Finite Group Databasebeta

← C43×#60204 #24980221

Subgroups — C43×#60204 #24980221

Order 11008.

2050 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3444C211yesmaximal, characteristic
2C43×#2966C218yesmaximal, complemented
3C43×#2965C214yesmaximal, complemented
4C8×#41×C43C214yesmaximal, complemented
5C43×#2960C212yesmaximal, complemented
6C43×#2931C212yesmaximal, complemented
7C43×#2929C214yesmaximal, complemented
8C43×#2922C212yesmaximal, complemented
9C43×#2920C211yesmaximal, characteristic, complemented
10C4×#131×C43C212yesmaximal, complemented
11C22×C4×C8×C43C211yesmaximal, characteristic, complemented
12C2×#131×C43C2214yes—
13C23×C8×C43C2212yes—
14C43×#533C412yes—
15C43×#533C2211yescharacteristic
16C43×#532C412yes—
17C43×#532C2211yescharacteristic
18C43×#529C414yes—
19C43×#529C414yes—
20C43×#529C2214yes—
21C43×#525C414yes—
22C43×#525C2212yes—
23C4×#41×C43C2214yes—
24C4×#41×C43C2212yes—
25C22×C42×C43C2211yescharacteristic
26C43×#446C2218yescomplemented
27C8×Q8×C43C2218yescomplemented
28C43×#436C2218yescomplemented
29C43×#435C22116yes—
30C8×D4×C43C22116yes—
31C8×D4×C43C2218yescomplemented
32C43×#433C2218yescomplemented
33C43×#432C2214yes—
34C43×#431C2214yes—
35C43×#431C2218yescomplemented
36C43×#424C2214yes—
37C43×#423C2212yes—
38C43×#408C2214yes—
39C43×#407C2212yes—
40C43×#405C2214yes—
41C43×#405C2218yescomplemented
42C4×M16×C43C2212yes—
43C4×M16×C43C2214yescomplemented
44C2×C4×C8×C43C2211yescharacteristic
45C2×C4×C8×C43C2212yes—
46C2×C4×C8×C43C2212yes—
47C2×C4×C8×C43C2214yes—
48C2×C4×C8×C43C2211yescharacteristic
49C2×C4×C8×C43C2212yes—
50C2×C4×C8×C43C2214yescomplemented
51C2×#41×C43C2×C414yes—
52C2×#41×C43C2312yes—
53C23×C4×C43C2×C412yes—
54C23×C4×C43C2311yescharacteristic
55#131×C43—216no—
56C2×M16×C43C2314yes—
57C2×M16×C43C2318yes—
58C22×C8×C43—28no—
59C22×C8×C43C2312yes—
60C22×C8×C43C2314yes—
61C22×C8×C43C2314yes—
62C22×C8×C43C2318yes—
63C22×C8×C43C2312yes—
64C4⋊Q8×C43C2×C412yes—
65C4⋊Q8×C43C2×C411yescharacteristic
66#127×C43C2×C411yescharacteristic
67#126×C43C2×C418yes—
68#125×C43C2×C412yes—
69#125×C43C2×C414yes—
70#124×C43C2×C412yes—
71#124×C43C2×C414yes—
72#123×C43C2×C418yes—
73#123×C43C2×C414yes—
74C22⋊Q8×C43C2×C414yes—
75C22⋊Q8×C43C2×C414yes—
76C22⋊Q8×C43C2×C414yes—
77#121×C43C2×C414yes—
78#121×C43C2×C414yes—
79#121×C43C2×C414yes—
80#120×C43C2×C414yes—
81C4×Q8×C43C2×C414yes—
82C4×Q8×C43C2×C414yes—
83C4×Q8×C43C2314yes—
84C4×D4×C43C2×C418yes—
85C4×D4×C43C2×C418yes—
86C4×D4×C43C2×C414yes—
87C4×D4×C43C2×C414yes—
88C4×D4×C43C2318yes—
89C4×D4×C43C2314yes—
90#117×C43C2×C414yes—
91#117×C43C2×C418yes—
