Finite Group Databasebeta

← C43×#24475 #24944492

Subgroups — C43×#24475 #24944492

Order 11008.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3585C211yesmaximal, characteristic
2C43×#3069C211yesmaximal, characteristic, complemented
3C43×#3040C211yesmaximal, characteristic, complemented
4C43×#3022C211yesmaximal, characteristic, complemented
5C2×C43×#455C211yesmaximal, characteristic, complemented
6C43×#2901C211yesmaximal, characteristic, complemented
7C43×#2050C211yesmaximal, characteristic, complemented
8C43×#2048C211yesmaximal, characteristic, complemented
9C43×#2009C211yesmaximal, characteristic, complemented
10C43×#2003C211yesmaximal, characteristic, complemented
11C43×#1906C211yesmaximal, characteristic, complemented
12C43×#1903C211yesmaximal, characteristic, complemented
13C43×#1902C211yesmaximal, characteristic, complemented
14C43×#1861C211yesmaximal, characteristic, complemented
15C43×#1795C211yesmaximal, characteristic, complemented
16C43×#585C2211yescharacteristic
17C2×H(5,𝔽2)×C43C2211yescharacteristic
18C43×#577—22no—
19C43×#577—22no—
20C43×#576—22no—
21C43×#576—22no—
22C43×#575—22no—
23C43×#575C2211yescharacteristic
24C43×#575C2211yescharacteristic
25C2×#137×C43C2211yescharacteristic
26C2×#137×C43C2211yescharacteristic, complemented
27C2×#137×C43C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C43—22no—
29C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
31C43×#568C2211yescharacteristic
32C43×#568C2211yescharacteristic, complemented
33C43×#536C2211yescharacteristic, complemented
34C2×#124×C43C2211yescharacteristic, complemented
35C4×#41×C43C2211yescharacteristic, complemented
36C43×#473—22no—
37C43×#471—22no—
38C43×#464—22no—
39C43×#463—22no—
40C43×#456—22no—
41C43×#455—22no—
42C43×#455—22no—
43C43×#455—22no—
44C43×#430C2211yescharacteristic, complemented
45C43×#423C2211yescharacteristic, complemented
46C43×#421—22no—
47C43×#421C2211yescharacteristic
48C43×#421C2211yescharacteristic
49C43×#421C2211yescharacteristic, complemented
50C43×#421C2211yescharacteristic, complemented
51C2×#104×C43—22no—
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic, complemented
54C2×#104×C43C2211yescharacteristic, complemented
55C43×#419C2211yescharacteristic, complemented
56C43×#418C2211yescharacteristic, complemented
57C43×#418C2211yescharacteristic, complemented
58C43×#413C2211yescharacteristic, complemented
59C43×#413C2211yescharacteristic, complemented
60C2×#101×C43C2211yescharacteristic, complemented
61C2×#100×C43C2211yescharacteristic, complemented
62C43×#410C2211yescharacteristic, complemented
63C43×#344C2211yescharacteristic, complemented
64C43×#344C2211yescharacteristic, complemented
65C43×#339C2211yescharacteristic, complemented
66C43×#338C2211yescharacteristic, complemented
672−1+4×C43—21no—
682−1+4×C43—21no—
692−1+4×C43D412yes—
70H(5,𝔽2)×C43—22no—
71H(5,𝔽2)×C43—21no—
72H(5,𝔽2)×C43—22no—
73H(5,𝔽2)×C43—21no—
74H(5,𝔽2)×C43—22no—
75H(5,𝔽2)×C43—41no—
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×C43C2311yescharacteristic
84C2×#41×C43C2311yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C2×#41×C43C2311yescharacteristic
87C22×Q8×C43C2311yescharacteristic
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—41no—
91C22×D4×C43C2311yescharacteristic
92#137×C43—24no—
93#137×C43—21no—
94#137×C43—21no—
95#137×C43—21no—
96#137×C43—22no—
97#137×C43—22no—
98#137×C43—22no—
99#137×C43—22no—
100#137×C43—22no—
101#137×C43—41no—
102#137×C43D412yes—
103AGL(1,ℤ/8)×C43—24no—
104AGL(1,ℤ/8)×C43—24no—
105AGL(1,ℤ/8)×C43—24no—
106AGL(1,ℤ/8)×C43—22no—
107AGL(1,ℤ/8)×C43—22no—
108AGL(1,ℤ/8)×C43—21no—
109AGL(1,ℤ/8)×C43—22no—
110AGL(1,ℤ/8)×C43—21no—
111AGL(1,ℤ/8)×C43—21no—
112AGL(1,ℤ/8)×C43—22no—
113AGL(1,ℤ/8)×C43D412yes—
114#135×C43—24no—
115#135×C43—24no—
116#135×C43—22no—
117#135×C43—22no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×SD16×C43—24no—
122C2×SD16×C43—21no—
123C2×SD16×C43—21no—
124C2×SD16×C43—21no—
125C2×SD16×C43—21no—
126C2×SD16×C43D412yes—
127C2×D8×C43—24no—
128C2×D8×C43—21no—
