Finite Group Databasebeta

← C43×#8422 #24928439

Subgroups — C43×#8422 #24928439

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3511C211yesmaximal, characteristic
2C43×#1987C211yesmaximal, characteristic, complemented
3C43×#1806C211yesmaximal, characteristic, complemented
4C43×#1549C211yesmaximal, characteristic, complemented
5C43×#1547C211yesmaximal, characteristic, complemented
6C43×#1502C211yesmaximal, characteristic, complemented
7C43×#1477C211yesmaximal, characteristic, complemented
8C43×#556C412yescomplemented
9C43×#555—21no—
10C43×#554—21no—
11C43×#553—22no—
12C43×#548—22no—
13C43×#547C412yescomplemented
14C43×#542—22no—
15C43×#537—21no—
16C43×#533—21no—
17C43×#532—21no—
18C43×#532C2211yescharacteristic
19C2×C4⋊Q8×C43C2211yescharacteristic
20C43×#520—21no—
21C4×#41×C43C2211yescharacteristic
22C43×#431C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#104×C43—21no—
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#340—22no—
28C43×#339—21no—
29C43×#332—21no—
30C43×#332—22no—
31C43×#331—21no—
32C43×#327—22no—
33C43×Q8⋊C8—21no—
34C43×D4⋊C8—21no—
35C2×#41×C43—22no—
36C2×#41×C43—21no—
37C2×#41×C43D411yescharacteristic
38C22×Q8×C43—21no—
39C2×M16×C43—21no—
40C22×C8×C43—21no—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43—21no—
43C4⋊Q8×C43C2×C412yes—
44C4⋊Q8×C43D412yes—
45C4⋊Q8×C43D411yescharacteristic
46#127×C43D411yescharacteristic
47#126×C43—24no—
48#125×C43—22no—
49#124×C43—24no—
50#124×C43—22no—
51#124×C43—21no—
52#123×C43—24no—
53C22⋊Q8×C43—22no—
54C22⋊Q8×C43—24no—
55C22⋊Q8×C43—22no—
56C22⋊Q8×C43—22no—
57#121×C43—22no—
58#121×C43—22no—
59#121×C43—24no—
60#121×C43—22no—
61#121×C43—21no—
62#121×C43D412yes—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×Q8×C43C2×C411yescharacteristic
66C4×Q8×C43D411yescharacteristic
67C4×D4×C43—22no—
68C4×D4×C43—24no—
69C4×D4×C43—22no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43C2×C411yescharacteristic
74C4×D4×C43C2×C412yes—
75C4×D4×C43D411yescharacteristic
76#117×C43—22no—
77#117×C43—22no—
78#117×C43—21no—
79#117×C43D411yescharacteristic
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D412yes—
84C2×C42×C43—21no—
85C2×C42×C43—21no—
86C2×C42×C43C2311yescharacteristic
87C4⋊C8×C43—21no—
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43—21no—
91C4⋊C8×C43—21no—
92#104×C43—42no—
93C22⋊C8×C43—21no—
94C4×C8×C43—21no—
95#95×C43—21no—
96#41×C43—21no—
97#41×C43—21no—
98#41×C43—21no—
99#41×C43—21no—
100#41×C43—41no—
101#41×C43—41no—
102#41×C43—41no—
103#41×C43—41no—
104#41×C43—84no—
105C2×Q8×C43—22no—
106C2×Q8×C43—21no—
107C2×Q8×C43—22no—
108C2×Q8×C43—82no—
109C2×Q8×C43C22⋊C411yescharacteristic
110C2×D4×C43—24no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—22no—
115C2×D4×C43C22⋊C411yescharacteristic
116C2×D4×C43C22⋊C412yes—
117C22×C4×C43—24no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127M16×C43—41no—
128M16×C43—41no—
129C2×C8×C43—42no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C2×C8×C43—41no—
133C4⋊C4×C43—24no—
134C4⋊C4×C43—24no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43C22⋊C411yescharacteristic
144C4⋊C4×C43C22⋊C414yes—
145C4⋊C4×C43C22⋊C411yescharacteristic
146C4⋊C4×C43C22⋊C412yes—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—24no—
149C22⋊C4×C43—24no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—21no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—21no—
155C42×C43—24no—
156C42×C43—21no—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—41no—
160C42×C43—41no—
