Finite Group Databasebeta

← C43×#61588 #24981605

Subgroups — C43×#61588 #24981605

Order 11008.

2150 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×#3501C211yesmaximal, characteristic, complemented
2C2×C43×#550C211yesmaximal, characteristic
3C43×#3333C218yesmaximal, complemented
4C43×#3278C218yesmaximal, complemented
5C43×#3208C212yesmaximal, complemented
6C43×#3193C214yesmaximal, complemented
7C43×#3104C212yesmaximal, complemented
8C43×#3007C214yesmaximal, complemented
9C43×#2975C211yesmaximal, characteristic, complemented
10C22×#41×C43C2212yes—
11C2×#137×C43C2218yescomplemented
12C43×#554—24no—
13C43×#554C2214yescomplemented
14C43×#550—24no—
15C43×#550C2218yes—
16D4×Q8×C43C2214yescomplemented
17C43×#544—21no—
18C43×#543—22no—
19C43×#533C2212yes—
20C2×#127×C43—21no—
21C2×#127×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2214yes—
23C2×#121×C43—22no—
24C2×#121×C43C2212yes—
25C43×#518—21no—
26C2×C4×Q8×C43C2211yescharacteristic
27C2×C4×D4×C43—21no—
28C2×C4×D4×C43C2211yescharacteristic
29C43×#492C2214yescomplemented
30C43×#486C2214yescomplemented
31C43×#484C2214yes—
32C43×#480C2218yescomplemented
33C43×#477C2214yescomplemented
34C43×#468C22116yescomplemented
35C43×#462C2214yescomplemented
36C43×#460C2218yescomplemented
37C43×#452C22116yescomplemented
38C43×#451C2214yes—
39C43×#450C2218yes—
40C43×#448C2218yescomplemented
41C4×Q16×C43C2218yescomplemented
42C43×#436C2218yescomplemented
43C43×#431C2212yes—
44C43×#417C2218yescomplemented
45C43×#407C2214yes—
46C2×#41×C43—24no—
47C2×#41×C43—48no—
48C2×#41×C43C2318yes—
49C22×Q8×C43C2311yescharacteristic
50C22×Q8×C43C2314yes—
51C22×D4×C43—22no—
52C22×D4×C43—22no—
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×D4×C43D411yescharacteristic
56C22×D4×C43C2312yes—
57C23×C4×C43—22no—
58C23×C4×C43C2312yes—
59#137×C43—416no—
60C2×Q16×C43C2318yes—
61C2×SD16×C43C23116yes—
62C2×M16×C43C2318yes—
63C4⋊Q8×C43—24no—
64C4⋊Q8×C43C2312yes—
65C4⋊Q8×C43C2312yes—
66#127×C43—28no—
67#127×C43—22no—
68#127×C43C2314yes—
69#125×C43—24no—
70#125×C43—22no—
71C22⋊Q8×C43—24no—
72C22⋊Q8×C43—24no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—28no—
75C22⋊Q8×C43—28no—
76C22⋊Q8×C43C2314yes—
77C22⋊Q8×C43C2318yes—
78#121×C43—24no—
79#121×C43—216no—
80#121×C43C2318yes—
81C4×Q8×C43—22no—
82C4×Q8×C43—22no—
83C4×Q8×C43C2314yes—
84C4×Q8×C43C2314yes—
85C4×D4×C43—24no—
86C4×D4×C43—24no—
87C4×D4×C43—28no—
88C4×D4×C43D414yes—
89C4×D4×C43C2314yes—
90#117×C43—22no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—24no—
93C2×C4⋊C4×C43D411yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2314yes—
96C2×C22⋊C4×C43—24no—
97C2×C22⋊C4×C43—22no—
98C2×C22⋊C4×C43D412yes—
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#107×C43C2318yes—
102C4⋊C8×C43C2314yes—
103#103×C43C2318yes—
104#103×C43C2318yes—
105#102×C43C23116yes—
106C22⋊C8×C43C2314yes—
107C22⋊C8×C43C2318yes—
108C4×C8×C43C2314yes—
109C24×C43—22no—
110C24×C43C2×D412yes—
111#41×C43—216no—
112#41×C43—48no—
113#41×C43—416no—
114C2×Q8×C43—24no—
