGL(1,ℤ/8)×C43—22no—
106#135×C43—28no—
107#135×C43—22no—
108#135×C43—22no—
109C2×Q16×C43—21no—
110C2×Q16×C43D411yescharacteristic, complemented
111C2×SD16×C43—28no—
112C2×SD16×C43—21no—
113C2×SD16×C43—22no—
114C2×SD16×C43—21no—
115C2×SD16×C43—22no—
116C2×SD16×C43—22no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—41no—
124C2×SD16×C43D411yescharacteristic, complemented
125C2×SD16×C43D411yescharacteristic, complemented
126C2×D8×C43—21no—
127C2×D8×C43—21no—
128C2×D8×C43—21no—
129C2×D8×C43D411yescharacteristic, complemented
130#131×C43—22no—
131#131×C43—22no—
132#131×C43—22no—
133#131×C43—41no—
134C2×M16×C43—21no—
135C2×M16×C43—21no—
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140C22×C8×C43—21no—
141C22×C8×C43—21no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#127×C43—22no—
145#127×C43—21no—
146#127×C43—41no—
147#124×C43—21no—
148#121×C43—21no—
149#121×C43—21no—
150#120×C43—41no—
151C4×Q8×C43—21no—
152C4×D4×C43—21no—
153C4×D4×C43—41no—
154#117×C43—21no—
155#117×C43C2311yescharacteristic
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C42×C43C2311yescharacteristic
159#108×C43—22no—
160C4⋊C8×C43—21no—
161C4⋊C8×C43—21no—
162#104×C43—22no—
163#104×C43—22no—
164#104×C43—41no—
165#103×C43—21no—
166#103×C43—21no—
167#103×C43—21no—
168#103×C43—21no—
169#103×C43D411yescharacteristic, complemented
170#103×C43D411yescharacteristic, complemented
171#102×C43—21no—
172#102×C43—21no—
173#102×C43—21no—
174#102×C43—21no—
175#102×C43—21no—
176#102×C43—21no—
177#102×C43—21no—
178#102×C43—21no—
179#102×C43D411yescharacteristic, complemented
180#102×C43D411yescharacteristic, complemented
181#101×C43—22no—
182#100×C43—22no—
183#100×C43—22no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186#95×C43—41no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—41no—
190#41×C43—21no—
191#41×C43—21no—
192#41×C43—21no—
193#41×C43—21no—
194#41×C43—24no—
195#41×C43—24no—
196#41×C43—24no—
197#41×C43—21no—
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—21no—
201#41×C43—42no—
202#41×C43—44no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—42no—
206#41×C43—44no—
207#41×C43—42no—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210#41×C43C2×D412yes—
211#41×C43#4112yes—
212C2×Q8×C43—21no—
213C2×Q8×C43—24no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—41no—
219C2×Q8×C43—42no—
220C2×Q8×C43—42no—
221C2×Q8×C43—42no—
222C2×Q8×C43C2×D412yes—
223C2×Q8×C43C2×D411yescharacteristic
224C2×Q8×C43C2×D411yescharacteristic
225C2×Q8×C43C2×D411yescharacteristic
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—24no—
231C2×D4×C43—24no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—21no—
241C2×D4×C43—21no—
242C2×D4×C43—41no—
243C2×D4×C43—41no—
244C2×D4×C43—41no—
245C2×D4×C43—41no—
246C2×D4×C43—41no—
247C2×D4×C43—44no—
248C2×D4×C43—44no—
249C2×D4×C43—42no—
250C2×D4×C43—42no—
251C2×D4×C43—44no—
252C2×D4×C43—82no—
253C2×D4×C43—82no—
254C2×D4×C43C2×D412yes—
255C2×D4×C43C2×D411yescharacteristic
256C2×D4×C43C2×D411yescharacteristic
257C2×D4×C43C2×D411yescharacteristic
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—41no—
265C22×C4×C43—41no—
266C22×C4×C43—41no—
267C22×C4×C43—41no—
268C22×C4×C43C2411yescharacteristic
269Q16×C43—24no—
270Q16×C43—22no—
271SD16×C43—24no—
272SD16×C43—24no—
273SD16×C43—24no—
274SD16×C43—22no—
275SD16×C43—22no—
276SD16×C43—24no—
277SD16×C43—42no—
278SD16×C43—42no—
279SD16×C43—42no—
280SD16×C43—42no—
281D8×C43—24no—
282D8×C43—22no—
283D8×C43—42no—
284D8×C43—42no—
285M16×C43—24no—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—21no—
293M16×C43—42no—
294M16×C43C2×D412yes—
295C2×C8×C43—24no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—21no—
303C2×C8×C43—21no—
304C2×C8×C43—42no—
305C2×C8×C43C2×D411yescharacteristic
306C2×C8×C43C2×D411yescharacteristic
307C2×C8×C43C2×D411yescharacteristic
308C2×C8×C43C2×D411yescharacteristic
309C4⋊C4×C43—21no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—41no—
