Finite Group Databasebeta

← C43×#24460 #24944477

Subgroups — C43×#24460 #24944477

Order 11008.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#577C211yesmaximal, characteristic, complemented
2C2×C43×#472C211yesmaximal, characteristic, complemented
3C43×#3045C211yesmaximal, characteristic, complemented
4C2×C43×#454C211yesmaximal, characteristic, complemented
5C43×#3008C211yesmaximal, characteristic, complemented
6C43×#2898C211yesmaximal, characteristic, complemented
7C43×#2052C211yesmaximal, characteristic, complemented
8C43×#2046C211yesmaximal, characteristic, complemented
9C43×#2012C211yesmaximal, characteristic, complemented
10C43×#2004C211yesmaximal, characteristic, complemented
11C43×#1907C211yesmaximal, characteristic, complemented
12C43×#1883C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic, complemented
14C43×#1866C211yesmaximal, characteristic, complemented
15C43×#1792C211yesmaximal, 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, complemented
26C2×#135×C43—21no—
27C2×#135×C43C2211yescharacteristic
28C22×SD16×C43—21no—
29C22×SD16×C43C2211yescharacteristic
30C22×D8×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C2×#131×C43C2211yescharacteristic, complemented
33C43×#535C2211yescharacteristic
34C2×#124×C43C2211yescharacteristic, complemented
35C43×#520C2211yescharacteristic, complemented
36C43×#472—24no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#460—21no—
40C43×#459—21no—
41C43×#454—24no—
42C43×#449—21no—
43C43×#449—21no—
44C43×#447—21no—
45C43×#447—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C43×#424C2211yescharacteristic, complemented
48C2×#104×C43C2211yescharacteristic
49C2×#104×C43C2211yescharacteristic
50C2×#104×C43C2211yescharacteristic, complemented
51C43×#419—21no—
52C43×#419C2211yescharacteristic, complemented
53C43×#418C2211yescharacteristic
54C43×#417—21no—
55C43×#417C2211yescharacteristic
56C43×#417C2211yescharacteristic
57C43×#416—21no—
58C43×#416C2211yescharacteristic
59C2×#103×C43—21no—
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C2×#100×C43C2211yescharacteristic
64C2×#100×C43C2211yescharacteristic, complemented
65C43×#408C2211yescharacteristic
66C43×#390C2211yescharacteristic
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—41no—
742−1+4×C43D414yescomplemented
75H(5,𝔽2)×C43—22no—
76H(5,𝔽2)×C43—22no—
77H(5,𝔽2)×C43—22no—
78H(5,𝔽2)×C43—41no—
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×C43C2311yescharacteristic
94C22×D4×C43C2311yescharacteristic
95#137×C43—28no—
96#137×C43—22no—
97#137×C43—22no—
98AGL(1,ℤ/8)×C43—28no—
99AGL(1,ℤ/8)×C43—22no—
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)×C43D414yescomplemented
105#135×C43—28no—
106#135×C43—22no—
107#135×C43—22no—
108C2×Q16×C43—21no—
109C2×Q16×C43D411yescharacteristic
110C2×SD16×C43—28no—
111C2×SD16×C43—21no—
112C2×SD16×C43—22no—
113C2×SD16×C43—21no—
114C2×SD16×C43—22no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C2×SD16×C43D411yescharacteristic
121C2×D8×C43—21no—
122C2×D8×C43—22no—
123C2×D8×C43—21no—
124C2×D8×C43—21no—
125C2×D8×C43—21no—
126C2×D8×C43—21no—
127C2×D8×C43—41no—
128C2×D8×C43D411yescharacteristic
129#131×C43—22no—
130#131×C43—22no—
131#131×C43—22no—
132#131×C43—41no—
133C2×M16×C43—21no—
134C2×M16×C43—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C22×C8×C43—21no—
140C22×C8×C43—21no—
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#127×C43—21no—
144#124×C43—22no—
145#124×C43—21no—
146#124×C43—41no—
147#121×C43—21no—
148#121×C43—21no—
149#120×C43—41no—
150C4×Q8×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—41no—
153#117×C43—21no—
154#117×C43C2311yescharacteristic
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—41no—
158C2×C22⋊C4×C43—41no—
159C2×C42×C43C2311yescharacteristic
160#108×C43—22no—
161C4⋊C8×C43—21no—
162C4⋊C8×C43—21no—
163#104×C43—22no—
164#104×C43—22no—
165#104×C43—41no—
166#103×C43—21no—
167#103×C43—21no—
168#103×C43—21no—
169#103×C43—21no—
170#103×C43—21no—
171#103×C43—21no—
172#103×C43D411yescharacteristic
173#103×C43D411yescharacteristic
