Finite Group Databasebeta

← C43×#61586 #24981603

Subgroups — C43×#61586 #24981603

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3501C211yesmaximal, characteristic, complemented
2C2×C43×#547C211yesmaximal, characteristic
3C43×#3331C218yesmaximal, complemented
4C43×#3276C218yesmaximal, complemented
5C43×#3209C212yesmaximal, complemented
6C43×#3195C214yesmaximal, complemented
7C43×#3101C212yesmaximal, complemented
8C43×#3007C214yesmaximal, complemented
9C43×#2975C211yesmaximal, characteristic, complemented
10C22×#41×C43C2212yes—
11C2×#137×C43C2218yescomplemented
12C43×#554—24no—
13C43×#554C2214yescomplemented
14D4×Q8×C43C2214yescomplemented
15C43×#547—24no—
16C43×#547C2218yes—
17C43×#544—21no—
18C43×#543—22no—
19C43×#533C2212yes—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C2×#123×C43—22no—
22C2×C22⋊Q8×C43C2212yes—
23C2×C22⋊Q8×C43C2214yes—
24C2×#121×C43—21no—
25C43×#518—21no—
26C2×C4×D4×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C22×C4⋊C4×C43—21no—
29C43×#494C2214yescomplemented
30C43×#487C2214yescomplemented
31C43×#483C2214yes—
32C43×#483C2218yescomplemented
33C43×#476C2214yescomplemented
34C43×#470C22116yescomplemented
35C43×#462C2218yescomplemented
36C43×#461C2214yescomplemented
37C43×#452C22116yescomplemented
38C43×#451C2218yes—
39C43×#451C2218yescomplemented
40C43×#450C2214yes—
41C4×SD16×C43C2218yescomplemented
42C43×#436C2218yescomplemented
43C43×#431C2212yes—
44C43×#417C2218yescomplemented
45C43×#407C2214yes—
46C2×#41×C43—24no—
47C2×#41×C43—48no—
48C2×#41×C43C2318yes—
49C22×Q8×C43C2312yes—
50C22×Q8×C43C2314yes—
51C22×D4×C43—22no—
52C22×D4×C43D411yescharacteristic
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43—21no—
55C23×C4×C43—22no—
56C23×C4×C43C2312yes—
57#137×C43—416no—
58C2×Q16×C43C23116yes—
59C2×SD16×C43C2318yes—
60C2×M16×C43C2318yes—
61C4⋊Q8×C43—24no—
62C4⋊Q8×C43—22no—
63C4⋊Q8×C43C2314yes—
64C4⋊Q8×C43C2312yes—
65C4⋊Q8×C43C2312yes—
66#125×C43—24no—
67#125×C43—22no—
68#123×C43—216no—
69C22⋊Q8×C43—24no—
70C22⋊Q8×C43—24no—
71C22⋊Q8×C43—24no—
72C22⋊Q8×C43—22no—
73C22⋊Q8×C43—28no—
74C22⋊Q8×C43—28no—
75C22⋊Q8×C43C2314yes—
76C22⋊Q8×C43C2318yes—
77C22⋊Q8×C43C2318yes—
78#121×C43—28no—
79C4×Q8×C43—22no—
80C4×Q8×C43C2314yes—
81C4×D4×C43—24no—
82C4×D4×C43—24no—
83C4×D4×C43—22no—
84C4×D4×C43D414yes—
85C4×D4×C43C2314yes—
86C4×D4×C43C2314yes—
87#117×C43—22no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—24no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—28no—
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×C43—21no—
99C2×C22⋊C4×C43D412yes—
100C2×C42×C43C2311yescharacteristic
101#106×C43C2318yes—
102C4⋊C8×C43C2314yes—
103#103×C43C23116yes—
104#103×C43C2318yes—
105#102×C43C2318yes—
106C22⋊C8×C43C2314yes—
107C22⋊C8×C43C2318yes—
108C4×C8×C43C2314yes—
109C24×C43—21no—
110C24×C43C2×D412yes—
111#41×C43—216no—
112#41×C43—48no—
113#41×C43—416no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—24no—