129C2×D8×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—21no—
143#124×C43—22no—
144#124×C43—21no—
145#124×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×C22⋊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#102×C43—22no—
172#102×C43—41no—
173#101×C43—21no—
174#101×C43—21no—
175#101×C43—22no—
176#100×C43—21no—
177#100×C43—21no—
178#100×C43—22no—
179#99×C43—41no—
180C24×C43—21no—
181C24×C43—41no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—21no—
186#41×C43—24no—
187#41×C43—22no—
188#41×C43—22no—
189#41×C43—22no—
190#41×C43—22no—
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—42no—
201#41×C43—42no—
202#41×C43—42no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—41no—
206#41×C43—41no—
207#41×C43—42no—
208#41×C43C2×D412yes—
209#41×C43C2×D412yes—
210#41×C43C2×D412yes—
211#41×C43C2×D412yes—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
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—41no—
221C2×Q8×C43C2×D411yescharacteristic
222C2×Q8×C43C2×D411yescharacteristic
223C2×Q8×C43C2×D411yescharacteristic
224C2×Q8×C43#4111yescharacteristic
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—24no—
231C2×D4×C43—22no—
232C2×D4×C43—22no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—41no—
238C2×D4×C43—41no—
239C2×D4×C43—42no—
240C2×D4×C43—44no—
241C2×D4×C43—42no—
242C2×D4×C43—42no—
243C2×D4×C43—42no—
244C2×D4×C43—42no—
245C2×D4×C43—41no—
246C2×D4×C43—44no—
247C2×D4×C43—42no—
248C2×D4×C43C2×D411yescharacteristic
249C2×D4×C43C2×D411yescharacteristic
250C2×D4×C43C2×D412yes—
251C2×D4×C43C2×D411yescharacteristic
252C2×D4×C43#4111yescharacteristic
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—41no—
260C22×C4×C43—41no—
261C22×C4×C43—42no—
262C22×C4×C43C2411yescharacteristic
263Q16×C43—22no—
264Q16×C43—22no—
265Q16×C43—42no—
266Q16×C43—42no—
267Q16×C43—42no—
268SD16×C43—24no—
269SD16×C43—22no—
270SD16×C43—22no—
271SD16×C43—22no—
272SD16×C43—24no—
273SD16×C43—22no—
274SD16×C43—42no—
275SD16×C43—42no—
276SD16×C43—42no—
277D8×C43—24no—
278D8×C43—22no—
279D8×C43—22no—
280D8×C43—24no—
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—41no—
306C4⋊C4×C43—42no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—42no—
310C22⋊C4×C43—42no—
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—22no—
323C23×C43—21no—
324C23×C43—42no—
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—21no—
334Q8×C43—21no—
335Q8×C43—21no—
336Q8×C43—21no—
337Q8×C43—42no—
338Q8×C43—41no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43—41no—
342Q8×C43#12012yes—
343Q8×C43#12112yes—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—21no—
349D4×C43—21no—
350D4×C43—22no—
351D4×C43—21no—
352D4×C43—21no—
353D4×C43—21no—
354D4×C43—21no—
355D4×C43—22no—
356D4×C43—42no—
357D4×C43—42no—
358D4×C43—44no—
359D4×C43—42no—
360D4×C43—44no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43#12012yes—
368D4×C43#12112yes—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
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—21no—
378C2×C4×C43—21no—
379C2×C4×C43—42no—
380C2×C4×C43—42no—
381C2×C4×C43—42no—
382C2×C4×C43—44no—
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—81no—
393C2×C4×C43—82no—
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C2×#4111yescharacteristic
399C2×C4×C43H(5,𝔽2)11yescharacteristic
400C8×C43—22no—
401C8×C43—22no—
402C8×C43—22no—
403C8×C43—41no—
404C8×C43—41no—
405C8×C43—41no—
406#24475C4311yesmaximal, characteristic, direct product factor, Sylow
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—41no—
410C22×C43—42no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43—81no—
416C22×C43—82no—
417C22×C43—81no—
418C22×C43—82no—
419C22×C43—161no—
420C22×C43—162no—
421C22×C43—164no—
422C22×C43#53411yescharacteristic
423C22×C43D4211yescharacteristic
424C22×C43#54611yescharacteristic
425C4×C43—22no—
426C4×C43—22no—
427C4×C43—41no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—81no—
432C4×C43—81no—
433C4×C43—81no—
434C4×C43C2×#12011yescharacteristic
435C4×C43C2×#12111yescharacteristic
