Finite Group Databasebeta

← C2×C11×#3529 #14639884

Subgroups — C2×C11×#3529 #14639884

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3529C2132yesmaximal, direct product factor
2C2×C11×#563C213yesmaximal, complemented
3C2×C11×#562C216yesmaximal, complemented
4C2×C11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
5C2×C11×#560C216yesmaximal, complemented
6C2×C11×#532C213yesmaximal, complemented
7C2×C11×#529C216yesmaximal, complemented
8C2×C11×#525C216yesmaximal, complemented
9C22×C11×#41C2213yes—
10C22×C11×#41C2211yescharacteristic, complemented
11C24×C4×C11C2212yescomplemented
12C11×#563C22148yescomplemented
13C11×#562C22196yescomplemented
14C11×H(3,𝔽4)C22116yescomplemented
15C11×#560C22196yescomplemented
16C11×#532C22148yescomplemented
17C2×C11×C4⋊Q8C2213yescomplemented
18C2×C11×#127C2213yes—
19C11×#529C22196yescomplemented
20C2×C11×#126C22112yescomplemented
21C2×C11×#125C2216yescomplemented
22C2×C11×#124C2216yes—
23C2×C11×#124C2213yes—
24C2×C11×#124C2213yescomplemented
25C11×#525C22196yescomplemented
26C2×C11×#123C2216yes—
27C2×C11×#123C2216yescomplemented
28C2×C11×#123C22112yescomplemented
29C2×C11×C22⋊Q8C22112yescomplemented
30C2×C11×C22⋊Q8C2216yescomplemented
31C2×C11×#121C22112yes—
32C2×C11×#121C2216yes—
33C2×C11×#121C22112yescomplemented
34C2×C11×#120C2216yes—
35C2×C11×#120C2216yescomplemented
36C2×C4×Q8×C11C2212yescomplemented
37C2×C4×D4×C11C2216yes—
38C2×C4×D4×C11C22112yescomplemented
39C2×C11×#117C2216yescomplemented
40C22×C42×C11C2213yescomplemented
41C25×C11C2312yes—
42C2×C11×#41—412no—
43C2×C11×#41—44no—
44C2×C11×#41C23124yes—
45C2×C11×#41C2318yescomplemented
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2313yes—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2316yes—
50C22×D4×C11C23112yes—
51C22×D4×C11C2313yes—
52C22×D4×C11C2316yes—
53C22×D4×C11C2313yes—
54C23×C4×C11—48no—
55C23×C4×C11C2313yes—
56C23×C4×C11C2316yes—
57C23×C4×C11C2316yes—
58C23×C4×C11C2316yes—
59C23×C4×C11C23116yescomplemented
60C11×C4⋊Q8C23124yescomplemented
61C11×#127C23124yes—
62C11×#126C23196yescomplemented
63C11×#125C23148yescomplemented
64C11×#124C23148yes—
65C11×#124C23124yes—
66C11×#124C23124yescomplemented
67C11×#123C23148yes—
68C11×#123C23148yescomplemented
69C11×#123C23196yescomplemented
70C11×C22⋊Q8C23196yescomplemented
71C11×C22⋊Q8C23148yescomplemented
72C11×#121C23196yes—
73C11×#121C23148yes—
74C11×#121C23196yescomplemented
75C11×#120C23148yes—
76C11×#120C23148yescomplemented
77C4×Q8×C11C23116yescomplemented
78C4×D4×C11C23148yes—
79C4×D4×C11C23196yescomplemented
80C11×#117C23148yescomplemented
81C2×C11×C4⋊C4C23112yes—