92#117×C43C2312yes—
93#117×C43C2314yes—
94C2×C42×C43C2×C412yes—
95C2×C42×C43C2×C412yes—
96C2×C42×C43C2×C412yes—
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2312yes—
99C2×C42×C43C2312yes—
100C2×C42×C43C2311yescharacteristic
101C2×C42×C43C2314yes—
102C4⋊C8×C43C2318yes—
103C4⋊C8×C43C23116yes—
104C22⋊C8×C43C2318yes—
105C22⋊C8×C43C23116yes—
106#97×C43C2314yes—
107#97×C43C2318yes—
108C4×C8×C43C2311yescharacteristic
109C4×C8×C43C2312yes—
110C4×C8×C43C2312yes—
111C4×C8×C43C2312yes—
112C4×C8×C43C2314yes—
113C4×C8×C43C2314yes—
114C4×C8×C43C2314yes—
115C4×C8×C43C2318yes—
116C4×C8×C43C2311yescharacteristic
117C24×C43C22×C411yescharacteristic
118#41×C43—216no—
119#41×C43—28no—
120C2×Q8×C43C22×C412yes—
121C2×Q8×C43C22×C414yes—
122C2×D4×C43C22×C414yes—
123C2×D4×C43C22×C412yes—
124C2×D4×C43C22×C418yes—
125C2×D4×C43C22×C414yes—
126C22×C4×C43—28no—
127C22×C4×C43—24no—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C22×C418yes—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C2412yes—
138C22×C4×C43C2414yes—
139C22×C4×C43C2411yescharacteristic
140M16×C43—28no—
141M16×C43—216no—
142C2×C8×C43—24no—
143C2×C8×C43—28no—
144C2×C8×C43—28no—
145C2×C8×C43—216no—
146C2×C8×C43#4118yescomplemented
147C2×C8×C43C2414yes—
148C2×C8×C43C2418yes—
149C2×C8×C43C2412yes—
150C2×C8×C43C2412yes—
151C4⋊C4×C43C22×C414yes—
152C4⋊C4×C43C22×C418yes—
153C4⋊C4×C43C22×C414yes—
154C4⋊C4×C43C22×C418yes—
155C4⋊C4×C43C22×C414yes—
156C4⋊C4×C43C22×C418yes—
157C22⋊C4×C43C22×C418yes—
158C22⋊C4×C43C22×C418yes—
159C22⋊C4×C43C22×C418yes—
160C22⋊C4×C43C22×C414yes—
161C22⋊C4×C43C22×C418yes—
162C42×C43C22×C412yes—
163C42×C43C22×C412yes—
164C42×C43C22×C412yes—
165C42×C43C22×C412yes—
166C42×C43C22×C411yescharacteristic
167C42×C43C22×C412yes—
168C42×C43C22×C411yescharacteristic
169C42×C43C22×C418yes—
170C42×C43C2411yescharacteristic
171C42×C43C2411yescharacteristic
172C42×C43C2412yes—
173C42×C43C2414yes—
174C23×C43—22no—
175C23×C43—24no—
176C23×C43C23×C414yes—
177C23×C43C23×C411yescharacteristic
178C23×C43C23×C412yes—
179Q8×C43—24no—
180Q8×C43—28no—
181D4×C43—28no—
182D4×C43—216no—
183D4×C43—24no—
184D4×C43—28no—
185C2×C4×C43—22no—
186C2×C4×C43—24no—
187C2×C4×C43—24no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—24no—
192C2×C4×C43—216no—
193C2×C4×C43—24no—
194C2×C4×C43—28no—
195C2×C4×C43#13118yescomplemented
196C2×C4×C43C23×C412yes—
197C2×C4×C43C23×C412yes—
198C2×C4×C43C23×C412yes—
199C2×C4×C43C23×C414yes—
200C2×C4×C43C23×C418yes—
201C2×C4×C43C23×C411yescharacteristic
202C2×C4×C43C23×C412yes—
203C2×C4×C43C23×C412yes—
204C2×C4×C43C2×#4114yes—