117C2×Q8×C43—44no—
118C2×Q8×C43—48no—
119C2×Q8×C43C2414yes—
120C2×Q8×C43C2414yes—
121C2×D4×C43—24no—
122C2×D4×C43—24no—
123C2×D4×C43—21no—
124C2×D4×C43—28no—
125C2×D4×C43—48no—
126C2×D4×C43C2×D414yes—
127C2×D4×C43C2412yes—
128C22×C4×C43—24no—
129C22×C4×C43—28no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—24no—
133C22×C4×C43—24no—
134C22×C4×C43—48no—
135C22×C4×C43—44no—
136C22×C4×C43—44no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D414yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×C4×C43C2414yes—
143Q16×C43—416no—
144SD16×C43—216no—
145M16×C43—48no—
146C2×C8×C43C2418yes—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—28no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—28no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43C2×D414yes—
159C4⋊C4×C43C2414yes—
160C4⋊C4×C43C2412yes—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—28no—
164C22⋊C4×C43—28no—
165C22⋊C4×C43C2×D418yes—
166C42×C43—24no—
167C42×C43C2×D412yes—
168C42×C43C2412yes—
169C23×C43—24no—
170C23×C43—22no—
171C23×C43—24no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43C22×D414yes—
177C23×C43C22×D411yescharacteristic
178Q8×C43—28no—
179Q8×C43—28no—
180Q8×C43—44no—
181Q8×C43—82no—
182Q8×C43—84no—
183D4×C43—24no—
184D4×C43—28no—
185D4×C43—22no—
186D4×C43—416no—
187D4×C43H(5,𝔽2)14yes—
188C2×C4×C43—28no—
189C2×C4×C43—22no—
190C2×C4×C43—24no—
191C2×C4×C43—24no—
192C2×C4×C43—22no—
193C2×C4×C43—24no—
194C2×C4×C43—42no—
195C2×C4×C43—44no—
196C2×C4×C43—41no—
197C2×C4×C43—416no—
198C2×C4×C43—44no—
199C2×C4×C43—42no—
200C2×C4×C43—48no—
201C2×C4×C43—84no—
202C2×C4×C43—84no—
203C2×C4×C43#13714yescomplemented
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D412yes—
206C2×C4×C43C22×D414yes—
207C2×C4×C43C22×D412yes—
208C2×C4×C43C2511yescharacteristic
209C8×C43—28no—
210#61586C4311yesmaximal, characteristic, direct product factor, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—24no—
214C22×C43—24no—
215C22×C43—24no—
216C22×C43—24no—
217C22×C43—48no—
218C22×C43—42no—
219C22×C43—42no—
220C22×C43—84no—
221C22×C43C2×#13712yes—
222C22×C43C23×D411yescharacteristic
223C4×C43—22no—
224C4×C43—24no—
225C4×C43—21no—
226C4×C43—44no—
227C4×C43—44no—
228C4×C43—44no—
229C4×C43—42no—
230C4×C43C2×#13714yes—
231C4×C43C2×H(5,𝔽2)12yes—
232#3501C2×C4311yescharacteristic, complemented
233C2×#547C2×C4311yescharacteristic
234#3331C2×C4318yescomplemented
235#3276C2×C4318yescomplemented
236#3209C2×C4312yescomplemented
237#3195C2×C4314yescomplemented
238#3101C2×C4312yescomplemented
239#3007C2×C4314yescomplemented
240#2975C2×C4311yescharacteristic, complemented
241C2×C43—22no—
242C2×C43—44no—
243C2×C43—44no—
244C2×C43#348411yescharacteristic
245C2×C43C22×#13711yescharacteristic
246C2×C43#358611yescharacteristic
247C22×#41C22×C4312yes—
248C2×#137C22×C4318yescomplemented
249#554—24no—
250#554C22×C4314yescomplemented
