Finite Group Databasebeta

← C43×#25809 #24945826

Subgroups — C43×#25809 #24945826

Order 11008.

1414 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#578C211yesmaximal, characteristic, complemented
2C43×#3154C211yesmaximal, characteristic, complemented
3C2×C43×#497C211yesmaximal, characteristic, complemented
4C2×C43×#471C211yesmaximal, characteristic, complemented
5C2×C43×#456C211yesmaximal, characteristic, complemented
6C2×C43×#454C211yesmaximal, characteristic, complemented
7C43×#3011C211yesmaximal, characteristic, complemented
8C43×#3010C211yesmaximal, characteristic, complemented
9C43×#2020C211yesmaximal, characteristic, complemented
10C43×#2019C211yesmaximal, characteristic, complemented
11C43×#2005C211yesmaximal, characteristic, complemented
12C43×#2004C211yesmaximal, characteristic, complemented
13C43×#1979C211yesmaximal, characteristic, complemented
14C43×#1975C211yesmaximal, characteristic, complemented
15C43×#1765C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C2×2−1+4×C43C2211yescharacteristic
18C43×#578—24no—
19C43×#578—24no—
20C2×#137×C43—21no—
21C2×#137×C43—21no—
22C2×#137×C43C2211yescharacteristic
23C2×#137×C43C2211yescharacteristic
24C2×#137×C43C2211yescharacteristic
25C2×#137×C43C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
28C2×#135×C43—21no—
29C2×#135×C43C2211yescharacteristic
30C22×Q16×C43—21no—
31C22×Q16×C43C2211yescharacteristic
32C22×Q16×C43C2211yescharacteristic
33C22×SD16×C43C2211yescharacteristic
34C22×SD16×C43C2211yescharacteristic
35C2×#131×C43C2211yescharacteristic
36C43×#536C2211yescharacteristic
37C43×#535C2211yescharacteristic
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×#124×C43C2211yescharacteristic
40C43×#497—21no—
41C43×#497—24no—
42C43×#496—21no—
43C43×#495—21no—
44C43×#492—21no—
45C43×#471—24no—
46C43×#456—24no—
47C43×#454—24no—
48C43×#452—22no—
49C43×#451—22no—
50C43×#449—22no—
51C43×#448—22no—
52C2×#108×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C2×#104×C43C2211yescharacteristic
56C43×#419C2211yescharacteristic
57C43×#419C2211yescharacteristic
58C43×#416C2211yescharacteristic
59C2×#101×C43C2211yescharacteristic
60C2×#101×C43C2211yescharacteristic
61C2×#101×C43C2211yescharacteristic
62C2×#100×C43C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C2×#97×C43C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C43×#339C2211yescharacteristic
692−1+4×C43—22no—
702−1+4×C43—22no—
712−1+4×C43—22no—
722−1+4×C43—22no—
732−1+4×C43—22no—
742−1+4×C43—22no—
752−1+4×C43—41no—
762−1+4×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—41no—
82C2×#41×C43—41no—
83C2×#41×C43C2311yescharacteristic
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C22×Q8×C43—21no—
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43—21no—
90C22×Q8×C43C2311yescharacteristic
91C22×Q8×C43C2311yescharacteristic
92C22×Q8×C43C2311yescharacteristic
93C22×D4×C43C2311yescharacteristic
94#137×C43—28no—
95#137×C43—28no—
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—
104AGL(1,ℤ/8)×C43—22no—
105AGL(1,ℤ/8)×C43—22no—
106AGL(1,ℤ/8)×C43—22no—
107AGL(1,ℤ/8)×C43—41no—
108#135×C43—28no—
109#135×C43—22no—
110#135×C43—22no—
111C2×Q16×C43—28no—
112C2×Q16×C43—21no—
113C2×Q16×C43—21no—
114C2×Q16×C43—22no—
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43—21no—
119C2×Q16×C43—22no—
