Finite Group Databasebeta

← C43×#8426 #24928443

Subgroups — C43×#8426 #24928443

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3508C211yesmaximal, characteristic
2C43×#1982C211yesmaximal, characteristic, complemented
3C43×#1806C211yesmaximal, characteristic, complemented
4C43×#1550C211yesmaximal, characteristic, complemented
5C43×#1545C211yesmaximal, characteristic, complemented
6C43×#1503C211yesmaximal, characteristic, complemented
7C43×#1477C211yesmaximal, characteristic, complemented
8C43×#559—21no—
9C43×#559C412yescomplemented
10C43×#550—21no—
11C43×#550C412yescomplemented
12C43×#546—22no—
13C43×#546—22no—
14C43×#540—22no—
15C43×#535—21no—
16C43×#533C2211yescharacteristic
17C43×#532—21no—
18C43×#532—21no—
19C2×#127×C43C2211yescharacteristic
20C43×#518—21no—
21C4×#41×C43C2211yescharacteristic
22C43×#431C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#104×C43—21no—
26C2×#102×C43—22no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#339—21no—
29C43×#333—21no—
30C43×#332—21no—
31C43×#331—22no—
32C43×#328—22no—
33C43×Q8⋊C8—21no—
34C43×D4⋊C8—21no—
35C2×#41×C43—22no—
36C2×#41×C43—22no—
37C2×#41×C43D411yescharacteristic
38C22×D4×C43—21no—
39C22×D4×C43—21no—
40C22×D4×C43D412yes—
41C2×M16×C43—21no—
42C22×C8×C43—21no—
43C4⋊Q8×C43D411yescharacteristic
44C4⋊Q8×C43D411yescharacteristic
45#127×C43—22no—
46#127×C43—21no—
47#127×C43—21no—
48#127×C43C2×C412yes—
49#127×C43D412yes—
50#125×C43—21no—
51#124×C43—22no—
52#124×C43—22no—
53#124×C43—22no—
54#123×C43—24no—
55#123×C43—24no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43D412yes—
58#121×C43—22no—
59#121×C43—22no—
60#121×C43—22no—
61#121×C43—24no—
62#121×C43—24no—
63#121×C43—22no—
64#120×C43—24no—
65C4×Q8×C43—21no—
66C4×Q8×C43C2×C411yescharacteristic
67C4×Q8×C43C2×C412yes—
68C4×Q8×C43D411yescharacteristic
69C4×D4×C43—22no—
70C4×D4×C43—22no—
71C4×D4×C43—22no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—22no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43C2×C411yescharacteristic
78C4×D4×C43D411yescharacteristic
79#117×C43—21no—
80#117×C43—21no—
81#117×C43D411yescharacteristic
82C2×C4⋊C4×C43—21no—
83C2×C22⋊C4×C43—24no—
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—
93#102×C43—44no—
94C22⋊C8×C43—21no—
95C4×C8×C43—21no—
96#95×C43—21no—
97C24×C43—22no—
98#41×C43—21no—
99#41×C43—21no—
100#41×C43—21no—
101#41×C43—21no—
102#41×C43—84no—
103#41×C43—82no—
104#41×C43—82no—
105C2×Q8×C43—21no—
106C2×Q8×C43C22⋊C411yescharacteristic
107C2×Q8×C43C22⋊C412yes—
108C2×D4×C43—24no—
109C2×D4×C43—24no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43—82no—
123C2×D4×C43C22⋊C411yescharacteristic
124C2×D4×C43C22⋊C414yes—
125C22×C4×C43—24no—
126C22×C4×C43—24no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—41no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134M16×C43—41no—
135M16×C43—41no—
136C2×C8×C43—42no—
137C2×C8×C43—41no—
138C2×C8×C43—41no—
139C2×C8×C43—41no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43C22⋊C411yescharacteristic
150C4⋊C4×C43C22⋊C411yescharacteristic
151C4⋊C4×C43C22⋊C412yes—
152C22⋊C4×C43—24no—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—24no—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—21no—
157C22⋊C4×C43—21no—
158C22⋊C4×C43—21no—
159C22⋊C4×C43—22no—
160C42×C43—21no—
161C42×C43—22no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—41no—
165C42×C43—41no—
166C42×C43C22×C411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C23×C43—24no—
