Finite Group Databasebeta

← C43×#24459 #24944476

Subgroups — C43×#24459 #24944476

Order 11008.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#576C211yesmaximal, characteristic
2C2×C43×#471C211yesmaximal, characteristic, complemented
3C43×#3046C211yesmaximal, characteristic, complemented
4C2×C43×#455C211yesmaximal, characteristic, complemented
5C43×#3009C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2051C211yesmaximal, characteristic, complemented
8C43×#2045C211yesmaximal, characteristic, complemented
9C43×#2012C211yesmaximal, characteristic, complemented
10C43×#2003C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1883C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic, complemented
14C43×#1866C211yesmaximal, characteristic, complemented
15C43×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C2×H(5,𝔽2)×C43C2211yescharacteristic
18C43×#576—24no—
19C43×#576—24no—
20C2×#137×C43C2211yescharacteristic
21C2×#137×C43C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C43—21no—
23C2×AGL(1,ℤ/8)×C43—21no—
24C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
26C2×#135×C43—21no—
27C2×#135×C43C2211yescharacteristic
28C22×SD16×C43C2211yescharacteristic, complemented
29C22×D8×C43—21no—
30C22×D8×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C2×#131×C43C2211yescharacteristic, complemented
33C43×#536C2211yescharacteristic, complemented
34C2×#124×C43C2211yescharacteristic, complemented
35C43×#520C2211yescharacteristic, complemented
36C43×#471—24no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#462—21no—
40C43×#461—21no—
41C43×#455—24no—
42C43×#452—21no—
43C43×#452—21no—
44C43×#450—21no—
45C43×#450—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C43×#424C2211yescharacteristic, complemented
48C2×#104×C43C2211yescharacteristic
49C2×#104×C43C2211yescharacteristic, complemented
50C2×#104×C43C2211yescharacteristic, complemented
51C43×#418—21no—
52C43×#418C2211yescharacteristic, complemented
53C43×#418C2211yescharacteristic, complemented
54C43×#417—21no—
55C43×#417C2211yescharacteristic
56C43×#417C2211yescharacteristic, complemented
57C43×#416—21no—
58C43×#416C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43—21no—
61C2×#102×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C2×#100×C43C2211yescharacteristic, complemented
64C2×#100×C43C2211yescharacteristic, complemented
65C43×#408C2211yescharacteristic, complemented
66C43×#390C2211yescharacteristic, complemented
67C43×#343C2211yescharacteristic, complemented
68C43×#341C2211yescharacteristic, complemented
69C43×#339C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
71H(5,𝔽2)×C43—22no—
72H(5,𝔽2)×C43—22no—
73H(5,𝔽2)×C43—22no—
74H(5,𝔽2)×C43—22no—
75H(5,𝔽2)×C43—22no—
76H(5,𝔽2)×C43—41no—
77H(5,𝔽2)×C43—41no—
78H(5,𝔽2)×C43D414yes—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43C2311yescharacteristic
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C22×Q8×C43C2311yescharacteristic
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43—41no—
92C22×D4×C43—41no—
93C22×D4×C43C2311yescharacteristic
94C22×D4×C43C2311yescharacteristic
95#137×C43—22no—
96#137×C43—22no—
97#137×C43—22no—
98#137×C43—22no—
99AGL(1,ℤ/8)×C43—28no—
100AGL(1,ℤ/8)×C43—28no—
101AGL(1,ℤ/8)×C43—22no—
102AGL(1,ℤ/8)×C43—22no—
103AGL(1,ℤ/8)×C43—22no—
104AGL(1,ℤ/8)×C43D414yes—
105#135×C43—28no—
106#135×C43—22no—
107#135×C43—22no—
108C2×Q16×C43—21no—
109C2×Q16×C43—21no—
110C2×Q16×C43D411yescharacteristic
111C2×SD16×C43—21no—
112C2×SD16×C43—21no—
113C2×SD16×C43—22no—
114C2×SD16×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—41no—
119C2×SD16×C43D411yescharacteristic
120C2×SD16×C43D411yescharacteristic
121C2×D8×C43—28no—
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43—22no—
125C2×D8×C43—22no—
126C2×D8×C43—21no—
127C2×D8×C43—21no—
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
143C4⋊Q8×C43—21no—
144#124×C43—22no—
145#124×C43—21no—
146#124×C43—41no—
147#123×C43—41no—
148C22⋊Q8×C43—21no—
149C22⋊Q8×C43—21no—
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×C43D411yescharacteristic
