Finite Group Databasebeta

← C2×C43×#3568 #24982753

Subgroups — C2×C43×#3568 #24982753

Order 11008.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3568C2132yesmaximal, direct product factor
2C2×C43×#563C213yesmaximal, complemented
3C2×C43×H(3,𝔽4)C211yesmaximal, characteristic, complemented
4C2×C43×#556C216yesmaximal, complemented
5C2×C43×#551C216yesmaximal, complemented
6C2×C43×#542C216yesmaximal, complemented
7C2×C43×#538C216yesmaximal, complemented
8C2×C43×#529C213yesmaximal, complemented
9C43×#563C22148yescomplemented
10C43×H(3,𝔽4)C22116yescomplemented
11C43×#556C22196yescomplemented
12C43×#551C22196yescomplemented
13C43×#542C22196yescomplemented
14C43×#538C22196yescomplemented
15C2×C4⋊Q8×C43C2216yescomplemented
16C43×#529C22148yescomplemented
17C2×#126×C43C2216yescomplemented
18C2×#126×C43C2216yescomplemented
19C2×#126×C43C2216yescomplemented
20C2×#126×C43C2212yescomplemented
21C2×#126×C43C2216yescomplemented
22C2×#125×C43C2213yescomplemented
23C2×#124×C43C2213yes—
24C2×#124×C43C2216yes—
25C2×#124×C43C2216yes—
26C2×#124×C43C2216yescomplemented
27C2×#123×C43C2216yes—
28C2×#123×C43C2216yes—
29C2×#123×C43C2216yescomplemented
30C2×C22⋊Q8×C43C2213yescomplemented
31C2×C22⋊Q8×C43C2216yescomplemented
32C2×C22⋊Q8×C43C2216yescomplemented
33C2×C22⋊Q8×C43C2216yescomplemented
34C2×#121×C43C2213yes—
35C2×#121×C43C2216yes—
36C2×#120×C43C2216yes—
37C2×#120×C43C2212yescomplemented
38C2×C4×Q8×C43C2213yescomplemented
39C2×C4×Q8×C43C2216yescomplemented
40C2×C4×D4×C43C2213yes—
41C2×C4×D4×C43C2216yes—
42C2×C4×D4×C43C2216yescomplemented
43C2×#117×C43C2216yescomplemented
44C2×#117×C43C2216yescomplemented
45C22×C22⋊C4×C43C2216yescomplemented
46C22×C42×C43C2211yescharacteristic, complemented
47C25×C43C2312yes—
48C22×Q8×C43C2316yes—
49C22×Q8×C43C2313yes—
50C22×D4×C43C2313yes—
51C22×D4×C43C2316yes—
52C22×D4×C43C2316yes—
53C23×C4×C43C2313yes—
54C23×C4×C43C2316yes—
55C23×C4×C43C2316yes—
56C4⋊Q8×C43C23148yescomplemented
57#126×C43C23148yescomplemented
58#126×C43C23148yescomplemented
59#126×C43C23148yescomplemented
60#126×C43C23116yescomplemented
61#126×C43C23148yescomplemented
62#125×C43C23124yescomplemented
63#124×C43C23124yes—
64#124×C43C23148yes—
65#124×C43C23148yes—
66#124×C43C23148yescomplemented
67#123×C43C23148yes—
68#123×C43C23148yes—
69#123×C43C23148yescomplemented
70C22⋊Q8×C43C23124yescomplemented
71C22⋊Q8×C43C23148yescomplemented
72C22⋊Q8×C43C23148yescomplemented
73C22⋊Q8×C43C23148yescomplemented
74#121×C43C23124yes—
75#121×C43C23148yes—
76#120×C43C23148yes—
77#120×C43C23116yescomplemented
78C4×Q8×C43C23124yescomplemented
79C4×Q8×C43C23148yescomplemented
80C4×D4×C43C23124yes—
81C4×D4×C43C23148yes—
82C4×D4×C43C23148yescomplemented
83#117×C43C23148yescomplemented
84#117×C43C23148yescomplemented
85C2×C4⋊C4×C43C2316yes—
86C2×C4⋊C4×C43C2316yes—
87C2×C4⋊C4×C43C2316yes—
88C2×C4⋊C4×C43C2316yes—
