Finite Group Databasebeta

← C43×#24474 #24944491

Subgroups — C43×#24474 #24944491

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3586C211yesmaximal, characteristic
2C43×#3069C211yesmaximal, characteristic, complemented
3C43×#3039C211yesmaximal, characteristic, complemented
4C43×#3022C211yesmaximal, characteristic, complemented
5C2×C43×#456C211yesmaximal, characteristic, complemented
6C43×#2901C211yesmaximal, characteristic, complemented
7C43×#2050C211yesmaximal, characteristic, complemented
8C43×#2049C211yesmaximal, characteristic, complemented
9C43×#2009C211yesmaximal, characteristic, complemented
10C43×#2005C211yesmaximal, characteristic, complemented
11C43×#1906C211yesmaximal, characteristic, complemented
12C43×#1902C211yesmaximal, characteristic, complemented
13C43×#1902C211yesmaximal, characteristic, complemented
14C43×#1861C211yesmaximal, characteristic, complemented
15C43×#1796C211yesmaximal, characteristic, complemented
16C43×#585C2211yescharacteristic
17C2×2−1+4×C43C2211yescharacteristic
18C43×#578—22no—
19C43×#578—22no—
20C43×#577—22no—
21C43×#577—22no—
22C43×#575—22no—
23C43×#575C2211yescharacteristic
24C43×#575C2211yescharacteristic
25C2×#137×C43—22no—
26C2×#137×C43C2211yescharacteristic
27C2×#137×C43C2211yescharacteristic
28C2×#137×C43C2211yescharacteristic
29C2×#137×C43C2211yescharacteristic
30C2×#137×C43C2211yescharacteristic, complemented
31C43×#568C2211yescharacteristic
32C43×#568C2211yescharacteristic
33C43×#536C2211yescharacteristic
34C2×C4⋊Q8×C43C2211yescharacteristic, complemented
35C4×#41×C43C2211yescharacteristic
36C43×#473—22no—
37C43×#471—22no—
38C43×#462—22no—
39C43×#461—22no—
40C43×#456—22no—
41C43×#456—22no—
42C43×#456—22no—
43C43×#455—22no—
44C43×#430C2211yescharacteristic, complemented
45C43×#423C2211yescharacteristic, complemented
46C43×#421—22no—
47C43×#421C2211yescharacteristic
48C43×#421C2211yescharacteristic
49C43×#421C2211yescharacteristic
50C43×#421C2211yescharacteristic
51C2×#104×C43—22no—
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic, complemented
55C43×#419C2211yescharacteristic, complemented
56C43×#419C2211yescharacteristic, complemented
57C43×#419C2211yescharacteristic, complemented
58C43×#413C2211yescharacteristic
59C43×#413C2211yescharacteristic, complemented
60C2×#101×C43C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C43×#410C2211yescharacteristic, complemented
63C43×#344C2211yescharacteristic, complemented
64C43×#344C2211yescharacteristic, complemented
65C43×#339C2211yescharacteristic, complemented
66C43×#338C2211yescharacteristic, complemented
672−1+4×C43—22no—
682−1+4×C43—22no—
692−1+4×C43—21no—
702−1+4×C43—21no—
712−1+4×C43—22no—
722−1+4×C43—41no—
732−1+4×C43D412yes—
74H(5,𝔽2)×C43—21no—
75H(5,𝔽2)×C43—21no—
76H(5,𝔽2)×C43—41no—
77H(5,𝔽2)×C43D412yes—
78C2×#41×C43—22no—
79C2×#41×C43—22no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—41no—
83C2×#41×C43—41no—
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C2×#41×C43C2311yescharacteristic
87C2×#41×C43C2311yescharacteristic
88C22×Q8×C43—21no—
89C22×Q8×C43—21no—
90C22×Q8×C43C2311yescharacteristic
91C22×Q8×C43C2311yescharacteristic
92#137×C43—24no—
93#137×C43—24no—
94#137×C43—24no—
95#137×C43—22no—
96#137×C43—22no—
97#137×C43—21no—
98#137×C43—22no—
99#137×C43—21no—
100#137×C43—21no—
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—22no—
104#137×C43—22no—
105#137×C43—22no—
106#137×C43—22no—
107#137×C43—41no—
108#137×C43D412yes—
109AGL(1,ℤ/8)×C43—24no—
110AGL(1,ℤ/8)×C43—21no—
111AGL(1,ℤ/8)×C43—21no—
112AGL(1,ℤ/8)×C43—21no—
113AGL(1,ℤ/8)×C43D412yes—
114#135×C43—24no—
115#135×C43—24no—
116#135×C43—22no—
117#135×C43—22no—
118C2×Q16×C43—24no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×Q16×C43—21no—
122C2×Q16×C43—21no—
123C2×Q16×C43D412yes—
124C2×SD16×C43—24no—
125C2×SD16×C43—21no—
126C2×SD16×C43—21no—
127C2×SD16×C43—21no—
128C2×SD16×C43—21no—
129C2×SD16×C43D412yes—
130#131×C43—22no—
131#131×C43—22no—
132#131×C43—22no—
133#131×C43—41no—
134C2×M16×C43—22no—
135C2×M16×C43—22no—
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C2×M16×C43C2311yescharacteristic
