Finite Group Databasebeta

← C43×#25192 #24945209

Subgroups — C43×#25192 #24945209

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3062C211yesmaximal, characteristic, complemented
2C43×#3045C211yesmaximal, characteristic, complemented
3C2×C43×#453C211yesmaximal, characteristic, complemented
4C43×#3012C211yesmaximal, characteristic, complemented
5C2×C43×#444C211yesmaximal, characteristic, complemented
6C43×#2897C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2040C211yesmaximal, characteristic, complemented
10C43×#2002C211yesmaximal, characteristic, complemented
11C43×#1961C211yesmaximal, characteristic, complemented
12C43×#1938C211yesmaximal, characteristic, complemented
13C43×#1907C211yesmaximal, characteristic, complemented
14C43×#1907C211yesmaximal, characteristic, complemented
15C43×#1860C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×#135×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic
22C2×#131×C43C2211yescharacteristic, complemented
23C43×#537C2211yescharacteristic
24C43×#535C2211yescharacteristic, complemented
25C2×#127×C43C2211yescharacteristic
26C43×#520C2211yescharacteristic
27C43×#469—21no—
28C43×#468—21no—
29C43×#466—21no—
30C43×#465—21no—
31C43×#464—21no—
32C43×#463—21no—
33C43×#460—21no—
34C43×#459—21no—
35C43×#453—24no—
36C43×#452—21no—
37C43×#450—21no—
38C43×#449—21no—
39C43×#447—21no—
40C43×#444—24no—
41C2×#108×C43C2211yescharacteristic, complemented
42C43×#428C2211yescharacteristic, complemented
43C43×#424C2211yescharacteristic, complemented
44C2×#104×C43C2211yescharacteristic
45C2×#104×C43C2211yescharacteristic
46C2×#104×C43C2211yescharacteristic, complemented
47C43×#418—21no—
48C43×#418C2211yescharacteristic
49C43×#417—21no—
50C43×#417C2211yescharacteristic
51C43×#417C2211yescharacteristic
52C43×#417C2211yescharacteristic, complemented
53C43×#416—21no—
54C43×#416C2211yescharacteristic
55C2×#102×C43—21no—
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#100×C43C2211yescharacteristic
61C2×#100×C43C2211yescharacteristic, complemented
62C43×#408C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic, complemented
64C43×#382C2211yescharacteristic, complemented
65C43×#343C2211yescharacteristic, complemented
66C43×#343C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
69H(5,𝔽2)×C43—22no—
70H(5,𝔽2)×C43—22no—
71H(5,𝔽2)×C43—22no—
72H(5,𝔽2)×C43—41no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43C2311yescharacteristic
76C2×#41×C43C2311yescharacteristic
77C2×#41×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—41no—
81C22×D4×C43—41no—
82C22×D4×C43C2311yescharacteristic
83C22×D4×C43C2311yescharacteristic
84AGL(1,ℤ/8)×C43—22no—
85AGL(1,ℤ/8)×C43—22no—
86AGL(1,ℤ/8)×C43—22no—
87AGL(1,ℤ/8)×C43—22no—
88AGL(1,ℤ/8)×C43—41no—
89AGL(1,ℤ/8)×C43—41no—
90#135×C43—22no—
91#135×C43—22no—
92C2×Q16×C43D411yescharacteristic, complemented
93C2×SD16×C43—21no—
94C2×SD16×C43—21no—
95C2×SD16×C43—21no—
96C2×SD16×C43D411yescharacteristic, complemented
97C2×SD16×C43D411yescharacteristic, complemented
98C2×D8×C43—21no—
99C2×D8×C43—21no—
100C2×D8×C43—21no—
101C2×D8×C43D411yescharacteristic, complemented
102#131×C43—22no—
103#131×C43—22no—
104#131×C43—41no—
105#131×C43—41no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43C2311yescharacteristic
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#127×C43—21no—
117#127×C43—22no—
118#127×C43—22no—
119#124×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—41no—
127#120×C43—41no—
128C4×Q8×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—41no—
131#117×C43—21no—
132#117×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#108×C43—22no—
138#107×C43—21no—
139#106×C43—21no—
140C4⋊C8×C43—21no—
141C4⋊C8×C43—21no—
142#104×C43—22no—
143#104×C43—22no—
144#104×C43D414yescomplemented
145#103×C43—21no—
146#103×C43—21no—
147#103×C43—21no—
148#103×C43D411yescharacteristic, complemented
149#103×C43D411yescharacteristic, complemented