174#102×C43—21no—
175#102×C43—21no—
176#102×C43—21no—
177#102×C43—21no—
178#102×C43—21no—
179#102×C43—21no—
180#102×C43D411yescharacteristic
181#102×C43D411yescharacteristic
182#101×C43—22no—
183#100×C43—22no—
184#100×C43—22no—
185C22⋊C8×C43—21no—
186C22⋊C8×C43—21no—
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—44no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—44no—
206#41×C43—42no—
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—24no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—41no—
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—21no—
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—41no—
242C2×D4×C43—41no—
243C2×D4×C43—41no—
244C2×D4×C43—41no—
245C2×D4×C43—41no—
246C2×D4×C43—44no—
247C2×D4×C43—42no—
248C2×D4×C43—42no—
249C2×D4×C43—44no—
250C2×D4×C43—42no—
251C2×D4×C43C2×D412yes—
252C2×D4×C43C2×D411yescharacteristic
253C2×D4×C43C2×D411yescharacteristic
254C2×D4×C43C2×D411yescharacteristic
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—41no—
262C22×C4×C43—41no—
263C22×C4×C43—41no—
264C22×C4×C43—41no—
265C22×C4×C43C2411yescharacteristic
266Q16×C43—24no—
267Q16×C43—22no—
268SD16×C43—24no—
269SD16×C43—24no—
270SD16×C43—24no—
271SD16×C43—22no—
272SD16×C43—24no—
273SD16×C43—22no—
274SD16×C43—42no—
275SD16×C43—42no—
276D8×C43—24no—
277D8×C43—22no—
278D8×C43—42no—
279D8×C43—42no—
280D8×C43—42no—
281D8×C43—42no—
282M16×C43—24no—
283M16×C43—21no—
284M16×C43—21no—
285M16×C43—21no—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—42no—
291M16×C43C2×D412yes—
292C2×C8×C43—24no—
293C2×C8×C43—21no—
294C2×C8×C43—21no—
295C2×C8×C43—21no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—42no—
302C2×C8×C43C2×D411yescharacteristic
303C2×C8×C43C2×D411yescharacteristic
304C2×C8×C43C2×D411yescharacteristic
305C2×C8×C43C2×D411yescharacteristic
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—41no—
309C4⋊C4×C43C2×D411yescharacteristic
310C4⋊C4×C43C2×D411yescharacteristic
311C22⋊C4×C43—21no—
312C22⋊C4×C43—41no—
313C22⋊C4×C43—41no—
314C22⋊C4×C43—41no—
315C22⋊C4×C43—44no—
316C22⋊C4×C43—82no—
317C42×C43—21no—
318C42×C43—21no—
319C42×C43—21no—
320C42×C43—41no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—22no—
325C23×C43—44no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—81no—
332C23×C43—81no—
333C23×C43—81no—
334C23×C43—81no—
335C23×C43—161no—
336C23×C43—161no—
337C23×C43H(5,𝔽2)11yescharacteristic
338Q8×C43—21no—
339Q8×C43—21no—
340Q8×C43—22no—
341Q8×C43—21no—
342Q8×C43—22no—
343Q8×C43—21no—
344Q8×C43—44no—
345Q8×C43—41no—
346Q8×C43—41no—
347Q8×C43#12012yes—
348Q8×C43#12112yes—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—21no—
355D4×C43—21no—
356D4×C43—22no—
357D4×C43—21no—
358D4×C43—21no—
359D4×C43—44no—
360D4×C43—44no—
361D4×C43—44no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—161no—
371D4×C43—161no—
372D4×C43#12012yes—
373D4×C43#12112yes—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—44no—
385C2×C4×C43—44no—
386C2×C4×C43—44no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—81no—
396C2×C4×C43—161no—
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43C2×#4111yescharacteristic
402C2×C4×C43H(5,𝔽2)11yescharacteristic
403C8×C43—21no—
404C8×C43—22no—
405C8×C43—21no—
406C8×C43—21no—
407C8×C43—21no—
408C8×C43—41no—
409C8×C43—41no—
410C8×C43—41no—
411#24460C4311yesmaximal, characteristic, direct product factor, Sylow
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—42no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—82no—
425C22×C43—82no—
426C22×C43—81no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—161no—
432C22×C43—161no—
433C22×C43—164no—
434C22×C43#53411yescharacteristic
435C22×C43D4211yescharacteristic
436C22×C43#54611yescharacteristic
437C4×C43—22no—
438C4×C43—22no—
439C4×C43—41no—
440C4×C43—42no—
441C4×C43—41no—
442C4×C43—41no—
443C4×C43—81no—
444C4×C43—81no—
445C4×C43C2×#12011yescharacteristic
446C4×C43C2×#12111yescharacteristic
447C4×C43D4211yescharacteristic
448C4×C43#54611yescharacteristic