89C2×C4⋊C4×C43C2313yes—
90C2×C4⋊C4×C43C2316yes—
91C2×C4⋊C4×C43C2313yes—
92C2×C4⋊C4×C43C2316yes—
93C2×C22⋊C4×C43C2316yes—
94C2×C22⋊C4×C43C2316yes—
95C2×C22⋊C4×C43C2316yes—
96C2×C22⋊C4×C43C2316yes—
97C2×C22⋊C4×C43C2316yes—
98C2×C22⋊C4×C43C2316yes—
99C2×C22⋊C4×C43C2316yes—
100C2×C22⋊C4×C43C2316yes—
101C2×C22⋊C4×C43C2316yes—
102C2×C22⋊C4×C43C23148yescomplemented
103C2×C42×C43C2313yes—
104C2×C42×C43C2311yescharacteristic
105C2×C42×C43C2316yes—
106C2×C42×C43C2316yes—
107C2×C42×C43C2312yes—
108C2×C42×C43C2318yescomplemented
109C24×C43—412no—
110C24×C43C2416yes—
111C24×C43C2411yescharacteristic
112C24×C43C2418yes—
113C2×Q8×C43—412no—
114C2×Q8×C43—46no—
115C2×Q8×C43C24124yes—
116C2×Q8×C43C24112yes—
117C2×D4×C43—412no—
118C2×D4×C43—46no—
119C2×D4×C43—412no—
120C2×D4×C43C24112yes—
121C2×D4×C43C24124yes—
122C2×D4×C43C24124yes—
123C22×C4×C43—46no—
124C22×C4×C43—412no—
125C22×C4×C43—412no—
126C22×C4×C43C24112yes—
127C22×C4×C43C24124yes—
128C22×C4×C43C24124yes—
129C22×C4×C43C2413yes—
130C22×C4×C43C2416yes—
131C22×C4×C43C2413yes—
132C22×C4×C43C2416yes—
133C22×C4×C43C2416yes—
134C4⋊C4×C43C24124yes—
135C4⋊C4×C43C24124yes—
136C4⋊C4×C43C24124yes—
137C4⋊C4×C43C24124yes—
138C4⋊C4×C43C24112yes—
139C4⋊C4×C43C24124yes—
140C4⋊C4×C43C24112yes—
141C4⋊C4×C43C24124yes—
142C22⋊C4×C43C24124yes—
143C22⋊C4×C43C24124yes—
144C22⋊C4×C43C24124yes—
145C22⋊C4×C43C24124yes—
146C22⋊C4×C43C24124yes—
147C22⋊C4×C43C24124yes—
148C22⋊C4×C43C24124yes—
149C22⋊C4×C43C24124yes—
150C22⋊C4×C43C24124yes—
151C42×C43C24112yes—
152C42×C43C2414yes—
153C42×C43C24124yes—
154C42×C43C24124yes—
155C42×C43C2418yes—
156C23×C43—26no—
157C23×C43—212no—
158C23×C43—212no—
159C23×C43—212no—
160C23×C43—424no—
161C23×C43—816no—
162C23×C43C25112yes—
163C23×C43C2512yes—
164C23×C43C2511yescharacteristic
165Q8×C43—424no—
166Q8×C43—412no—
167D4×C43—412no—
168D4×C43—424no—
169D4×C43—424no—
170C2×C4×C43—26no—
171C2×C4×C43—212no—
172C2×C4×C43—26no—
173C2×C4×C43—212no—
174C2×C4×C43—212no—
175C2×C4×C43—424no—
176C2×C4×C43—412no—
177C2×C4×C43—424no—
178C2×C4×C43C2516yes—
179C2×C4×C43C25112yes—
180C2×C4×C43C2516yes—
181C2×C4×C43C25112yes—
182C2×C4×C43C25112yes—
183C2×#3568C4311yesmaximal, characteristic, direct product factor, Sylow
184C22×C43—212no—
185C22×C43—212no—
186C22×C43—212no—
187C22×C43—26no—
188C22×C43—44no—
189C22×C43—424no—
190C22×C43—816no—
191C22×C43#58516yes—
192C22×C43C2611yescharacteristic
193C4×C43—26no—
194C4×C43—212no—
195C4×C43—26no—
196C4×C43—212no—
197C4×C43—212no—
198#3568C2×C43132yesdirect product factor
199C2×#563C2×C4313yescomplemented
200C2×H(3,𝔽4)C2×C4311yescharacteristic, complemented
201C2×#556C2×C4316yescomplemented
202C2×#551C2×C4316yescomplemented
203C2×#542C2×C4316yescomplemented
204C2×#538C2×C4316yescomplemented
205C2×#529C2×C4313yescomplemented
206C2×C43—42no—
207C2×C43—412no—
208C2×C43#356814yesdirect product factor