82C2×C11×C4⋊C4C2316yes—
83C2×C11×C4⋊C4C23112yes—
84C2×C11×C4⋊C4C2316yes—
85C2×C11×C22⋊C4C2316yes—
86C2×C11×C22⋊C4C2316yes—
87C2×C11×C22⋊C4C23112yes—
88C2×C11×C22⋊C4C23112yes—
89C2×C11×C22⋊C4C23112yes—
90C2×C42×C11C2313yes—
91C2×C42×C11C2313yes—
92C2×C42×C11C2316yes—
93C2×C42×C11C23124yescomplemented
94C2×#3529C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—44no—
96C24×C11—48no—
97C24×C11C2416yes—
98C24×C11C2413yes—
99C24×C11C2418yes—
100C11×#41—448no—
101C11×#41—416no—
102C2×Q8×C11—44no—
103C2×Q8×C11—46no—
104C2×Q8×C11—42no—
105C2×Q8×C11C2418yes—
106C2×Q8×C11C24112yes—
107C2×Q8×C11C2414yes—
108C2×D4×C11—424no—
109C2×D4×C11—412no—
110C2×D4×C11—412no—
111C2×D4×C11—46no—
112C2×D4×C11—46no—
113C2×D4×C11C24124yes—
114C2×D4×C11C24148yes—
115C2×D4×C11C24112yes—
116C2×D4×C11C24124yes—
117C2×D4×C11C24112yes—
118C22×C4×C11—224no—
119C22×C4×C11—212no—
120C22×C4×C11—432no—
121C22×C4×C11—412no—
122C22×C4×C11—412no—
123C22×C4×C11C2416yes—
124C22×C4×C11C2416yes—
125C22×C4×C11C2413yes—
126C22×C4×C11C24112yes—
127C22×C4×C11C2416yes—
128C22×C4×C11C24124yes—
129C22×C4×C11C24124yes—
130C22×C4×C11C24124yes—
131C22×C4×C11C2411yescharacteristic
132C11×C4⋊C4C24148yes—
133C11×C4⋊C4C24124yes—
134C11×C4⋊C4C24148yes—
135C11×C4⋊C4C24124yes—
136C11×C22⋊C4C24124yes—
137C11×C22⋊C4C24124yes—
138C11×C22⋊C4C24148yes—
139C11×C22⋊C4C24148yes—
140C11×C22⋊C4C24148yes—
141C42×C11C24124yes—
142C42×C11C24112yes—
143C42×C11C24112yes—
144#3529C2×C11132yesdirect product factor
145C2×#563C2×C1113yescomplemented
146C2×#562C2×C1116yescomplemented
147C2×H(3,𝔽4)C2×C1111yescharacteristic, complemented
148C2×#560C2×C1116yescomplemented
149C2×#532C2×C1113yescomplemented
150C2×#529C2×C1116yescomplemented
151C2×#525C2×C1116yescomplemented
152C23×C11—212no—
153C23×C11—26no—
154C23×C11—212no—
155C23×C11—224no—
156C23×C11—48no—
157C23×C11—416no—
158C23×C11—432no—
159C23×C11C25112yes—
160C23×C11C2516yes—
161C23×C11C2511yescharacteristic
162Q8×C11—48no—
163Q8×C11—412no—
164Q8×C11—44no—
165D4×C11—448no—
166D4×C11—424no—
167D4×C11—424no—
168D4×C11—412no—
169D4×C11—412no—
170C2×C4×C11—212no—
171C2×C4×C11—26no—
172C2×C4×C11—212no—
173C2×C4×C11—212no—
174C2×C4×C11—248no—
175C2×C4×C11—224no—
176C2×C4×C11—424no—
177C2×C4×C11—424no—
178C2×C4×C11H(5,𝔽2)14yes—
179C2×C4×C11C25112yes—
180C2×C4×C11C25112yes—
181C2×C4×C11C2516yes—
182C2×C4×C11C25112yes—
183C2×C4×C11C2512yes—
184C22×#41C22×C1113yes—
185C22×#41C22×C1111yescharacteristic, complemented
186C24×C4C22×C1112yescomplemented
187#563C22×C11148yescomplemented
188#562C22×C11196yescomplemented
189H(3,𝔽4)C22×C11116yescomplemented
