Finite Group Databasebeta

← C43×#19002 #24939019

Subgroups — C43×#19002 #24939019

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#563C211yesmaximal, characteristic, complemented
2C43×#3234C211yesmaximal, characteristic, complemented
3C43×#3213C211yesmaximal, characteristic
4C43×#3142C211yesmaximal, characteristic, complemented
5C43×#1664C214yesmaximal, complemented
6C43×#1657C214yesmaximal, complemented
7C43×#1534C211yesmaximal, characteristic, complemented
8C43×#1528C211yesmaximal, characteristic, complemented
9C43×#1527C211yesmaximal, characteristic, complemented
10C43×#563—22no—
11C43×#563—22no—
12C43×#563—22no—
13C43×#563C2214yes—
14C43×#532C2211yescharacteristic
15C2×C4⋊Q8×C43—21no—
16C2×#126×C43—21no—
17C2×#126×C43—21no—
18C2×#125×C43C2211yescharacteristic
19C2×#125×C43C2211yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×#123×C43—21no—
22C2×C22⋊Q8×C43—21no—
23C2×C22⋊Q8×C43—21no—
24C43×#501C2212yescomplemented
25C43×#496C2212yes—
26C43×#491C2212yescomplemented
27C43×#490C2212yescomplemented
28C43×#490C2212yescomplemented
29C43×#489C2212yes—
30C43×#488—22no—
31C43×#481—21no—
32C43×#480—21no—
33C43×#478—22no—
34C43×#463—22no—
35C43×#448—21no—
36C43×#447—21no—
37C43×#432C2211yescharacteristic
38C43×#432C2211yescharacteristic
39C43×#417—21no—
40C43×#417—21no—
41C4×M16×C43C2211yescharacteristic
42C43×#330C2214yescomplemented
43C43×#330C2214yescomplemented
44C43×#329C2214yes—
45C2×#41×C43—21no—
46C22×Q8×C43—21no—
47C22×Q8×C43D411yescharacteristic
48C22×D4×C43D411yescharacteristic
49C23×C4×C43—21no—
50C2×SD16×C43—22no—
51C2×D8×C43—22no—
52C2×M16×C43—21no—
53C4⋊Q8×C43—24no—
54C4⋊Q8×C43—24no—
55C4⋊Q8×C43C2311yescharacteristic
56#127×C43C2311yescharacteristic
57#126×C43—24no—
58#126×C43—24no—
59#126×C43—24no—
60#126×C43—24no—
61#125×C43—21no—
62#125×C43—21no—
63#125×C43—21no—
64#125×C43—21no—
65#125×C43D412yes—
66#125×C43D412yes—
67#125×C43C2312yes—
68#125×C43C2312yes—
69#124×C43—21no—
70#124×C43—21no—
71#124×C43—21no—
72#124×C43D412yes—
73#124×C43C2312yes—
74#123×C43—24no—
75#123×C43—24no—
76C22⋊Q8×C43—24no—
77C22⋊Q8×C43—24no—
78C22⋊Q8×C43—24no—
79C22⋊Q8×C43—24no—
80#121×C43—21no—
81#121×C43—21no—
82C4×D4×C43—21no—
83C4×D4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43D411yescharacteristic
93C2×C4⋊C4×C43D411yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#107×C43—22no—
102#106×C43—22no—
103C4⋊C8×C43—21no—
104C4⋊C8×C43—21no—
105#103×C43—22no—
106#103×C43—22no—
107#103×C43—22no—
108#102×C43—22no—
109#102×C43—22no—
110#102×C43—22no—
111#102×C43—22no—
112#102×C43—22no—
113C22⋊C8×C43—21no—
114C22⋊C8×C43—21no—
115#97×C43C2312yes—
116#97×C43C2312yes—
117#97×C43C2312yes—
118C4×C8×C43—21no—
119C24×C43—21no—
120#41×C43—44no—
121C2×Q8×C43—24no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—81no—
125C2×Q8×C43—82no—
126C2×Q8×C43C2×D412yes—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—41no—
132C2×D4×C43—81no—
133C2×D4×C43C2×D412yes—
134C22×C4×C43—24no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—41no—
141C22×C4×C43—82no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145SD16×C43—82no—
146D8×C43—82no—
147M16×C43—42no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C2×C8×C43—22no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×D412yes—
169C4⋊C4×C43C2×D412yes—
170C4⋊C4×C43C2×D412yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—24no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2411yescharacteristic
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—41no—
190C23×C43#12011yescharacteristic
191Q8×C43—42no—
192Q8×C43—42no—
193Q8×C43—81no—
194Q8×C43—84no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43—81no—
200D4×C43—82no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—82no—
216C2×C4×C43—84no—
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C8×C43—42no—
224C8×C43—42no—
225C8×C43—42no—
226#19002C4311yesmaximal, characteristic, direct product factor, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—84no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43#45412yes—
237C22×C43C2×#12011yescharacteristic
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—42no—
245C4×C43—42no—
246C4×C43—42no—
247C4×C43—42no—
248C4×C43—42no—
249C4×C43—81no—
250C2×#563C2×C4311yescharacteristic, complemented
251#3234C2×C4311yescharacteristic, complemented
252#3213C2×C4311yescharacteristic
253#3142C2×C4311yescharacteristic, complemented
254#1664C2×C4314yescomplemented
255#1657C2×C4314yescomplemented
256#1534C2×C4311yescharacteristic, complemented
257#1528C2×C4311yescharacteristic, complemented
258#1527C2×C4311yescharacteristic, complemented
259C2×C43—22no—
260C2×C43—82no—
261C2×C43—161no—
262C2×C43C2×#45411yescharacteristic
263C2×C43#301911yescharacteristic
264C2×C43#302011yescharacteristic
265#563—22no—