209C2×C43C2×#58513yes—
210#563C22×C43148yescomplemented
211H(3,𝔽4)C22×C43116yescomplemented
212#556C22×C43196yescomplemented
213#551C22×C43196yescomplemented
214#542C22×C43196yescomplemented
215#538C22×C43196yescomplemented
216C2×C4⋊Q8C22×C4316yescomplemented
217#529C22×C43148yescomplemented
218C2×#126C22×C4316yescomplemented
219C2×#126C22×C4316yescomplemented
220C2×#126C22×C4316yescomplemented
221C2×#126C22×C4312yescomplemented
222C2×#126C22×C4316yescomplemented
223C2×#125C22×C4313yescomplemented
224C2×#124C22×C4313yes—
225C2×#124C22×C4316yes—
226C2×#124C22×C4316yes—
227C2×#124C22×C4316yescomplemented
228C2×#123C22×C4316yes—
229C2×#123C22×C4316yes—
230C2×#123C22×C4316yescomplemented
231C2×C22⋊Q8C22×C4313yescomplemented
232C2×C22⋊Q8C22×C4316yescomplemented
233C2×C22⋊Q8C22×C4316yescomplemented
234C2×C22⋊Q8C22×C4316yescomplemented
235C2×#121C22×C4313yes—
236C2×#121C22×C4316yes—
237C2×#120C22×C4316yes—
238C2×#120C22×C4312yescomplemented
239C2×C4×Q8C22×C4313yescomplemented
240C2×C4×Q8C22×C4316yescomplemented
241C2×C4×D4C22×C4313yes—
242C2×C4×D4C22×C4316yes—
243C2×C4×D4C22×C4316yescomplemented
244C2×#117C22×C4316yescomplemented
245C2×#117C22×C4316yescomplemented
246C22×C22⋊C4C22×C4316yescomplemented
247C22×C42C22×C4311yescharacteristic, complemented
248C43C2×#356811yescharacteristic, direct product factor, Sylow
249C25C23×C4312yes—
250C22×Q8C23×C4316yes—
251C22×Q8C23×C4313yes—
252C22×D4C23×C4313yes—
253C22×D4C23×C4316yes—
254C22×D4C23×C4316yes—
255C23×C4C23×C4316yes—
256C23×C4C23×C4316yes—
257C23×C4C23×C4313yes—
258C4⋊Q8C23×C43148yescomplemented
259#126C23×C43148yescomplemented
260#126C23×C43148yescomplemented
261#126C23×C43148yescomplemented
262#126C23×C43116yescomplemented
263#126C23×C43148yescomplemented
264#125C23×C43124yescomplemented
265#124C23×C43124yes—
266#124C23×C43148yes—
267#124C23×C43148yes—
268#124C23×C43148yescomplemented
269#123C23×C43148yes—
270#123C23×C43148yes—
271#123C23×C43148yescomplemented
272C22⋊Q8C23×C43124yescomplemented
273C22⋊Q8C23×C43148yescomplemented
274C22⋊Q8C23×C43148yescomplemented
275C22⋊Q8C23×C43148yescomplemented
276#121C23×C43124yes—
277#121C23×C43148yes—
278#120C23×C43148yes—
279#120C23×C43116yescomplemented
280C4×Q8C23×C43124yescomplemented
281C4×Q8C23×C43148yescomplemented
282C4×D4C23×C43124yes—
283C4×D4C23×C43148yes—
284C4×D4C23×C43148yescomplemented
285#117C23×C43148yescomplemented
286#117C23×C43148yescomplemented
287C2×C4⋊C4C23×C4316yes—
288C2×C4⋊C4C23×C4316yes—
289C2×C4⋊C4C23×C4316yes—
290C2×C4⋊C4C23×C4316yes—
291C2×C4⋊C4C23×C4313yes—
292C2×C4⋊C4C23×C4316yes—
293C2×C4⋊C4C23×C4313yes—
294C2×C4⋊C4C23×C4316yes—
295C2×C22⋊C4C23×C4316yes—
296C2×C22⋊C4C23×C4316yes—
297C2×C22⋊C4C23×C4316yes—
298C2×C22⋊C4C23×C4316yes—
299C2×C22⋊C4C23×C4316yes—
300C2×C22⋊C4C23×C4316yes—
301C2×C22⋊C4C23×C4316yes—
302C2×C22⋊C4C23×C4316yes—
303C2×C22⋊C4C23×C4316yes—