436C4×C43D4211yescharacteristic
437C4×C43#54611yescharacteristic
438#3585C2×C4311yescharacteristic
439#3069C2×C4311yescharacteristic, complemented
440#3040C2×C4311yescharacteristic, complemented
441#3022C2×C4311yescharacteristic, complemented
442C2×#455C2×C4311yescharacteristic, complemented
443#2901C2×C4311yescharacteristic, complemented
444#2050C2×C4311yescharacteristic, complemented
445#2048C2×C4311yescharacteristic, complemented
446#2009C2×C4311yescharacteristic, complemented
447#2003C2×C4311yescharacteristic, complemented
448#1906C2×C4311yescharacteristic, complemented
449#1903C2×C4311yescharacteristic, complemented
450#1902C2×C4311yescharacteristic, complemented
451#1861C2×C4311yescharacteristic, complemented
452#1795C2×C4311yescharacteristic, complemented
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—21no—
456C2×C43—42no—
457C2×C43—42no—
458C2×C43—82no—
459C2×C43—81no—
460C2×C43—81no—
461C2×C43#241011yescharacteristic
462#585C22×C4311yescharacteristic
463C2×H(5,𝔽2)C22×C4311yescharacteristic
464#577—22no—
465#577—22no—
466#576—22no—
467#576—22no—
468#575—22no—
469#575C22×C4311yescharacteristic
470#575C22×C4311yescharacteristic
471C2×#137C22×C4311yescharacteristic
472C2×#137C22×C4311yescharacteristic, complemented
473C2×#137C22×C4311yescharacteristic, complemented
474C2×AGL(1,ℤ/8)—22no—
475C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
476C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
477#568C22×C4311yescharacteristic
478#568C22×C4311yescharacteristic, complemented
479#536C22×C4311yescharacteristic, complemented
480C2×#124C22×C4311yescharacteristic, complemented
481C4×#41C22×C4311yescharacteristic, complemented
482#473—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#456—22no—
487#455—22no—
488#455—22no—
489#455—22no—
490#430C22×C4311yescharacteristic, complemented
491#423C22×C4311yescharacteristic, complemented
492#421—22no—
493#421C22×C4311yescharacteristic
494#421C22×C4311yescharacteristic
495#421C22×C4311yescharacteristic, complemented
496#421C22×C4311yescharacteristic, complemented
497C2×#104—22no—
498C2×#104C22×C4311yescharacteristic
499C2×#104C22×C4311yescharacteristic, complemented
500C2×#104C22×C4311yescharacteristic, complemented
501#419C22×C4311yescharacteristic, complemented
502#418C22×C4311yescharacteristic, complemented
503#418C22×C4311yescharacteristic, complemented
504#413C22×C4311yescharacteristic, complemented
505#413C22×C4311yescharacteristic, complemented
506C2×#101C22×C4311yescharacteristic, complemented
507C2×#100C22×C4311yescharacteristic, complemented
508#410C22×C4311yescharacteristic, complemented
509#344C22×C4311yescharacteristic, complemented
510#344C22×C4311yescharacteristic, complemented
511#339C22×C4311yescharacteristic, complemented
512#338C22×C4311yescharacteristic, complemented
513C43#2447511yescharacteristic, direct product factor, Sylow
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C4312yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C4312yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C4311yescharacteristic
531C2×#41C23×C4311yescharacteristic
532C2×#41C23×C4311yescharacteristic
533C2×#41C23×C4311yescharacteristic
534C22×Q8C23×C4311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C4311yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C4312yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C4312yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C4312yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C4312yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C4311yescharacteristic
584C2×M16C23×C4311yescharacteristic
585C2×M16C23×C4311yescharacteristic
586C2×M16C23×C4311yescharacteristic
587C2×M16C23×C4311yescharacteristic
588C2×M16C23×C4311yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C4311yescharacteristic
601#117C23×C4311yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C4311yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C4312yes—
616#104D4×C4312yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C4312yes—