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#102×C43—21no—
159#102×C43—21no—
160#102×C43—21no—
161#102×C43—21no—
162#102×C43—21no—
163#102×C43D411yescharacteristic, complemented
164#102×C43D411yescharacteristic, complemented
165#100×C43—22no—
166#100×C43—41no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43—21no—
169#97×C43—22no—
170#95×C43—41no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—41no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—24no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—42no—
186#41×C43—42no—
187#41×C43—42no—
188#41×C43C2×D412yes—
189#41×C43#4112yes—
190C2×Q8×C43C2×D411yescharacteristic
191C2×Q8×C43C2×D411yescharacteristic
192C2×Q8×C43C2×D411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—24no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—41no—
209C2×D4×C43—41no—
210C2×D4×C43—41no—
211C2×D4×C43—44no—
212C2×D4×C43—41no—
213C2×D4×C43—41no—
214C2×D4×C43—44no—
215C2×D4×C43—42no—
216C2×D4×C43—42no—
217C2×D4×C43—44no—
218C2×D4×C43—42no—
219C2×D4×C43—82no—
220C2×D4×C43—82no—
221C2×D4×C43C2×D411yescharacteristic
222C2×D4×C43C2×D411yescharacteristic
223C2×D4×C43C2×D411yescharacteristic
224C2×D4×C43#4112yes—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—41no—
232C22×C4×C43—41no—
233C22×C4×C43C2411yescharacteristic
234Q16×C43—22no—
235SD16×C43—22no—
236SD16×C43—22no—
237SD16×C43—42no—
238SD16×C43—42no—
239SD16×C43—42no—
240D8×C43—22no—
241D8×C43—42no—
242D8×C43—42no—
243D8×C43—42no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—42no—
252M16×C43—42no—
253M16×C43C2×D412yes—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—42no—
263C2×C8×C43—42no—
264C2×C8×C43C2×D411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C2×C8×C43C2×D411yescharacteristic
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—41no—
273C4⋊C4×C43—41no—
274C4⋊C4×C43C2×D411yescharacteristic
275C4⋊C4×C43C2×D411yescharacteristic
276C22⋊C4×C43—21no—
277C22⋊C4×C43—41no—
278C22⋊C4×C43—41no—
279C22⋊C4×C43—41no—
280C22⋊C4×C43—41no—
281C22⋊C4×C43—41no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43—41no—
285C42×C43C2×D412yes—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—44no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—81no—
297C23×C43—81no—
298C23×C43—81no—
299C23×C43—81no—
300C23×C43—161no—
301C23×C43—161no—
302C23×C43H(5,𝔽2)11yescharacteristic
303Q8×C43—21no—
304Q8×C43—21no—
305Q8×C43—21no—
306Q8×C43—21no—
307Q8×C43—21no—
308Q8×C43#12112yes—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—21no—
312D4×C43—21no—
313D4×C43—22no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—21no—
317D4×C43—22no—
318D4×C43—44no—
319D4×C43—44no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—88no—
331D4×C43—161no—
332D4×C43—161no—
333D4×C43—161no—
334D4×C43#12112yes—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—44no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—81no—
353C2×C4×C43—81no—
354C2×C4×C43—161no—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C8×C43—21no—
362C8×C43—21no—
363C8×C43—21no—
364C8×C43—21no—
365C8×C43—22no—
366C8×C43—41no—
367C8×C43—41no—
368C8×C43—41no—
369#25192C4311yesmaximal, characteristic, direct product factor, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—22no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—82no—
383C22×C43—82no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—161no—
390C22×C43—161no—
391C22×C43—164no—
392C22×C43#53811yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C4×C43—22no—
396C4×C43—42no—
397C4×C43—41no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—41no—
401C4×C43—81no—
402C4×C43—81no—
403C4×C43C2×#12111yescharacteristic
404C4×C43#52511yescharacteristic
405C4×C43D4211yescharacteristic
406C4×C43#54611yescharacteristic
407#3062C2×C4311yescharacteristic, complemented
408#3045C2×C4311yescharacteristic, complemented
409C2×#453C2×C4311yescharacteristic, complemented
410#3012C2×C4311yescharacteristic, complemented