304C2×C22⋊C4C23×C43148yescomplemented
305C2×C42C23×C4313yes—
306C2×C42C23×C4316yes—
307C2×C42C23×C4316yes—
308C2×C42C23×C4312yes—
309C2×C42C23×C4311yescharacteristic
310C2×C42C23×C4318yescomplemented
311C24—412no—
312C24C24×C4316yes—
313C24C24×C4311yescharacteristic
314C24C24×C4318yes—
315C2×Q8—412no—
316C2×Q8—46no—
317C2×Q8C24×C43124yes—
318C2×Q8C24×C43112yes—
319C2×D4—412no—
320C2×D4—46no—
321C2×D4—412no—
322C2×D4C24×C43112yes—
323C2×D4C24×C43124yes—
324C2×D4C24×C43124yes—
325C22×C4—412no—
326C22×C4—46no—
327C22×C4—412no—
328C22×C4C24×C4313yes—
329C22×C4C24×C4316yes—
330C22×C4C24×C4313yes—
331C22×C4C24×C4316yes—
332C22×C4C24×C4316yes—
333C22×C4C24×C43112yes—
334C22×C4C24×C43124yes—
335C22×C4C24×C43124yes—
336C4⋊C4C24×C43124yes—
337C4⋊C4C24×C43124yes—
338C4⋊C4C24×C43124yes—
339C4⋊C4C24×C43124yes—
340C4⋊C4C24×C43112yes—
341C4⋊C4C24×C43124yes—
342C4⋊C4C24×C43112yes—
343C4⋊C4C24×C43124yes—
344C22⋊C4C24×C43124yes—
345C22⋊C4C24×C43124yes—
346C22⋊C4C24×C43124yes—
347C22⋊C4C24×C43124yes—
348C22⋊C4C24×C43124yes—
349C22⋊C4C24×C43124yes—
350C22⋊C4C24×C43124yes—
351C22⋊C4C24×C43124yes—
352C22⋊C4C24×C43124yes—
353C42C24×C43112yes—
354C42C24×C4314yes—
355C42C24×C43124yes—
356C42C24×C43124yes—
357C42C24×C4318yes—
358C23—26no—
359C23—212no—
360C23—212no—
361C23—212no—
362C23—424no—
363C23—816no—
364C23C25×C43112yes—
365C23C25×C4312yes—
366C23C25×C4311yescharacteristic
367Q8—424no—
368Q8—412no—
369D4—424no—
370D4—412no—
371D4—424no—
372C2×C4—26no—
373C2×C4—212no—
374C2×C4—26no—
375C2×C4—212no—
376C2×C4—212no—
377C2×C4—424no—
378C2×C4—412no—
379C2×C4—424no—
380C2×C4C25×C4316yes—
381C2×C4C25×C43112yes—
382C2×C4C25×C4316yes—
383C2×C4C25×C43112yes—
384C2×C4C25×C43112yes—
385C22—26no—
386C22—212no—
387C22—212no—
388C22—212no—
389C22—424no—
390C22—44no—
391C22—816no—
392C22C43×#58516yes—
393C22C26×C4311yescharacteristic
394C4—26no—
395C4—212no—
396C4—26no—
397C4—212no—
398C4—212no—
399C2—412no—
400C2—42no—
401C2C43×#356814yesdirect product factor
402C2C2×C43×#58513yes—
subgroupG/H
center, socleC23×C43C25
commutator, Frattini, cosocleC22C26×C43
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3568C2direct (N × H)
2. C2×C43×#563C2semidirect
3. C2×C43×H(3,𝔽4)C2semidirect
4. C2×C43×#556C2semidirect
5. C2×C43×#551C2semidirect
6. C2×C43×#542C2semidirect
7. C2×C43×#538C2semidirect
8. C2×C43×#529C2semidirect
9. C43×#563C22semidirect
10. C43×H(3,𝔽4)C22semidirect
11. C43×#556C22semidirect
12. C43×#551C22semidirect
13. C43×#542C22semidirect
14. C43×#538C22semidirect
15. C2×C4⋊Q8×C43C22semidirect
16. C43×#529C22semidirect
17. C2×#126×C43C22semidirect
18. C2×#126×C43C22semidirect
19. C2×#126×C43C22semidirect
20. C2×#126×C43C22semidirect
21. C2×#126×C43C22semidirect
22. C2×#125×C43C22semidirect
26. C2×#124×C43C22semidirect
29. C2×#123×C43C22semidirect
30. C2×C22⋊Q8×C43C22semidirect