171#103×C43D411yescharacteristic
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×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—
190C24×C43—41no—
191#41×C43—21no—
192#41×C43—21no—
193#41×C43—21no—
194#41×C43—21no—
195#41×C43—24no—
196#41×C43—24no—
197#41×C43—24no—
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—21no—
201#41×C43—21no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—42no—
206#41×C43—42no—
207#41×C43C2×D412yes—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210#41×C43#4112yes—
211C2×Q8×C43—21no—
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43C2×D411yescharacteristic
218C2×Q8×C43C2×D411yescharacteristic
219C2×Q8×C43C2×D411yescharacteristic
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—24no—
226C2×D4×C43—24no—
227C2×D4×C43—24no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—41no—
237C2×D4×C43—41no—
238C2×D4×C43—41no—
239C2×D4×C43—41no—
240C2×D4×C43—44no—
241C2×D4×C43—44no—
242C2×D4×C43—42no—
243C2×D4×C43—42no—
244C2×D4×C43—42no—
245C2×D4×C43—42no—
246C2×D4×C43—44no—
247C2×D4×C43—44no—
248C2×D4×C43—42no—
249C2×D4×C43C2×D412yes—
250C2×D4×C43C2×D412yes—
251C2×D4×C43C2×D411yescharacteristic
252C2×D4×C43C2×D411yescharacteristic
253C2×D4×C43C2×D411yescharacteristic
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—41no—
261C22×C4×C43—41no—
262C22×C4×C43—41no—
263C22×C4×C43C2411yescharacteristic
264Q16×C43—22no—
265Q16×C43—42no—
266Q16×C43—42no—
267SD16×C43—24no—
268SD16×C43—24no—
269SD16×C43—22no—
270SD16×C43—22no—
271SD16×C43—42no—
272SD16×C43—42no—
273SD16×C43—42no—
274SD16×C43—42no—
275D8×C43—24no—
276D8×C43—24no—
277D8×C43—24no—
278D8×C43—22no—
279D8×C43—24no—
280M16×C43—24no—
281M16×C43—21no—
282M16×C43—21no—
283M16×C43—21no—
284M16×C43—21no—
285M16×C43—21no—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—42no—
289M16×C43C2×D412yes—
290C2×C8×C43—24no—
291C2×C8×C43—21no—
292C2×C8×C43—21no—
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—42no—
300C2×C8×C43C2×D411yescharacteristic
301C2×C8×C43C2×D411yescharacteristic
302C2×C8×C43C2×D411yescharacteristic
303C2×C8×C43C2×D411yescharacteristic
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—41no—
307C4⋊C4×C43—41no—
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—22no—
326C23×C43—44no—
327C23×C43—44no—
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×C43—161no—
339C23×C43—161no—
340C23×C43H(5,𝔽2)11yescharacteristic
341Q8×C43—21no—
342Q8×C43—21no—
343Q8×C43—21no—
344Q8×C43—21no—
345Q8×C43—41no—
346Q8×C43—41no—
347Q8×C43—41no—
348Q8×C43—41no—
349Q8×C43#12012yes—
350Q8×C43#12112yes—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—22no—
355D4×C43—22no—
356D4×C43—22no—
357D4×C43—21no—
358D4×C43—22no—
359D4×C43—21no—
360D4×C43—22no—
361D4×C43—21no—
362D4×C43—21no—
363D4×C43—44no—
364D4×C43—44no—
365D4×C43—44no—
366D4×C43—44no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43#12012yes—
374D4×C43#12112yes—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
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—41no—
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#24459C4311yesmaximal, 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—42no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—82no—
426C22×C43—82no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—161no—
432C22×C43—161no—
433C22×C43—164no—
434C22×C43—164no—
435C22×C43#53411yescharacteristic
436C22×C43D4211yescharacteristic
437C22×C43#54611yescharacteristic
438C4×C43—22no—
439C4×C43—22no—
440C4×C43—41no—
441C4×C43—41no—
442C4×C43—41no—
443C4×C43—81no—
444C4×C43—81no—
445C4×C43—81no—
446C4×C43C2×#12011yescharacteristic
447C4×C43C2×#12111yescharacteristic
448C4×C43D4211yescharacteristic
449C4×C43#54611yescharacteristic
450C2×#576C2×C4311yescharacteristic
451C2×#471C2×C4311yescharacteristic, complemented
452#3046C2×C4311yescharacteristic, complemented
453C2×#455C2×C4311yescharacteristic, complemented
454#3009C2×C4311yescharacteristic, complemented
455#2897C2×C4311yescharacteristic, complemented
456#2051C2×C4311yescharacteristic, complemented