312C4⋊C4×C43C2×D411yescharacteristic
313C4⋊C4×C43C2×D411yescharacteristic
314C22⋊C4×C43—21no—
315C22⋊C4×C43—41no—
316C22⋊C4×C43—41no—
317C22⋊C4×C43—41no—
318C42×C43—21no—
319C42×C43—21no—
320C42×C43—21no—
321C42×C43—41no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—21no—
325C23×C43—22no—
326C23×C43—44no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—81no—
333C23×C43—81no—
334C23×C43—81no—
335C23×C43—81no—
336C23×C43—161no—
337C23×C43—161no—
338C23×C43H(5,𝔽2)11yescharacteristic
339Q8×C43—21no—
340Q8×C43—21no—
341Q8×C43—22no—
342Q8×C43—21no—
343Q8×C43—22no—
344Q8×C43—21no—
345Q8×C43—44no—
346Q8×C43—41no—
347Q8×C43—41no—
348Q8×C43#12012yes—
349Q8×C43#12112yes—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—21no—
355D4×C43—22no—
356D4×C43—22no—
357D4×C43—21no—
358D4×C43—21no—
359D4×C43—21no—
360D4×C43—44no—
361D4×C43—44no—
362D4×C43—44no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—88no—
372D4×C43—161no—
373D4×C43—161no—
374D4×C43#12012yes—
375D4×C43#12112yes—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—22no—
387C2×C4×C43—44no—
388C2×C4×C43—44no—
389C2×C4×C43—41no—
390C2×C4×C43—44no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—81no—
398C2×C4×C43—161no—
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×C4×C43C2×#4111yescharacteristic
404C2×C4×C43H(5,𝔽2)11yescharacteristic
405C8×C43—21no—
406C8×C43—22no—
407C8×C43—21no—
408C8×C43—21no—
409C8×C43—21no—
410C8×C43—41no—
411C8×C43—41no—
412C8×C43—41no—
413#24457C4311yesmaximal, characteristic, direct product factor, Sylow
414C22×C43—21no—
415C22×C43—21no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—42no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—82no—
427C22×C43—82no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—81no—
432C22×C43—81no—
433C22×C43—161no—
434C22×C43—161no—
435C22×C43—164no—
436C22×C43#53411yescharacteristic
437C22×C43D4211yescharacteristic
438C22×C43#54611yescharacteristic
439C4×C43—22no—
440C4×C43—22no—
441C4×C43—42no—
442C4×C43—41no—
443C4×C43—42no—
444C4×C43—41no—
445C4×C43—41no—
446C4×C43—81no—
447C4×C43C2×#12011yescharacteristic
448C4×C43C2×#12111yescharacteristic
449C4×C43D4211yescharacteristic
450C4×C43#54611yescharacteristic
451C2×#577C2×C4311yescharacteristic, complemented
452C2×#471C2×C4311yescharacteristic, complemented
453#3045C2×C4311yescharacteristic, complemented
454C2×#453C2×C4311yescharacteristic, complemented
455#3010C2×C4311yescharacteristic, complemented
456#2897C2×C4311yescharacteristic, complemented
457#2051C2×C4311yescharacteristic, complemented
458#2046C2×C4311yescharacteristic, complemented
459#2014C2×C4311yescharacteristic, complemented
460#2002C2×C4311yescharacteristic, complemented
461#1907C2×C4311yescharacteristic, complemented
462#1882C2×C4311yescharacteristic, complemented
463#1876C2×C4311yescharacteristic, complemented
464#1866C2×C4311yescharacteristic, complemented
465#1793C2×C4311yescharacteristic, complemented
466C2×C43—21no—
467C2×C43—21no—
468C2×C43—42no—
469C2×C43—42no—
470C2×C43—81no—
471C2×C43—82no—
472C2×C43—161no—
473C2×C43#241011yescharacteristic
474C2×C43#328811yescharacteristic
475C2×C43#329111yescharacteristic
476C2×2−1+4C22×C4311yescharacteristic
477C2×H(5,𝔽2)C22×C4311yescharacteristic
478#577—24no—
479#577—24no—
480C2×#137—21no—
481C2×#137C22×C4311yescharacteristic
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
484C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
485C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
486C2×#135—21no—
487C2×#135C22×C4311yescharacteristic
488C22×SD16—21no—
489C22×SD16C22×C4311yescharacteristic
490C22×SD16C22×C4311yescharacteristic, complemented
491C2×#131C22×C4311yescharacteristic
492C2×#131C22×C4311yescharacteristic
493#535C22×C4311yescharacteristic, complemented
494C2×#127C22×C4311yescharacteristic
495#520C22×C4311yescharacteristic
496#471—24no—
497#464—21no—
498#463—21no—
499#460—21no—
500#459—21no—
501#453—24no—
502#449—21no—
