Finite Group Databasebeta

← C43×#19650 #24939667

Subgroups — C43×#19650 #24939667

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3228C211yesmaximal, characteristic, complemented
2C43×#3210C211yesmaximal, characteristic, complemented
3C43×#3185C211yesmaximal, characteristic, complemented
4C43×#3184C211yesmaximal, characteristic
5C43×#3167C211yesmaximal, characteristic, complemented
6C43×#3131C211yesmaximal, characteristic, complemented
7C43×#1720C211yesmaximal, characteristic, complemented
8C43×#1719C211yesmaximal, characteristic, complemented
9C43×#1716C211yesmaximal, characteristic, complemented
10C43×#1715C211yesmaximal, characteristic, complemented
11C43×#1711C211yesmaximal, characteristic, complemented
12C43×#1709C211yesmaximal, characteristic, complemented
13C43×#1708C211yesmaximal, characteristic, complemented
14C43×#1707C211yesmaximal, characteristic, complemented
15C8×M16×C43C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#532C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#498C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#494C2211yescharacteristic
27C43×#493C2211yescharacteristic
28C43×#492C2211yescharacteristic
29C43×#492C2211yescharacteristic
30C43×#488—22no—
31C43×#487C2211yescharacteristic
32C43×#487C2211yescharacteristic
33C43×#487C2211yescharacteristic
34C43×#487C2211yescharacteristic
35C43×#487C2211yescharacteristic
36C43×#487C2211yescharacteristic
37C43×#486C2211yescharacteristic
38C43×#486C2211yescharacteristic
39C43×#486C2211yescharacteristic
40C43×#486C2211yescharacteristic
41C43×#486C2211yescharacteristic
42C43×#486C2211yescharacteristic
43C43×#486C2211yescharacteristic
44C43×#486C2211yescharacteristic
45C43×#482—22no—
46C43×#478—22no—
47C43×#470—22no—
48C43×#469—22no—
49C43×#465—22no—
50C43×#464—22no—
51C43×#452—22no—
52C43×#442—22no—
53C43×#441—22no—
54C4×SD16×C43—22no—
55C43×#431C2211yescharacteristic
56C43×#416—22no—
57C4×M16×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#322C2211yescharacteristic
60C43×#322C2211yescharacteristic
61C82×C43C2211yescharacteristic
62C82×C43C2211yescharacteristic
63C2×#41×C43—21no—
64C2×#41×C43—21no—
65C2×Q16×C43—22no—
66C2×Q16×C43—22no—
67C2×SD16×C43—22no—
68C2×SD16×C43—22no—
69C2×D8×C43—22no—
70C2×M16×C43D412yes—
71C22×C8×C43D412yes—
72C4⋊Q8×C43C2311yescharacteristic
73C4⋊Q8×C43C2311yescharacteristic
74C4⋊Q8×C43C2311yescharacteristic
75C4⋊Q8×C43C2311yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78#127×C43C2311yescharacteristic
79#127×C43C2311yescharacteristic
80#125×C43—21no—
81#125×C43—21no—
82#124×C43—21no—
83#124×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104#106×C43—22no—
105#106×C43—22no—
106#106×C43—22no—
107#106×C43—22no—
108C4⋊C8×C43D412yes—
109#103×C43—22no—
110#103×C43—22no—
111#103×C43—22no—
112#103×C43—22no—
113#103×C43—22no—
114#103×C43—22no—
115#102×C43—22no—
116#102×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#102×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123C22⋊C8×C43D412yes—
124#97×C43D412yes—
125C4×C8×C43D412yes—
126C4×C8×C43C2311yescharacteristic
127C4×C8×C43C2311yescharacteristic
128C4×C8×C43C2311yescharacteristic
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132#41×C43—44no—
133#41×C43—82no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153Q16×C43—44no—
154Q16×C43—82no—
155SD16×C43—44no—
156SD16×C43—82no—
157D8×C43—44no—
158M16×C43—24no—
159C2×C8×C43—42no—
160C2×C8×C43C2×D412yes—
161C2×C8×C43C2×D412yes—
162C2×C8×C43C2×D412yes—
163C2×C8×C43C2×D412yes—
164C2×C8×C43C2×D412yes—
