Finite Group Databasebeta

← C43×#8513 #24928530

Subgroups — C43×#8513 #24928530

Order 11008.

724 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×#3559C211yesmaximal, characteristic
2C43×#1989C211yesmaximal, characteristic, complemented
3C43×#1980C211yesmaximal, characteristic, complemented
4C43×#1551C211yesmaximal, characteristic, complemented
5C43×#1528C211yesmaximal, characteristic, complemented
6C43×#1509C211yesmaximal, characteristic, complemented
7C43×#1483C211yesmaximal, characteristic, complemented
8C43×#563C412yescomplemented
9C43×#562C412yescomplemented
10C43×#554—21no—
11C43×#553—21no—
12C43×#553—21no—
13C43×#547—22no—
14C43×#547—21no—
15C43×#544—21no—
16C43×#540—21no—
17C43×#539—22no—
18C43×#539—21no—
19C43×#537—21no—
20C43×#532C2211yescharacteristic
21C43×#529C2211yescharacteristic
22C2×#125×C43C2211yescharacteristic
23C43×#432C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#104×C43—22no—
26C4×M16×C43C2211yescharacteristic
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#340—21no—
29C43×#340—21no—
30C43×#333—21no—
31C43×#331—21no—
32C43×#330—22no—
33C43×#328—21no—
34C43×#327—21no—
35C43×Q8⋊C8—21no—
36C43×D4⋊C8—21no—
37C2×#41×C43—22no—
38C2×#41×C43D412yes—
39C2×M16×C43—21no—
40C22×C8×C43—21no—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43—22no—
43C4⋊Q8×C43D411yescharacteristic
44#127×C43D411yescharacteristic
45#126×C43—22no—
46#126×C43—22no—
47#126×C43—21no—
48#125×C43—22no—
49#125×C43—21no—
50#125×C43—21no—
51#125×C43—21no—
52#125×C43C2×C412yes—
53#125×C43C2×C411yescharacteristic
54#125×C43D412yes—
55#124×C43C2×C411yescharacteristic
56#124×C43C2×C412yes—
57#123×C43—22no—
58#123×C43—22no—
59#123×C43—22no—
60#123×C43—22no—
61#123×C43—21no—
62#123×C43—22no—
63#123×C43—22no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—22no—
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43—22no—
68C22⋊Q8×C43—22no—
69C22⋊Q8×C43—22no—
70C22⋊Q8×C43D411yescharacteristic
71#121×C43—22no—
72#121×C43—22no—
73#121×C43—21no—
74#121×C43—21no—
75#121×C43—22no—
76#121×C43—22no—
77#121×C43—21no—
78#121×C43—21no—
79#121×C43D411yescharacteristic
80C4×Q8×C43D411yescharacteristic
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43—21no—
86C4×D4×C43—21no—
87C4×D4×C43—21no—
88C4×D4×C43D411yescharacteristic
89#117×C43—21no—
90#117×C43—21no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43D411yescharacteristic
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C42×C43—21no—
99C2×C42×C43C2311yescharacteristic
100C4⋊C8×C43—21no—
101C4⋊C8×C43—21no—
102C4⋊C8×C43—21no—
103#104×C43—44no—
104C22⋊C8×C43—21no—
105#97×C43—21no—
106#97×C43—21no—
107C4×C8×C43—21no—
108#95×C43—21no—
109#41×C43—42no—
110#41×C43—42no—
111#41×C43—82no—
112#41×C43—82no—
113C2×Q8×C43—22no—
114C2×Q8×C43C22⋊C411yescharacteristic
115C2×Q8×C43C22⋊C412yes—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—21no—
122C2×D4×C43C22⋊C411yescharacteristic
123C2×D4×C43C22⋊C412yes—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135M16×C43—22no—
136M16×C43—41no—
137C2×C8×C43—41no—
138C2×C8×C43—42no—
139C2×C8×C43—41no—
140C2×C8×C43—41no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43C22⋊C412yes—
160C4⋊C4×C43C22⋊C412yes—
161C4⋊C4×C43C22⋊C411yescharacteristic