190#560C22×C11196yescomplemented
191#532C22×C11148yescomplemented
192C2×C4⋊Q8C22×C1113yescomplemented
193C2×#127C22×C1113yes—
194#529C22×C11196yescomplemented
195C2×#126C22×C11112yescomplemented
196C2×#125C22×C1116yescomplemented
197C2×#124C22×C1116yes—
198C2×#124C22×C1113yes—
199C2×#124C22×C1113yescomplemented
200#525C22×C11196yescomplemented
201C2×#123C22×C1116yes—
202C2×#123C22×C1116yescomplemented
203C2×#123C22×C11112yescomplemented
204C2×C22⋊Q8C22×C11112yescomplemented
205C2×C22⋊Q8C22×C1116yescomplemented
206C2×#121C22×C11112yes—
207C2×#121C22×C1116yes—
208C2×#121C22×C11112yescomplemented
209C2×#120C22×C1116yes—
210C2×#120C22×C1116yescomplemented
211C2×C4×Q8C22×C1112yescomplemented
212C2×C4×D4C22×C1116yes—
213C2×C4×D4C22×C11112yescomplemented
214C2×#117C22×C1116yescomplemented
215C22×C42C22×C1113yescomplemented
216C22×C11—212no—
217C22×C11—26no—
218C22×C11—212no—
219C22×C11—224no—
220C22×C11—432no—
221C22×C11—412no—
222C22×C11—424no—
223C22×C11C2×H(5,𝔽2)12yes—
224C22×C11#58514yes—
225C22×C11C2611yescharacteristic
226C4×C11—212no—
227C4×C11—26no—
228C4×C11—212no—
229C4×C11—212no—
230C4×C11C2×H(5,𝔽2)14yes—
231C25C23×C1112yes—
232C2×#41—412no—
233C2×#41—44no—
234C2×#41C23×C11124yes—
235C2×#41C23×C1118yescomplemented
236C22×Q8C23×C1112yes—
237C22×Q8C23×C1113yes—
238C22×Q8C23×C1111yescharacteristic
239C22×D4C23×C1116yes—
240C22×D4C23×C11112yes—
241C22×D4C23×C1113yes—
242C22×D4C23×C1116yes—
243C22×D4C23×C1113yes—
244C23×C4—48no—
245C23×C4C23×C1116yes—
246C23×C4C23×C1113yes—
247C23×C4C23×C1116yes—
248C23×C4C23×C1116yes—
249C23×C4C23×C11116yescomplemented
250C4⋊Q8C23×C11124yescomplemented
251#127C23×C11124yes—
252#126C23×C11196yescomplemented
253#125C23×C11148yescomplemented
254#124C23×C11148yes—
255#124C23×C11124yes—
256#124C23×C11124yescomplemented
257#123C23×C11148yes—
258#123C23×C11148yescomplemented
259#123C23×C11196yescomplemented
260C22⋊Q8C23×C11196yescomplemented
261C22⋊Q8C23×C11148yescomplemented
262#121C23×C11196yes—
263#121C23×C11148yes—
264#121C23×C11196yescomplemented
265#120C23×C11148yes—
266#120C23×C11148yescomplemented
267C4×Q8C23×C11116yescomplemented
268C4×D4C23×C11148yes—
269C4×D4C23×C11196yescomplemented
270#117C23×C11148yescomplemented
271C2×C4⋊C4C23×C11112yes—
272C2×C4⋊C4C23×C1116yes—
273C2×C4⋊C4C23×C11112yes—
274C2×C4⋊C4C23×C1116yes—
275C2×C22⋊C4C23×C1116yes—
276C2×C22⋊C4C23×C1116yes—
277C2×C22⋊C4C23×C11112yes—
278C2×C22⋊C4C23×C11112yes—
279C2×C22⋊C4C23×C11112yes—
280C2×C42C23×C1116yes—
281C2×C42C23×C1113yes—
282C2×C42C23×C1113yes—
283C2×C42C23×C11124yescomplemented
284C2×C11—46no—
285C2×C11—412no—