251D4×Q8C22×C4314yescomplemented
252#547—24no—
253#547C22×C4318yes—
254#544—21no—
255#543—22no—
256#533C22×C4312yes—
257C2×C4⋊Q8C22×C4311yescharacteristic
258C2×#123—22no—
259C2×C22⋊Q8C22×C4312yes—
260C2×C22⋊Q8C22×C4314yes—
261C2×#121—21no—
262#518—21no—
263C2×C4×D4C22×C4311yescharacteristic
264C2×C4×D4C22×C4311yescharacteristic
265C22×C4⋊C4—21no—
266#494C22×C4314yescomplemented
267#487C22×C4314yescomplemented
268#483C22×C4314yes—
269#483C22×C4318yescomplemented
270#476C22×C4314yescomplemented
271#470C22×C43116yescomplemented
272#462C22×C4318yescomplemented
273#461C22×C4314yescomplemented
274#452C22×C43116yescomplemented
275#451C22×C4318yes—
276#451C22×C4318yescomplemented
277#450C22×C4314yes—
278C4×SD16C22×C4318yescomplemented
279#436C22×C4318yescomplemented
280#431C22×C4312yes—
281#417C22×C4318yescomplemented
282#407C22×C4314yes—
283C43#6158611yescharacteristic, direct product factor, Sylow
284C2×#41—24no—
285C2×#41—48no—
286C2×#41C23×C4318yes—
287C22×Q8C23×C4312yes—
288C22×Q8C23×C4314yes—
289C22×D4—22no—
290C22×D4D4×C4311yescharacteristic
291C22×D4C23×C4311yescharacteristic
292C23×C4—21no—
293C23×C4—22no—
294C23×C4C23×C4312yes—
295#137—416no—
296C2×Q16C23×C43116yes—
297C2×SD16C23×C4318yes—
298C2×M16C23×C4318yes—
299C4⋊Q8—24no—
300C4⋊Q8—22no—
301C4⋊Q8C23×C4314yes—
302C4⋊Q8C23×C4312yes—
303C4⋊Q8C23×C4312yes—
304#125—24no—
305#125—22no—
306#123—216no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—28no—
312C22⋊Q8—28no—
313C22⋊Q8C23×C4314yes—
314C22⋊Q8C23×C4318yes—
315C22⋊Q8C23×C4318yes—
316#121—28no—
317C4×Q8—22no—
318C4×Q8C23×C4314yes—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4D4×C4314yes—
323C4×D4C23×C4314yes—
324C4×D4C23×C4314yes—
325#117—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4D4×C4311yescharacteristic
332C2×C4⋊C4C23×C4311yescharacteristic
333C2×C4⋊C4C23×C4314yes—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4D4×C4312yes—
338C2×C42C23×C4311yescharacteristic
339#106C23×C4318yes—
340C4⋊C8C23×C4314yes—
341#103C23×C43116yes—
342#103C23×C4318yes—
343#102C23×C4318yes—
344C22⋊C8C23×C4314yes—
345C22⋊C8C23×C4318yes—
346C4×C8C23×C4314yes—
347C24—21no—
348C24C2×D4×C4312yes—
349#41—216no—
350#41—48no—
351#41—416no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—24no—
355C2×Q8—44no—
356C2×Q8—48no—
357C2×Q8C24×C4314yes—
358C2×Q8C24×C4314yes—
359C2×D4—24no—
360C2×D4—28no—
361C2×D4—24no—
362C2×D4—21no—
363C2×D4—48no—
364C2×D4C2×D4×C4314yes—
365C2×D4C24×C4312yes—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—28no—
372C22×C4—44no—
373C22×C4—48no—
374C22×C4—44no—
375C22×C4C2×D4×C4311yescharacteristic
376C22×C4C2×D4×C4312yes—
377C22×C4C2×D4×C4314yes—
378C22×C4C2×D4×C4311yescharacteristic
379C22×C4C24×C4311yescharacteristic
380C22×C4C24×C4314yes—
381Q16—416no—
382SD16—216no—
383M16—48no—
384C2×C8C24×C4318yes—
385C4⋊C4—24no—
386C4⋊C4—28no—
387C4⋊C4—24no—
388C4⋊C4—28no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—24no—