449C2×#577C2×C4311yescharacteristic, complemented
450C2×#472C2×C4311yescharacteristic, complemented
451#3045C2×C4311yescharacteristic, complemented
452C2×#454C2×C4311yescharacteristic, complemented
453#3008C2×C4311yescharacteristic, complemented
454#2898C2×C4311yescharacteristic, complemented
455#2052C2×C4311yescharacteristic, complemented
456#2046C2×C4311yescharacteristic, complemented
457#2012C2×C4311yescharacteristic, complemented
458#2004C2×C4311yescharacteristic, complemented
459#1907C2×C4311yescharacteristic, complemented
460#1883C2×C4311yescharacteristic, complemented
461#1876C2×C4311yescharacteristic, complemented
462#1866C2×C4311yescharacteristic, complemented
463#1792C2×C4311yescharacteristic, complemented
464C2×C43—21no—
465C2×C43—21no—
466C2×C43—42no—
467C2×C43—42no—
468C2×C43—81no—
469C2×C43—82no—
470C2×C43—161no—
471C2×C43#241011yescharacteristic
472C2×C43#328811yescharacteristic
473C2×C43#329011yescharacteristic
474C2×2−1+4C22×C4311yescharacteristic
475C2×H(5,𝔽2)C22×C4311yescharacteristic
476#577—24no—
477#577—24no—
478C2×#137—21no—
479C2×#137C22×C4311yescharacteristic
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
482C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
483C2×AGL(1,ℤ/8)C22×C4311yescharacteristic, complemented
484C2×#135—21no—
485C2×#135C22×C4311yescharacteristic
486C22×SD16—21no—
487C22×SD16C22×C4311yescharacteristic
488C22×D8C22×C4311yescharacteristic
489C2×#131C22×C4311yescharacteristic
490C2×#131C22×C4311yescharacteristic, complemented
491#535C22×C4311yescharacteristic
492C2×#124C22×C4311yescharacteristic, complemented
493#520C22×C4311yescharacteristic, complemented
494#472—24no—
495#464—21no—
496#463—21no—
497#460—21no—
498#459—21no—
499#454—24no—
500#449—21no—
501#449—21no—
502#447—21no—
503#447—21no—
504C2×#108C22×C4311yescharacteristic, complemented
505#424C22×C4311yescharacteristic, complemented
506C2×#104C22×C4311yescharacteristic
507C2×#104C22×C4311yescharacteristic
508C2×#104C22×C4311yescharacteristic, complemented
509#419—21no—
510#419C22×C4311yescharacteristic, complemented
511#418C22×C4311yescharacteristic
512#417—21no—
513#417C22×C4311yescharacteristic
514#417C22×C4311yescharacteristic
515#416—21no—
516#416C22×C4311yescharacteristic
517C2×#103—21no—
518C2×#103C22×C4311yescharacteristic, complemented
519C2×#102C22×C4311yescharacteristic, complemented
520C2×#101C22×C4311yescharacteristic, complemented
521C2×#100C22×C4311yescharacteristic
522C2×#100C22×C4311yescharacteristic, complemented
523#408C22×C4311yescharacteristic
524#390C22×C4311yescharacteristic
525#343C22×C4311yescharacteristic, complemented
526#341C22×C4311yescharacteristic, complemented
527#339C22×C4311yescharacteristic, complemented
528#336C22×C4311yescharacteristic, complemented
529C43#2446011yescharacteristic, direct product factor, Sylow
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C4314yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C4311yescharacteristic
544C2×#41C23×C4311yescharacteristic
545C2×#41C23×C4311yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C4311yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C4311yescharacteristic
553C22×D4C23×C4311yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C4314yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C4311yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C4311yescharacteristic
579C2×SD16D4×C4311yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C4311yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C4311yescharacteristic
595C2×M16C23×C4311yescharacteristic
596C2×M16C23×C4311yescharacteristic
597C2×M16C23×C4311yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C4311yescharacteristic
601C22×C8C23×C4311yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C4311yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C4311yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C4311yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C4311yescharacteristic
632#103D4×C4311yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C4311yescharacteristic
