Finite Group Databasebeta

← C43×#25808 #24945825

Subgroups — C43×#25808 #24945825

Order 11008.

1424 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#577C211yesmaximal, characteristic
2C43×#3156C211yesmaximal, characteristic, complemented
3C2×C43×#497C211yesmaximal, characteristic, complemented
4C2×C43×#473C211yesmaximal, characteristic, complemented
5C2×C43×#456C211yesmaximal, characteristic, complemented
6C2×C43×#455C211yesmaximal, characteristic, complemented
7C43×#3011C211yesmaximal, characteristic, complemented
8C43×#3009C211yesmaximal, characteristic, complemented
9C43×#2020C211yesmaximal, characteristic, complemented
10C43×#2019C211yesmaximal, characteristic, complemented
11C43×#2005C211yesmaximal, characteristic, complemented
12C43×#2003C211yesmaximal, characteristic, complemented
13C43×#1977C211yesmaximal, characteristic, complemented
14C43×#1975C211yesmaximal, characteristic, complemented
15C43×#1765C211yesmaximal, 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×#137×C43C2211yescharacteristic
23C2×#137×C43C2211yescharacteristic
24C2×#137×C43C2211yescharacteristic
25C2×#137×C43C2211yescharacteristic, complemented
26C2×AGL(1,ℤ/8)×C43—21no—
27C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
28C2×#135×C43—21no—
29C2×#135×C43C2211yescharacteristic
30C22×Q16×C43C2211yescharacteristic, complemented
31C22×Q16×C43C2211yescharacteristic, complemented
32C22×SD16×C43—21no—
33C22×SD16×C43C2211yescharacteristic
34C22×SD16×C43C2211yescharacteristic
35C2×#131×C43C2211yescharacteristic
36C43×#536C2211yescharacteristic
37C43×#536C2211yescharacteristic, complemented
38C2×C4⋊Q8×C43C2211yescharacteristic, complemented
39C2×#124×C43C2211yescharacteristic
40C43×#497—24no—
41C43×#497—21no—
42C43×#497—21no—
43C43×#495—21no—
44C43×#494—21no—
45C43×#473—24no—
46C43×#456—24no—
47C43×#455—24no—
48C43×#452—22no—
49C43×#452—22no—
50C43×#451—22no—
51C43×#450—22no—
52C2×#108×C43C2211yescharacteristic, complemented
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C2×#104×C43C2211yescharacteristic, complemented
56C43×#419C2211yescharacteristic, complemented
57C43×#418C2211yescharacteristic
58C43×#416C2211yescharacteristic
59C2×#101×C43C2211yescharacteristic, complemented
60C2×#101×C43C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C2×#100×C43C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic, complemented
65C43×#405C2211yescharacteristic, complemented
66C2×#97×C43C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
692−1+4×C43—22no—
702−1+4×C43—22no—
712−1+4×C43—22no—
722−1+4×C43—41no—
73H(5,𝔽2)×C43—22no—
74H(5,𝔽2)×C43—22no—
75H(5,𝔽2)×C43—22no—
76H(5,𝔽2)×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—41no—
82C2×#41×C43C2311yescharacteristic
83C2×#41×C43C2311yescharacteristic
84C2×#41×C43C2311yescharacteristic
85C22×Q8×C43—21no—
86C22×Q8×C43—21no—
87C22×Q8×C43C2311yescharacteristic
88C22×Q8×C43C2311yescharacteristic
89C22×Q8×C43C2311yescharacteristic
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—41no—
93C22×D4×C43C2311yescharacteristic
94#137×C43—28no—
95#137×C43—22no—
96#137×C43—22no—
97#137×C43—22no—
98#137×C43—22no—
99#137×C43—22no—
100#137×C43—22no—
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—41no—
104#137×C43—41no—
105AGL(1,ℤ/8)×C43—28no—
106AGL(1,ℤ/8)×C43—22no—
107AGL(1,ℤ/8)×C43—22no—
108#135×C43—28no—
109#135×C43—22no—
110#135×C43—22no—
111C2×Q16×C43—21no—
112C2×Q16×C43—22no—
113C2×Q16×C43—21no—
114C2×Q16×C43—21no—
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43—22no—
119C2×Q16×C43—22no—
120C2×Q16×C43—22no—
121C2×Q16×C43—21no—
122C2×Q16×C43—41no—
123C2×Q16×C43D411yescharacteristic
124C2×SD16×C43—28no—
125C2×SD16×C43—21no—
126C2×SD16×C43—21no—
127C2×SD16×C43—22no—
128C2×SD16×C43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C2×SD16×C43—21no—