457#2045C2×C4311yescharacteristic, complemented
458#2012C2×C4311yescharacteristic, complemented
459#2003C2×C4311yescharacteristic, complemented
460#1908C2×C4311yescharacteristic, complemented
461#1883C2×C4311yescharacteristic, complemented
462#1876C2×C4311yescharacteristic, complemented
463#1866C2×C4311yescharacteristic, complemented
464#1792C2×C4311yescharacteristic, complemented
465C2×C43—21no—
466C2×C43—21no—
467C2×C43—42no—
468C2×C43—42no—
469C2×C43—81no—
470C2×C43—82no—
471C2×C43—82no—
472C2×C43#241011yescharacteristic
473C2×C43#328811yescharacteristic
474C2×C43#329011yescharacteristic
475C2×H(5,𝔽2)C22×C4311yescharacteristic
476C2×H(5,𝔽2)C22×C4311yescharacteristic
477#576—24no—
478#576—24no—
479C2×#137C22×C4311yescharacteristic
480C2×#137C22×C4311yescharacteristic, complemented
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
484C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
485C2×#135—21no—
486C2×#135C22×C4311yescharacteristic
487C22×SD16C22×C4311yescharacteristic, complemented
488C22×D8—21no—
489C22×D8C22×C4311yescharacteristic
490C2×#131C22×C4311yescharacteristic
491C2×#131C22×C4311yescharacteristic, complemented
492#536C22×C4311yescharacteristic, complemented
493C2×#124C22×C4311yescharacteristic, complemented
494#520C22×C4311yescharacteristic, complemented
495#471—24no—
496#464—21no—
497#463—21no—
498#462—21no—
499#461—21no—
500#455—24no—
501#452—21no—
502#452—21no—
503#450—21no—
504#450—21no—
505C2×#108C22×C4311yescharacteristic, complemented
506#424C22×C4311yescharacteristic, complemented
507C2×#104C22×C4311yescharacteristic
508C2×#104C22×C4311yescharacteristic, complemented
509C2×#104C22×C4311yescharacteristic, complemented
510#418—21no—
511#418C22×C4311yescharacteristic, complemented
512#418C22×C4311yescharacteristic, complemented
513#417—21no—
514#417C22×C4311yescharacteristic
515#417C22×C4311yescharacteristic, complemented
516#416—21no—
517#416C22×C4311yescharacteristic
518C2×#103C22×C4311yescharacteristic, complemented
519C2×#102—21no—
520C2×#102C22×C4311yescharacteristic, complemented
521C2×#101C22×C4311yescharacteristic, complemented
522C2×#100C22×C4311yescharacteristic, complemented
523C2×#100C22×C4311yescharacteristic, complemented
524#408C22×C4311yescharacteristic, complemented
525#390C22×C4311yescharacteristic, complemented
526#343C22×C4311yescharacteristic, complemented
527#341C22×C4311yescharacteristic, complemented
528#339C22×C4311yescharacteristic, complemented
529#336C22×C4311yescharacteristic, complemented
530C43#2445911yescharacteristic, direct product factor, Sylow
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C4314yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C4311yescharacteristic
544C2×#41C23×C4311yescharacteristic
545C2×#41C23×C4311yescharacteristic
546C22×Q8C23×C4311yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C4311yescharacteristic
554C22×D4C23×C4311yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C4314yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C4311yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C4311yescharacteristic
580C2×SD16D4×C4311yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C4311yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C4311yescharacteristic
596C2×M16C23×C4311yescharacteristic
597C2×M16C23×C4311yescharacteristic
598C2×M16C23×C4311yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C4311yescharacteristic
602C22×C8C23×C4311yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C4311yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C4311yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
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
631#103D4×C4311yescharacteristic
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
641#102D4×C4311yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
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—42no—
664#41—42no—
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—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C4311yescharacteristic
678C2×Q8C2×D4×C4311yescharacteristic