396C4⋊C4C2×D4×C4314yes—
397C4⋊C4C24×C4314yes—
398C4⋊C4C24×C4312yes—
399C22⋊C4—24no—
400C22⋊C4—28no—
401C22⋊C4—28no—
402C22⋊C4—24no—
403C22⋊C4C2×D4×C4318yes—
404C42—24no—
405C42C2×D4×C4312yes—
406C42C24×C4312yes—
407C23—24no—
408C23—22no—
409C23—24no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23C22×D4×C4314yes—
415C23C22×D4×C4311yescharacteristic
416Q8—28no—
417Q8—28no—
418Q8—44no—
419Q8—84no—
420Q8—82no—
421D4—24no—
422D4—28no—
423D4—22no—
424D4—416no—
425D4H(5,𝔽2)×C4314yes—
426C2×C4—28no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—416no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—48no—
439C2×C4—84no—
440C2×C4—84no—
441C2×C4#137×C4314yescomplemented
442C2×C4C22×D4×C4311yescharacteristic
443C2×C4C22×D4×C4312yes—
444C2×C4C22×D4×C4314yes—
445C2×C4C22×D4×C4312yes—
446C2×C4C25×C4311yescharacteristic
447C8—28no—
448C22—21no—
449C22—21no—
450C22—24no—
451C22—24no—
452C22—24no—
453C22—24no—
454C22—48no—
455C22—42no—
456C22—42no—
457C22—84no—
458C22C2×#137×C4312yes—
459C22C23×D4×C4311yescharacteristic
460C4—24no—
461C4—21no—
462C4—22no—
463C4—44no—
464C4—44no—
465C4—42no—
466C4—44no—
467C4C2×#137×C4314yes—
468C4C2×H(5,𝔽2)×C4312yes—
469C2—22no—
470C2—44no—
471C2—44no—
472C2C43×#348411yescharacteristic
473C2C22×#137×C4311yescharacteristic
474C2C43×#358611yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×C43×#547C2
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×#3331C2semidirect
4. C43×#3276C2semidirect
5. C43×#3209C2semidirect
6. C43×#3195C2semidirect
7. C43×#3101C2semidirect
8. C43×#3007C2semidirect
9. C43×#2975C2semidirect
11. C2×#137×C43C22semidirect
13. C43×#554C22semidirect
14. D4×Q8×C43C22semidirect
29. C43×#494C22semidirect
30. C43×#487C22semidirect
32. C43×#483C22semidirect
33. C43×#476C22semidirect
34. C43×#470C22semidirect
35. C43×#462C22semidirect
36. C43×#461C22semidirect
37. C43×#452C22semidirect
39. C43×#451C22semidirect
41. C4×SD16×C43C22semidirect
42. C43×#436C22semidirect
44. C43×#417C22semidirect
203. C2×C4×C43#137semidirect
210. #61586C43direct (N × H)
232. #3501C2×C43semidirect
234. #3331C2×C43semidirect
235. #3276C2×C43semidirect
236. #3209C2×C43semidirect
237. #3195C2×C43semidirect
238. #3101C2×C43semidirect
239. #3007C2×C43semidirect
240. #2975C2×C43semidirect
248. C2×#137C22×C43semidirect
250. #554C22×C43semidirect
251. D4×Q8C22×C43semidirect
266. #494C22×C43semidirect
267. #487C22×C43semidirect
269. #483C22×C43semidirect
270. #476C22×C43semidirect
271. #470C22×C43semidirect
272. #462C22×C43semidirect
273. #461C22×C43semidirect
274. #452C22×C43semidirect
276. #451C22×C43semidirect
278. C4×SD16C22×C43semidirect
279. #436C22×C43semidirect
281. #417C22×C43semidirect
283. C43#61586direct (N × H)
441. 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×#5472
C43×#33312
C43×#32762
C43×#32092
C43×#31952
C43×#31012
C43×#30072
C43×#29752
#6158643