640#102D4×C4311yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C4312yes—
668#41C2×D4×C4312yes—
669#41C2×D4×C4312yes—
670#41#41×C4312yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C4312yes—
682C2×Q8C2×D4×C4311yescharacteristic
683C2×Q8C2×D4×C4311yescharacteristic
684C2×Q8C2×D4×C4311yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
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—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C4312yes—
711C2×D4C2×D4×C4311yescharacteristic
712C2×D4C2×D4×C4311yescharacteristic
713C2×D4C2×D4×C4311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C4311yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C4312yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C4311yescharacteristic
762C2×C8C2×D4×C4311yescharacteristic
763C2×C8C2×D4×C4311yescharacteristic
764C2×C8C2×D4×C4311yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C4311yescharacteristic
769C4⋊C4C2×D4×C4311yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C4311yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C4312yes—
807Q8#121×C4312yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C4312yes—
832D4#121×C4312yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C4311yescharacteristic
857C2×C4C22×D4×C4311yescharacteristic
858C2×C4C22×D4×C4311yescharacteristic
859C2×C4C22×D4×C4311yescharacteristic
860C2×C4C2×#41×C4311yescharacteristic
861C2×C4H(5,𝔽2)×C4311yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22C43×#53411yescharacteristic
893C22D42×C4311yescharacteristic
894C22C43×#54611yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4C2×#120×C4311yescharacteristic
904C4C2×#121×C4311yescharacteristic
905C4D42×C4311yescharacteristic
906C4C43×#54611yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C43×#241011yescharacteristic
915C2C43×#328811yescharacteristic
916C2C43×#329011yescharacteristic
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×#472C2semidirect
3. C43×#3045C2semidirect
4. C2×C43×#454C2semidirect
5. C43×#3008C2semidirect
6. C43×#2898C2semidirect
7. C43×#2052C2semidirect
8. C43×#2046C2semidirect
9. C43×#2012C2semidirect
10. C43×#2004C2semidirect
11. C43×#1907C2semidirect
12. C43×#1883C2semidirect
13. C43×#1876C2semidirect
14. C43×#1866C2semidirect
15. C43×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C43C22semidirect
32. C2×#131×C43C22semidirect
34. C2×#124×C43C22semidirect
35. C43×#520C22semidirect
46. C2×#108×C43C22semidirect
47. C43×#424C22semidirect
50. C2×#104×C43C22semidirect
52. C43×#419C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#102×C43C22semidirect
62. C2×#101×C43C22semidirect
64. C2×#100×C43C22semidirect
67. C43×#343C22semidirect
68. C43×#341C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
74. 2−1+4×C43D4semidirect
104. AGL(1,ℤ/8)×C43D4semidirect
411. #24460C43direct (N × H)
449. C2×#577C2×C43semidirect
450. C2×#472C2×C43semidirect
451. #3045C2×C43semidirect
452. C2×#454C2×C43semidirect
453. #3008C2×C43semidirect
454. #2898C2×C43semidirect
455. #2052C2×C43semidirect
456. #2046C2×C43semidirect
457. #2012C2×C43semidirect
458. #2004C2×C43semidirect
459. #1907C2×C43semidirect
460. #1883C2×C43semidirect
461. #1876C2×C43semidirect
462. #1866C2×C43semidirect
463. #1792C2×C43semidirect
483. C2×AGL(1,ℤ/8)C22×C43semidirect
490. C2×#131C22×C43semidirect
492. C2×#124C22×C43semidirect
493. #520C22×C43semidirect
504. C2×#108C22×C43semidirect
505. #424C22×C43semidirect
508. C2×#104C22×C43semidirect
510. #419C22×C43semidirect
518. C2×#103C22×C43semidirect
519. C2×#102C22×C43semidirect
520. C2×#101C22×C43semidirect
522. C2×#100C22×C43semidirect
525. #343C22×C43semidirect
526. #341C22×C43semidirect
527. #339C22×C43semidirect
528. #336C22×C43semidirect
529. C43#24460direct (N × H)
533. 2−1+4D4×C43semidirect
563. AGL(1,ℤ/8)D4×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×#4722
C43×#30452
C2×C43×#4542
C43×#30082
C43×#28982
C43×#20522
C43×#20462
C43×#20122
C43×#20042
C43×#19072
C43×#18832
C43×#18762
C43×#18662
C43×#17922
#2446043