503#449—21no—
504#448—21no—
505#448—21no—
506C2×#108C22×C4311yescharacteristic, complemented
507#424C22×C4311yescharacteristic, complemented
508C2×#104C22×C4311yescharacteristic
509C2×#104C22×C4311yescharacteristic
510C2×#104C22×C4311yescharacteristic, complemented
511#419C22×C4311yescharacteristic, complemented
512#418—21no—
513#418C22×C4311yescharacteristic
514#417—21no—
515#417C22×C4311yescharacteristic
516#417C22×C4311yescharacteristic, complemented
517#416—21no—
518#416C22×C4311yescharacteristic
519C2×#102—21no—
520C2×#102C22×C4311yescharacteristic
521C2×#102C22×C4311yescharacteristic, complemented
522C2×#101C22×C4311yescharacteristic, complemented
523C2×#100C22×C4311yescharacteristic
524C2×#100C22×C4311yescharacteristic, complemented
525#408C22×C4311yescharacteristic, complemented
526#391C22×C4311yescharacteristic, complemented
527#343C22×C4311yescharacteristic, complemented
528#341C22×C4311yescharacteristic, complemented
529#339C22×C4311yescharacteristic, complemented
530#336C22×C4311yescharacteristic, complemented
531C43#2445711yescharacteristic, direct product factor, Sylow
5322−1+4—22no—
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—41no—
539H(5,𝔽2)D4×C4314yescomplemented
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41C23×C4311yescharacteristic
546C2×#41C23×C4311yescharacteristic
547C2×#41C23×C4311yescharacteristic
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8C23×C4311yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C4311yescharacteristic
556C22×D4C23×C4311yescharacteristic
557#137—28no—
558#137—22no—
559#137D4×C4314yescomplemented
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567#135—28no—
568#135—22no—
569#135—22no—
570C2×Q16—21no—
571C2×Q16D4×C4311yescharacteristic, complemented
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—22no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C4311yescharacteristic, complemented
586C2×SD16D4×C4311yescharacteristic, complemented
587C2×D8—21no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8D4×C4311yescharacteristic, complemented
591#131—22no—
592#131—22no—
593#131—22no—
594#131—41no—
595C2×M16—21no—
596C2×M16—21no—
597C2×M16C23×C4311yescharacteristic
598C2×M16C23×C4311yescharacteristic
599C2×M16C23×C4311yescharacteristic
600C2×M16C23×C4311yescharacteristic
601C22×C8—21no—
602C22×C8—21no—
603C22×C8C23×C4311yescharacteristic
604C22×C8C23×C4311yescharacteristic
605#127—22no—
606#127—21no—
607#127—41no—
608#124—21no—
609#121—21no—
610#121—21no—
611#120—41no—
612C4×Q8—21no—
613C4×D4—21no—
614C4×D4—41no—
615#117—21no—
616#117C23×C4311yescharacteristic
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C4311yescharacteristic
619C2×C42C23×C4311yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C4311yescharacteristic, complemented
631#103D4×C4311yescharacteristic, complemented
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C4311yescharacteristic, complemented
641#102D4×C4311yescharacteristic, complemented
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#95—41no—
648C24—21no—
649C24—21no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41C2×D4×C4312yes—
670#41C2×D4×C4312yes—
671#41C2×D4×C4312yes—
672#41#41×C4312yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C4312yes—
684C2×Q8C2×D4×C4311yescharacteristic
685C2×Q8C2×D4×C4311yescharacteristic
686C2×Q8C2×D4×C4311yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4C2×D4×C4312yes—
716C2×D4C2×D4×C4311yescharacteristic
717C2×D4C2×D4×C4311yescharacteristic
718C2×D4C2×D4×C4311yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4C24×C4311yescharacteristic
730Q16—24no—
731Q16—22no—
732SD16—24no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—22no—
737SD16—24no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741SD16—42no—
742D8—24no—
743D8—22no—
744D8—42no—
745D8—42no—
746M16—24no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—21no—
754M16—42no—