165C2×C8×C43C2×D412yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—41no—
189C42×C43—41no—
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2411yescharacteristic
194C23×C43—41no—
195C23×C43—41no—
196C23×C43#12711yescharacteristic
197Q8×C43—42no—
198Q8×C43—42no—
199Q8×C43—42no—
200Q8×C43—42no—
201Q8×C43—42no—
202Q8×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—82no—
210D4×C43—82no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—82no—
221C2×C4×C43—82no—
222C2×C4×C43#12711yescharacteristic
223C2×C4×C43#12711yescharacteristic
224C2×C4×C43#12711yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C8×C43—22no—
229C8×C43—22no—
230C8×C43—22no—
231C8×C43—22no—
232C8×C43—22no—
233C8×C43#13514yes—
234#19650C4311yesmaximal, characteristic, direct product factor, Sylow
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43C2×#12711yescharacteristic
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43—81no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43C2×#13512yes—
255C4×C43#57512yes—
256C4×C43#57712yes—
257#3228C2×C4311yescharacteristic, complemented
258#3210C2×C4311yescharacteristic, complemented
259#3185C2×C4311yescharacteristic, complemented
260#3184C2×C4311yescharacteristic
261#3167C2×C4311yescharacteristic, complemented
262#3131C2×C4311yescharacteristic, complemented
263#1720C2×C4311yescharacteristic, complemented
264#1719C2×C4311yescharacteristic, complemented
265#1716C2×C4311yescharacteristic, complemented
266#1715C2×C4311yescharacteristic, complemented
267#1711C2×C4311yescharacteristic, complemented
268#1709C2×C4311yescharacteristic, complemented
269#1708C2×C4311yescharacteristic, complemented
270#1707C2×C4311yescharacteristic, complemented
271C8×M16C2×C4311yescharacteristic, complemented
272C2×C43—41no—
273C2×C43—161no—
274C2×C43—161no—
275C2×C43#314711yescharacteristic
276C2×C43#315311yescharacteristic
277C2×C43#315411yescharacteristic
278#533C22×C4311yescharacteristic
279#533C22×C4311yescharacteristic
280#532C22×C4311yescharacteristic
281#532C22×C4311yescharacteristic
282#500C22×C4311yescharacteristic
283#498C22×C4311yescharacteristic
284#498C22×C4311yescharacteristic
285#498C22×C4311yescharacteristic
286#498C22×C4311yescharacteristic
287#494C22×C4311yescharacteristic
288#494C22×C4311yescharacteristic
289#493C22×C4311yescharacteristic
290#492C22×C4311yescharacteristic
291#492C22×C4311yescharacteristic
292#488—22no—
293#487C22×C4311yescharacteristic
294#487C22×C4311yescharacteristic
295#487C22×C4311yescharacteristic
296#487C22×C4311yescharacteristic
297#487C22×C4311yescharacteristic
298#487C22×C4311yescharacteristic
299#486C22×C4311yescharacteristic
300#486C22×C4311yescharacteristic
301#486C22×C4311yescharacteristic
302#486C22×C4311yescharacteristic
303#486C22×C4311yescharacteristic
304#486C22×C4311yescharacteristic
305#486C22×C4311yescharacteristic
306#486C22×C4311yescharacteristic
307#482—22no—
308#478—22no—
309#470—22no—
310#469—22no—
311#465—22no—
312#464—22no—
313#452—22no—
314#442—22no—
315#441—22no—
316C4×SD16—22no—
317#431C22×C4311yescharacteristic
318#416—22no—
319C4×M16C22×C4311yescharacteristic
320C2×C4×C8C22×C4311yescharacteristic
321#322C22×C4311yescharacteristic
322#322C22×C4311yescharacteristic
323C82C22×C4311yescharacteristic
324C82C22×C4311yescharacteristic
325C43#1965011yescharacteristic, direct product factor, Sylow
326C2×#41—21no—
327C2×#41—21no—
328C2×Q16—22no—
329C2×Q16—22no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×D8—22no—
333C2×M16D4×C4312yes—
334C22×C8D4×C4312yes—