142C4⋊Q8×C43—22no—
143C4⋊Q8×C43—21no—
144C4⋊Q8×C43—21no—
145C4⋊Q8×C43—21no—
146#124×C43—21no—
147#123×C43—41no—
148C22⋊Q8×C43—41no—
149C4×Q8×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—41no—
152#117×C43—21no—
153#117×C43C2311yescharacteristic
154#117×C43C2311yescharacteristic
155C2×C4⋊C4×C43—41no—
156C2×C42×C43—21no—
157C2×C42×C43C2311yescharacteristic
158#108×C43—22no—
159C4⋊C8×C43—22no—
160#104×C43—22no—
161#104×C43—22no—
162#104×C43—22no—
163#104×C43—22no—
164#104×C43—21no—
165#104×C43—21no—
166#104×C43—21no—
167#104×C43—21no—
168#104×C43D412yes—
169#104×C43D412yes—
170#103×C43—22no—
171#103×C43—22no—
172#103×C43—41no—
173#101×C43—21no—
174#101×C43—21no—
175#101×C43—22no—
176#101×C43—22no—
177#100×C43—21no—
178#100×C43—21no—
179#99×C43—41no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—24no—
185#41×C43—22no—
186#41×C43—22no—
187#41×C43—22no—
188#41×C43—22no—
189#41×C43—21no—
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—42no—
198#41×C43—42no—
199#41×C43—42no—
200#41×C43—42no—
201#41×C43—42no—
202#41×C43—44no—
203#41×C43—42no—
204#41×C43—41no—
205#41×C43—41no—
206#41×C43—44no—
207#41×C43—42no—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210#41×C43C2×D412yes—
211#41×C43C2×D412yes—
212C2×Q8×C43—21no—
213C2×Q8×C43—24no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
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—41no—
227C2×Q8×C43—42no—
228C2×Q8×C43—42no—
229C2×Q8×C43—41no—
230C2×Q8×C43—42no—
231C2×Q8×C43C2×D411yescharacteristic
232C2×Q8×C43C2×D411yescharacteristic
233C2×Q8×C43C2×D412yes—
234C2×Q8×C43C2×D411yescharacteristic
235C2×Q8×C43#4111yescharacteristic
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—22no—
241C2×D4×C43—22no—
242C2×D4×C43—41no—
243C2×D4×C43—42no—
244C2×D4×C43—42no—
245C2×D4×C43—42no—
246C2×D4×C43—41no—
247C2×D4×C43C2×D411yescharacteristic
248C2×D4×C43C2×D411yescharacteristic
249C2×D4×C43C2×D411yescharacteristic
250C2×D4×C43#4111yescharacteristic
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—41no—
259C22×C4×C43—41no—
260C22×C4×C43—41no—
261C22×C4×C43—42no—
262C22×C4×C43C2411yescharacteristic
263Q16×C43—24no—
264Q16×C43—22no—
265Q16×C43—22no—
266Q16×C43—24no—
267Q16×C43—42no—
268Q16×C43—42no—
269Q16×C43—42no—
270SD16×C43—24no—
271SD16×C43—22no—
272SD16×C43—22no—
273SD16×C43—22no—
274SD16×C43—22no—
275SD16×C43—24no—
276SD16×C43—42no—
277SD16×C43—42no—
278SD16×C43—42no—
279D8×C43—22no—
280D8×C43—22no—
281M16×C43—24no—
282M16×C43—21no—
283M16×C43—21no—
284M16×C43—21no—
285M16×C43—21no—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—42no—
293M16×C43C2×D412yes—
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—42no—
302C2×C8×C43C2×D412yes—
303C4⋊C4×C43—21no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—42no—
306C4⋊C4×C43—42no—
307C4⋊C4×C43—41no—
308C4⋊C4×C43—42no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—41no—
312C22⋊C4×C43—42no—
313C42×C43—21no—
314C42×C43—21no—
315C42×C43—21no—
316C42×C43—41no—
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—42no—
324C23×C43H(5,𝔽2)11yescharacteristic
325Q8×C43—21no—
326Q8×C43—21no—
327Q8×C43—21no—
328Q8×C43—22no—
329Q8×C43—21no—
330Q8×C43—21no—
331Q8×C43—21no—
332Q8×C43—22no—
333Q8×C43—42no—
334Q8×C43—44no—
335Q8×C43—41no—
336Q8×C43—41no—
337Q8×C43—41no—
338Q8×C43—41no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43#12012yes—
342Q8×C43#12112yes—
343D4×C43—22no—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—21no—
348D4×C43—21no—
349D4×C43—21no—
350D4×C43—21no—
351D4×C43—21no—
352D4×C43—21no—
353D4×C43—42no—
354D4×C43—42no—
355D4×C43—42no—
356D4×C43—44no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43#12012yes—
362D4×C43#12112yes—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—22no—
373C2×C4×C43—21no—
374C2×C4×C43—42no—
375C2×C4×C43—42no—
376C2×C4×C43—42no—
377C2×C4×C43—42no—
378C2×C4×C43—44no—
379C2×C4×C43—44no—
380C2×C4×C43—41no—
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—82no—
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C2×#4111yescharacteristic
397C2×C4×C43H(5,𝔽2)11yescharacteristic
398C8×C43—22no—
