Finite Group Databasebeta

← C43×#19554 #24939571

Subgroups — C43×#19554 #24939571

Order 11008.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3253C211yesmaximal, characteristic, complemented
2C43×#3205C211yesmaximal, characteristic, complemented
3C43×#3205C211yesmaximal, characteristic, complemented
4C43×#2979C211yesmaximal, characteristic, complemented
5C43×#1697C212yesmaximal, complemented
6C43×#1687C212yesmaximal, complemented
7C43×#1677C212yesmaximal, complemented
8C43×#1667C212yesmaximal, complemented
9C43×#1574C211yesmaximal, characteristic, complemented
10C43×#1545C211yesmaximal, characteristic, complemented
11C43×#1543C211yesmaximal, characteristic, complemented
12C43×#532C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C2×#127×C43C2211yescharacteristic
15C43×#493—21no—
16C43×#493C2212yes—
17C43×#486—21no—
18C43×#486C2212yes—
19C43×#476—21no—
20C43×#476C2212yescomplemented
21C43×#469—22no—
22C43×#459—21no—
23C43×#459—21no—
24C43×#459—21no—
25C43×#459C2212yes—
26C43×#459C2212yes—
27C43×#459C2212yescomplemented
28C43×#447—22no—
29C43×#447—22no—
30C43×#436—21no—
31C43×#436C2212yescomplemented
32C8×D4×C43—21no—
33C8×D4×C43C2212yescomplemented
34C43×#431C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#431C2211yescharacteristic
37C43×#423C2211yescharacteristic
38C43×#408—22no—
39C43×#335C2212yescomplemented
40C43×#334C2212yescomplemented
41C43×#333C2211yescharacteristic, complemented
42C43×#333C2211yescharacteristic, complemented
43C43×#331C2212yes—
44C43×#331C2212yes—
45C43×#331C2211yescharacteristic, complemented
46C43×#331C2211yescharacteristic, complemented
47C2×#41×C43—21no—
48C2×#41×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C22×D4×C43—21no—
52C2×D8×C43—22no—
53C2×D8×C43—22no—
54C2×D8×C43—22no—
55C2×D8×C43—22no—
56C2×D8×C43—22no—
57C2×M16×C43—21no—
58C2×M16×C43—22no—
59C22×C8×C43—22no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43C2311yescharacteristic
62#127×C43—21no—
63#127×C43—21no—
64#127×C43—21no—
65#127×C43D411yescharacteristic
66#127×C43C2312yes—
67#127×C43C2311yescharacteristic
68#124×C43—21no—
69#124×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73#121×C43D412yes—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43C2312yes—
78C2×C42×C43C2311yescharacteristic
79#106×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C4⋊C8×C43C2311yescharacteristic
84C4⋊C8×C43C2311yescharacteristic
85C4⋊C8×C43C2312yes—
86C4⋊C8×C43C2311yescharacteristic
87C4⋊C8×C43C2311yescharacteristic
88#102×C43—22no—
89#102×C43—22no—
90#102×C43—22no—
91#102×C43—22no—
92#102×C43—22no—
93#102×C43—22no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96C22⋊C8×C43—22no—
97C22⋊C8×C43—22no—
98C22⋊C8×C43D412yes—
99C4×C8×C43—21no—
100C4×C8×C43—21no—
101C4×C8×C43C2312yes—
102C24×C43—41no—
103#41×C43—81no—
104#41×C43—81no—
105#41×C43—82no—
106C2×Q8×C43—21no—
107C2×Q8×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—22no—
111C2×D4×C43—21no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—81no—
122C2×D4×C43—81no—
123C2×D4×C43—81no—
124C2×D4×C43—81no—
125C2×D4×C43—82no—
126C2×D4×C43C2×D412yes—
127C22×C4×C43—22no—
128C22×C4×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4111yescharacteristic
132D8×C43—82no—
133D8×C43—82no—
134D8×C43—82no—
135D8×C43—82no—
136D8×C43—82no—
137M16×C43—82no—
138M16×C43—81no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—22no—
144C2×C8×C43—82no—
145C2×C8×C43C2×D412yes—
146C2×C8×C43C2×D412yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43C2×D412yes—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43#4111yescharacteristic
158C42×C43C2411yescharacteristic
159C23×C43—22no—
160C23×C43—41no—
161C23×C43—42no—