335C4⋊Q8C23×C4311yescharacteristic
336C4⋊Q8C23×C4311yescharacteristic
337C4⋊Q8C23×C4311yescharacteristic
338C4⋊Q8C23×C4311yescharacteristic
339C4⋊Q8C23×C4311yescharacteristic
340C4⋊Q8C23×C4311yescharacteristic
341#127C23×C4311yescharacteristic
342#127C23×C4311yescharacteristic
343#125—21no—
344#125—21no—
345#124—21no—
346#124—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363#117—21no—
364#117—21no—
365C2×C42C23×C4311yescharacteristic
366#107—22no—
367#106—22no—
368#106—22no—
369#106—22no—
370#106—22no—
371C4⋊C8D4×C4312yes—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379#102—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386C22⋊C8D4×C4312yes—
387#97D4×C4312yes—
388C4×C8D4×C4312yes—
389C4×C8C23×C4311yescharacteristic
390C4×C8C23×C4311yescharacteristic
391C4×C8C23×C4311yescharacteristic
392C4×C8C23×C4311yescharacteristic
393C4×C8C23×C4311yescharacteristic
394C4×C8C23×C4311yescharacteristic
395#41—44no—
396#41—82no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4C2×D4×C4311yescharacteristic
414C22×C4C2×D4×C4311yescharacteristic
415C22×C4C2×D4×C4311yescharacteristic
416Q16—44no—
417Q16—82no—
418SD16—44no—
419SD16—82no—
420D8—44no—
421M16—24no—
422C2×C8—42no—
423C2×C8C2×D4×C4312yes—
424C2×C8C2×D4×C4312yes—
425C2×C8C2×D4×C4312yes—
426C2×C8C2×D4×C4312yes—
427C2×C8C2×D4×C4312yes—
428C2×C8C2×D4×C4312yes—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C42—41no—
452C42—41no—
453C42C2×D4×C4311yescharacteristic
454C42C2×D4×C4311yescharacteristic
455C42C2×D4×C4311yescharacteristic
456C42C24×C4311yescharacteristic
457C23—41no—
458C23—41no—
459C23#127×C4311yescharacteristic
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—82no—
473D4—82no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4#127×C4311yescharacteristic
486C2×C4#127×C4311yescharacteristic
487C2×C4#127×C4311yescharacteristic
488C2×C4C22×D4×C4311yescharacteristic
489C2×C4C22×D4×C4311yescharacteristic
490C2×C4C22×D4×C4311yescharacteristic
491C8—22no—
492C8—22no—
493C8—22no—
494C8—22no—
495C8—22no—
496C8#135×C4314yes—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C2×#127×C4311yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4C2×#135×C4312yes—
517C4C43×#57512yes—
518C4C43×#57712yes—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C43×#314711yescharacteristic
523C2C43×#315311yescharacteristic
524C2C43×#315411yescharacteristic
subgroupG/H
center, socleC22×C43C2×#127
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3184C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3228C2semidirect
2. C43×#3210C2semidirect
3. C43×#3185C2semidirect
5. C43×#3167C2semidirect
6. C43×#3131C2semidirect
7. C43×#1720C2semidirect
8. C43×#1719C2semidirect
9. C43×#1716C2semidirect
10. C43×#1715C2semidirect
11. C43×#1711C2semidirect
12. C43×#1709C2semidirect
13. C43×#1708C2semidirect
14. C43×#1707C2semidirect
15. C8×M16×C43C2semidirect
234. #19650C43direct (N × H)
257. #3228C2×C43semidirect
258. #3210C2×C43semidirect
259. #3185C2×C43semidirect
261. #3167C2×C43semidirect
262. #3131C2×C43semidirect
263. #1720C2×C43semidirect
264. #1719C2×C43semidirect
265. #1716C2×C43semidirect
266. #1715C2×C43semidirect
267. #1711C2×C43semidirect
268. #1709C2×C43semidirect
269. #1708C2×C43semidirect
270. #1707C2×C43semidirect
271. C8×M16C2×C43semidirect
325. C43#19650direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32282
C43×#32102
C43×#31852
C43×#31842
C43×#31672
C43×#31312
C43×#17202
C43×#17192
C43×#17162
C43×#17152
C43×#17112
C43×#17092
C43×#17082
C43×#17072
C8×M16×C432
#1965043