Finite Group Databasebeta

← C43×#60401 #24980418

Subgroups — C43×#60401 #24980418

Order 11008.

4854 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×H(7,𝔽2)C211yesmaximal, characteristic, complemented
2C43×#3485C213yesmaximal, complemented
3C43×#3028C214yesmaximal, complemented
4C43×#3026C218yesmaximal, complemented
5C43×#3025C214yesmaximal, complemented
6C2×C43×#458C218yesmaximal, complemented
7C43×#2883C213yesmaximal, complemented
8C43×#585—212no—
9C43×#585C2214yes—
10C2×H(5,𝔽2)×C43—212no—
11C2×H(5,𝔽2)×C43C2218yes—
12C2×H(5,𝔽2)×C43C2213yes—
13C22×#41×C43C2211yescharacteristic, complemented
14C43×#547—212no—
15C43×#546—212no—
16C43×#536C2216yescomplemented
17C43×#534C22112yescomplemented
18C43×#525C2216yescomplemented
19C2×#123×C43C22112yescomplemented
20C43×#518C2213yescomplemented
21C43×#458C22116yescomplemented
22C43×#458C22132yescomplemented
23C43×B(4,𝔽2)C22116yescomplemented
24C43×#410C22112yescomplemented
25C2×#99×C43C22124yescomplemented
262−1+4×C43—216no—
272−1+4×C43—212no—
28H(5,𝔽2)×C43—248no—
29H(5,𝔽2)×C43—212no—
30H(5,𝔽2)×C43—248no—
31H(5,𝔽2)×C43—224no—
32H(5,𝔽2)×C43C23116yes—
33C2×#41×C43—248no—
34C2×#41×C43—212no—
35C2×#41×C43—224no—
36C2×#41×C43—224no—
37C2×#41×C43D4112yescomplemented
38C2×#41×C43C2316yes—
39C22×Q8×C43C2311yescharacteristic, complemented
40C22×D4×C43—216no—
41C22×D4×C43—224no—
42C22×D4×C43D4112yescomplemented
43C22×D4×C43C23112yes—
44C22×D4×C43C2311yescharacteristic
45C22×D4×C43C2312yescomplemented
46C23×C4×C43C2312yescomplemented
47C23×C4×C43C2311yescharacteristic, complemented
48C4⋊Q8×C43—26no—
49#124×C43—26no—
50#123×C43—224no—
51#123×C43—212no—
52#123×C43C23112yescomplemented
53#123×C43C23124yescomplemented
54C22⋊Q8×C43—26no—
55C22⋊Q8×C43—212no—
56#121×C43—26no—
57#121×C43—224no—
58#120×C43—212no—
59#120×C43C23112yescomplemented
60C4×D4×C43—212no—
61C4×D4×C43—212no—
62#117×C43C2316yescomplemented
63C2×C4⋊C4×C43—212no—
64C2×C22⋊C4×C43—212no—
65C2×C22⋊C4×C43C23112yescomplemented
66#99×C43C23148yescomplemented
67C24×C43—28no—
68C24×C43C2×D4112yes—
69C24×C43C2411yescharacteristic
70C24×C43C2412yes—
71#41×C43—296no—
72#41×C43—248no—
73#41×C43—216no—
74#41×C43—248no—
75#41×C43—248no—
76#41×C43—224no—
77#41×C43—416no—
78C2×Q8×C43—224no—
79C2×Q8×C43—28no—
80C2×Q8×C43—26no—
81C2×Q8×C43C2×D416yes—
82C2×D4×C43—224no—
83C2×D4×C43—296no—
84C2×D4×C43—224no—
85C2×D4×C43—248no—
86C2×D4×C43—248no—
87C2×D4×C43—248no—
88C2×D4×C43—212no—
89C2×D4×C43—212no—
90C2×D4×C43C2×D4124yes—
91C2×D4×C43C2×D416yes—
92C2×D4×C43C2×D4112yes—
93C2×D4×C43C24112yes—
94C22×C4×C43—216no—
95C22×C4×C43—224no—
96C22×C4×C43—26no—
97C22×C4×C43—212no—
98C22×C4×C43—212no—
99C22×C4×C43C2×D4112yes—
100C22×C4×C43C2×D4112yes—
101C22×C4×C43C2411yescharacteristic
102C22×C4×C43C2412yes—
103C22×C4×C43C2411yescharacteristic
104C4⋊C4×C43—212no—
105C4⋊C4×C43—224no—
106C4⋊C4×C43—26no—
107C22⋊C4×C43—212no—
108C22⋊C4×C43—212no—
109C22⋊C4×C43—224no—
110C22⋊C4×C43—212no—
111C22⋊C4×C43C24112yes—
112C42×C43—26no—
113C23×C43—216no—
114C23×C43—224no—
115C23×C43—23no—
116C23×C43—82no—
117C23×C43—81no—
118C23×C43—812no—
119C23×C43—168no—
120C23×C43C22×D4112yes—
121C23×C43C22×D4112yes—
122C23×C43C2511yescharacteristic
