Finite Group Databasebeta

← C43×#18536 #24938553

Subgroups — C43×#18536 #24938553

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#556C211yesmaximal, characteristic, complemented
2C43×#3141C211yesmaximal, characteristic, complemented
3C43×#3112C211yesmaximal, characteristic, complemented
4C43×#3109C211yesmaximal, characteristic
5C43×#1638C214yesmaximal, complemented
6C43×#1628C214yesmaximal, complemented
7C43×#1556C211yesmaximal, characteristic, complemented
8C43×#1491C211yesmaximal, characteristic, complemented
9C43×#1490C211yesmaximal, characteristic, complemented
10C43×#556—22no—
11C43×#556—22no—
12C43×#556—22no—
13C43×#556C2214yes—
14C43×#532C2211yescharacteristic
15C2×C4⋊Q8×C43C2211yescharacteristic
16C2×#126×C43—22no—
17C2×#124×C43—21no—
18C2×C22⋊Q8×C43—21no—
19C2×C4×Q8×C43—21no—
20C2×C4×Q8×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C2×#117×C43—21no—
23C43×#489—22no—
24C43×#487C2212yescomplemented
25C43×#486C2212yescomplemented
26C43×#481—21no—
27C43×#480—21no—
28C43×#477C2212yescomplemented
29C43×#476C2212yes—
30C43×#460C2212yescomplemented
31C43×#459C2212yes—
32C43×#448—21no—
33C43×#447—21no—
34C43×#442—22no—
35C43×#440—22no—
36C43×#432C2211yescharacteristic
37C43×#432C2211yescharacteristic
38C43×#417—22no—
39C4×M16×C43C2211yescharacteristic
40C43×#332C2214yescomplemented
41C43×Q8⋊C8C2214yescomplemented
42C43×D4⋊C8C2214yes—
43C2×#41×C43—21no—
44C22×Q8×C43—21no—
45C22×Q8×C43D411yescharacteristic
46C22×D4×C43D411yescharacteristic
47C23×C4×C43—21no—
48C2×SD16×C43—22no—
49C2×D8×C43—22no—
50C2×M16×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43D412yes—
54C4⋊Q8×C43C2311yescharacteristic
55C4⋊Q8×C43C2312yes—
56#127×C43C2311yescharacteristic
57#126×C43—28no—
58#126×C43—28no—
59#124×C43—24no—
60#124×C43—24no—
61#124×C43—21no—
62C22⋊Q8×C43—24no—
63C22⋊Q8×C43—24no—
64#121×C43—21no—
65#121×C43—21no—
66C4×Q8×C43—24no—
67C4×Q8×C43—24no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43D412yes—
71C4×Q8×C43C2312yes—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43D412yes—
77C4×D4×C43C2312yes—
78#117×C43—24no—
79#117×C43—24no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43D412yes—
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43—22no—
88C2×C22⋊C4×C43—21no—
89C2×C42×C43—22no—
90C2×C42×C43—21no—
91C2×C42×C43C2311yescharacteristic
92#107×C43—22no—
93#106×C43—22no—
94C4⋊C8×C43C2312yes—
95C4⋊C8×C43C2312yes—
96#103×C43—22no—
97#103×C43—24no—
98#102×C43—22no—
99#102×C43—24no—
100#102×C43—22no—
101#102×C43—22no—
102C22⋊C8×C43—21no—
103C22⋊C8×C43—21no—
104#97×C43—21no—
105#97×C43—21no—
106#97×C43—21no—
107C4×C8×C43C2312yes—
108C24×C43—21no—
109#41×C43—44no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—21no—
114C2×Q8×C43—42no—
115C2×Q8×C43—44no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—41no—
123C2×D4×C43C2×D412yes—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—44no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135SD16×C43—44no—
136D8×C43—44no—
137M16×C43—42no—
138C2×C8×C43—22no—
139C2×C8×C43—22no—
140C2×C8×C43—22no—
141C4⋊C4×C43—28no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43C2×D414yes—
152C4⋊C4×C43C2×D412yes—
153C4⋊C4×C43C2×D412yes—
154C22⋊C4×C43—28no—
155C22⋊C4×C43—28no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—41no—
160C42×C43—28no—
161C42×C43—22no—
162C42×C43—22no—
163C42×C43C2×D411yescharacteristic
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43C2411yescharacteristic
167C23×C43—22no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—41no—
172C23×C43#12011yescharacteristic
173Q8×C43—22no—
174Q8×C43—22no—
175Q8×C43—42no—
176Q8×C43—44no—
177Q8×C43—42no—
178Q8×C43—44no—
179D4×C43—22no—
180D4×C43—22no—
181D4×C43—42no—
182D4×C43—42no—
183D4×C43—42no—
184D4×C43—42no—
185D4×C43—82no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—44no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—44no—
197C2×C4×C43—42no—
198C2×C4×C43—44no—
199C2×C4×C43—41no—
200C2×C4×C43—82no—
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C8×C43—42no—
208C8×C43—42no—
209C8×C43—42no—
210#18536C4311yesmaximal, characteristic, direct product factor, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—42no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—84no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43#45412yes—
221C22×C43C2×#12011yescharacteristic
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—42no—
228C4×C43—44no—
229C4×C43—42no—
230C4×C43—81no—
231C4×C43#57512yes—
232C4×C43#57512yes—
233C2×#556C2×C4311yescharacteristic, complemented
234#3141C2×C4311yescharacteristic, complemented
235#3112C2×C4311yescharacteristic, complemented
236#3109C2×C4311yescharacteristic
237#1638C2×C4314yescomplemented
238#1628C2×C4314yescomplemented
239#1556C2×C4311yescharacteristic, complemented
240#1491C2×C4311yescharacteristic, complemented
241#1490C2×C4311yescharacteristic, complemented
242C2×C43—22no—