411C2×#444C2×C4311yescharacteristic, complemented
412#2897C2×C4311yescharacteristic, complemented
413#2063C2×C4311yescharacteristic, complemented
414#2051C2×C4311yescharacteristic, complemented
415#2040C2×C4311yescharacteristic, complemented
416#2002C2×C4311yescharacteristic, complemented
417#1961C2×C4311yescharacteristic, complemented
418#1938C2×C4311yescharacteristic, complemented
419#1907C2×C4311yescharacteristic, complemented
420#1907C2×C4311yescharacteristic, complemented
421#1860C2×C4311yescharacteristic, complemented
422C2×C43—21no—
423C2×C43—21no—
424C2×C43—42no—
425C2×C43—81no—
426C2×C43—81no—
427C2×C43—82no—
428C2×C43—161no—
429C2×C43#242411yescharacteristic
430C2×C43#328811yescharacteristic
431C2×C43#328811yescharacteristic
432C2×H(5,𝔽2)C22×C4311yescharacteristic
433C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
436C2×#135C22×C4311yescharacteristic
437C2×#131C22×C4311yescharacteristic
438C2×#131C22×C4311yescharacteristic, complemented
439#537C22×C4311yescharacteristic
440#535C22×C4311yescharacteristic, complemented
441C2×#127C22×C4311yescharacteristic
442#520C22×C4311yescharacteristic
443#469—21no—
444#468—21no—
445#466—21no—
446#465—21no—
447#464—21no—
448#463—21no—
449#460—21no—
450#459—21no—
451#453—24no—
452#452—21no—
453#450—21no—
454#449—21no—
455#447—21no—
456#444—24no—
457C2×#108C22×C4311yescharacteristic, complemented
458#428C22×C4311yescharacteristic, complemented
459#424C22×C4311yescharacteristic, complemented
460C2×#104C22×C4311yescharacteristic
461C2×#104C22×C4311yescharacteristic
462C2×#104C22×C4311yescharacteristic, complemented
463#418—21no—
464#418C22×C4311yescharacteristic
465#417—21no—
466#417C22×C4311yescharacteristic
467#417C22×C4311yescharacteristic
468#417C22×C4311yescharacteristic, complemented
469#416—21no—
470#416C22×C4311yescharacteristic
471C2×#102—21no—
472C2×#102C22×C4311yescharacteristic
473C2×#102C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic, complemented
475C2×#102C22×C4311yescharacteristic, complemented
476C2×#100C22×C4311yescharacteristic
477C2×#100C22×C4311yescharacteristic, complemented
478#408C22×C4311yescharacteristic
479C2×#97C22×C4311yescharacteristic, complemented
480#382C22×C4311yescharacteristic, complemented
481#343C22×C4311yescharacteristic, complemented
482#343C22×C4311yescharacteristic, complemented
483#341C22×C4311yescharacteristic, complemented
484#339C22×C4311yescharacteristic, complemented
485C43#2519211yescharacteristic, direct product factor, Sylow
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C4311yescharacteristic
493C2×#41C23×C4311yescharacteristic
494C2×#41C23×C4311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C4311yescharacteristic
500C22×D4C23×C4311yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C4311yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C4311yescharacteristic, complemented
514C2×SD16D4×C4311yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C4311yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C4311yescharacteristic
526C2×M16C23×C4311yescharacteristic
527C2×M16C23×C4311yescharacteristic
528C2×M16C23×C4311yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C4311yescharacteristic
532C22×C8C23×C4311yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C4311yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C4311yescharacteristic
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C42C23×C4311yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C4314yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C4311yescharacteristic, complemented
566#103D4×C4311yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C4311yescharacteristic, complemented
581#102D4×C4311yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C4312yes—
606#41#41×C4312yes—
607C2×Q8C2×D4×C4311yescharacteristic
608C2×Q8C2×D4×C4311yescharacteristic
609C2×Q8C2×D4×C4311yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C4311yescharacteristic