134C2×SD16×C43—22no—
135C2×SD16×C43—22no—
136C2×SD16×C43—41no—
137C2×SD16×C43D411yescharacteristic
138C2×SD16×C43D414yes—
139C2×SD16×C43D411yescharacteristic
140C2×D8×C43—21no—
141C2×D8×C43D411yescharacteristic
142#131×C43—22no—
143#131×C43D414yes—
144C2×M16×C43—21no—
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43—21no—
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C4⋊Q8×C43—22no—
153C4⋊Q8×C43—21no—
154C4⋊Q8×C43—21no—
155C4⋊Q8×C43—22no—
156#124×C43—22no—
157#124×C43—21no—
158#124×C43—21no—
159#124×C43—22no—
160#123×C43—41no—
161#123×C43—41no—
162C22⋊Q8×C43—22no—
163C22⋊Q8×C43—22no—
164#117×C43C2311yescharacteristic
165C2×C4⋊C4×C43—41no—
166C2×C22⋊C4×C43—41no—
167C2×C42×C43C2311yescharacteristic
168#108×C43—22no—
169#104×C43—22no—
170#104×C43—22no—
171#104×C43D414yes—
172#103×C43—22no—
173#103×C43D412yes—
174#102×C43—22no—
175#102×C43D412yes—
176#101×C43—22no—
177#101×C43—22no—
178#101×C43—22no—
179#100×C43—22no—
180C22⋊C8×C43—22no—
181C22⋊C8×C43—22no—
182#97×C43—22no—
183#97×C43—21no—
184C4×C8×C43—21no—
185C24×C43—21no—
186C24×C43—41no—
187#41×C43—21no—
188#41×C43—21no—
189#41×C43—24no—
190#41×C43—24no—
191#41×C43—21no—
192#41×C43—21no—
193#41×C43—21no—
194#41×C43—21no—
195#41×C43—21no—
196#41×C43—21no—
197#41×C43—21no—
198#41×C43—21no—
199#41×C43—42no—
200#41×C43—44no—
201#41×C43—42no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—44no—
205#41×C43—42no—
206#41×C43—42no—
207#41×C43C2×D412yes—
208#41×C43C2×D412yes—
209C2×Q8×C43—21no—
210C2×Q8×C43—24no—
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×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—21no—
220C2×Q8×C43—21no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—21no—
226C2×Q8×C43—21no—
227C2×Q8×C43—41no—
228C2×Q8×C43—42no—
229C2×Q8×C43—42no—
230C2×Q8×C43—42no—
231C2×Q8×C43C2×D411yescharacteristic
232C2×Q8×C43C2×D412yes—
233C2×Q8×C43C2×D411yescharacteristic
234C2×Q8×C43C2×D411yescharacteristic
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—24no—
240C2×D4×C43—21no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—41no—
245C2×D4×C43—41no—
246C2×D4×C43—41no—
247C2×D4×C43—44no—
248C2×D4×C43—42no—
249C2×D4×C43—42no—
250C2×D4×C43—44no—
251C2×D4×C43—42no—
252C2×D4×C43C2×D411yescharacteristic
253C2×D4×C43C2×D411yescharacteristic
254C2×D4×C43C2×D412yes—
255C2×D4×C43C2×D411yescharacteristic
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—41no—
264C22×C4×C43—41no—
265C22×C4×C43—41no—
266C22×C4×C43C2411yescharacteristic
267Q16×C43—24no—
268Q16×C43—22no—
269Q16×C43—44no—
270Q16×C43—42no—
271Q16×C43—42no—
272Q16×C43—42no—
273Q16×C43—42no—
274Q16×C43—42no—
275Q16×C43—42no—
276SD16×C43—24no—
277SD16×C43—24no—
278SD16×C43—22no—
279SD16×C43—24no—
280SD16×C43—24no—
281SD16×C43—22no—
282SD16×C43—44no—
283SD16×C43—42no—
284SD16×C43—42no—
285SD16×C43—42no—
286SD16×C43—42no—
287D8×C43—24no—
288D8×C43—22no—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—24no—
292M16×C43—21no—
293M16×C43—21no—
294M16×C43—21no—
295M16×C43—21no—
296M16×C43C2×D412yes—
297M16×C43C2×D412yes—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—24no—
303C2×C8×C43—21no—
304C2×C8×C43—21no—
305C2×C8×C43C2×D412yes—
306C2×C8×C43C2×D411yescharacteristic
307C2×C8×C43C2×D411yescharacteristic
308C2×C8×C43C2×D412yes—
309C2×C8×C43C2×D412yes—
310C4⋊C4×C43—44no—
311C4⋊C4×C43—42no—
312C4⋊C4×C43—42no—
313C4⋊C4×C43C2×D412yes—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—44no—
316C22⋊C4×C43—42no—
317C22⋊C4×C43—42no—
318C42×C43—21no—
319C42×C43—21no—
320C42×C43C2×D412yes—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—22no—
325C23×C43—44no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—82no—
329C23×C43—162no—
330C23×C43H(5,𝔽2)11yescharacteristic
331Q8×C43—21no—
332Q8×C43—21no—
333Q8×C43—22no—
334Q8×C43—21no—