399C8×C43—22no—
400C8×C43—22no—
401C8×C43—41no—
402C8×C43—41no—
403C8×C43—41no—
404#24474C4311yesmaximal, characteristic, direct product factor, Sylow
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—162no—
415C22×C43#53411yescharacteristic
416C22×C43D4211yescharacteristic
417C22×C43#54611yescharacteristic
418C4×C43—22no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—41no—
422C4×C43—41no—
423C4×C43—42no—
424C4×C43—41no—
425C4×C43—81no—
426C4×C43—81no—
427C4×C43—81no—
428C4×C43C2×#12011yescharacteristic
429C4×C43C2×#12111yescharacteristic
430C4×C43D4211yescharacteristic
431C4×C43#54611yescharacteristic
432#3586C2×C4311yescharacteristic
433#3069C2×C4311yescharacteristic, complemented
434#3039C2×C4311yescharacteristic, complemented
435#3022C2×C4311yescharacteristic, complemented
436C2×#456C2×C4311yescharacteristic, complemented
437#2901C2×C4311yescharacteristic, complemented
438#2050C2×C4311yescharacteristic, complemented
439#2049C2×C4311yescharacteristic, complemented
440#2009C2×C4311yescharacteristic, complemented
441#2005C2×C4311yescharacteristic, complemented
442#1906C2×C4311yescharacteristic, complemented
443#1902C2×C4311yescharacteristic, complemented
444#1902C2×C4311yescharacteristic, complemented
445#1861C2×C4311yescharacteristic, complemented
446#1796C2×C4311yescharacteristic, complemented
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—42no—
451C2×C43—42no—
452C2×C43—81no—
453C2×C43—81no—
454C2×C43#241011yescharacteristic
455#585C22×C4311yescharacteristic
456C2×2−1+4C22×C4311yescharacteristic
457#578—22no—
458#578—22no—
459#577—22no—
460#577—22no—
461#575—22no—
462#575C22×C4311yescharacteristic
463#575C22×C4311yescharacteristic
464C2×#137—22no—
465C2×#137C22×C4311yescharacteristic
466C2×#137C22×C4311yescharacteristic
467C2×#137C22×C4311yescharacteristic
468C2×#137C22×C4311yescharacteristic
469C2×#137C22×C4311yescharacteristic, complemented
470#568C22×C4311yescharacteristic
471#568C22×C4311yescharacteristic
472#536C22×C4311yescharacteristic
473C2×C4⋊Q8C22×C4311yescharacteristic, complemented
474C4×#41C22×C4311yescharacteristic
475#473—22no—
476#471—22no—
477#462—22no—
478#461—22no—
479#456—22no—
480#456—22no—
481#456—22no—
482#455—22no—
483#430C22×C4311yescharacteristic, complemented
484#423C22×C4311yescharacteristic, complemented
485#421—22no—
486#421C22×C4311yescharacteristic
487#421C22×C4311yescharacteristic
488#421C22×C4311yescharacteristic
489#421C22×C4311yescharacteristic
490C2×#104—22no—
491C2×#104C22×C4311yescharacteristic
492C2×#104C22×C4311yescharacteristic
493C2×#104C22×C4311yescharacteristic, complemented
494#419C22×C4311yescharacteristic, complemented
495#419C22×C4311yescharacteristic, complemented
496#419C22×C4311yescharacteristic, complemented
497#413C22×C4311yescharacteristic
498#413C22×C4311yescharacteristic, complemented
499C2×#101C22×C4311yescharacteristic, complemented
500C2×#101C22×C4311yescharacteristic, complemented
501#410C22×C4311yescharacteristic, complemented
502#344C22×C4311yescharacteristic, complemented
503#344C22×C4311yescharacteristic, complemented
504#339C22×C4311yescharacteristic, complemented
505#338C22×C4311yescharacteristic, complemented
506C43#2447411yescharacteristic, direct product factor, Sylow
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C4312yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C4312yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C4311yescharacteristic
525C2×#41C23×C4311yescharacteristic
526C2×#41C23×C4311yescharacteristic
527C2×#41C23×C4311yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C4311yescharacteristic
531C22×Q8C23×C4311yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C4312yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C4312yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C4312yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C4312yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C4311yescharacteristic
577C2×M16C23×C4311yescharacteristic
578C2×M16C23×C4311yescharacteristic
579C2×M16C23×C4311yescharacteristic
580C2×M16C23×C4311yescharacteristic
