Finite Group Databasebeta

← C43×#9520 #24929537

Subgroups — C43×#9520 #24929537

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3003C211yesmaximal, characteristic
2C43×#2976C211yesmaximal, characteristic, complemented
3C43×#1786C211yesmaximal, characteristic, complemented
4C43×#1783C211yesmaximal, characteristic, complemented
5C43×#1513C211yesmaximal, characteristic, complemented
6C43×#1305C211yesmaximal, characteristic, complemented
7C43×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C43C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C43—21no—
10C43×#525C2211yescharacteristic
11C43×#450—21no—
12C43×#450C412yescomplemented
13C43×#447—21no—
14C43×#447C412yescomplemented
15C43×#436—21no—
16C43×#435—21no—
17C43×#435—21no—
18C8×D4×C43—21no—
19C43×#433—21no—
20C43×#418—21no—
21C2×#102×C43—21no—
22C2×#102×C43—21no—
23C2×#100×C43—21no—
24C2×#100×C43—21no—
25C43×#408—21no—
26C43×#407C2211yescharacteristic
27C43×#407C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C43×#328—21no—
32C43×#327—21no—
33C25×C43—21no—
34C2×#41×C43D411yescharacteristic
35C22×D4×C43—21no—
36C22×D4×C43—21no—
37C22×D4×C43—21no—
38C22×D4×C43—21no—
39C22×D4×C43—21no—
40C22×D4×C43—42no—
41C22×D4×C43—42no—
42C22×D4×C43C2×C412yes—
43C23×C4×C43C2311yescharacteristic
44AGL(1,ℤ/8)×C43—42no—
45AGL(1,ℤ/8)×C43—42no—
46C2×SD16×C43—22no—
47C2×D8×C43—22no—
48C2×M16×C43—21no—
49C2×M16×C43—21no—
50C2×M16×C43—21no—
51C2×M16×C43D411yescharacteristic
52C2×M16×C43D411yescharacteristic
53C22×C8×C43—21no—
54C22×C8×C43D411yescharacteristic
55C22×C8×C43D411yescharacteristic
56#123×C43—21no—
57C22⋊Q8×C43C2×C411yescharacteristic
58C22⋊Q8×C43D411yescharacteristic
59#121×C43C2×C411yescharacteristic
60#121×C43D411yescharacteristic
61#120×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64#117×C43D411yescharacteristic
65C2×C4⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69#102×C43—22no—
70#102×C43—22no—
71#102×C43—42no—
72#102×C43—42no—
73#100×C43—42no—
74#100×C43—42no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—21no—
84C22⋊C8×C43C2×C412yes—
85#97×C43—21no—
86C4×C8×C43—21no—
87#95×C43—21no—
88C24×C43—22no—
89C24×C43—44no—
90C24×C43—41no—
91C24×C43—41no—
92C24×C43—81no—
93C24×C43—81no—
94C24×C43—82no—
95C24×C43#4111yescharacteristic
96#41×C43—41no—
97#41×C43—41no—
98C2×Q8×C43C22⋊C411yescharacteristic
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—21no—
102C2×D4×C43—21no—
103C2×D4×C43—21no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—44no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—44no—
118C2×D4×C43—44no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43C22⋊C411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4111yescharacteristic
132SD16×C43—44no—
133D8×C43—44no—
134M16×C43—41no—
135M16×C43—41no—
136M16×C43—41no—
137M16×C43—41no—
138M16×C43—41no—
139M16×C43—41no—
140M16×C43—81no—
141C2×C8×C43—22no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C2×C8×C43—81no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43C22⋊C411yescharacteristic
155C4⋊C4×C43C22⋊C411yescharacteristic
156C22⋊C4×C43—21no—
157C22⋊C4×C43—21no—
158C22⋊C4×C43—21no—
159C22⋊C4×C43—21no—
160C22⋊C4×C43—21no—
161C22⋊C4×C43—81no—
162C42×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—24no—
166C23×C43—21no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—82no—
176C23×C43—82no—
177C23×C43—82no—
178C23×C43—81no—
179C23×C43—81no—
180C23×C43—82no—
181C23×C43—88no—
182C23×C43—88no—
183C23×C43—81no—
184C23×C43—81no—
185C23×C43C4×D411yescharacteristic
186C23×C43#12111yescharacteristic
187C23×C43#12311yescharacteristic
188Q8×C43—41no—
189D4×C43—24no—
190D4×C43—24no—
191D4×C43—41no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—42no—
195D4×C43—42no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—42no—
199D4×C43—42no—
200D4×C43—81no—
201D4×C43—81no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—81no—
217C2×C4×C43—81no—
218C2×C4×C43—81no—
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C8×C43—42no—
224C8×C43—41no—
225C8×C43—41no—
226C8×C43—41no—
227C8×C43—41no—
228C8×C43—81no—
229#9520C4311yesmaximal, characteristic, direct product factor, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—44no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—41no—
