Finite Group Databasebeta

← C43×#18995 #24939012

Subgroups — C43×#18995 #24939012

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3529C211yesmaximal, characteristic, complemented
2C43×#3217C212yesmaximal, complemented
3C43×#3151C211yesmaximal, characteristic, complemented
4C43×#1657C212yesmaximal, complemented
5C43×#1656C214yesmaximal, complemented
6C43×#1655C212yesmaximal, complemented
7C43×#1536C211yesmaximal, characteristic, complemented
8C43×#1529C212yesmaximal, complemented
9C2×AGL(1,ℤ/8)×C43—21no—
10C2×AGL(1,ℤ/8)×C43—21no—
11C43×#563—21no—
12C43×#563C2211yescharacteristic, complemented
13C43×#562—22no—
14C43×#562C2212yescomplemented
15C43×H(3,𝔽4)C2211yescharacteristic, complemented
16C43×#560—21no—
17C43×#560—22no—
18C43×#532—21no—
19C43×#532C2211yescharacteristic
20C2×#127×C43C2211yescharacteristic, complemented
21C43×#529—22no—
22C43×#529C2212yes—
23C43×#525—21no—
24C43×#525—22no—
25C43×#496C2212yes—
26C43×#496C2214yes—
27C43×#496C2212yescomplemented
28C43×#493—21no—
29C43×#492—21no—
30C43×#490C2214yescomplemented
31C43×#460—22no—
32C43×#459—22no—
33C43×#450—22no—
34C43×#447—22no—
35C43×#432C2212yescomplemented
36C4×M16×C43C2211yescharacteristic, complemented
37C43×#330C2214yescomplemented
38C43×#329C2214yescomplemented
39C43×#329C2212yescomplemented
40C43×#329C2212yescomplemented
41C2×#41×C43—21no—
42C2×#41×C43D411yescharacteristic
43C2×#41×C43D411yescharacteristic
44C22×D4×C43—21no—
45C22×D4×C43—22no—
46C23×C4×C43—21no—
47AGL(1,ℤ/8)×C43—44no—
48AGL(1,ℤ/8)×C43—44no—
49C2×SD16×C43—22no—
50C2×SD16×C43—22no—
51C2×SD16×C43—24no—
52C2×D8×C43—22no—
53C2×D8×C43—22no—
54C2×D8×C43—24no—
55C2×M16×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43D411yescharacteristic
58#127×C43—21no—
59#127×C43—22no—
60#127×C43—21no—
61#127×C43D411yescharacteristic
62#127×C43C2312yes—
63#126×C43—22no—
64#126×C43—22no—
65#126×C43—22no—
66#125×C43—22no—
67#125×C43C2312yes—
68#124×C43—21no—
69#124×C43—22no—
70#124×C43—21no—
71#124×C43C2312yes—
72#124×C43C2311yescharacteristic
73#124×C43C2311yescharacteristic
74#123×C43—22no—
75#123×C43—21no—
76#123×C43—22no—
77#123×C43—21no—
78#123×C43—22no—
79#123×C43—22no—
80#123×C43—22no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43D412yes—
86#121×C43—22no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43D412yes—
94#120×C43—21no—
95#120×C43—22no—
96#120×C43—21no—
97#120×C43—22no—
98C4×Q8×C43D412yes—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43D412yes—
104#117×C43—21no—
105#117×C43—22no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C4⋊C8×C43—22no—
109#102×C43—24no—
110#102×C43—24no—
111C22⋊C8×C43—22no—
112#97×C43C2314yes—
113#97×C43C2312yes—
114C4×C8×C43—21no—
115C24×C43—21no—
116C24×C43—41no—
117#41×C43—42no—
118#41×C43—42no—
119#41×C43—82no—
120C2×Q8×C43—21no—
121C2×Q8×C43C2×D412yes—
122C2×Q8×C43C2×D411yescharacteristic
123C2×Q8×C43C2×D411yescharacteristic
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—24no—
133C2×D4×C43—22no—
134C2×D4×C43—42no—
135C2×D4×C43—41no—
136C2×D4×C43—42no—
137C2×D4×C43—42no—
138C2×D4×C43—84no—
139C2×D4×C43C2×D412yes—
140C2×D4×C43C2×D411yescharacteristic
141C2×D4×C43C2×D411yescharacteristic
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—82no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151SD16×C43—44no—
152SD16×C43—44no—
153SD16×C43—84no—
154D8×C43—44no—
155D8×C43—44no—
156D8×C43—84no—
157M16×C43—24no—
158C2×C8×C43—22no—
159C2×C8×C43—24no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C2×D412yes—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—22no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D412yes—