162C23×C43—82no—
163C23×C43—82no—
164C23×C43—82no—
165C23×C43#12111yescharacteristic
166Q8×C43—81no—
167Q8×C43—81no—
168D4×C43—22no—
169D4×C43—22no—
170D4×C43—41no—
171D4×C43—41no—
172D4×C43—41no—
173D4×C43—42no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—42no—
177D4×C43—41no—
178D4×C43—42no—
179D4×C43—81no—
180D4×C43—82no—
181D4×C43—81no—
182D4×C43—82no—
183D4×C43—82no—
184D4×C43—82no—
185D4×C43—82no—
186D4×C43—82no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—41no—
196C2×C4×C43—82no—
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C8×C43—22no—
204C8×C43—22no—
205C8×C43—41no—
206C8×C43—41no—
207C8×C43—42no—
208C8×C43—41no—
209C8×C43—41no—
210#19554C4311yesmaximal, characteristic, direct product factor, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—42no—
217C22×C43—82no—
218C22×C43—81no—
219C22×C43—82no—
220C22×C43—81no—
221C22×C43—82no—
222C22×C43—81no—
223C22×C43—164no—
224C22×C43C2×#12111yescharacteristic
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—42no—
229C4×C43—81no—
230C4×C43#47212yes—
231C4×C43#57611yescharacteristic
232C4×C43#57611yescharacteristic
233C4×C43#57611yescharacteristic
234C4×C43#57711yescharacteristic
235#3253C2×C4311yescharacteristic, complemented
236#3205C2×C4311yescharacteristic, complemented
237#3205C2×C4311yescharacteristic, complemented
238#2979C2×C4311yescharacteristic, complemented
239#1697C2×C4312yescomplemented
240#1687C2×C4312yescomplemented
241#1677C2×C4312yescomplemented
242#1667C2×C4312yescomplemented
243#1574C2×C4311yescharacteristic, complemented
244#1545C2×C4311yescharacteristic, complemented
245#1543C2×C4311yescharacteristic, complemented
246C2×C43—41no—
247C2×C43—82no—
248C2×C43—161no—
249C2×C43—162no—
250C2×C43#304111yescharacteristic
251C2×C43#306211yescharacteristic
252C2×C43C2×#47211yescharacteristic
253#532C22×C4311yescharacteristic
254#532C22×C4311yescharacteristic
255C2×#127C22×C4311yescharacteristic
256#493—21no—
257#493C22×C4312yes—
258#486—21no—
259#486C22×C4312yes—
260#476—21no—
261#476C22×C4312yescomplemented
262#469—22no—
263#459—21no—
264#459—21no—
265#459—21no—
266#459C22×C4312yes—
267#459C22×C4312yes—
268#459C22×C4312yescomplemented
269#447—22no—
270#447—22no—
271#436—21no—
272#436C22×C4312yescomplemented
273C8×D4—21no—
274C8×D4C22×C4312yescomplemented
275#431C22×C4311yescharacteristic
276#431C22×C4311yescharacteristic
277#431C22×C4311yescharacteristic
278#423C22×C4311yescharacteristic
279#408—22no—
280#335C22×C4312yescomplemented
281#334C22×C4312yescomplemented
282#333C22×C4311yescharacteristic, complemented
283#333C22×C4311yescharacteristic, complemented
284#331C22×C4312yes—
285#331C22×C4312yes—
286#331C22×C4311yescharacteristic, complemented
287#331C22×C4311yescharacteristic, complemented
288C43#1955411yescharacteristic, direct product factor, Sylow
289C2×#41—21no—
290C2×#41—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C2×D8—22no—
295C2×D8—22no—
296C2×D8—22no—
297C2×D8—22no—
298C2×D8—22no—
299C2×M16—21no—
300C2×M16—22no—
301C22×C8—22no—
302C4⋊Q8D4×C4311yescharacteristic
303C4⋊Q8C23×C4311yescharacteristic
304#127—21no—
305#127—21no—
306#127—21no—
307#127D4×C4311yescharacteristic
308#127C23×C4312yes—
309#127C23×C4311yescharacteristic
310#124—21no—
311#124—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121D4×C4312yes—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4C23×C4312yes—
320C2×C42C23×C4311yescharacteristic
321#106—22no—
322C4⋊C8—21no—
323C4⋊C8D4×C4311yescharacteristic
324C4⋊C8D4×C4311yescharacteristic
325C4⋊C8C23×C4311yescharacteristic
326C4⋊C8C23×C4311yescharacteristic
327C4⋊C8C23×C4312yes—
328C4⋊C8C23×C4311yescharacteristic
329C4⋊C8C23×C4311yescharacteristic