205C2×C4×C43C2511yescharacteristic
206C8×C43—24no—
207C8×C43—28no—
208C8×C43C2×#4114yes—
209C8×C43C2×#4114yes—
210#60204C4311yesmaximal, characteristic, direct product factor, Sylow
211C22×C43—28no—
212C22×C43—22no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—24no—
216C22×C43—28no—
217C22×C43C4×#4112yes—
218C22×C43C2×#13114yes—
219C22×C43C24×C411yescharacteristic
220C4×C43—22no—
221C4×C43—24no—
222C4×C43—22no—
223C4×C43—22no—
224C4×C43—28no—
225C4×C43C4×#4112yes—
226C4×C43C2×#13114yes—
227C4×C43C2×#13114yes—
228C4×C43C22×#4112yes—
229#3444C2×C4311yescharacteristic
230#2966C2×C4318yescomplemented
231#2965C2×C4314yescomplemented
232C8×#41C2×C4314yescomplemented
233#2960C2×C4312yescomplemented
234#2931C2×C4312yescomplemented
235#2929C2×C4314yescomplemented
236#2922C2×C4312yescomplemented
237#2920C2×C4311yescharacteristic, complemented
238C4×#131C2×C4312yescomplemented
239C22×C4×C8C2×C4311yescharacteristic, complemented
240C2×C43—22no—
241C2×C43—24no—
242C2×C43—44no—
243C2×C43C2×C4×#4111yescharacteristic
244C2×C43C22×#13112yes—
245C2×#131C22×C4314yes—
246C23×C8C22×C4312yes—
247#533C4×C4312yes—
248#533C22×C4311yescharacteristic
249#532C4×C4312yes—
250#532C22×C4311yescharacteristic
251#529C4×C4314yes—
252#529C4×C4314yes—
253#529C22×C4314yes—
254#525C4×C4314yes—
255#525C22×C4312yes—
256C4×#41C22×C4312yes—
257C4×#41C22×C4314yes—
258C22×C42C22×C4311yescharacteristic
259#446C22×C4318yescomplemented
260C8×Q8C22×C4318yescomplemented
261#436C22×C4318yescomplemented
262#435C22×C43116yes—
263C8×D4C22×C43116yes—
264C8×D4C22×C4318yescomplemented
265#433C22×C4318yescomplemented
266#432C22×C4314yes—
267#431C22×C4314yes—
268#431C22×C4318yescomplemented
269#424C22×C4314yes—
270#423C22×C4312yes—
271#408C22×C4314yes—
272#407C22×C4312yes—
273#405C22×C4314yes—
274#405C22×C4318yescomplemented
275C4×M16C22×C4312yes—
276C4×M16C22×C4314yescomplemented
277C2×C4×C8C22×C4311yescharacteristic
278C2×C4×C8C22×C4311yescharacteristic
279C2×C4×C8C22×C4312yes—
280C2×C4×C8C22×C4312yes—
281C2×C4×C8C22×C4312yes—
282C2×C4×C8C22×C4314yes—
283C2×C4×C8C22×C4314yescomplemented
284C43#6020411yescharacteristic, direct product factor, Sylow
285C2×#41C2×C4×C4314yes—
286C2×#41C23×C4312yes—
287C23×C4C2×C4×C4312yes—
288C23×C4C23×C4311yescharacteristic
289#131—216no—
290C2×M16C23×C4314yes—
291C2×M16C23×C4318yes—
292C22×C8—28no—
293C22×C8C23×C4312yes—
294C22×C8C23×C4314yes—
295C22×C8C23×C4314yes—
296C22×C8C23×C4318yes—
297C22×C8C23×C4312yes—
298C4⋊Q8C2×C4×C4312yes—
299C4⋊Q8C2×C4×C4311yescharacteristic
300#127C2×C4×C4311yescharacteristic
301#126C2×C4×C4318yes—