639C2×D4C2×D4×C4311yescharacteristic
640C2×D4C2×D4×C4311yescharacteristic
641C2×D4#41×C4312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C4311yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C4312yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C4311yescharacteristic
682C2×C8C2×D4×C4311yescharacteristic
683C2×C8C2×D4×C4311yescharacteristic
684C2×C8C2×D4×C4311yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C4311yescharacteristic
692C4⋊C4C2×D4×C4311yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C4312yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C4311yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C4312yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C4312yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C4311yescharacteristic
773C2×C4C22×D4×C4311yescharacteristic
774C2×C4C22×D4×C4311yescharacteristic
775C2×C4C2×#41×C4311yescharacteristic
776C2×C4C2×#41×C4311yescharacteristic
777C2×C4H(5,𝔽2)×C4311yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22C43×#53811yescharacteristic
809C22D42×C4311yescharacteristic
810C22C43×#54611yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C4311yescharacteristic
820C4C43×#52511yescharacteristic
821C4D42×C4311yescharacteristic
822C4C43×#54611yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C43×#242411yescharacteristic
831C2C43×#328811yescharacteristic
832C2C43×#328811yescharacteristic
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. C43×#3062C2semidirect
2. C43×#3045C2semidirect
3. C2×C43×#453C2semidirect
4. C43×#3012C2semidirect
5. C2×C43×#444C2semidirect
6. C43×#2897C2semidirect
7. C43×#2063C2semidirect
8. C43×#2051C2semidirect
9. C43×#2040C2semidirect
10. C43×#2002C2semidirect
11. C43×#1961C2semidirect
12. C43×#1938C2semidirect
13. C43×#1907C2semidirect
14. C43×#1907C2semidirect
15. C43×#1860C2semidirect
22. C2×#131×C43C22semidirect
24. C43×#535C22semidirect
41. C2×#108×C43C22semidirect
42. C43×#428C22semidirect
43. C43×#424C22semidirect
46. C2×#104×C43C22semidirect
52. C43×#417C22semidirect
58. C2×#102×C43C22semidirect
59. C2×#102×C43C22semidirect
61. C2×#100×C43C22semidirect
63. C2×#97×C43C22semidirect
64. C43×#382C22semidirect
65. C43×#343C22semidirect
66. C43×#343C22semidirect
67. C43×#341C22semidirect
68. C43×#339C22semidirect
92. C2×Q16×C43D4semidirect
96. C2×SD16×C43D4semidirect
97. C2×SD16×C43D4semidirect
101. C2×D8×C43D4semidirect
144. #104×C43D4semidirect
148. #103×C43D4semidirect
149. #103×C43D4semidirect
163. #102×C43D4semidirect
164. #102×C43D4semidirect
369. #25192C43direct (N × H)
407. #3062C2×C43semidirect
408. #3045C2×C43semidirect
409. C2×#453C2×C43semidirect
410. #3012C2×C43semidirect
411. C2×#444C2×C43semidirect
412. #2897C2×C43semidirect
413. #2063C2×C43semidirect
414. #2051C2×C43semidirect
415. #2040C2×C43semidirect
416. #2002C2×C43semidirect
417. #1961C2×C43semidirect
418. #1938C2×C43semidirect
419. #1907C2×C43semidirect
420. #1907C2×C43semidirect
421. #1860C2×C43semidirect
438. C2×#131C22×C43semidirect
440. #535C22×C43semidirect
457. C2×#108C22×C43semidirect
458. #428C22×C43semidirect
459. #424C22×C43semidirect
462. C2×#104C22×C43semidirect
468. #417C22×C43semidirect
474. C2×#102C22×C43semidirect
475. C2×#102C22×C43semidirect
477. C2×#100C22×C43semidirect
479. C2×#97C22×C43semidirect
480. #382C22×C43semidirect
481. #343C22×C43semidirect
482. #343C22×C43semidirect
483. #341C22×C43semidirect
484. #339C22×C43semidirect
485. C43#25192direct (N × H)
509. C2×Q16D4×C43semidirect
513. C2×SD16D4×C43semidirect
514. C2×SD16D4×C43semidirect
518. C2×D8D4×C43semidirect
561. #104D4×C43semidirect
565. #103D4×C43semidirect
566. #103D4×C43semidirect
580. #102D4×C43semidirect
581. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#30622
C43×#30452
C2×C43×#4532
C43×#30122
C2×C43×#4442
C43×#28972
C43×#20632
C43×#20512
C43×#20402
C43×#20022
C43×#19612
C43×#19382
C43×#19072
C43×#18602
#2519243