330#102—22no—
331#102—22no—
332#102—22no—
333#102—22no—
334#102—22no—
335#102—22no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340C22⋊C8D4×C4312yes—
341C4×C8—21no—
342C4×C8—21no—
343C4×C8C23×C4312yes—
344C24—41no—
345#41—81no—
346#41—81no—
347#41—82no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—81no—
364C2×D4—81no—
365C2×D4—81no—
366C2×D4—81no—
367C2×D4—82no—
368C2×D4C2×D4×C4312yes—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4C2×D4×C4311yescharacteristic
372C22×C4C2×D4×C4311yescharacteristic
373C22×C4#41×C4311yescharacteristic
374D8—82no—
375D8—82no—
376D8—82no—
377D8—82no—
378D8—82no—
379M16—82no—
380M16—81no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—82no—
387C2×C8C2×D4×C4312yes—
388C2×C8C2×D4×C4312yes—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4C2×D4×C4312yes—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C42C2×D4×C4311yescharacteristic
398C42C2×D4×C4311yescharacteristic
399C42#41×C4311yescharacteristic
400C42C24×C4311yescharacteristic
401C23—22no—
402C23—41no—
403C23—42no—
404C23—82no—
405C23—82no—
406C23—82no—
407C23#121×C4311yescharacteristic
408Q8—81no—
409Q8—81no—
410D4—22no—
411D4—22no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—42no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423D4—81no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—82no—
428D4—82no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4#121×C4311yescharacteristic
440C2×C4#121×C4311yescharacteristic
441C2×C4#121×C4311yescharacteristic
442C2×C4C22×D4×C4311yescharacteristic
443C2×C4C22×D4×C4311yescharacteristic
444C2×C4C2×#41×C4311yescharacteristic
445C8—22no—
446C8—22no—
447C8—41no—
448C8—41no—
449C8—42no—
450C8—41no—
451C8—41no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—82no—
459C22—81no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—82no—
464C22—164no—
465C22C2×#121×C4311yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—81no—
471C4C43×#47212yes—
472C4C43×#57611yescharacteristic
473C4C43×#57611yescharacteristic
474C4C43×#57611yescharacteristic
475C4C43×#57711yescharacteristic
476C2—41no—
477C2—82no—
478C2—162no—
479C2—161no—
480C2C43×#304111yescharacteristic
481C2C43×#306211yescharacteristic
482C2C2×C43×#47211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
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×#3253C2semidirect
2. C43×#3205C2semidirect
3. C43×#3205C2semidirect
4. C43×#2979C2semidirect
5. C43×#1697C2semidirect
6. C43×#1687C2semidirect
7. C43×#1677C2semidirect
8. C43×#1667C2semidirect
9. C43×#1574C2semidirect
10. C43×#1545C2semidirect
11. C43×#1543C2semidirect
20. C43×#476C22semidirect
27. C43×#459C22semidirect
31. C43×#436C22semidirect
33. C8×D4×C43C22semidirect
39. C43×#335C22semidirect
40. C43×#334C22semidirect
41. C43×#333C22semidirect
42. C43×#333C22semidirect
45. C43×#331C22semidirect
46. C43×#331C22semidirect
210. #19554C43direct (N × H)
235. #3253C2×C43semidirect
236. #3205C2×C43semidirect
237. #3205C2×C43semidirect
238. #2979C2×C43semidirect
239. #1697C2×C43semidirect
240. #1687C2×C43semidirect
241. #1677C2×C43semidirect
242. #1667C2×C43semidirect
243. #1574C2×C43semidirect
244. #1545C2×C43semidirect
245. #1543C2×C43semidirect
261. #476C22×C43semidirect
268. #459C22×C43semidirect
272. #436C22×C43semidirect
274. C8×D4C22×C43semidirect
280. #335C22×C43semidirect
281. #334C22×C43semidirect
282. #333C22×C43semidirect
283. #333C22×C43semidirect
286. #331C22×C43semidirect
287. #331C22×C43semidirect
288. C43#19554direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32532
C43×#32052
C43×#29792
C43×#16972
C43×#16872
C43×#16772
C43×#16672
C43×#15742
C43×#15452
C43×#15432
#1955443