244C22×C43—82no—
245C22×C43—82no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43—84no—
249C22×C43—84no—
250C22×C43—84no—
251C22×C43—84no—
252C22×C43—82no—
253C22×C43—82no—
254C22×C43#38611yescharacteristic
255C22×C43#47111yescharacteristic
256C22×C43#47211yescharacteristic
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—161no—
264C4×C43B(4,𝔽2)11yescharacteristic
265C4×C43B(4,𝔽2)11yescharacteristic
266#3003C2×C4311yescharacteristic
267#2976C2×C4311yescharacteristic, complemented
268#1786C2×C4311yescharacteristic, complemented
269#1783C2×C4311yescharacteristic, complemented
270#1513C2×C4311yescharacteristic, complemented
271#1305C2×C4311yescharacteristic, complemented
272#1293C2×C4311yescharacteristic, complemented
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—41no—
276C2×C43—41no—
277C2×C43—81no—
278C2×C43—84no—
279C2×C43#188911yescharacteristic
280C2×C43#190311yescharacteristic
281C2×C43#190711yescharacteristic
282C23×D4C22×C4311yescharacteristic
283C2×AGL(1,ℤ/8)—21no—
284#525C22×C4311yescharacteristic
285#450—21no—
286#450C4×C4312yescomplemented
287#447—21no—
288#447C4×C4312yescomplemented
289#436—21no—
290#435—21no—
291#435—21no—
292C8×D4—21no—
293#433—21no—
294#418—21no—
295C2×#102—21no—
296C2×#102—21no—
297C2×#100—21no—
298C2×#100—21no—
299#408—21no—
300#407C22×C4311yescharacteristic
301#407C22×C4311yescharacteristic
302#407C22×C4311yescharacteristic
303C2×C22⋊C8C22×C4311yescharacteristic
304#380C22×C4311yescharacteristic
305#328—21no—
306#327—21no—
307C43#952011yescharacteristic, direct product factor, Sylow
308C25—21no—
309C2×#41D4×C4311yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C4312yes—
318C23×C4C23×C4311yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C4311yescharacteristic
327C2×M16D4×C4311yescharacteristic
328C22×C8—21no—
329C22×C8D4×C4311yescharacteristic
330C22×C8D4×C4311yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C4311yescharacteristic
333C22⋊Q8D4×C4311yescharacteristic
334#121C2×C4×C4311yescharacteristic
335#121D4×C4311yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C4311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C4312yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C4311yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C4311yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C4311yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C4311yescharacteristic
402C22×C4C2×D4×C4311yescharacteristic
403C22×C4C2×D4×C4311yescharacteristic
404C22×C4C2×D4×C4311yescharacteristic
405C22×C4C2×D4×C4311yescharacteristic
406C22×C4#41×C4311yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C4311yescharacteristic
430C4⋊C4C22⋊C4×C4311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—81no—
454C23—81no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C4311yescharacteristic
461C23#121×C4311yescharacteristic
462C23#123×C4311yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C4311yescharacteristic
495C2×C4C4×D4×C4311yescharacteristic
496C2×C4#120×C4311yescharacteristic
497C2×C4#121×C4311yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C43×#38611yescharacteristic
529C22C43×#47111yescharacteristic
530C22C43×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C43×B(4,𝔽2)11yescharacteristic
539C4C43×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C43×#188911yescharacteristic
547C2C43×#190311yescharacteristic
548C2C43×#190711yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC43×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2976C2semidirect
3. C43×#1786C2semidirect
4. C43×#1783C2semidirect
5. C43×#1513C2semidirect
6. C43×#1305C2semidirect
7. C43×#1293C2semidirect
12. C43×#450C4semidirect
14. C43×#447C4semidirect
229. #9520C43direct (N × H)
267. #2976C2×C43semidirect
268. #1786C2×C43semidirect
269. #1783C2×C43semidirect
270. #1513C2×C43semidirect
271. #1305C2×C43semidirect
272. #1293C2×C43semidirect
286. #450C4×C43semidirect
288. #447C4×C43semidirect
307. C43#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30032
C43×#29762
C43×#17862
C43×#17832
C43×#15132
C43×#13052
C43×#12932
#952043