171C23×C43—21no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—82no—
175C23×C43—82no—
176C23×C43#12011yescharacteristic
177Q8×C43—21no—
178Q8×C43—21no—
179Q8×C43—42no—
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—21no—
183D4×C43—21no—
184D4×C43—44no—
185D4×C43—44no—
186D4×C43—41no—
187D4×C43—41no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—82no—
195D4×C43—84no—
196D4×C43—84no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—84no—
212C2×C4×C43—84no—
213C2×C4×C43—81no—
214C2×C4×C43—81no—
215C2×C4×C43C2×C22⋊C411yescharacteristic
216C2×C4×C43C2×C22⋊C411yescharacteristic
217C2×C4×C43C2×C22⋊C411yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#13511yescharacteristic
222C2×C4×C43#13511yescharacteristic
223C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C43#13711yescharacteristic
225C8×C43—81no—
226C8×C43—81no—
227C8×C43—81no—
228#8426C4311yesmaximal, characteristic, direct product factor, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—44no—
232C22×C43—41no—
233C22×C43—44no—
234C22×C43—41no—
235C22×C43—44no—
236C22×C43—41no—
237C22×C43—162no—
238C22×C43—162no—
239C22×C43#37911yescharacteristic
240C22×C43#44911yescharacteristic
241C22×C43#45211yescharacteristic
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—41no—
246C4×C43—42no—
247C4×C43—41no—
248C4×C43—42no—
249C4×C43—41no—
250C4×C43—82no—
251C4×C43#41611yescharacteristic
252C4×C43#41711yescharacteristic
253C4×C43#44911yescharacteristic
254C4×C43#45211yescharacteristic
255C4×C43#45311yescharacteristic
256C4×C43#45511yescharacteristic
257#3508C2×C4311yescharacteristic
258#1982C2×C4311yescharacteristic, complemented
259#1806C2×C4311yescharacteristic, complemented
260#1550C2×C4311yescharacteristic, complemented
261#1545C2×C4311yescharacteristic, complemented
262#1503C2×C4311yescharacteristic, complemented
263#1477C2×C4311yescharacteristic, complemented
264C2×C43—21no—
265C2×C43—21no—
266C2×C43—81no—
267C2×C43—84no—
268C2×C43#178811yescharacteristic
269C2×C43#179211yescharacteristic
270C2×C43#179511yescharacteristic
271#559—21no—
272#559C4×C4312yescomplemented
273#550—21no—
274#550C4×C4312yescomplemented
275#546—22no—
276#546—22no—
277#540—22no—
278#535—21no—
279#533C22×C4311yescharacteristic
280#532—21no—
281#532—21no—
282C2×#127C22×C4311yescharacteristic
283#518—21no—
284C4×#41C22×C4311yescharacteristic
285#431C22×C4311yescharacteristic
286#423C22×C4311yescharacteristic
287C2×C4⋊C8C22×C4311yescharacteristic
288C2×#104—21no—
289C2×#102—22no—
290C4×C4⋊C4C22×C4311yescharacteristic
291#339—21no—
292#333—21no—
293#332—21no—
294#331—22no—
295#328—22no—
296Q8⋊C8—21no—
297D4⋊C8—21no—
298C43#842611yescharacteristic, direct product factor, Sylow
299C2×#41—22no—
300C2×#41—22no—
301C2×#41D4×C4311yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4D4×C4312yes—
305C2×M16—21no—
306C22×C8—21no—
307C4⋊Q8D4×C4311yescharacteristic
308C4⋊Q8D4×C4311yescharacteristic
309#127—22no—
310#127—21no—
311#127—21no—
312#127C2×C4×C4312yes—
313#127D4×C4312yes—
314#125—21no—
315#124—22no—
316#124—22no—
317#124—22no—
318#123—24no—
319#123—24no—
320C22⋊Q8—21no—
321C22⋊Q8D4×C4312yes—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—24no—
326#121—24no—
327#121—22no—
328#120—24no—
329C4×Q8—21no—
330C4×Q8C2×C4×C4311yescharacteristic
331C4×Q8C2×C4×C4312yes—
332C4×Q8D4×C4311yescharacteristic
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4C2×C4×C4311yescharacteristic
342C4×D4D4×C4311yescharacteristic
343#117—21no—
344#117—21no—
345#117D4×C4311yescharacteristic
346C2×C4⋊C4—21no—