188C42×C43C2411yescharacteristic
189C23×C43—21no—
190C23×C43—22no—
191C23×C43—21no—
192C23×C43—42no—
193C23×C43—82no—
194C23×C43—84no—
195C23×C43—81no—
196C23×C43—82no—
197C23×C43#12011yescharacteristic
198Q8×C43—41no—
199Q8×C43—41no—
200Q8×C43—42no—
201Q8×C43—81no—
202D4×C43—41no—
203D4×C43—41no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—44no—
208D4×C43—44no—
209D4×C43—82no—
210D4×C43—84no—
211D4×C43—82no—
212D4×C43—81no—
213D4×C43—81no—
214D4×C43—82no—
215D4×C43—82no—
216D4×C43—82no—
217D4×C43—81no—
218D4×C43—82no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—44no—
228C2×C4×C43—42no—
229C2×C4×C43—82no—
230C2×C4×C43—82no—
231C2×C4×C43—81no—
232C2×C4×C43#12012yes—
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43C22×D412yes—
235C2×C4×C43C22×D411yescharacteristic
236C8×C43—24no—
237C8×C43—44no—
238#18995C4311yesmaximal, characteristic, direct product factor, Sylow
239C22×C43—21no—
240C22×C43—22no—
241C22×C43—41no—
242C22×C43—42no—
243C22×C43—41no—
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—84no—
249C22×C43—82no—
250C22×C43—84no—
251C22×C43—164no—
252C22×C43C2×#12011yescharacteristic
253C4×C43—21no—
254C4×C43—22no—
255C4×C43—22no—
256C4×C43—41no—
257C4×C43—42no—
258C4×C43—41no—
259C4×C43—42no—
260C4×C43—42no—
261C4×C43#45312yes—
262#3529C2×C4311yescharacteristic, complemented
263#3217C2×C4312yescomplemented
264#3151C2×C4311yescharacteristic, complemented
265#1657C2×C4312yescomplemented
266#1656C2×C4314yescomplemented
267#1655C2×C4312yescomplemented
268#1536C2×C4311yescharacteristic, complemented
269#1529C2×C4312yescomplemented
270C2×C43—41no—
271C2×C43—81no—
272C2×C43—81no—
273C2×C43—82no—
274C2×C43—162no—
275C2×C43C2×#45311yescharacteristic
276C2×C43#302112yes—
277C2×AGL(1,ℤ/8)—21no—
278C2×AGL(1,ℤ/8)—21no—
279#563—21no—
280#563C22×C4311yescharacteristic, complemented
281#562—22no—
282#562C22×C4312yescomplemented
283H(3,𝔽4)C22×C4311yescharacteristic, complemented
284#560—21no—
285#560—22no—
286#532—21no—
287#532C22×C4311yescharacteristic
288C2×#127C22×C4311yescharacteristic, complemented
289#529—22no—
290#529C22×C4312yes—
291#525—21no—
292#525—22no—
293#496C22×C4312yes—
294#496C22×C4314yes—
295#496C22×C4312yescomplemented
296#493—21no—
297#492—21no—
298#490C22×C4314yescomplemented
299#460—22no—
300#459—22no—
301#450—22no—
302#447—22no—
303#432C22×C4312yescomplemented
304C4×M16C22×C4311yescharacteristic, complemented
305#330C22×C4314yescomplemented
306#329C22×C4312yescomplemented
307#329C22×C4312yescomplemented
308#329C22×C4314yescomplemented
309C43#1899511yescharacteristic, direct product factor, Sylow
310C2×#41—21no—
311C2×#41D4×C4311yescharacteristic
312C2×#41D4×C4311yescharacteristic
313C22×D4—21no—
314C22×D4—22no—
315C23×C4—21no—
316AGL(1,ℤ/8)—44no—
317AGL(1,ℤ/8)—44no—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×SD16—24no—
321C2×D8—22no—
322C2×D8—22no—
323C2×D8—24no—
324C2×M16—21no—
325C4⋊Q8—21no—
326C4⋊Q8D4×C4311yescharacteristic
327#127—21no—
328#127—22no—
329#127—21no—
330#127D4×C4311yescharacteristic
331#127C23×C4312yes—
332#126—22no—
333#126—22no—
334#126—22no—
335#125—22no—
336#125C23×C4312yes—
337#124—21no—
338#124—22no—
339#124—21no—
340#124C23×C4312yes—
341#124C23×C4311yescharacteristic
342#124C23×C4311yescharacteristic
343#123—22no—
344#123—21no—
345#123—22no—
346#123—21no—
347#123—22no—
348#123—22no—
349#123—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8D4×C4312yes—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121D4×C4312yes—
363#120—21no—
364#120—22no—
365#120—21no—