335Q8×C43—22no—
336Q8×C43—21no—
337Q8×C43—21no—
338Q8×C43—44no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43—41no—
342Q8×C43—41no—
343Q8×C43—41no—
344Q8×C43—41no—
345Q8×C43—41no—
346Q8×C43—41no—
347Q8×C43—41no—
348Q8×C43—41no—
349Q8×C43#12712yes—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—21no—
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#12712yes—
369C2×C4×C43—21no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—44no—
378C2×C4×C43—44no—
379C2×C4×C43—42no—
380C2×C4×C43—44no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43H(5,𝔽2)11yescharacteristic
399C8×C43—22no—
400C8×C43—22no—
401C8×C43—22no—
402C8×C43—41no—
403C8×C43—41no—
404C8×C43#12012yes—
405C8×C43#12012yes—
406#25808C4311yesmaximal, characteristic, direct product factor, Sylow
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—42no—
410C22×C43—41no—
411C22×C43—42no—
412C22×C43—41no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—82no—
416C22×C43—82no—
417C22×C43—161no—
418C22×C43—164no—
419C22×C43#53511yescharacteristic
420C22×C43D4211yescharacteristic
421C22×C43D4211yescharacteristic
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—41no—
425C4×C43—42no—
426C4×C43—41no—
427C4×C43—42no—
428C4×C43—81no—
429C4×C43—81no—
430C4×C43C2×#12011yescharacteristic
431C4×C43C2×#12711yescharacteristic
432C4×C43D4211yescharacteristic
433C4×C43D4211yescharacteristic
434C2×#577C2×C4311yescharacteristic
435#3156C2×C4311yescharacteristic, complemented
436C2×#497C2×C4311yescharacteristic, complemented
437C2×#473C2×C4311yescharacteristic, complemented
438C2×#456C2×C4311yescharacteristic, complemented
439C2×#455C2×C4311yescharacteristic, complemented
440#3011C2×C4311yescharacteristic, complemented
441#3009C2×C4311yescharacteristic, complemented
442#2020C2×C4311yescharacteristic, complemented
443#2019C2×C4311yescharacteristic, complemented
444#2005C2×C4311yescharacteristic, complemented
445#2003C2×C4311yescharacteristic, complemented
446#1977C2×C4311yescharacteristic, complemented
447#1975C2×C4311yescharacteristic, complemented
448#1765C2×C4311yescharacteristic, complemented
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—42no—
452C2×C43—81no—
453C2×C43—81no—
454C2×C43—82no—
455C2×C43#243311yescharacteristic
456C2×C43#328912yes—
457C2×2−1+4C22×C4311yescharacteristic
458C2×H(5,𝔽2)C22×C4311yescharacteristic
459#577—24no—
460#577—24no—
461C2×#137—21no—
462C2×#137C22×C4311yescharacteristic
463C2×#137C22×C4311yescharacteristic
464C2×#137C22×C4311yescharacteristic
465C2×#137C22×C4311yescharacteristic
466C2×#137C22×C4311yescharacteristic, complemented
467C2×AGL(1,ℤ/8)—21no—
468C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
469C2×#135—21no—
470C2×#135C22×C4311yescharacteristic
471C22×Q16C22×C4311yescharacteristic, complemented
472C22×Q16C22×C4311yescharacteristic, complemented
473C22×SD16—21no—
474C22×SD16C22×C4311yescharacteristic
475C22×SD16C22×C4311yescharacteristic
476C2×#131C22×C4311yescharacteristic
477#536C22×C4311yescharacteristic
478#536C22×C4311yescharacteristic, complemented
479C2×C4⋊Q8C22×C4311yescharacteristic, complemented
480C2×#124C22×C4311yescharacteristic
481#497—24no—
482#497—21no—
483#497—21no—
484#495—21no—
485#494—21no—
486#473—24no—
487#456—24no—
488#455—24no—
489#452—22no—
490#452—22no—
491#451—22no—
492#450—22no—
493C2×#108C22×C4311yescharacteristic, complemented
494C2×#104C22×C4311yescharacteristic
495C2×#104C22×C4311yescharacteristic
496C2×#104C22×C4311yescharacteristic, complemented
497#419C22×C4311yescharacteristic, complemented
498#418C22×C4311yescharacteristic
499#416C22×C4311yescharacteristic
500C2×#101C22×C4311yescharacteristic, complemented
501C2×#101C22×C4311yescharacteristic, complemented
502C2×#101C22×C4311yescharacteristic, complemented