347C2×C22⋊C4—24no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C23×C4311yescharacteristic
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356#104—42no—
357#102—44no—
358C22⋊C8—21no—
359C4×C8—21no—
360#95—21no—
361C24—22no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—21no—
366#41—84no—
367#41—82no—
368#41—82no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C4311yescharacteristic
371C2×Q8C22⋊C4×C4312yes—
372C2×D4—21no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—82no—
387C2×D4C22⋊C4×C4311yescharacteristic
388C2×D4C22⋊C4×C4314yes—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—41no—
395C22×C4C2×D4×C4311yescharacteristic
396C22×C4C2×D4×C4311yescharacteristic
397C22×C4C2×D4×C4311yescharacteristic
398M16—41no—
399M16—41no—
400C2×C8—42no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4C22⋊C4×C4311yescharacteristic
414C4⋊C4C22⋊C4×C4311yescharacteristic
415C4⋊C4C22⋊C4×C4312yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—21no—
421C22⋊C4—22no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C42—21no—
425C42—22no—
426C42—21no—
427C42—21no—
428C42—41no—
429C42—41no—
430C42C22×C4×C4311yescharacteristic
431C42C2×D4×C4311yescharacteristic
432C42C2×D4×C4311yescharacteristic
433C42C2×D4×C4311yescharacteristic
434C23—24no—
435C23—21no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23#120×C4311yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446D4—21no—
447D4—21no—
448D4—44no—
449D4—44no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—84no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—84no—
476C2×C4—84no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4C2×C22⋊C4×C4311yescharacteristic
480C2×C4C2×C22⋊C4×C4311yescharacteristic
481C2×C4C2×C22⋊C4×C4311yescharacteristic
482C2×C4#120×C4311yescharacteristic
483C2×C4#120×C4311yescharacteristic
484C2×C4#120×C4311yescharacteristic
485C2×C4#135×C4311yescharacteristic
486C2×C4#135×C4311yescharacteristic
487C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
488C2×C4#137×C4311yescharacteristic
489C8—81no—
490C8—81no—
491C8—81no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—44no—
496C22—41no—
497C22—44no—
498C22—41no—
499C22—44no—
500C22—162no—
501C22—162no—
502C22C43×#37911yescharacteristic
503C22C43×#44911yescharacteristic
504C22C43×#45211yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4—41no—
512C4—42no—
513C4—82no—
514C4C43×#41611yescharacteristic
515C4C43×#41711yescharacteristic
516C4C43×#44911yescharacteristic
517C4C43×#45211yescharacteristic
518C4C43×#45311yescharacteristic
519C4C43×#45511yescharacteristic
520C2—21no—
521C2—21no—
522C2—84no—
523C2—81no—
524C2C43×#178811yescharacteristic
525C2C43×#179211yescharacteristic
526C2C43×#179511yescharacteristic
subgroupG/H
center, socleC22×C43#379
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3508C2
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×#1982C2semidirect
3. C43×#1806C2semidirect
4. C43×#1550C2semidirect
5. C43×#1545C2semidirect
6. C43×#1503C2semidirect
7. C43×#1477C2semidirect
9. C43×#559C4semidirect
11. C43×#550C4semidirect
228. #8426C43direct (N × H)
258. #1982C2×C43semidirect
259. #1806C2×C43semidirect
260. #1550C2×C43semidirect
261. #1545C2×C43semidirect
262. #1503C2×C43semidirect
263. #1477C2×C43semidirect
272. #559C4×C43semidirect
274. #550C4×C43semidirect
298. C43#8426direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35082
C43×#19822
C43×#18062
C43×#15502
C43×#15452
C43×#15032
C43×#14772
#842643