656#41C2×D4×C4312yes—
657#41C2×D4×C4312yes—
658#41C2×D4×C4312yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C4311yescharacteristic
669C2×Q8C2×D4×C4311yescharacteristic
670C2×Q8C2×D4×C4311yescharacteristic
671C2×Q8#41×C4311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C4311yescharacteristic
696C2×D4C2×D4×C4311yescharacteristic
697C2×D4C2×D4×C4312yes—
698C2×D4C2×D4×C4311yescharacteristic
699C2×D4#41×C4311yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C4311yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C4312yes—
741M16C2×D4×C4312yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C4312yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C4311yescharacteristic
765C42C2×D4×C4311yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C4311yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C4312yes—
790Q8#121×C4312yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C4312yes—
815D4#121×C4312yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C4311yescharacteristic
842C2×C4C22×D4×C4311yescharacteristic
843C2×C4C22×D4×C4311yescharacteristic
844C2×C4C22×D4×C4311yescharacteristic
845C2×C4C2×#41×C4311yescharacteristic
846C2×C4H(5,𝔽2)×C4311yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22C43×#53411yescharacteristic
869C22D42×C4311yescharacteristic
870C22C43×#54611yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C4311yescharacteristic
881C4C2×#121×C4311yescharacteristic
882C4D42×C4311yescharacteristic
883C4C43×#54611yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C43×#241011yescharacteristic
subgroupG/H
center, socleC2×C43#2410
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3585C2
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×#3040C2semidirect
4. C43×#3022C2semidirect
5. C2×C43×#455C2semidirect
6. C43×#2901C2semidirect
7. C43×#2050C2semidirect
8. C43×#2048C2semidirect
9. C43×#2009C2semidirect
10. C43×#2003C2semidirect
11. C43×#1906C2semidirect
12. C43×#1903C2semidirect
13. C43×#1902C2semidirect
14. C43×#1861C2semidirect
15. C43×#1795C2semidirect
26. C2×#137×C43C22semidirect
27. C2×#137×C43C22semidirect
32. C43×#568C22semidirect
33. C43×#536C22semidirect
34. C2×#124×C43C22semidirect
35. C4×#41×C43C22semidirect
44. C43×#430C22semidirect
45. C43×#423C22semidirect
49. C43×#421C22semidirect
50. C43×#421C22semidirect
53. C2×#104×C43C22semidirect
54. C2×#104×C43C22semidirect
55. C43×#419C22semidirect
56. C43×#418C22semidirect
57. C43×#418C22semidirect
58. C43×#413C22semidirect
59. C43×#413C22semidirect
60. C2×#101×C43C22semidirect
61. C2×#100×C43C22semidirect
62. C43×#410C22semidirect
63. C43×#344C22semidirect
64. C43×#344C22semidirect
65. C43×#339C22semidirect
66. C43×#338C22semidirect
406. #24475C43direct (N × H)
439. #3069C2×C43semidirect
440. #3040C2×C43semidirect
441. #3022C2×C43semidirect
442. C2×#455C2×C43semidirect
443. #2901C2×C43semidirect
444. #2050C2×C43semidirect
445. #2048C2×C43semidirect
446. #2009C2×C43semidirect
447. #2003C2×C43semidirect
448. #1906C2×C43semidirect
449. #1903C2×C43semidirect
450. #1902C2×C43semidirect
451. #1861C2×C43semidirect
452. #1795C2×C43semidirect
472. C2×#137C22×C43semidirect
473. C2×#137C22×C43semidirect
478. #568C22×C43semidirect
479. #536C22×C43semidirect
480. C2×#124C22×C43semidirect
481. C4×#41C22×C43semidirect
490. #430C22×C43semidirect
491. #423C22×C43semidirect
495. #421C22×C43semidirect
496. #421C22×C43semidirect
499. C2×#104C22×C43semidirect
500. C2×#104C22×C43semidirect
501. #419C22×C43semidirect
502. #418C22×C43semidirect
503. #418C22×C43semidirect
504. #413C22×C43semidirect
505. #413C22×C43semidirect
506. C2×#101C22×C43semidirect
507. C2×#100C22×C43semidirect
508. #410C22×C43semidirect
509. #344C22×C43semidirect
510. #344C22×C43semidirect
511. #339C22×C43semidirect
512. #338C22×C43semidirect
513. C43#24475direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35852
C43×#30692
C43×#30402
C43×#30222
C2×C43×#4552
C43×#29012
C43×#20502
C43×#20482
C43×#20092
C43×#20032
C43×#19062
C43×#19032
C43×#19022
C43×#18612
C43×#17952
#2447543