120C2×Q16×C43—22no—
121C2×Q16×C43—41no—
122C2×Q16×C43D411yescharacteristic
123C2×Q16×C43D414yescomplemented
124C2×SD16×C43—21no—
125C2×SD16×C43—21no—
126C2×SD16×C43—22no—
127C2×SD16×C43—21no—
128C2×SD16×C43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—22no—
132C2×SD16×C43—21no—
133C2×SD16×C43—22no—
134C2×SD16×C43—22no—
135C2×SD16×C43—21no—
136C2×SD16×C43—41no—
137C2×SD16×C43D411yescharacteristic
138C2×SD16×C43D411yescharacteristic
139C2×D8×C43—21no—
140C2×D8×C43—21no—
141C2×D8×C43D411yescharacteristic
142#131×C43—22no—
143#131×C43D414yescomplemented
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—22no—
155#127×C43—21no—
156#124×C43—22no—
157#124×C43—21no—
158#124×C43—21no—
159#124×C43—22no—
160#123×C43—41no—
161C22⋊Q8×C43—22no—
162#121×C43—22no—
163#120×C43—41no—
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×C43D414yescomplemented
172#103×C43—22no—
173#103×C43—22no—
174#103×C43D412yes—
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—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—24no—
189#41×C43—24no—
190#41×C43—21no—
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—42no—
199#41×C43—42no—
200#41×C43—44no—
201#41×C43—44no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—44no—
205#41×C43—44no—
206#41×C43—42no—
207#41×C43—42no—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43—24no—
213C2×Q8×C43—24no—
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—21no—
228C2×Q8×C43—41no—
229C2×Q8×C43—41no—
230C2×Q8×C43—42no—
231C2×Q8×C43—42no—
232C2×Q8×C43—42no—
233C2×Q8×C43—42no—
234C2×Q8×C43—42no—
235C2×Q8×C43—42no—
236C2×Q8×C43C2×D411yescharacteristic
237C2×Q8×C43C2×D412yes—
238C2×Q8×C43C2×D411yescharacteristic
239C2×Q8×C43C2×D412yes—
240C2×Q8×C43C2×D411yescharacteristic
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—21no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43—21no—
250C2×D4×C43—41no—
251C2×D4×C43—41no—
252C2×D4×C43—42no—
253C2×D4×C43C2×D411yescharacteristic
254C2×D4×C43C2×D411yescharacteristic
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×C43—41no—
267C22×C4×C43C2411yescharacteristic
268Q16×C43—24no—
269Q16×C43—24no—
270Q16×C43—22no—
271Q16×C43—24no—
272Q16×C43—24no—
273Q16×C43—44no—
274Q16×C43—42no—
275Q16×C43—42no—
276SD16×C43—24no—
277SD16×C43—24no—
278SD16×C43—22no—
279SD16×C43—22no—
280SD16×C43—42no—
281SD16×C43—44no—
282SD16×C43—42no—
283SD16×C43—42no—
284SD16×C43—42no—
285SD16×C43—42no—
286SD16×C43—42no—
287D8×C43—22no—
288D8×C43—42no—
289D8×C43—42no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—24no—
293M16×C43—21no—
294M16×C43—21no—
295M16×C43—21no—
296M16×C43—21no—
297M16×C43C2×D412yes—
298M16×C43C2×D412yes—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—21no—
303C2×C8×C43—24no—
304C2×C8×C43—21no—
305C2×C8×C43—21no—
306C2×C8×C43C2×D412yes—
307C2×C8×C43C2×D411yescharacteristic
308C2×C8×C43C2×D411yescharacteristic
309C2×C8×C43C2×D412yes—
310C2×C8×C43C2×D412yes—
311C4⋊C4×C43—44no—
312C4⋊C4×C43—42no—
313C4⋊C4×C43C2×D412yes—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—42no—
316C22⋊C4×C43—44no—
317C22⋊C4×C43—42no—
318C42×C43—21no—
319C42×C43—21no—
320C42×C43C2×D412yes—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—82no—
328C23×C43H(5,𝔽2)11yescharacteristic
329Q8×C43—21no—
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—21no—