161C42×C43C22×C411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43C2×D411yescharacteristic
164C42×C43C2×D411yescharacteristic
165C23×C43—21no—
166C23×C43—22no—
167C23×C43#12011yescharacteristic
168Q8×C43—21no—
169Q8×C43—21no—
170Q8×C43—44no—
171Q8×C43—41no—
172Q8×C43—41no—
173Q8×C43—82no—
174D4×C43—21no—
175D4×C43—21no—
176D4×C43—42no—
177D4×C43—41no—
178D4×C43—42no—
179D4×C43—41no—
180D4×C43—42no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—84no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—22no—
191C2×C4×C43—21no—
192C2×C4×C43—24no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—82no—
203C2×C4×C43—84no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#13511yescharacteristic
213C2×C4×C43#13511yescharacteristic
214C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
215C2×C4×C43#13711yescharacteristic
216C8×C43—81no—
217C8×C43—81no—
218C8×C43—81no—
219#8422C4311yesmaximal, characteristic, direct product factor, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—41no—
223C22×C43—42no—
224C22×C43—41no—
225C22×C43—42no—
226C22×C43—41no—
227C22×C43—42no—
228C22×C43#37911yescharacteristic
229C22×C43#44911yescharacteristic
230C22×C43#45211yescharacteristic
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—41no—
235C4×C43—41no—
236C4×C43—44no—
237C4×C43—41no—
238C4×C43—42no—
239C4×C43—82no—
240C4×C43#41611yescharacteristic
241C4×C43#41711yescharacteristic
242C4×C43#44911yescharacteristic
243C4×C43#45211yescharacteristic
244C4×C43#45411yescharacteristic
245C4×C43#45611yescharacteristic
246#3511C2×C4311yescharacteristic
247#1987C2×C4311yescharacteristic, complemented
248#1806C2×C4311yescharacteristic, complemented
249#1549C2×C4311yescharacteristic, complemented
250#1547C2×C4311yescharacteristic, complemented
251#1502C2×C4311yescharacteristic, complemented
252#1477C2×C4311yescharacteristic, complemented
253C2×C43—21no—
254C2×C43—21no—
255C2×C43—81no—
256C2×C43—82no—
257C2×C43#178811yescharacteristic
258C2×C43#179311yescharacteristic
259C2×C43#179511yescharacteristic
260#556C4×C4312yescomplemented
261#555—21no—
262#554—21no—
263#553—22no—
264#548—22no—
265#547C4×C4312yescomplemented
266#542—22no—
267#537—21no—
268#533—21no—
269#532—21no—
270#532C22×C4311yescharacteristic
271C2×C4⋊Q8C22×C4311yescharacteristic
272#520—21no—
273C4×#41C22×C4311yescharacteristic
274#431C22×C4311yescharacteristic
275#423C22×C4311yescharacteristic
276C2×C4⋊C8C22×C4311yescharacteristic
277C2×#104—21no—
278C4×C4⋊C4C22×C4311yescharacteristic
279#340—22no—
280#339—21no—
281#332—21no—
282#332—22no—
283#331—21no—
284#327—22no—
285Q8⋊C8—21no—
286D4⋊C8—21no—
287C43#842211yescharacteristic, direct product factor, Sylow
288C2×#41—22no—
289C2×#41—21no—
290C2×#41D4×C4311yescharacteristic
291C22×Q8—21no—
292C2×M16—21no—
293C22×C8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8C2×C4×C4312yes—
297C4⋊Q8D4×C4312yes—
298C4⋊Q8D4×C4311yescharacteristic
299#127D4×C4311yescharacteristic
300#126—24no—
301#125—22no—
302#124—24no—
303#124—22no—
304#124—21no—
305#123—24no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310#121—22no—
311#121—22no—
312#121—24no—
313#121—22no—
314#121—21no—
315#121D4×C4312yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8C2×C4×C4311yescharacteristic
319C4×Q8D4×C4311yescharacteristic
320C4×D4—22no—
321C4×D4—24no—
322C4×D4—22no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4C2×C4×C4311yescharacteristic
327C4×D4C2×C4×C4312yes—
328C4×D4D4×C4311yescharacteristic