123Q8×C43—216no—
124Q8×C43—212no—
125Q8×C43—44no—
126D4×C43—248no—
127D4×C43—248no—
128D4×C43—224no—
129D4×C43—212no—
130D4×C43—48no—
131D4×C43—812no—
132D4×C43#120116yes—
133C2×C4×C43—248no—
134C2×C4×C43—224no—
135C2×C4×C43—224no—
136C2×C4×C43—212no—
137C2×C4×C43—23no—
138C2×C4×C43—26no—
139C2×C4×C43—48no—
140C2×C4×C43—44no—
141C2×C4×C43—812no—
142C2×C4×C43C22×D4112yes—
143C2×C4×C43C22×D416yes—
144#60401C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—212no—
146C22×C43—41no—
147C22×C43—412no—
148C22×C43—412no—
149C22×C43—46no—
150C22×C43—41no—
151C22×C43—824no—
152C22×C43—816no—
153C22×C43C2×#12018yes—
154C22×C43C23×D413yes—
155C4×C43—212no—
156C4×C43—412no—
157C4×C43—41no—
158C4×C43—42no—
159C4×C43C2×#12014yes—
160H(7,𝔽2)C2×C4311yescharacteristic, complemented
161#3485C2×C4313yescomplemented
162#3028C2×C4314yescomplemented
163#3026C2×C4318yescomplemented
164#3025C2×C4314yescomplemented
165C2×#458C2×C4318yescomplemented
166#2883C2×C4313yescomplemented
167C2×C43—23no—
168C2×C43—28no—
169C2×C43—412no—
170C2×C43—81no—
171C2×C43C22×#12011yescharacteristic
172#585—212no—
173#585C22×C4314yes—
174C2×H(5,𝔽2)—212no—
175C2×H(5,𝔽2)C22×C4318yes—
176C2×H(5,𝔽2)C22×C4313yes—
177C22×#41C22×C4311yescharacteristic, complemented
178#547—212no—
179#546—212no—
180#536C22×C4316yescomplemented
181#534C22×C43112yescomplemented
182#525C22×C4316yescomplemented
183C2×#123C22×C43112yescomplemented
184#518C22×C4313yescomplemented
185#458C22×C43116yescomplemented
186#458C22×C43132yescomplemented
187B(4,𝔽2)C22×C43116yescomplemented
188#410C22×C43112yescomplemented
189C2×#99C22×C43124yescomplemented
190C43#6040111yescharacteristic, direct product factor, Sylow
1912−1+4—216no—
1922−1+4—212no—
193H(5,𝔽2)—248no—
194H(5,𝔽2)—212no—
195H(5,𝔽2)—248no—
196H(5,𝔽2)—224no—
197H(5,𝔽2)C23×C43116yes—
198C2×#41—248no—
199C2×#41—212no—
200C2×#41—224no—
201C2×#41—224no—
202C2×#41D4×C43112yescomplemented
203C2×#41C23×C4316yes—
204C22×Q8C23×C4311yescharacteristic, complemented
205C22×D4—216no—
206C22×D4—224no—
207C22×D4D4×C43112yescomplemented
208C22×D4C23×C43112yes—
209C22×D4C23×C4311yescharacteristic
210C22×D4C23×C4312yescomplemented
211C23×C4C23×C4312yescomplemented
212C23×C4C23×C4311yescharacteristic, complemented
213C4⋊Q8—26no—
214#124—26no—
215#123—224no—
216#123—212no—
217#123C23×C43112yescomplemented
218#123C23×C43124yescomplemented
219C22⋊Q8—26no—
220C22⋊Q8—212no—
221#121—26no—
222#121—224no—
223#120—212no—
224#120C23×C43112yescomplemented
225C4×D4—212no—
226C4×D4—212no—
227#117C23×C4316yescomplemented
228C2×C4⋊C4—212no—
229C2×C22⋊C4—212no—
230C2×C22⋊C4C23×C43112yescomplemented
231#99C23×C43148yescomplemented
232C24—28no—
233C24C2×D4×C43112yes—
234C24C24×C4311yescharacteristic
235C24C24×C4312yes—
236#41—296no—
237#41—248no—
238#41—216no—
239#41—248no—
240#41—248no—
241#41—224no—
242#41—416no—
243C2×Q8—224no—
244C2×Q8—28no—
245C2×Q8—26no—
246C2×Q8C2×D4×C4316yes—
247C2×D4—296no—
248C2×D4—224no—
249C2×D4—224no—
250C2×D4—248no—
251C2×D4—248no—
252C2×D4—248no—
253C2×D4—212no—
254C2×D4—212no—
255C2×D4C2×D4×C43124yes—
256C2×D4C2×D4×C4316yes—
257C2×D4C2×D4×C43112yes—
258C2×D4C24×C43112yes—
259C22×C4—224no—
260C22×C4—216no—
261C22×C4—212no—