115C2×Q8×C43—21no—
116C2×Q8×C43—22no—
117C2×Q8×C43—24no—
118C2×Q8×C43—48no—
119C2×Q8×C43C2414yes—
120C2×Q8×C43C2412yes—
121C2×D4×C43—24no—
122C2×D4×C43—24no—
123C2×D4×C43—22no—
124C2×D4×C43—24no—
125C2×D4×C43—28no—
126C2×D4×C43—28no—
127C2×D4×C43—44no—
128C2×D4×C43—48no—
129C2×D4×C43—44no—
130C2×D4×C43—84no—
131C2×D4×C43—82no—
132C2×D4×C43C2×D414yes—
133C2×D4×C43C2414yes—
134C22×C4×C43—28no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—24no—
138C22×C4×C43—24no—
139C22×C4×C43—44no—
140C22×C4×C43—48no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D414yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×C4×C43C2414yes—
147Q16×C43—216no—
148SD16×C43—416no—
149M16×C43—48no—
150C2×C8×C43C2418yes—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—28no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43C2×D414yes—
161C4⋊C4×C43C2414yes—
162C4⋊C4×C43C2412yes—
163C22⋊C4×C43—28no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—28no—
166C22⋊C4×C43C2×D418yes—
167C42×C43—24no—
168C42×C43—24no—
169C42×C43C2×D412yes—
170C42×C43C2412yes—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—44no—
176C23×C43—44no—
177C23×C43—44no—
178C23×C43C22×D414yes—
179C23×C43C22×D411yescharacteristic
180Q8×C43—24no—
181Q8×C43—22no—
182Q8×C43—28no—
183Q8×C43—82no—
184Q8×C43—84no—
185Q8×C43H(5,𝔽2)14yes—
186D4×C43—28no—
187D4×C43—28no—
188D4×C43—416no—
189D4×C43—44no—
190D4×C43—48no—
191D4×C43—84no—
192D4×C43—88no—
193C2×C4×C43—24no—
194C2×C4×C43—22no—
195C2×C4×C43—28no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—42no—
201C2×C4×C43—44no—
202C2×C4×C43—41no—
203C2×C4×C43—416no—
204C2×C4×C43—42no—
205C2×C4×C43—84no—
206C2×C4×C43—84no—
207C2×C4×C43#13714yescomplemented
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D412yes—
210C2×C4×C43C22×D414yes—
211C2×C4×C43C22×D412yes—
212C2×C4×C43C2511yescharacteristic
213C8×C43—28no—
214#61588C4311yesmaximal, characteristic, direct product factor, Sylow
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—24no—
218C22×C43—24no—
219C22×C43—24no—
220C22×C43—44no—
221C22×C43—44no—
222C22×C43—44no—
223C22×C43—84no—
224C22×C43—88no—
225C22×C43C2×#13712yes—
226C22×C43C23×D411yescharacteristic
227C4×C43—22no—
228C4×C43—24no—
229C4×C43—24no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—44no—
233C4×C43—44no—
234C4×C43C2×#13714yes—
235C4×C43C2×H(5,𝔽2)12yes—
236#3501C2×C4311yescharacteristic, complemented
237C2×#550C2×C4311yescharacteristic
238#3333C2×C4318yescomplemented
239#3278C2×C4318yescomplemented
240#3208C2×C4312yescomplemented
241#3193C2×C4314yescomplemented
242#3104C2×C4312yescomplemented
243#3007C2×C4314yescomplemented
244#2975C2×C4311yescharacteristic, complemented
245C2×C43—22no—
246C2×C43—44no—
247C2×C43—84no—
248C2×C43#348411yescharacteristic
249C2×C43C22×#13711yescharacteristic
250C2×C43#358511yescharacteristic
251C22×#41C22×C4312yes—
252C2×#137C22×C4318yescomplemented
253#554—24no—
254#554C22×C4314yescomplemented
255#550—24no—
256#550C22×C4318yes—