333Q8×C43—21no—
334Q8×C43—22no—
335Q8×C43—21no—
336Q8×C43—22no—
337Q8×C43—21no—
338Q8×C43—44no—
339Q8×C43—44no—
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#12712yes—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—21no—
352D4×C43—21no—
353D4×C43—21no—
354D4×C43—21no—
355D4×C43—21no—
356D4×C43—44no—
357D4×C43—44no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—162no—
367D4×C43#12712yes—
368C2×C4×C43—21no—
369C2×C4×C43—22no—
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—44no—
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#25809C4311yesmaximal, characteristic, direct product factor, Sylow
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—42no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—82no—
415C22×C43—81no—
416C22×C43—82no—
417C22×C43—161no—
418C22×C43#53511yescharacteristic
419C22×C43D4211yescharacteristic
420C22×C43D4211yescharacteristic
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—42no—
425C4×C43—41no—
426C4×C43—41no—
427C4×C43—42no—
428C4×C43—81no—
429C4×C43C2×#12011yescharacteristic
430C4×C43C2×#12711yescharacteristic
431C4×C43D4211yescharacteristic
432C4×C43D4211yescharacteristic
433C2×#578C2×C4311yescharacteristic, complemented
434#3154C2×C4311yescharacteristic, complemented
435C2×#497C2×C4311yescharacteristic, complemented
436C2×#471C2×C4311yescharacteristic, complemented
437C2×#456C2×C4311yescharacteristic, complemented
438C2×#454C2×C4311yescharacteristic, complemented
439#3011C2×C4311yescharacteristic, complemented
440#3010C2×C4311yescharacteristic, complemented
441#2020C2×C4311yescharacteristic, complemented
442#2019C2×C4311yescharacteristic, complemented
443#2005C2×C4311yescharacteristic, complemented
444#2004C2×C4311yescharacteristic, complemented
445#1979C2×C4311yescharacteristic, complemented
446#1975C2×C4311yescharacteristic, complemented
447#1765C2×C4311yescharacteristic, complemented
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—42no—
451C2×C43—81no—
452C2×C43—81no—
453C2×C43—161no—
454C2×C43#243311yescharacteristic
455C2×C43#328912yes—
456C2×2−1+4C22×C4311yescharacteristic
457C2×2−1+4C22×C4311yescharacteristic
458#578—24no—
459#578—24no—
460C2×#137—21no—
461C2×#137—21no—
462C2×#137C22×C4311yescharacteristic
463C2×#137C22×C4311yescharacteristic
464C2×#137C22×C4311yescharacteristic
465C2×#137C22×C4311yescharacteristic
466C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
467C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
468C2×#135—21no—
469C2×#135C22×C4311yescharacteristic
470C22×Q16—21no—
471C22×Q16C22×C4311yescharacteristic
472C22×Q16C22×C4311yescharacteristic
473C22×SD16C22×C4311yescharacteristic
474C22×SD16C22×C4311yescharacteristic
475C2×#131C22×C4311yescharacteristic
476#536C22×C4311yescharacteristic
477#535C22×C4311yescharacteristic
478C2×C4⋊Q8C22×C4311yescharacteristic
479C2×#124C22×C4311yescharacteristic
480#497—21no—
481#497—24no—
482#496—21no—
483#495—21no—
484#492—21no—
485#471—24no—
486#456—24no—
487#454—24no—
488#452—22no—
489#451—22no—
490#449—22no—
491#448—22no—
492C2×#108C22×C4311yescharacteristic
493C2×#104C22×C4311yescharacteristic
494C2×#104C22×C4311yescharacteristic
495C2×#104C22×C4311yescharacteristic
496#419C22×C4311yescharacteristic
497#419C22×C4311yescharacteristic
498#416C22×C4311yescharacteristic