162C4⋊C4×C43C22⋊C411yescharacteristic
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—22no—
176C42×C43—21no—
177C42×C43—42no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C23×C43—22no—
183C23×C43—21no—
184C23×C43#12011yescharacteristic
185Q8×C43—41no—
186Q8×C43—42no—
187Q8×C43—82no—
188D4×C43—41no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—41no—
192D4×C43—42no—
193D4×C43—41no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—81no—
197D4×C43—82no—
198D4×C43—82no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—82no—
216C2×C4×C43—81no—
217C2×C4×C43—82no—
218C2×C4×C43—82no—
219C2×C4×C43—82no—
220C2×C4×C43—81no—
221C2×C4×C43—81no—
222C2×C4×C43C2×C22⋊C411yescharacteristic
223C2×C4×C43C2×C22⋊C411yescharacteristic
224C2×C4×C43C2×C22⋊C411yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C8×C43—42no—
229C8×C43—81no—
230C8×C43—81no—
231#8513C4311yesmaximal, characteristic, direct product factor, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—42no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—41no—
240C22×C43#37911yescharacteristic
241C22×C43#45311yescharacteristic
242C22×C43#45511yescharacteristic
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—42no—
249C4×C43—42no—
250C4×C43—41no—
251C4×C43—41no—
252C4×C43—42no—
253C4×C43—41no—
254C4×C43—82no—
255C4×C43#45411yescharacteristic
256C4×C43#45611yescharacteristic
257#3559C2×C4311yescharacteristic
258#1989C2×C4311yescharacteristic, complemented
259#1980C2×C4311yescharacteristic, complemented
260#1551C2×C4311yescharacteristic, complemented
261#1528C2×C4311yescharacteristic, complemented
262#1509C2×C4311yescharacteristic, complemented
263#1483C2×C4311yescharacteristic, complemented
264C2×C43—21no—
265C2×C43—21no—
266C2×C43—82no—
267C2×C43—81no—
268C2×C43#179211yescharacteristic
269C2×C43#179311yescharacteristic
270C2×C43#179411yescharacteristic
271#563C4×C4312yescomplemented
272#562C4×C4312yescomplemented
273#554—21no—
274#553—21no—
275#553—21no—
276#547—22no—
277#547—21no—
278#544—21no—
279#540—21no—
280#539—22no—
281#539—21no—
282#537—21no—
283#532C22×C4311yescharacteristic
284#529C22×C4311yescharacteristic
285C2×#125C22×C4311yescharacteristic
286#432C22×C4311yescharacteristic
287C2×C4⋊C8C22×C4311yescharacteristic
288C2×#104—22no—
289C4×M16C22×C4311yescharacteristic
290C4×C4⋊C4C22×C4311yescharacteristic
291#340—21no—
292#340—21no—
293#333—21no—
294#331—21no—
295#330—22no—
296#328—21no—
297#327—21no—
298Q8⋊C8—21no—
299D4⋊C8—21no—
300C43#851311yescharacteristic, direct product factor, Sylow
301C2×#41—22no—
302C2×#41D4×C4312yes—
303C2×M16—21no—
304C22×C8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—22no—
307C4⋊Q8D4×C4311yescharacteristic
308#127D4×C4311yescharacteristic
309#126—22no—
310#126—22no—
311#126—21no—
312#125—22no—
313#125—21no—
314#125—21no—
315#125—21no—
316#125C2×C4×C4312yes—
317#125C2×C4×C4311yescharacteristic
318#125D4×C4312yes—
319#124C2×C4×C4311yescharacteristic
320#124C2×C4×C4312yes—
321#123—22no—
322#123—22no—
323#123—22no—
324#123—22no—
325#123—21no—
326#123—22no—
327#123—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C4311yescharacteristic
335#121—22no—
336#121—22no—
337#121—21no—
338#121—21no—
339#121—22no—
340#121—22no—
341#121—21no—
342#121—21no—