257D4×Q8C22×C4314yescomplemented
258#544—21no—
259#543—22no—
260#533C22×C4312yes—
261C2×#127—21no—
262C2×#127C22×C4311yescharacteristic
263C2×C22⋊Q8C22×C4314yes—
264C2×#121—22no—
265C2×#121C22×C4312yes—
266#518—21no—
267C2×C4×Q8C22×C4311yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4C22×C4311yescharacteristic
270#492C22×C4314yescomplemented
271#486C22×C4314yescomplemented
272#484C22×C4314yes—
273#480C22×C4318yescomplemented
274#477C22×C4314yescomplemented
275#468C22×C43116yescomplemented
276#462C22×C4314yescomplemented
277#460C22×C4318yescomplemented
278#452C22×C43116yescomplemented
279#451C22×C4314yes—
280#450C22×C4318yes—
281#448C22×C4318yescomplemented
282C4×Q16C22×C4318yescomplemented
283#436C22×C4318yescomplemented
284#431C22×C4312yes—
285#417C22×C4318yescomplemented
286#407C22×C4314yes—
287C43#6158811yescharacteristic, direct product factor, Sylow
288C2×#41—24no—
289C2×#41—48no—
290C2×#41C23×C4318yes—
291C22×Q8C23×C4311yescharacteristic
292C22×Q8C23×C4314yes—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4D4×C4311yescharacteristic
298C22×D4C23×C4312yes—
299C23×C4—22no—
300C23×C4C23×C4312yes—
301#137—416no—
302C2×Q16C23×C4318yes—
303C2×SD16C23×C43116yes—
304C2×M16C23×C4318yes—
305C4⋊Q8—24no—
306C4⋊Q8C23×C4312yes—
307C4⋊Q8C23×C4312yes—
308#127—28no—
309#127—22no—
310#127C23×C4314yes—
311#125—24no—
312#125—22no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—22no—
316C22⋊Q8—28no—
317C22⋊Q8—28no—
318C22⋊Q8C23×C4314yes—
319C22⋊Q8C23×C4318yes—
320#121—24no—
321#121—216no—
322#121C23×C4318yes—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8C23×C4314yes—
326C4×Q8C23×C4314yes—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—28no—
330C4×D4D4×C4314yes—
331C4×D4C23×C4314yes—
332#117—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4D4×C4311yescharacteristic
336C2×C4⋊C4C23×C4311yescharacteristic
337C2×C4⋊C4C23×C4314yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4D4×C4312yes—
341C2×C42—21no—
342C2×C42C23×C4311yescharacteristic
343#107C23×C4318yes—
344C4⋊C8C23×C4314yes—
345#103C23×C4318yes—
346#103C23×C4318yes—
347#102C23×C43116yes—
348C22⋊C8C23×C4314yes—
349C22⋊C8C23×C4318yes—
350C4×C8C23×C4314yes—
351C24—22no—
352C24C2×D4×C4312yes—
353#41—216no—
354#41—48no—
355#41—416no—
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—24no—
360C2×Q8—48no—
361C2×Q8C24×C4314yes—
362C2×Q8C24×C4312yes—
363C2×D4—28no—
364C2×D4—28no—
365C2×D4—24no—
366C2×D4—24no—
367C2×D4—22no—
368C2×D4—24no—
369C2×D4—44no—
370C2×D4—48no—
371C2×D4—44no—
372C2×D4—82no—
373C2×D4—84no—
374C2×D4C2×D4×C4314yes—
375C2×D4C24×C4314yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—44no—
382C22×C4—48no—
383C22×C4C2×D4×C4311yescharacteristic
384C22×C4C2×D4×C4312yes—
385C22×C4C2×D4×C4314yes—
386C22×C4C2×D4×C4311yescharacteristic
387C22×C4C24×C4311yescharacteristic
388C22×C4C24×C4314yes—
389Q16—216no—
390SD16—416no—
391M16—48no—
392C2×C8C24×C4318yes—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—28no—