286C2×C11#352914yesdirect product factor
287C2×C11C22×H(5,𝔽2)11yescharacteristic
288C2×C11C2×#58512yes—
289C24—44no—
290C24—48no—
291C24C24×C1116yes—
292C24C24×C1113yes—
293C24C24×C1118yes—
294#41—448no—
295#41—416no—
296C2×Q8—46no—
297C2×Q8—42no—
298C2×Q8—44no—
299C2×Q8C24×C1118yes—
300C2×Q8C24×C11112yes—
301C2×Q8C24×C1114yes—
302C2×D4—412no—
303C2×D4—46no—
304C2×D4—46no—
305C2×D4—424no—
306C2×D4—412no—
307C2×D4C24×C11124yes—
308C2×D4C24×C11148yes—
309C2×D4C24×C11112yes—
310C2×D4C24×C11124yes—
311C2×D4C24×C11112yes—
312C22×C4—224no—
313C22×C4—212no—
314C22×C4—432no—
315C22×C4—412no—
316C22×C4—412no—
317C22×C4C24×C1116yes—
318C22×C4C24×C1116yes—
319C22×C4C24×C1113yes—
320C22×C4C24×C11112yes—
321C22×C4C24×C1116yes—
322C22×C4C24×C11124yes—
323C22×C4C24×C11124yes—
324C22×C4C24×C11124yes—
325C22×C4C24×C1111yescharacteristic
326C4⋊C4C24×C11148yes—
327C4⋊C4C24×C11124yes—
328C4⋊C4C24×C11148yes—
329C4⋊C4C24×C11124yes—
330C22⋊C4C24×C11124yes—
331C22⋊C4C24×C11124yes—
332C22⋊C4C24×C11148yes—
333C22⋊C4C24×C11148yes—
334C22⋊C4C24×C11148yes—
335C42C24×C11124yes—
336C42C24×C11112yes—
337C42C24×C11112yes—
338C11C2×#352911yescharacteristic, direct product factor, Sylow
339C23—212no—
340C23—26no—
341C23—212no—
342C23—224no—
343C23—48no—
344C23—416no—
345C23—432no—
346C23C25×C11112yes—
347C23C25×C1116yes—
348C23C25×C1111yescharacteristic
349Q8—48no—
350Q8—412no—
351Q8—44no—
352D4—448no—
353D4—424no—
354D4—424no—
355D4—412no—
356D4—412no—
357C2×C4—212no—
358C2×C4—26no—
359C2×C4—212no—
360C2×C4—212no—
361C2×C4—248no—
362C2×C4—224no—
363C2×C4—424no—
364C2×C4—424no—
365C2×C4C11×H(5,𝔽2)14yes—
366C2×C4C25×C11112yes—
367C2×C4C25×C11112yes—
368C2×C4C25×C1116yes—
369C2×C4C25×C11112yes—
370C2×C4C25×C1112yes—
371C22—212no—
372C22—26no—
373C22—212no—
374C22—224no—
375C22—432no—
376C22—424no—
377C22—412no—
378C22C2×C11×H(5,𝔽2)12yes—
379C22C11×#58514yes—
380C22C26×C1111yescharacteristic
381C4—212no—
382C4—26no—
383C4—212no—
384C4—212no—
385C4C2×C11×H(5,𝔽2)14yes—
386C2—412no—
387C2—46no—
388C2C11×#352914yesdirect product factor
389C2C22×C11×H(5,𝔽2)11yescharacteristic
390C2C2×C11×#58512yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC22C26×C11
socleC23×C11C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3529C2direct (N × H)
2. C2×C11×#563C2semidirect
3. C2×C11×#562C2semidirect
4. C2×C11×H(3,𝔽4)C2semidirect
5. C2×C11×#560C2semidirect
6. C2×C11×#532C2semidirect
7. C2×C11×#529C2semidirect
8. C2×C11×#525C2semidirect
10. C22×C11×#41C22semidirect
11. C24×C4×C11C22semidirect
12. C11×#563C22semidirect
13. C11×#562C22semidirect
14. C11×H(3,𝔽4)C22semidirect
15. C11×#560C22semidirect