329#117—22no—
330#117—22no—
331#117—21no—
332#117D4×C4311yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C4312yes—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C23×C4311yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345#104—42no—
346C22⋊C8—21no—
347C4×C8—21no—
348#95—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352#41—21no—
353#41—41no—
354#41—41no—
355#41—41no—
356#41—41no—
357#41—84no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—82no—
362C2×Q8C22⋊C4×C4311yescharacteristic
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22⋊C4×C4311yescharacteristic
369C2×D4C22⋊C4×C4312yes—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4C2×D4×C4311yescharacteristic
378C22×C4C2×D4×C4311yescharacteristic
379C22×C4C2×D4×C4311yescharacteristic
380M16—41no—
381M16—41no—
382C2×C8—42no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4C22⋊C4×C4311yescharacteristic
397C4⋊C4C22⋊C4×C4314yes—
398C4⋊C4C22⋊C4×C4311yescharacteristic
399C4⋊C4C22⋊C4×C4312yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—22no—
406C22⋊C4—21no—
407C22⋊C4—22no—
408C42—24no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—41no—
413C42—41no—
414C42C22×C4×C4311yescharacteristic
415C42C2×D4×C4311yescharacteristic
416C42C2×D4×C4311yescharacteristic
417C42C2×D4×C4311yescharacteristic
418C23—21no—
419C23—22no—
420C23#120×C4311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—44no—
424Q8—41no—
425Q8—41no—
426Q8—82no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—42no—
432D4—41no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—84no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—84no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4C2×C22⋊C4×C4311yescharacteristic
460C2×C4C2×C22⋊C4×C4311yescharacteristic
461C2×C4C2×C22⋊C4×C4311yescharacteristic
462C2×C4#120×C4311yescharacteristic
463C2×C4#120×C4311yescharacteristic
464C2×C4#120×C4311yescharacteristic
465C2×C4#135×C4311yescharacteristic
466C2×C4#135×C4311yescharacteristic
467C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
468C2×C4#137×C4311yescharacteristic
469C8—81no—
470C8—81no—
471C8—81no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—42no—
476C22—41no—
477C22—42no—
478C22—41no—
479C22—42no—
480C22C43×#37911yescharacteristic
481C22C43×#44911yescharacteristic
482C22C43×#45211yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—82no—
492C4C43×#41611yescharacteristic
493C4C43×#41711yescharacteristic
494C4C43×#44911yescharacteristic
495C4C43×#45211yescharacteristic
496C4C43×#45411yescharacteristic
497C4C43×#45611yescharacteristic
498C2—21no—
499C2—21no—
500C2—81no—
501C2—82no—
502C2C43×#178811yescharacteristic
503C2C43×#179311yescharacteristic
504C2C43×#179511yescharacteristic
subgroupG/H
center, socleC22×C43#379
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3511C2
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
2. C43×#1987C2semidirect
3. C43×#1806C2semidirect
4. C43×#1549C2semidirect
5. C43×#1547C2semidirect
6. C43×#1502C2semidirect
7. C43×#1477C2semidirect
8. C43×#556C4semidirect
13. C43×#547C4semidirect
219. #8422C43direct (N × H)
247. #1987C2×C43semidirect
248. #1806C2×C43semidirect
249. #1549C2×C43semidirect
250. #1547C2×C43semidirect
251. #1502C2×C43semidirect
252. #1477C2×C43semidirect
260. #556C4×C43semidirect
265. #547C4×C43semidirect
287. C43#8422direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35112
C43×#19872
C43×#18062
C43×#15492
C43×#15472
C43×#15022
C43×#14772
#842243