302#125C2×C4×C4312yes—
303#125C2×C4×C4314yes—
304#124C2×C4×C4312yes—
305#124C2×C4×C4314yes—
306#123C2×C4×C4318yes—
307#123C2×C4×C4314yes—
308C22⋊Q8C2×C4×C4314yes—
309C22⋊Q8C2×C4×C4314yes—
310C22⋊Q8C2×C4×C4314yes—
311#121C2×C4×C4314yes—
312#121C2×C4×C4314yes—
313#121C2×C4×C4314yes—
314#120C2×C4×C4314yes—
315C4×Q8C2×C4×C4314yes—
316C4×Q8C2×C4×C4314yes—
317C4×Q8C23×C4314yes—
318C4×D4C2×C4×C4318yes—
319C4×D4C2×C4×C4318yes—
320C4×D4C2×C4×C4314yes—
321C4×D4C2×C4×C4314yes—
322C4×D4C23×C4318yes—
323C4×D4C23×C4314yes—
324#117C2×C4×C4314yes—
325#117C2×C4×C4318yes—
326#117C23×C4312yes—
327#117C23×C4314yes—
328C2×C42C2×C4×C4312yes—
329C2×C42C2×C4×C4312yes—
330C2×C42C2×C4×C4312yes—
331C2×C42C23×C4314yes—
332C2×C42C23×C4311yescharacteristic
333C2×C42C23×C4312yes—
334C2×C42C23×C4312yes—
335C2×C42C23×C4311yescharacteristic
336C4⋊C8C23×C4318yes—
337C4⋊C8C23×C43116yes—
338C22⋊C8C23×C4318yes—
339C22⋊C8C23×C43116yes—
340#97C23×C4314yes—
341#97C23×C4318yes—
342C4×C8C23×C4311yescharacteristic
343C4×C8C23×C4312yes—
344C4×C8C23×C4312yes—
345C4×C8C23×C4312yes—
346C4×C8C23×C4314yes—
347C4×C8C23×C4314yes—
348C4×C8C23×C4314yes—
349C4×C8C23×C4318yes—
350C4×C8C23×C4311yescharacteristic
351C24C22×C4×C4311yescharacteristic
352#41—216no—
353#41—28no—
354C2×Q8C22×C4×C4314yes—
355C2×Q8C22×C4×C4312yes—
356C2×D4C22×C4×C4318yes—
357C2×D4C22×C4×C4314yes—
358C2×D4C22×C4×C4314yes—
359C2×D4C22×C4×C4312yes—
360C22×C4—28no—
361C22×C4—24no—
362C22×C4C22×C4×C4312yes—
363C22×C4C22×C4×C4312yes—
364C22×C4C22×C4×C4312yes—
365C22×C4C22×C4×C4312yes—
366C22×C4C22×C4×C4312yes—
367C22×C4C22×C4×C4318yes—
368C22×C4C22×C4×C4312yes—
369C22×C4C22×C4×C4311yescharacteristic
370C22×C4C22×C4×C4312yes—
371C22×C4C24×C4312yes—
372C22×C4C24×C4314yes—
373C22×C4C24×C4311yescharacteristic
374M16—28no—
375M16—216no—
376C2×C8—24no—
377C2×C8—28no—
378C2×C8—28no—
379C2×C8—216no—
380C2×C8#41×C4318yescomplemented
381C2×C8C24×C4314yes—
382C2×C8C24×C4318yes—
383C2×C8C24×C4312yes—
384C2×C8C24×C4312yes—
385C4⋊C4C22×C4×C4314yes—
386C4⋊C4C22×C4×C4318yes—
387C4⋊C4C22×C4×C4314yes—
388C4⋊C4C22×C4×C4318yes—
389C4⋊C4C22×C4×C4314yes—
390C4⋊C4C22×C4×C4318yes—
391C22⋊C4C22×C4×C4314yes—
392C22⋊C4C22×C4×C4318yes—
393C22⋊C4C22×C4×C4318yes—
394C22⋊C4C22×C4×C4318yes—
395C22⋊C4C22×C4×C4318yes—
396C42C22×C4×C4312yes—
397C42C22×C4×C4312yes—
398C42C22×C4×C4312yes—
399C42C22×C4×C4312yes—
400C42C22×C4×C4311yescharacteristic
401C42C22×C4×C4312yes—
402C42C22×C4×C4311yescharacteristic
403C42C22×C4×C4318yes—
404C42C24×C4311yescharacteristic
405C42C24×C4311yescharacteristic
406C42C24×C4312yes—
407C42C24×C4314yes—
408C23—22no—