503C2×#100C22×C4311yescharacteristic
504#408C22×C4311yescharacteristic
505#408C22×C4311yescharacteristic, complemented
506#405C22×C4311yescharacteristic, complemented
507C2×#97C22×C4311yescharacteristic, complemented
508#341C22×C4311yescharacteristic, complemented
509#339C22×C4311yescharacteristic, complemented
510C43#2580811yescharacteristic, direct product factor, Sylow
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—41no—
515H(5,𝔽2)—22no—
516H(5,𝔽2)—22no—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—41no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—21no—
523C2×#41—41no—
524C2×#41C23×C4311yescharacteristic
525C2×#41C23×C4311yescharacteristic
526C2×#41C23×C4311yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8C23×C4311yescharacteristic
530C22×Q8C23×C4311yescharacteristic
531C22×Q8C23×C4311yescharacteristic
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—41no—
535C22×D4C23×C4311yescharacteristic
536#137—28no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—41no—
546#137—41no—
547AGL(1,ℤ/8)—28no—
548AGL(1,ℤ/8)—22no—
549AGL(1,ℤ/8)—22no—
550#135—28no—
551#135—22no—
552#135—22no—
553C2×Q16—21no—
554C2×Q16—22no—
555C2×Q16—21no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16—22no—
564C2×Q16—41no—
565C2×Q16D4×C4311yescharacteristic
566C2×SD16—28no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—22no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16D4×C4311yescharacteristic
580C2×SD16D4×C4314yes—
581C2×SD16D4×C4311yescharacteristic
582C2×D8—21no—
583C2×D8D4×C4311yescharacteristic
584#131—22no—
585#131D4×C4314yes—
586C2×M16—21no—
587C2×M16C23×C4311yescharacteristic
588C2×M16C23×C4311yescharacteristic
589C2×M16C23×C4311yescharacteristic
590C2×M16C23×C4311yescharacteristic
591C22×C8—21no—
592C22×C8C23×C4311yescharacteristic
593C22×C8C23×C4311yescharacteristic
594C4⋊Q8—22no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597C4⋊Q8—22no—
598#124—22no—
599#124—21no—
600#124—21no—
601#124—22no—
602#123—41no—
603#123—41no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606#117C23×C4311yescharacteristic
607C2×C4⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C42C23×C4311yescharacteristic
610#108—22no—
611#104—22no—
612#104—22no—
613#104D4×C4314yes—
614#103—22no—
615#103D4×C4312yes—
616#102—22no—
617#102D4×C4312yes—
618#101—22no—
619#101—22no—
620#101—22no—
621#100—22no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#97—22no—
625#97—21no—
626C4×C8—21no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—24no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—42no—
645#41—42no—
646#41—44no—
647#41—42no—
648#41—42no—
649#41C2×D4×C4312yes—
650#41C2×D4×C4312yes—
651C2×Q8—21no—
652C2×Q8—24no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8C2×D4×C4311yescharacteristic
674C2×Q8C2×D4×C4312yes—
675C2×Q8C2×D4×C4311yescharacteristic
676C2×Q8C2×D4×C4311yescharacteristic
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—42no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4C2×D4×C4311yescharacteristic
695C2×D4C2×D4×C4311yescharacteristic
696C2×D4C2×D4×C4312yes—
697C2×D4C2×D4×C4311yescharacteristic
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4C24×C4311yescharacteristic
709Q16—24no—
710Q16—22no—
711Q16—44no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715Q16—42no—
716Q16—42no—
717Q16—42no—
718SD16—24no—
719SD16—24no—
720SD16—22no—
721SD16—24no—
722SD16—24no—
723SD16—22no—
724SD16—44no—
725SD16—42no—
726SD16—42no—
727SD16—42no—
728SD16—42no—
729D8—24no—
730D8—22no—
731M16—21no—
732M16—21no—
733M16—24no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16C2×D4×C4312yes—
739M16C2×D4×C4312yes—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—24no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8C2×D4×C4312yes—