262C22×C4—212no—
263C22×C4—26no—
264C22×C4C2×D4×C43112yes—
265C22×C4C2×D4×C43112yes—
266C22×C4C24×C4311yescharacteristic
267C22×C4C24×C4312yes—
268C22×C4C24×C4311yescharacteristic
269C4⋊C4—212no—
270C4⋊C4—224no—
271C4⋊C4—26no—
272C22⋊C4—212no—
273C22⋊C4—224no—
274C22⋊C4—212no—
275C22⋊C4—212no—
276C22⋊C4C24×C43112yes—
277C42—26no—
278C23—216no—
279C23—224no—
280C23—23no—
281C23—82no—
282C23—81no—
283C23—812no—
284C23—168no—
285C23C22×D4×C43112yes—
286C23C22×D4×C43112yes—
287C23C25×C4311yescharacteristic
288Q8—216no—
289Q8—212no—
290Q8—44no—
291D4—248no—
292D4—248no—
293D4—224no—
294D4—212no—
295D4—48no—
296D4—812no—
297D4#120×C43116yes—
298C2×C4—248no—
299C2×C4—224no—
300C2×C4—224no—
301C2×C4—212no—
302C2×C4—23no—
303C2×C4—26no—
304C2×C4—48no—
305C2×C4—44no—
306C2×C4—812no—
307C2×C4C22×D4×C43112yes—
308C2×C4C22×D4×C4316yes—
309C22—212no—
310C22—412no—
311C22—41no—
312C22—412no—
313C22—46no—
314C22—41no—
315C22—824no—
316C22—816no—
317C22C2×#120×C4318yes—
318C22C23×D4×C4313yes—
319C4—212no—
320C4—412no—
321C4—41no—
322C4—42no—
323C4C2×#120×C4314yes—
324C2—23no—
325C2—28no—
326C2—412no—
327C2—81no—
328C2C22×#120×C4311yescharacteristic
subgroupG/H
center, socleC2×C43C22×#120
commutator, Frattini, cosocleC23C25×C43
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×H(7,𝔽2)C2semidirect
2. C43×#3485C2semidirect
3. C43×#3028C2semidirect
4. C43×#3026C2semidirect
5. C43×#3025C2semidirect
6. C2×C43×#458C2semidirect
7. C43×#2883C2semidirect
13. C22×#41×C43C22semidirect
16. C43×#536C22semidirect
17. C43×#534C22semidirect
18. C43×#525C22semidirect
19. C2×#123×C43C22semidirect
20. C43×#518C22semidirect
21. C43×#458C22semidirect
22. C43×#458C22semidirect
23. C43×B(4,𝔽2)C22semidirect
24. C43×#410C22semidirect
25. C2×#99×C43C22semidirect
37. C2×#41×C43D4semidirect
39. C22×Q8×C43C23semidirect
42. C22×D4×C43D4semidirect
45. C22×D4×C43C23semidirect
46. C23×C4×C43C23semidirect
47. C23×C4×C43C23semidirect
52. #123×C43C23semidirect
53. #123×C43C23semidirect
59. #120×C43C23semidirect
62. #117×C43C23semidirect
65. C2×C22⋊C4×C43C23semidirect
66. #99×C43C23semidirect
144. #60401C43direct (N × H)
160. H(7,𝔽2)C2×C43semidirect
161. #3485C2×C43semidirect
162. #3028C2×C43semidirect
163. #3026C2×C43semidirect
164. #3025C2×C43semidirect
165. C2×#458C2×C43semidirect
166. #2883C2×C43semidirect
177. C22×#41C22×C43semidirect
180. #536C22×C43semidirect
181. #534C22×C43semidirect
182. #525C22×C43semidirect
183. C2×#123C22×C43semidirect
184. #518C22×C43semidirect
185. #458C22×C43semidirect
186. #458C22×C43semidirect
187. B(4,𝔽2)C22×C43semidirect
188. #410C22×C43semidirect
189. C2×#99C22×C43semidirect
190. C43#60401direct (N × H)
202. C2×#41D4×C43semidirect
204. C22×Q8C23×C43semidirect
207. C22×D4D4×C43semidirect
210. C22×D4C23×C43semidirect
211. C23×C4C23×C43semidirect
212. C23×C4C23×C43semidirect
217. #123C23×C43semidirect
218. #123C23×C43semidirect
224. #120C23×C43semidirect
227. #117C23×C43semidirect
230. C2×C22⋊C4C23×C43semidirect
231. #99C23×C43semidirect

Maximal subgroups

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

subgroupindex
C43×H(7,𝔽2)2
C43×#34852
C43×#30282
C43×#30262
C43×#30252
C2×C43×#4582
C43×#28832
#6040143