16. C11×#532C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
19. C11×#529C22semidirect
20. C2×C11×#126C22semidirect
21. C2×C11×#125C22semidirect
24. C2×C11×#124C22semidirect
25. C11×#525C22semidirect
27. C2×C11×#123C22semidirect
28. C2×C11×#123C22semidirect
29. C2×C11×C22⋊Q8C22semidirect
30. C2×C11×C22⋊Q8C22semidirect
33. C2×C11×#121C22semidirect
35. C2×C11×#120C22semidirect
36. C2×C4×Q8×C11C22semidirect
38. C2×C4×D4×C11C22semidirect
39. C2×C11×#117C22semidirect
40. C22×C42×C11C22semidirect
45. C2×C11×#41C23semidirect
59. C23×C4×C11C23semidirect
60. C11×C4⋊Q8C23semidirect
62. C11×#126C23semidirect
63. C11×#125C23semidirect
66. C11×#124C23semidirect
68. C11×#123C23semidirect
69. C11×#123C23semidirect
70. C11×C22⋊Q8C23semidirect
71. C11×C22⋊Q8C23semidirect
74. C11×#121C23semidirect
76. C11×#120C23semidirect
77. C4×Q8×C11C23semidirect
79. C4×D4×C11C23semidirect
80. C11×#117C23semidirect
93. C2×C42×C11C23semidirect
94. C2×#3529C11direct (N × H)
144. #3529C2×C11direct (N × H)
145. C2×#563C2×C11semidirect
146. C2×#562C2×C11semidirect
147. C2×H(3,𝔽4)C2×C11semidirect
148. C2×#560C2×C11semidirect
149. C2×#532C2×C11semidirect
150. C2×#529C2×C11semidirect
151. C2×#525C2×C11semidirect
185. C22×#41C22×C11semidirect
186. C24×C4C22×C11semidirect
187. #563C22×C11semidirect
188. #562C22×C11semidirect
189. H(3,𝔽4)C22×C11semidirect
190. #560C22×C11semidirect
191. #532C22×C11semidirect
192. C2×C4⋊Q8C22×C11semidirect
194. #529C22×C11semidirect
195. C2×#126C22×C11semidirect
196. C2×#125C22×C11semidirect
199. C2×#124C22×C11semidirect
200. #525C22×C11semidirect
202. C2×#123C22×C11semidirect
203. C2×#123C22×C11semidirect
204. C2×C22⋊Q8C22×C11semidirect
205. C2×C22⋊Q8C22×C11semidirect
208. C2×#121C22×C11semidirect
210. C2×#120C22×C11semidirect
211. C2×C4×Q8C22×C11semidirect
213. C2×C4×D4C22×C11semidirect
214. C2×#117C22×C11semidirect
215. C22×C42C22×C11semidirect
235. C2×#41C23×C11semidirect
249. C23×C4C23×C11semidirect
250. C4⋊Q8C23×C11semidirect
252. #126C23×C11semidirect
253. #125C23×C11semidirect
256. #124C23×C11semidirect
258. #123C23×C11semidirect
259. #123C23×C11semidirect
260. C22⋊Q8C23×C11semidirect
261. C22⋊Q8C23×C11semidirect
264. #121C23×C11semidirect
266. #120C23×C11semidirect
267. C4×Q8C23×C11semidirect
269. C4×D4C23×C11semidirect
270. #117C23×C11semidirect
283. C2×C42C23×C11semidirect
286. C2×C11#3529direct (N × H)
338. C11C2×#3529direct (N × H)
388. C2C11×#3529direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35292
C2×C11×#5632
C2×C11×#5622
C2×C11×H(3,𝔽4)2
C2×C11×#5602
C2×C11×#5322
C2×C11×#5292
C2×C11×#5252
C2×#352911