581C2×M16C23×C4311yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C4311yescharacteristic
594#117C23×C4311yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C4311yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C4312yes—
609#104D4×C4312yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C4312yes—
649#41C2×D4×C4312yes—
650#41C2×D4×C4312yes—
651#41C2×D4×C4312yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
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—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C4311yescharacteristic
672C2×Q8C2×D4×C4311yescharacteristic
673C2×Q8C2×D4×C4312yes—
674C2×Q8C2×D4×C4311yescharacteristic
675C2×Q8#41×C4311yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C4311yescharacteristic
688C2×D4C2×D4×C4311yescharacteristic
689C2×D4C2×D4×C4311yescharacteristic
690C2×D4#41×C4311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C4311yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C4312yes—
734M16C2×D4×C4312yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C4312yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C4311yescharacteristic
758C42C2×D4×C4311yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C4311yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C4312yes—
782Q8#121×C4312yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C4312yes—
802D4#121×C4312yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
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—82no—
832C2×C4C22×D4×C4311yescharacteristic
833C2×C4C22×D4×C4311yescharacteristic
834C2×C4C22×D4×C4311yescharacteristic
835C2×C4C22×D4×C4311yescharacteristic
836C2×C4C2×#41×C4311yescharacteristic
837C2×C4H(5,𝔽2)×C4311yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22C43×#53411yescharacteristic
855C22D42×C4311yescharacteristic
856C22C43×#54611yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C4311yescharacteristic
868C4C2×#121×C4311yescharacteristic
869C4D42×C4311yescharacteristic
870C4C43×#54611yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C43×#241011yescharacteristic
subgroupG/H
center, socleC2×C43#2410
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3586C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C43×#3069C2semidirect
3. C43×#3039C2semidirect
4. C43×#3022C2semidirect
5. C2×C43×#456C2semidirect
6. C43×#2901C2semidirect
7. C43×#2050C2semidirect
8. C43×#2049C2semidirect
9. C43×#2009C2semidirect
10. C43×#2005C2semidirect
11. C43×#1906C2semidirect
12. C43×#1902C2semidirect
13. C43×#1902C2semidirect
14. C43×#1861C2semidirect
15. C43×#1796C2semidirect
30. C2×#137×C43C22semidirect
34. C2×C4⋊Q8×C43C22semidirect
44. C43×#430C22semidirect
45. C43×#423C22semidirect
54. C2×#104×C43C22semidirect
55. C43×#419C22semidirect
56. C43×#419C22semidirect
57. C43×#419C22semidirect
59. C43×#413C22semidirect
60. C2×#101×C43C22semidirect
61. C2×#101×C43C22semidirect
62. C43×#410C22semidirect
63. C43×#344C22semidirect
64. C43×#344C22semidirect
65. C43×#339C22semidirect
66. C43×#338C22semidirect
404. #24474C43direct (N × H)
433. #3069C2×C43semidirect
434. #3039C2×C43semidirect
435. #3022C2×C43semidirect
436. C2×#456C2×C43semidirect
437. #2901C2×C43semidirect
438. #2050C2×C43semidirect
439. #2049C2×C43semidirect
440. #2009C2×C43semidirect
441. #2005C2×C43semidirect
442. #1906C2×C43semidirect
443. #1902C2×C43semidirect
444. #1902C2×C43semidirect
445. #1861C2×C43semidirect
446. #1796C2×C43semidirect
469. C2×#137C22×C43semidirect
473. C2×C4⋊Q8C22×C43semidirect
483. #430C22×C43semidirect
484. #423C22×C43semidirect
493. C2×#104C22×C43semidirect
494. #419C22×C43semidirect
495. #419C22×C43semidirect
496. #419C22×C43semidirect
498. #413C22×C43semidirect
499. C2×#101C22×C43semidirect
500. C2×#101C22×C43semidirect
501. #410C22×C43semidirect
502. #344C22×C43semidirect
503. #344C22×C43semidirect
504. #339C22×C43semidirect
505. #338C22×C43semidirect
506. C43#24474direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35862
C43×#30692
C43×#30392
C43×#30222
C2×C43×#4562
C43×#29012
C43×#20502
C43×#20492
C43×#20092
C43×#20052
C43×#19062
C43×#19022
C43×#18612
C43×#17962
#2447443