366#120—22no—
367C4×Q8D4×C4312yes—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4D4×C4312yes—
373#117—21no—
374#117—22no—
375C2×C42—21no—
376C2×C42C23×C4311yescharacteristic
377C4⋊C8—22no—
378#102—24no—
379#102—24no—
380C22⋊C8—22no—
381#97C23×C4314yes—
382#97C23×C4312yes—
383C4×C8—21no—
384C24—21no—
385C24—41no—
386#41—42no—
387#41—42no—
388#41—82no—
389C2×Q8—21no—
390C2×Q8C2×D4×C4312yes—
391C2×Q8C2×D4×C4311yescharacteristic
392C2×Q8C2×D4×C4311yescharacteristic
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—41no—
407C2×D4—84no—
408C2×D4C2×D4×C4312yes—
409C2×D4C2×D4×C4311yescharacteristic
410C2×D4C2×D4×C4311yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—82no—
418C22×C4C2×D4×C4311yescharacteristic
419C22×C4C2×D4×C4312yes—
420SD16—44no—
421SD16—44no—
422SD16—84no—
423D8—44no—
424D8—44no—
425D8—84no—
426M16—24no—
427C2×C8—22no—
428C2×C8—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4C2×D4×C4312yes—
438C4⋊C4C2×D4×C4312yes—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C42—21no—
453C42—21no—
454C42—22no—
455C42C2×D4×C4311yescharacteristic
456C42C2×D4×C4312yes—
457C42C24×C4311yescharacteristic
458C23—21no—
459C23—22no—
460C23—21no—
461C23—42no—
462C23—82no—
463C23—84no—
464C23—81no—
465C23—82no—
466C23#120×C4311yescharacteristic
467Q8—41no—
468Q8—41no—
469Q8—42no—
470Q8—81no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—44no—
477D4—44no—
478D4—82no—
479D4—84no—
480D4—81no—
481D4—81no—
482D4—82no—
483D4—82no—
484D4—81no—
485D4—82no—
486D4—82no—
487D4—82no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—82no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4#120×C4312yes—
502C2×C4#120×C4311yescharacteristic
503C2×C4C22×D4×C4312yes—
504C2×C4C22×D4×C4311yescharacteristic
505C8—24no—
506C8—44no—
507C22—21no—
508C22—22no—
509C22—41no—
510C22—42no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—84no—
517C22—82no—
518C22—84no—
519C22—164no—
520C22C2×#120×C4311yescharacteristic
521C4—21no—
522C4—22no—
523C4—22no—
524C4—41no—
525C4—42no—
526C4—41no—
527C4—42no—
528C4—42no—
529C4C43×#45312yes—
530C2—41no—
531C2—81no—
532C2—82no—
533C2—81no—
534C2—162no—
535C2C2×C43×#45311yescharacteristic
536C2C43×#302112yes—
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
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×#3529C2semidirect
2. C43×#3217C2semidirect
3. C43×#3151C2semidirect
4. C43×#1657C2semidirect
5. C43×#1656C2semidirect
6. C43×#1655C2semidirect
7. C43×#1536C2semidirect
8. C43×#1529C2semidirect
12. C43×#563C22semidirect
14. C43×#562C22semidirect
15. C43×H(3,𝔽4)C22semidirect
20. C2×#127×C43C22semidirect
27. C43×#496C22semidirect
30. C43×#490C22semidirect
35. C43×#432C22semidirect
36. C4×M16×C43C22semidirect
37. C43×#330C22semidirect
38. C43×#329C22semidirect
39. C43×#329C22semidirect
40. C43×#329C22semidirect
238. #18995C43direct (N × H)
262. #3529C2×C43semidirect
263. #3217C2×C43semidirect
264. #3151C2×C43semidirect
265. #1657C2×C43semidirect
266. #1656C2×C43semidirect
267. #1655C2×C43semidirect
268. #1536C2×C43semidirect
269. #1529C2×C43semidirect
280. #563C22×C43semidirect
282. #562C22×C43semidirect
283. H(3,𝔽4)C22×C43semidirect
288. C2×#127C22×C43semidirect
295. #496C22×C43semidirect
298. #490C22×C43semidirect
303. #432C22×C43semidirect
304. C4×M16C22×C43semidirect
305. #330C22×C43semidirect
306. #329C22×C43semidirect
307. #329C22×C43semidirect
308. #329C22×C43semidirect
309. C43#18995direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35292
C43×#32172
C43×#31512
C43×#16572
C43×#16562
C43×#16552
C43×#15362
C43×#15292
#1899543