499C2×#101C22×C4311yescharacteristic
500C2×#101C22×C4311yescharacteristic
501C2×#101C22×C4311yescharacteristic
502C2×#100C22×C4311yescharacteristic
503#408C22×C4311yescharacteristic
504#408C22×C4311yescharacteristic
505#405C22×C4311yescharacteristic
506C2×#97C22×C4311yescharacteristic
507#341C22×C4311yescharacteristic
508#339C22×C4311yescharacteristic
509C43#2580911yescharacteristic, direct product factor, Sylow
5102−1+4—22no—
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—22no—
5162−1+4—41no—
5172−1+4—41no—
518C2×#41—21no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C4311yescharacteristic
525C2×#41C23×C4311yescharacteristic
526C2×#41C23×C4311yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8C23×C4311yescharacteristic
532C22×Q8C23×C4311yescharacteristic
533C22×Q8C23×C4311yescharacteristic
534C22×D4C23×C4311yescharacteristic
535#137—28no—
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—41no—
545AGL(1,ℤ/8)—22no—
546AGL(1,ℤ/8)—22no—
547AGL(1,ℤ/8)—22no—
548AGL(1,ℤ/8)—41no—
549#135—28no—
550#135—22no—
551#135—22no—
552C2×Q16—28no—
553C2×Q16—21no—
554C2×Q16—21no—
555C2×Q16—22no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—21no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—41no—
563C2×Q16D4×C4311yescharacteristic
564C2×Q16D4×C4314yescomplemented
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—22no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×SD16D4×C4311yescharacteristic
579C2×SD16D4×C4311yescharacteristic
580C2×D8—21no—
581C2×D8—21no—
582C2×D8D4×C4311yescharacteristic
583#131—22no—
584#131D4×C4314yescomplemented
585C2×M16—21no—
586C2×M16C23×C4311yescharacteristic
587C2×M16C23×C4311yescharacteristic
588C2×M16C23×C4311yescharacteristic
589C2×M16C23×C4311yescharacteristic
590C22×C8—21no—
591C22×C8C23×C4311yescharacteristic
592C22×C8C23×C4311yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—21no—
595C4⋊Q8—22no—
596#127—21no—
597#124—22no—
598#124—21no—
599#124—21no—
600#124—22no—
601#123—41no—
602C22⋊Q8—22no—
603#121—22no—
604#120—41no—
605#117C23×C4311yescharacteristic
606C2×C4⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C42C23×C4311yescharacteristic
609#108—22no—
610#104—22no—
611#104—22no—
612#104D4×C4314yescomplemented
613#103—22no—
614#103—22no—
615#103D4×C4312yes—
616#102D4×C4312yes—
617#101—22no—
618#101—22no—
619#101—22no—
620#100—22no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623#97—22no—
624#97—21no—
625C4×C8—21no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—24no—
630#41—24no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—42no—
640#41—42no—
641#41—44no—
642#41—44no—
643#41—42no—
644#41—42no—
645#41—44no—
646#41—44no—
647#41—42no—
648#41—42no—
649#41C2×D4×C4312yes—
650#41C2×D4×C4312yes—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—24no—
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—41no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8C2×D4×C4311yescharacteristic
678C2×Q8C2×D4×C4312yes—
679C2×Q8C2×D4×C4311yescharacteristic
680C2×Q8C2×D4×C4312yes—
681C2×Q8C2×D4×C4311yescharacteristic
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—42no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4C2×D4×C4311yescharacteristic
695C2×D4C2×D4×C4311yescharacteristic