755M16C2×D4×C4312yes—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—42no—
766C2×C8C2×D4×C4311yescharacteristic
767C2×C8C2×D4×C4311yescharacteristic
768C2×C8C2×D4×C4311yescharacteristic
769C2×C8C2×D4×C4311yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—41no—
773C4⋊C4C2×D4×C4311yescharacteristic
774C4⋊C4C2×D4×C4311yescharacteristic
775C22⋊C4—21no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—41no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23H(5,𝔽2)×C4311yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8#120×C4312yes—
810Q8#121×C4312yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4#120×C4312yes—
836D4#121×C4312yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C4311yescharacteristic
861C2×C4C22×D4×C4311yescharacteristic
862C2×C4C22×D4×C4311yescharacteristic
863C2×C4C22×D4×C4311yescharacteristic
864C2×C4C2×#41×C4311yescharacteristic
865C2×C4H(5,𝔽2)×C4311yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22C43×#53411yescharacteristic
897C22D42×C4311yescharacteristic
898C22C43×#54611yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—42no—
904C4—41no—
905C4—41no—
906C4—81no—
907C4C2×#120×C4311yescharacteristic
908C4C2×#121×C4311yescharacteristic
909C4D42×C4311yescharacteristic
910C4C43×#54611yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2C43×#241011yescharacteristic
919C2C43×#328811yescharacteristic
920C2C43×#329111yescharacteristic
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. C2×C43×#577C2semidirect
2. C2×C43×#471C2semidirect
3. C43×#3045C2semidirect
4. C2×C43×#453C2semidirect
5. C43×#3010C2semidirect
6. C43×#2897C2semidirect
7. C43×#2051C2semidirect
8. C43×#2046C2semidirect
9. C43×#2014C2semidirect
10. C43×#2002C2semidirect
11. C43×#1907C2semidirect
12. C43×#1882C2semidirect
13. C43×#1876C2semidirect
14. C43×#1866C2semidirect
15. C43×#1793C2semidirect
30. C22×SD16×C43C22semidirect
33. C43×#535C22semidirect
46. C2×#108×C43C22semidirect
47. C43×#424C22semidirect
50. C2×#104×C43C22semidirect
51. C43×#419C22semidirect
56. C43×#417C22semidirect
61. C2×#102×C43C22semidirect
62. C2×#101×C43C22semidirect
64. C2×#100×C43C22semidirect
65. C43×#408C22semidirect
66. C43×#391C22semidirect
67. C43×#343C22semidirect
68. C43×#341C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
78. H(5,𝔽2)×C43D4semidirect
98. #137×C43D4semidirect
110. C2×Q16×C43D4semidirect
124. C2×SD16×C43D4semidirect
125. C2×SD16×C43D4semidirect
129. C2×D8×C43D4semidirect
169. #103×C43D4semidirect
170. #103×C43D4semidirect
179. #102×C43D4semidirect
180. #102×C43D4semidirect
413. #24457C43direct (N × H)
451. C2×#577C2×C43semidirect
452. C2×#471C2×C43semidirect
453. #3045C2×C43semidirect
454. C2×#453C2×C43semidirect
455. #3010C2×C43semidirect
456. #2897C2×C43semidirect
457. #2051C2×C43semidirect
458. #2046C2×C43semidirect
459. #2014C2×C43semidirect
460. #2002C2×C43semidirect
461. #1907C2×C43semidirect
462. #1882C2×C43semidirect
463. #1876C2×C43semidirect
464. #1866C2×C43semidirect
465. #1793C2×C43semidirect
490. C22×SD16C22×C43semidirect
493. #535C22×C43semidirect
506. C2×#108C22×C43semidirect
507. #424C22×C43semidirect
510. C2×#104C22×C43semidirect
511. #419C22×C43semidirect
516. #417C22×C43semidirect
521. C2×#102C22×C43semidirect
522. C2×#101C22×C43semidirect
524. C2×#100C22×C43semidirect
525. #408C22×C43semidirect
526. #391C22×C43semidirect
527. #343C22×C43semidirect
528. #341C22×C43semidirect
529. #339C22×C43semidirect
530. #336C22×C43semidirect
531. C43#24457direct (N × H)
539. H(5,𝔽2)D4×C43semidirect
559. #137D4×C43semidirect
571. C2×Q16D4×C43semidirect
585. C2×SD16D4×C43semidirect
586. C2×SD16D4×C43semidirect
590. C2×D8D4×C43semidirect
630. #103D4×C43semidirect
631. #103D4×C43semidirect
640. #102D4×C43semidirect
641. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5772
C2×C43×#4712
C43×#30452
C2×C43×#4532
C43×#30102
C43×#28972
C43×#20512
C43×#20462
C43×#20142
C43×#20022
C43×#19072
C43×#18822
C43×#18762
C43×#18662
C43×#17932
#2445743