243C2×C43—82no—
244C2×C43—161no—
245C2×C43#300511yescharacteristic
246C2×C43#300511yescharacteristic
247C2×C43C2×#45411yescharacteristic
248#556—22no—
249#556—22no—
250#556—22no—
251#556C22×C4314yes—
252#532C22×C4311yescharacteristic
253C2×C4⋊Q8C22×C4311yescharacteristic
254C2×#126—22no—
255C2×#124—21no—
256C2×C22⋊Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C22×C4311yescharacteristic
259C2×C4×D4C22×C4311yescharacteristic
260C2×#117—21no—
261#489—22no—
262#487C22×C4312yescomplemented
263#486C22×C4312yescomplemented
264#481—21no—
265#480—21no—
266#477C22×C4312yescomplemented
267#476C22×C4312yes—
268#460C22×C4312yescomplemented
269#459C22×C4312yes—
270#448—21no—
271#447—21no—
272#442—22no—
273#440—22no—
274#432C22×C4311yescharacteristic
275#432C22×C4311yescharacteristic
276#417—22no—
277C4×M16C22×C4311yescharacteristic
278#332C22×C4314yescomplemented
279Q8⋊C8C22×C4314yescomplemented
280D4⋊C8C22×C4314yes—
281C43#1853611yescharacteristic, direct product factor, Sylow
282C2×#41—21no—
283C22×Q8—21no—
284C22×Q8D4×C4311yescharacteristic
285C22×D4D4×C4311yescharacteristic
286C23×C4—21no—
287C2×SD16—22no—
288C2×D8—22no—
289C2×M16—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8D4×C4312yes—
293C4⋊Q8C23×C4311yescharacteristic
294C4⋊Q8C23×C4312yes—
295#127C23×C4311yescharacteristic
296#126—28no—
297#126—28no—
298#124—24no—
299#124—24no—
300#124—21no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303#121—21no—
304#121—21no—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8D4×C4312yes—
310C4×Q8C23×C4312yes—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C4312yes—
316C4×D4C23×C4312yes—
317#117—24no—
318#117—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C4311yescharacteristic
323C2×C4⋊C4D4×C4311yescharacteristic
324C2×C4⋊C4D4×C4312yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—22no—
329C2×C42—21no—
330C2×C42C23×C4311yescharacteristic
331#107—22no—
332#106—22no—
333C4⋊C8C23×C4312yes—
334C4⋊C8C23×C4312yes—
335#103—22no—
336#103—24no—
337#102—22no—
338#102—24no—
339#102—22no—
340#102—22no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343#97—21no—
344#97—21no—
345#97—21no—
346C4×C8C23×C4312yes—
347C24—21no—
348#41—44no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—42no—
354C2×Q8—44no—
355C2×Q8C2×D4×C4312yes—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4C2×D4×C4312yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—41no—
371C22×C4C2×D4×C4311yescharacteristic
372C22×C4C2×D4×C4311yescharacteristic
373C22×C4C2×D4×C4311yescharacteristic
374SD16—44no—
375D8—44no—
376M16—42no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C4⋊C4—28no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4C2×D4×C4314yes—
391C4⋊C4C2×D4×C4312yes—
392C4⋊C4C2×D4×C4312yes—
393C22⋊C4—28no—
394C22⋊C4—28no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C42—28no—
400C42—22no—
401C42—22no—
402C42C2×D4×C4311yescharacteristic
403C42C2×D4×C4311yescharacteristic
404C42C2×D4×C4311yescharacteristic
405C42C24×C4311yescharacteristic
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—41no—
411C23#120×C4311yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—44no—
416Q8—42no—
417Q8—44no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—82no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—41no—
439C2×C4—82no—
440C2×C4#120×C4311yescharacteristic
441C2×C4#120×C4311yescharacteristic
442C2×C4#120×C4311yescharacteristic
443C2×C4C22×D4×C4311yescharacteristic
444C2×C4C22×D4×C4311yescharacteristic
445C2×C4C22×D4×C4311yescharacteristic
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22C43×#45412yes—
459C22C2×#120×C4311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—42no—
468C4—81no—
469C4C43×#57512yes—
470C4C43×#57512yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C43×#300511yescharacteristic
475C2C43×#300511yescharacteristic
476C2C2×C43×#45411yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3109C2
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×#556C2semidirect
2. C43×#3141C2semidirect
3. C43×#3112C2semidirect
5. C43×#1638C2semidirect
6. C43×#1628C2semidirect
7. C43×#1556C2semidirect
8. C43×#1491C2semidirect
9. C43×#1490C2semidirect
24. C43×#487C22semidirect
25. C43×#486C22semidirect
28. C43×#477C22semidirect
30. C43×#460C22semidirect
40. C43×#332C22semidirect
41. C43×Q8⋊C8C22semidirect
210. #18536C43direct (N × H)
233. C2×#556C2×C43semidirect
234. #3141C2×C43semidirect
235. #3112C2×C43semidirect
237. #1638C2×C43semidirect
238. #1628C2×C43semidirect
239. #1556C2×C43semidirect
240. #1491C2×C43semidirect
241. #1490C2×C43semidirect
262. #487C22×C43semidirect
263. #486C22×C43semidirect
266. #477C22×C43semidirect
268. #460C22×C43semidirect
278. #332C22×C43semidirect
279. Q8⋊C8C22×C43semidirect
281. C43#18536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5562
C43×#31412
C43×#31122
C43×#31092
C43×#16382
C43×#16282
C43×#15562
C43×#14912
C43×#14902
#1853643