31. C2×C22⋊Q8×C43C22semidirect
32. C2×C22⋊Q8×C43C22semidirect
33. C2×C22⋊Q8×C43C22semidirect
37. C2×#120×C43C22semidirect
38. C2×C4×Q8×C43C22semidirect
39. C2×C4×Q8×C43C22semidirect
42. C2×C4×D4×C43C22semidirect
43. C2×#117×C43C22semidirect
44. C2×#117×C43C22semidirect
45. C22×C22⋊C4×C43C22semidirect
46. C22×C42×C43C22semidirect
56. C4⋊Q8×C43C23semidirect
57. #126×C43C23semidirect
58. #126×C43C23semidirect
59. #126×C43C23semidirect
60. #126×C43C23semidirect
61. #126×C43C23semidirect
62. #125×C43C23semidirect
66. #124×C43C23semidirect
69. #123×C43C23semidirect
70. C22⋊Q8×C43C23semidirect
71. C22⋊Q8×C43C23semidirect
72. C22⋊Q8×C43C23semidirect
73. C22⋊Q8×C43C23semidirect
77. #120×C43C23semidirect
78. C4×Q8×C43C23semidirect
79. C4×Q8×C43C23semidirect
82. C4×D4×C43C23semidirect
83. #117×C43C23semidirect
84. #117×C43C23semidirect
102. C2×C22⋊C4×C43C23semidirect
108. C2×C42×C43C23semidirect
183. C2×#3568C43direct (N × H)
198. #3568C2×C43direct (N × H)
199. C2×#563C2×C43semidirect
200. C2×H(3,𝔽4)C2×C43semidirect
201. C2×#556C2×C43semidirect
202. C2×#551C2×C43semidirect
203. C2×#542C2×C43semidirect
204. C2×#538C2×C43semidirect
205. C2×#529C2×C43semidirect
208. C2×C43#3568direct (N × H)
210. #563C22×C43semidirect
211. H(3,𝔽4)C22×C43semidirect
212. #556C22×C43semidirect
213. #551C22×C43semidirect
214. #542C22×C43semidirect
215. #538C22×C43semidirect
216. C2×C4⋊Q8C22×C43semidirect
217. #529C22×C43semidirect
218. C2×#126C22×C43semidirect
219. C2×#126C22×C43semidirect
220. C2×#126C22×C43semidirect
221. C2×#126C22×C43semidirect
222. C2×#126C22×C43semidirect
223. C2×#125C22×C43semidirect
227. C2×#124C22×C43semidirect
230. C2×#123C22×C43semidirect
231. C2×C22⋊Q8C22×C43semidirect
232. C2×C22⋊Q8C22×C43semidirect
233. C2×C22⋊Q8C22×C43semidirect
234. C2×C22⋊Q8C22×C43semidirect
238. C2×#120C22×C43semidirect
239. C2×C4×Q8C22×C43semidirect
240. C2×C4×Q8C22×C43semidirect
243. C2×C4×D4C22×C43semidirect
244. C2×#117C22×C43semidirect
245. C2×#117C22×C43semidirect
246. C22×C22⋊C4C22×C43semidirect
247. C22×C42C22×C43semidirect
248. C43C2×#3568direct (N × H)
258. C4⋊Q8C23×C43semidirect
259. #126C23×C43semidirect
260. #126C23×C43semidirect
261. #126C23×C43semidirect
262. #126C23×C43semidirect
263. #126C23×C43semidirect
264. #125C23×C43semidirect
268. #124C23×C43semidirect
271. #123C23×C43semidirect
272. C22⋊Q8C23×C43semidirect
273. C22⋊Q8C23×C43semidirect
274. C22⋊Q8C23×C43semidirect
275. C22⋊Q8C23×C43semidirect
279. #120C23×C43semidirect
280. C4×Q8C23×C43semidirect
281. C4×Q8C23×C43semidirect
284. C4×D4C23×C43semidirect
285. #117C23×C43semidirect
286. #117C23×C43semidirect
304. C2×C22⋊C4C23×C43semidirect
310. C2×C42C23×C43semidirect
401. C2C43×#3568direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35682
C2×C43×#5632
C2×C43×H(3,𝔽4)2
C2×C43×#5562
C2×C43×#5512
C2×C43×#5422
C2×C43×#5382
C2×C43×#5292
C2×#356843