396C4⋊C4—21no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4C2×D4×C4314yes—
403C4⋊C4C24×C4314yes—
404C4⋊C4C24×C4312yes—
405C22⋊C4—24no—
406C22⋊C4—28no—
407C22⋊C4—28no—
408C22⋊C4C2×D4×C4318yes—
409C42—24no—
410C42—24no—
411C42C2×D4×C4312yes—
412C42C24×C4312yes—
413C23—24no—
414C23—24no—
415C23—42no—
416C23—42no—
417C23—44no—
418C23—44no—
419C23—44no—
420C23C22×D4×C4314yes—
421C23C22×D4×C4311yescharacteristic
422Q8—24no—
423Q8—22no—
424Q8—28no—
425Q8—84no—
426Q8—82no—
427Q8H(5,𝔽2)×C4314yes—
428D4—28no—
429D4—28no—
430D4—416no—
431D4—44no—
432D4—48no—
433D4—84no—
434D4—88no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—28no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—41no—
445C2×C4—416no—
446C2×C4—42no—
447C2×C4—84no—
448C2×C4—84no—
449C2×C4#137×C4314yescomplemented
450C2×C4C22×D4×C4311yescharacteristic
451C2×C4C22×D4×C4312yes—
452C2×C4C22×D4×C4314yes—
453C2×C4C22×D4×C4312yes—
454C2×C4C25×C4311yescharacteristic
455C8—28no—
456C22—21no—
457C22—21no—
458C22—24no—
459C22—24no—
460C22—24no—
461C22—44no—
462C22—44no—
463C22—44no—
464C22—84no—
465C22—88no—
466C22C2×#137×C4312yes—
467C22C23×D4×C4311yescharacteristic
468C4—24no—
469C4—24no—
470C4—21no—
471C4—22no—
472C4—44no—
473C4—42no—
474C4—44no—
475C4C2×#137×C4314yes—
476C4C2×H(5,𝔽2)×C4312yes—
477C2—22no—
478C2—44no—
479C2—84no—
480C2C43×#348411yescharacteristic
481C2C22×#137×C4311yescharacteristic
482C2C43×#358511yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×C43×#550C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C43×#3501C2semidirect
3. C43×#3333C2semidirect
4. C43×#3278C2semidirect
5. C43×#3208C2semidirect
6. C43×#3193C2semidirect
7. C43×#3104C2semidirect
8. C43×#3007C2semidirect
9. C43×#2975C2semidirect
11. C2×#137×C43C22semidirect
13. C43×#554C22semidirect
16. D4×Q8×C43C22semidirect
29. C43×#492C22semidirect
30. C43×#486C22semidirect
32. C43×#480C22semidirect
33. C43×#477C22semidirect
34. C43×#468C22semidirect
35. C43×#462C22semidirect
36. C43×#460C22semidirect
37. C43×#452C22semidirect
40. C43×#448C22semidirect
41. C4×Q16×C43C22semidirect
42. C43×#436C22semidirect
44. C43×#417C22semidirect
207. C2×C4×C43#137semidirect
214. #61588C43direct (N × H)
236. #3501C2×C43semidirect
238. #3333C2×C43semidirect
239. #3278C2×C43semidirect
240. #3208C2×C43semidirect
241. #3193C2×C43semidirect
242. #3104C2×C43semidirect
243. #3007C2×C43semidirect
244. #2975C2×C43semidirect
252. C2×#137C22×C43semidirect
254. #554C22×C43semidirect
257. D4×Q8C22×C43semidirect
270. #492C22×C43semidirect
271. #486C22×C43semidirect
273. #480C22×C43semidirect
274. #477C22×C43semidirect
275. #468C22×C43semidirect
276. #462C22×C43semidirect
277. #460C22×C43semidirect
278. #452C22×C43semidirect
281. #448C22×C43semidirect
282. C4×Q16C22×C43semidirect
283. #436C22×C43semidirect
285. #417C22×C43semidirect
287. C43#61588direct (N × H)
449. C2×C4#137×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35012
C2×C43×#5502
C43×#33332
C43×#32782
C43×#32082
C43×#31932
C43×#31042
C43×#30072
C43×#29752
#6158843