748C2×C8C2×D4×C4311yescharacteristic
749C2×C8C2×D4×C4311yescharacteristic
750C2×C8C2×D4×C4312yes—
751C2×C8C2×D4×C4312yes—
752C4⋊C4—44no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4C2×D4×C4312yes—
756C22⋊C4—21no—
757C22⋊C4—44no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42C2×D4×C4312yes—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—44no—
768C23—41no—
769C23—41no—
770C23—82no—
771C23—162no—
772C23H(5,𝔽2)×C4311yescharacteristic
773Q8—21no—
774Q8—21no—
775Q8—22no—
776Q8—21no—
777Q8—22no—
778Q8—21no—
779Q8—21no—
780Q8—44no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8#127×C4312yes—
792D4—22no—
793D4—22no—
794D4—21no—
795D4—22no—
796D4—21no—
797D4—21no—
798D4—22no—
799D4—21no—
800D4—21no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4#127×C4312yes—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4C22×D4×C4311yescharacteristic
836C2×C4C22×D4×C4311yescharacteristic
837C2×C4C22×D4×C4311yescharacteristic
838C2×C4C22×D4×C4311yescharacteristic
839C2×C4C22×D4×C4311yescharacteristic
840C2×C4H(5,𝔽2)×C4311yescharacteristic
841C8—22no—
842C8—22no—
843C8—22no—
844C8—41no—
845C8—41no—
846C8#120×C4312yes—
847C8#120×C4312yes—
848C22—22no—
849C22—22no—
850C22—42no—
851C22—41no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—82no—
857C22—82no—
858C22—161no—
859C22—164no—
860C22C43×#53511yescharacteristic
861C22D42×C4311yescharacteristic
862C22D42×C4311yescharacteristic
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4C2×#120×C4311yescharacteristic
872C4C2×#127×C4311yescharacteristic
873C4D42×C4311yescharacteristic
874C4D42×C4311yescharacteristic
875C2—21no—
876C2—21no—
877C2—42no—
878C2—81no—
879C2—81no—
880C2—82no—
881C2C43×#243311yescharacteristic
882C2C43×#328912yes—
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#577C2
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. C43×#3156C2semidirect
3. C2×C43×#497C2semidirect
4. C2×C43×#473C2semidirect
5. C2×C43×#456C2semidirect
6. C2×C43×#455C2semidirect
7. C43×#3011C2semidirect
8. C43×#3009C2semidirect
9. C43×#2020C2semidirect
10. C43×#2019C2semidirect
11. C43×#2005C2semidirect
12. C43×#2003C2semidirect
13. C43×#1977C2semidirect
14. C43×#1975C2semidirect
15. C43×#1765C2semidirect
25. C2×#137×C43C22semidirect
30. C22×Q16×C43C22semidirect
31. C22×Q16×C43C22semidirect
37. C43×#536C22semidirect
38. C2×C4⋊Q8×C43C22semidirect
52. C2×#108×C43C22semidirect
55. C2×#104×C43C22semidirect
56. C43×#419C22semidirect
59. C2×#101×C43C22semidirect
60. C2×#101×C43C22semidirect
61. C2×#101×C43C22semidirect
64. C43×#408C22semidirect
65. C43×#405C22semidirect
66. C2×#97×C43C22semidirect
67. C43×#341C22semidirect
68. C43×#339C22semidirect
406. #25808C43direct (N × H)
435. #3156C2×C43semidirect
436. C2×#497C2×C43semidirect
437. C2×#473C2×C43semidirect
438. C2×#456C2×C43semidirect
439. C2×#455C2×C43semidirect
440. #3011C2×C43semidirect
441. #3009C2×C43semidirect
442. #2020C2×C43semidirect
443. #2019C2×C43semidirect
444. #2005C2×C43semidirect
445. #2003C2×C43semidirect
446. #1977C2×C43semidirect
447. #1975C2×C43semidirect
448. #1765C2×C43semidirect
466. C2×#137C22×C43semidirect
471. C22×Q16C22×C43semidirect
472. C22×Q16C22×C43semidirect
478. #536C22×C43semidirect
479. C2×C4⋊Q8C22×C43semidirect
493. C2×#108C22×C43semidirect
496. C2×#104C22×C43semidirect
497. #419C22×C43semidirect
500. C2×#101C22×C43semidirect
501. C2×#101C22×C43semidirect
502. C2×#101C22×C43semidirect
505. #408C22×C43semidirect
506. #405C22×C43semidirect
507. C2×#97C22×C43semidirect
508. #341C22×C43semidirect
509. #339C22×C43semidirect
510. C43#25808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5772
C43×#31562
C2×C43×#4972
C2×C43×#4732
C2×C43×#4562
C2×C43×#4552
C43×#30112
C43×#30092
C43×#20202
C43×#20192
C43×#20052
C43×#20032
C43×#19772
C43×#19752
C43×#17652
#2580843