343#121D4×C4311yescharacteristic
344C4×Q8D4×C4311yescharacteristic
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4D4×C4311yescharacteristic
353#117—21no—
354#117—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4D4×C4311yescharacteristic
361C2×C4⋊C4D4×C4311yescharacteristic
362C2×C42—21no—
363C2×C42C23×C4311yescharacteristic
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367#104—44no—
368C22⋊C8—21no—
369#97—21no—
370#97—21no—
371C4×C8—21no—
372#95—21no—
373#41—42no—
374#41—42no—
375#41—82no—
376#41—82no—
377C2×Q8—22no—
378C2×Q8C22⋊C4×C4311yescharacteristic
379C2×Q8C22⋊C4×C4312yes—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4C22⋊C4×C4311yescharacteristic
387C2×D4C22⋊C4×C4312yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—41no—
396C22×C4C2×D4×C4311yescharacteristic
397C22×C4C2×D4×C4311yescharacteristic
398C22×C4C2×D4×C4311yescharacteristic
399M16—22no—
400M16—41no—
401C2×C8—41no—
402C2×C8—42no—
403C2×C8—41no—
404C2×C8—41no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—41no—
423C4⋊C4C22⋊C4×C4312yes—
424C4⋊C4C22⋊C4×C4312yes—
425C4⋊C4C22⋊C4×C4311yescharacteristic
426C4⋊C4C22⋊C4×C4311yescharacteristic
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C42—22no—
440C42—21no—
441C42—42no—
442C42C22×C4×C4311yescharacteristic
443C42C2×D4×C4311yescharacteristic
444C42C2×D4×C4311yescharacteristic
445C42C2×D4×C4311yescharacteristic
446C23—22no—
447C23—21no—
448C23#120×C4311yescharacteristic
449Q8—42no—
450Q8—41no—
451Q8—82no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—41no—
456D4—42no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—81no—
461D4—82no—
462D4—82no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—82no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4C2×C22⋊C4×C4311yescharacteristic
487C2×C4C2×C22⋊C4×C4311yescharacteristic
488C2×C4C2×C22⋊C4×C4311yescharacteristic
489C2×C4#120×C4311yescharacteristic
490C2×C4#120×C4311yescharacteristic
491C2×C4#120×C4311yescharacteristic
492C8—42no—
493C8—81no—
494C8—81no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—42no—
502C22—41no—
503C22C43×#37911yescharacteristic
504C22C43×#45311yescharacteristic
505C22C43×#45511yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—42no—
512C4—42no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—82no—
518C4C43×#45411yescharacteristic
519C4C43×#45611yescharacteristic
520C2—21no—
521C2—21no—
522C2—82no—
523C2—81no—
524C2C43×#179211yescharacteristic
525C2C43×#179311yescharacteristic
526C2C43×#179411yescharacteristic
subgroupG/H
center, socleC22×C43#379
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3559C2
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×#1989C2semidirect
3. C43×#1980C2semidirect
4. C43×#1551C2semidirect
5. C43×#1528C2semidirect
6. C43×#1509C2semidirect
7. C43×#1483C2semidirect
8. C43×#563C4semidirect
9. C43×#562C4semidirect
231. #8513C43direct (N × H)
258. #1989C2×C43semidirect
259. #1980C2×C43semidirect
260. #1551C2×C43semidirect
261. #1528C2×C43semidirect
262. #1509C2×C43semidirect
263. #1483C2×C43semidirect
271. #563C4×C43semidirect
272. #562C4×C43semidirect
300. C43#8513direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35592
C43×#19892
C43×#19802
C43×#15512
C43×#15282
C43×#15092
C43×#14832
#851343