409C23—24no—
410C23C23×C4×C4314yes—
411C23C23×C4×C4311yescharacteristic
412C23C23×C4×C4312yes—
413Q8—24no—
414Q8—28no—
415D4—28no—
416D4—216no—
417D4—24no—
418D4—28no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—216no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4#131×C4318yescomplemented
430C2×C4C23×C4×C4312yes—
431C2×C4C23×C4×C4312yes—
432C2×C4C23×C4×C4312yes—
433C2×C4C23×C4×C4314yes—
434C2×C4C23×C4×C4318yes—
435C2×C4C23×C4×C4311yescharacteristic
436C2×C4C23×C4×C4312yes—
437C2×C4C23×C4×C4312yes—
438C2×C4C2×#41×C4314yes—
439C2×C4C25×C4311yescharacteristic
440C8—24no—
441C8—28no—
442C8C2×#41×C4314yes—
443C8C2×#41×C4314yes—
444C22—28no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—28no—
450C22C4×#41×C4312yes—
451C22C2×#131×C4314yes—
452C22C24×C4×C4311yescharacteristic
453C4—22no—
454C4—24no—
455C4—22no—
456C4—22no—
457C4—28no—
458C4C4×#41×C4312yes—
459C4C2×#131×C4314yes—
460C4C2×#131×C4314yes—
461C4C22×#41×C4312yes—
462C2—22no—
463C2—24no—
464C2—44no—
465C2C2×C4×#41×C4311yescharacteristic
466C2C22×#131×C4312yes—
subgroupG/H
centerC4×C8×C43C23
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC43×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2966C2semidirect
3. C43×#2965C2semidirect
4. C8×#41×C43C2semidirect
5. C43×#2960C2semidirect
6. C43×#2931C2semidirect
7. C43×#2929C2semidirect
8. C43×#2922C2semidirect
9. C43×#2920C2semidirect
10. C4×#131×C43C2semidirect
11. C22×C4×C8×C43C2semidirect
26. C43×#446C22semidirect
27. C8×Q8×C43C22semidirect
28. C43×#436C22semidirect
31. C8×D4×C43C22semidirect
32. C43×#433C22semidirect
35. C43×#431C22semidirect
41. C43×#405C22semidirect
43. C4×M16×C43C22semidirect
50. C2×C4×C8×C43C22semidirect
146. C2×C8×C43#41semidirect
195. C2×C4×C43#131semidirect
210. #60204C43direct (N × H)
230. #2966C2×C43semidirect
231. #2965C2×C43semidirect
232. C8×#41C2×C43semidirect
233. #2960C2×C43semidirect
234. #2931C2×C43semidirect
235. #2929C2×C43semidirect
236. #2922C2×C43semidirect
237. #2920C2×C43semidirect
238. C4×#131C2×C43semidirect
239. C22×C4×C8C2×C43semidirect
259. #446C22×C43semidirect
260. C8×Q8C22×C43semidirect
261. #436C22×C43semidirect
264. C8×D4C22×C43semidirect
265. #433C22×C43semidirect
268. #431C22×C43semidirect
274. #405C22×C43semidirect
276. C4×M16C22×C43semidirect
283. C2×C4×C8C22×C43semidirect
284. C43#60204direct (N × H)
380. C2×C8#41×C43semidirect
429. C2×C4#131×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34442
C43×#29662
C43×#29652
C8×#41×C432
C43×#29602
C43×#29312
C43×#29292
C43×#29222
C43×#29202
C4×#131×C432
C22×C4×C8×C432
#6020443