696C2×D4C2×D4×C4311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4C24×C4311yescharacteristic
709Q16—24no—
710Q16—24no—
711Q16—22no—
712Q16—24no—
713Q16—24no—
714Q16—44no—
715Q16—42no—
716Q16—42no—
717SD16—24no—
718SD16—24no—
719SD16—22no—
720SD16—22no—
721SD16—42no—
722SD16—44no—
723SD16—42no—
724SD16—42no—
725SD16—42no—
726SD16—42no—
727SD16—42no—
728D8—22no—
729D8—42no—
730D8—42no—
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⋊C4C2×D4×C4312yes—
755C22⋊C4—21no—
756C22⋊C4—44no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42C2×D4×C4312yes—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—82no—
769C23H(5,𝔽2)×C4311yescharacteristic
770Q8—21no—
771Q8—22no—
772Q8—22no—
773Q8—21no—
774Q8—21no—
775Q8—22no—
776Q8—21no—
777Q8—22no—
778Q8—21no—
779Q8—44no—
780Q8—44no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#127×C4312yes—
790D4—22no—
791D4—22no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—44no—
798D4—44no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—162no—
808D4#127×C4312yes—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—44no—
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×C4C22×D4×C4311yescharacteristic
835C2×C4C22×D4×C4311yescharacteristic
836C2×C4C22×D4×C4311yescharacteristic
837C2×C4C22×D4×C4311yescharacteristic
838C2×C4C22×D4×C4311yescharacteristic
839C2×C4H(5,𝔽2)×C4311yescharacteristic
840C8—22no—
841C8—22no—
842C8—22no—
843C8—41no—
844C8—41no—
845C8#120×C4312yes—
846C8#120×C4312yes—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—82no—
855C22—81no—
856C22—82no—
857C22—161no—
858C22C43×#53511yescharacteristic
859C22D42×C4311yescharacteristic
860C22D42×C4311yescharacteristic
861C4—22no—
862C4—42no—
863C4—41no—
864C4—42no—
865C4—41no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4C2×#120×C4311yescharacteristic
870C4C2×#127×C4311yescharacteristic
871C4D42×C4311yescharacteristic
872C4D42×C4311yescharacteristic
873C2—21no—
874C2—21no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2—161no—
879C2C43×#243311yescharacteristic
880C2C43×#328912yes—
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×#578C2semidirect
2. C43×#3154C2semidirect
3. C2×C43×#497C2semidirect
4. C2×C43×#471C2semidirect
5. C2×C43×#456C2semidirect
6. C2×C43×#454C2semidirect
7. C43×#3011C2semidirect
8. C43×#3010C2semidirect
9. C43×#2020C2semidirect
10. C43×#2019C2semidirect
11. C43×#2005C2semidirect
12. C43×#2004C2semidirect
13. C43×#1979C2semidirect
14. C43×#1975C2semidirect
15. C43×#1765C2semidirect
123. C2×Q16×C43D4semidirect
143. #131×C43D4semidirect
171. #104×C43D4semidirect
406. #25809C43direct (N × H)
433. C2×#578C2×C43semidirect
434. #3154C2×C43semidirect
435. C2×#497C2×C43semidirect
436. C2×#471C2×C43semidirect
437. C2×#456C2×C43semidirect
438. C2×#454C2×C43semidirect
439. #3011C2×C43semidirect
440. #3010C2×C43semidirect
441. #2020C2×C43semidirect
442. #2019C2×C43semidirect
443. #2005C2×C43semidirect
444. #2004C2×C43semidirect
445. #1979C2×C43semidirect
446. #1975C2×C43semidirect
447. #1765C2×C43semidirect
509. C43#25809direct (N × H)
564. C2×Q16D4×C43semidirect
584. #131D4×C43semidirect
612. #104D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5782
C43×#31542
C2×C43×#4972
C2×C43×#4712
C2×C43×#4562
C2×C43×#4542
C43×#30112
C43×#30102
C43×#20202
C43×#20192
C43×#20052
C43×#20042
C43×#19792
C43×#19752
C43×#17652
#2580943