679C2×Q8C2×D4×C4311yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
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—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C4312yes—
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×C4C24×C4311yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C4312yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C4311yescharacteristic
761C2×C8C2×D4×C4311yescharacteristic
762C2×C8C2×D4×C4311yescharacteristic
763C2×C8C2×D4×C4311yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C4311yescharacteristic
770C4⋊C4C2×D4×C4311yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C4311yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C4312yes—
810Q8#121×C4312yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C4312yes—
834D4#121×C4312yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
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—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C4311yescharacteristic
858C2×C4C22×D4×C4311yescharacteristic
859C2×C4C22×D4×C4311yescharacteristic
860C2×C4C22×D4×C4311yescharacteristic
861C2×C4C2×#41×C4311yescharacteristic
862C2×C4H(5,𝔽2)×C4311yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22C43×#53411yescharacteristic
895C22D42×C4311yescharacteristic
896C22C43×#54611yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C4311yescharacteristic
906C4C2×#121×C4311yescharacteristic
907C4D42×C4311yescharacteristic
908C4C43×#54611yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2C43×#241011yescharacteristic
917C2C43×#328811yescharacteristic
918C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#576C2
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
2. C2×C43×#471C2semidirect
3. C43×#3046C2semidirect
4. C2×C43×#455C2semidirect
5. C43×#3009C2semidirect
6. C43×#2897C2semidirect
7. C43×#2051C2semidirect
8. C43×#2045C2semidirect
9. C43×#2012C2semidirect
10. C43×#2003C2semidirect
11. C43×#1908C2semidirect
12. C43×#1883C2semidirect
13. C43×#1876C2semidirect
14. C43×#1866C2semidirect
15. C43×#1792C2semidirect
21. C2×#137×C43C22semidirect
28. C22×SD16×C43C22semidirect
32. C2×#131×C43C22semidirect
33. C43×#536C22semidirect
34. C2×#124×C43C22semidirect
35. C43×#520C22semidirect
46. C2×#108×C43C22semidirect
47. C43×#424C22semidirect
49. C2×#104×C43C22semidirect
50. C2×#104×C43C22semidirect
52. C43×#418C22semidirect
53. C43×#418C22semidirect
56. C43×#417C22semidirect
59. C2×#103×C43C22semidirect
61. C2×#102×C43C22semidirect
62. C2×#101×C43C22semidirect
63. C2×#100×C43C22semidirect
64. C2×#100×C43C22semidirect
65. C43×#408C22semidirect
66. C43×#390C22semidirect
67. C43×#343C22semidirect
68. C43×#341C22semidirect
69. C43×#339C22semidirect
70. C43×#336C22semidirect
411. #24459C43direct (N × H)
451. C2×#471C2×C43semidirect
452. #3046C2×C43semidirect
453. C2×#455C2×C43semidirect
454. #3009C2×C43semidirect
455. #2897C2×C43semidirect
456. #2051C2×C43semidirect
457. #2045C2×C43semidirect
458. #2012C2×C43semidirect
459. #2003C2×C43semidirect
460. #1908C2×C43semidirect
461. #1883C2×C43semidirect
462. #1876C2×C43semidirect
463. #1866C2×C43semidirect
464. #1792C2×C43semidirect
480. C2×#137C22×C43semidirect
487. C22×SD16C22×C43semidirect
491. C2×#131C22×C43semidirect
492. #536C22×C43semidirect
493. C2×#124C22×C43semidirect
494. #520C22×C43semidirect
505. C2×#108C22×C43semidirect
506. #424C22×C43semidirect
508. C2×#104C22×C43semidirect
509. C2×#104C22×C43semidirect
511. #418C22×C43semidirect
512. #418C22×C43semidirect
515. #417C22×C43semidirect
518. C2×#103C22×C43semidirect
520. C2×#102C22×C43semidirect
521. C2×#101C22×C43semidirect
522. C2×#100C22×C43semidirect
523. C2×#100C22×C43semidirect
524. #408C22×C43semidirect
525. #390C22×C43semidirect
526. #343C22×C43semidirect
527. #341C22×C43semidirect
528. #339C22×C43semidirect
529. #336C22×C43semidirect
530. C43#24459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5762
C2×C43×#4712
C43×#30462
C2×C43×#4552
C43×#30092
C43×#28972
C43×#20512
C43×#20452
C43×#20122
C43×#20032
C43×#19082
C43×#18832
C43×#18762
C43×#18662
C43×#17922
#2445943