266#563—22no—
267#563—22no—
268#563C22×C4314yes—
269#532C22×C4311yescharacteristic
270C2×C4⋊Q8—21no—
271C2×#126—21no—
272C2×#126—21no—
273C2×#125C22×C4311yescharacteristic
274C2×#125C22×C4311yescharacteristic
275C2×#124C22×C4311yescharacteristic
276C2×#123—21no—
277C2×C22⋊Q8—21no—
278C2×C22⋊Q8—21no—
279#501C22×C4312yescomplemented
280#496C22×C4312yes—
281#491C22×C4312yescomplemented
282#490C22×C4312yescomplemented
283#490C22×C4312yescomplemented
284#489C22×C4312yes—
285#488—22no—
286#481—21no—
287#480—21no—
288#478—22no—
289#463—22no—
290#448—21no—
291#447—21no—
292#432C22×C4311yescharacteristic
293#432C22×C4311yescharacteristic
294#417—21no—
295#417—21no—
296C4×M16C22×C4311yescharacteristic
297#330C22×C4314yescomplemented
298#330C22×C4314yescomplemented
299#329C22×C4314yes—
300C43#1900211yescharacteristic, direct product factor, Sylow
301C2×#41—21no—
302C22×Q8—21no—
303C22×Q8D4×C4311yescharacteristic
304C22×D4D4×C4311yescharacteristic
305C23×C4—21no—
306C2×SD16—22no—
307C2×D8—22no—
308C2×M16—21no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8C23×C4311yescharacteristic
312#127C23×C4311yescharacteristic
313#126—24no—
314#126—24no—
315#126—24no—
316#126—24no—
317#125—21no—
318#125—21no—
319#125—21no—
320#125—21no—
321#125D4×C4312yes—
322#125D4×C4312yes—
323#125C23×C4312yes—
324#125C23×C4312yes—
325#124—21no—
326#124—21no—
327#124—21no—
328#124D4×C4312yes—
329#124C23×C4312yes—
330#123—24no—
331#123—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336#121—21no—
337#121—21no—
338C4×D4—21no—
339C4×D4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4D4×C4311yescharacteristic
347C2×C4⋊C4D4×C4311yescharacteristic
348C2×C4⋊C4D4×C4311yescharacteristic
349C2×C4⋊C4D4×C4311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—21no—
356C2×C42C23×C4311yescharacteristic
357#107—22no—
358#106—22no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361#103—22no—
362#103—22no—
363#103—22no—
364#102—22no—
365#102—22no—
366#102—22no—
367#102—22no—
368#102—22no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371#97C23×C4312yes—
372#97C23×C4312yes—
373#97C23×C4312yes—
374C4×C8—21no—
375C24—21no—
376#41—44no—
377C2×Q8—24no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—81no—
381C2×Q8—82no—
382C2×Q8C2×D4×C4312yes—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—81no—
389C2×D4C2×D4×C4312yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—41no—
397C22×C4—82no—
398C22×C4C2×D4×C4311yescharacteristic
399C22×C4C2×D4×C4311yescharacteristic
400C22×C4C2×D4×C4311yescharacteristic
401SD16—82no—
402D8—82no—
403M16—42no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4C2×D4×C4312yes—
424C4⋊C4C2×D4×C4312yes—
425C4⋊C4C2×D4×C4312yes—
426C4⋊C4C2×D4×C4312yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C42—24no—
437C42C2×D4×C4311yescharacteristic
438C42C2×D4×C4311yescharacteristic
439C42C2×D4×C4311yescharacteristic
440C42C24×C4311yescharacteristic
441C23—22no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23#120×C4311yescharacteristic
447Q8—42no—
448Q8—42no—
449Q8—81no—
450Q8—84no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—81no—
456D4—82no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—84no—
473C2×C4#120×C4311yescharacteristic
474C2×C4#120×C4311yescharacteristic
475C2×C4#120×C4311yescharacteristic
476C2×C4C22×D4×C4311yescharacteristic
477C2×C4C22×D4×C4311yescharacteristic
478C2×C4C22×D4×C4311yescharacteristic
479C8—42no—
480C8—42no—
481C8—42no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C43×#45412yes—
492C22C2×#120×C4311yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C2—22no—
506C2—82no—
507C2—161no—
508C2C2×C43×#45411yescharacteristic
509C2C43×#301911yescharacteristic
510C2C43×#302011yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3213C2
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. C2×C43×#563C2semidirect
2. C43×#3234C2semidirect
4. C43×#3142C2semidirect
5. C43×#1664C2semidirect
6. C43×#1657C2semidirect
7. C43×#1534C2semidirect
8. C43×#1528C2semidirect
9. C43×#1527C2semidirect
24. C43×#501C22semidirect
26. C43×#491C22semidirect
27. C43×#490C22semidirect
28. C43×#490C22semidirect
42. C43×#330C22semidirect
43. C43×#330C22semidirect
226. #19002C43direct (N × H)
250. C2×#563C2×C43semidirect
251. #3234C2×C43semidirect
253. #3142C2×C43semidirect
254. #1664C2×C43semidirect
255. #1657C2×C43semidirect
256. #1534C2×C43semidirect
257. #1528C2×C43semidirect
258. #1527C2×C43semidirect
279. #501C22×C43semidirect
281. #491C22×C43semidirect
282. #490C22×C43semidirect
283. #490C22×C43semidirect
297. #330C22×C43semidirect
298. #330C22×C43semidirect
300. C43#19002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5632
C43×#32342
C43×#32132
C43×#31422
C43×#16642
C43×#16572
C43×#15342
C43×#15282
C43×#15272
#1900243