Finite Group Databasebeta

← C11×#35033 #14612226

Subgroups — C11×#35033 #14612226

Order 2816.

1986 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2857C212yesmaximal, complemented
2C11×#2851C212yesmaximal, complemented
3C11×#2626C214yesmaximal
4C11×#2608C214yesmaximal, complemented
5C11×#2607C214yesmaximal, complemented
6C11×#2441C214yesmaximal, complemented
7C11×#2439C214yesmaximal, complemented
8C11×#2329C214yesmaximal, complemented
9C11×#2280C212yesmaximal
10C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×C4⋊Q8C2212yescomplemented
13C2×C11×#125C2212yescomplemented
14C2×C11×C22⋊Q8C2214yes—
15C2×C11×#117C2212yes—
16C2×C11×#117C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#399C2218yes—
21C11×#396C2218yes—
22C11×#396C2218yes—
23C11×#393C2218yes—
24C11×#391C2218yescomplemented
25C11×#391C2214yescomplemented
26C11×#389C2214yescomplemented
27C11×#389C2214yescomplemented
28C11×#389C2218yescomplemented
29C11×#389C2214yescomplemented
30C11×#387C2218yescomplemented
31C11×#387C2218yescomplemented
32C11×#387C2218yescomplemented
33C11×#385C2218yes—
34C11×#384C2212yescomplemented
35C11×#382C2212yescomplemented
36C11×#381C2214yes—
37C11×#380C2214yes—
38C11×#380C2214yes—
39C11×#380C2214yes—
40C11×#379C2214yes—
41C4×C11×C22⋊C4C2214yes—
42C4×C11×C22⋊C4C2212yes—
43C4×C11×C22⋊C4C2212yes—
44C4×C11×C22⋊C4C2214yes—
45C4×C11×C22⋊C4C2214yes—
46C2×C11×#95C2212yes—
47C25×C11C2311yescharacteristic
48C22×Q8×C11C2314yes—
49C23×C4×C11—42no—
50C23×C4×C11—42no—
51C23×C4×C11Q818yescomplemented
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C11×C4⋊Q8—44no—
59C11×#125—44no—
60C11×C22⋊Q8—216no—
61C11×#117—44no—
62C11×#117—44no—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2318yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C4⋊C4C2318yes—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2318yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C42×C11—42no—
79C2×C42×C11—42no—
80C2×C42×C11C2312yes—
81C2×C42×C11C2312yes—
82C2×C42×C11C2312yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2314yes—
86C2×C42×C11C2314yes—
87C11×#95C2314yes—
88C11×#95C2314yes—
89C11×#95C2318yes—
90C11×#95C2318yes—
91C11×#95C2318yes—
92C11×#95C2318yes—
93C11×#95C2318yes—
94#35033C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—24no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—42no—
99C24×C11C2×Q814yes—
100C24×C11C2412yes—
101C24×C11C2411yescharacteristic
102C2×Q8×C11—28no—
103C2×Q8×C11—44no—
104C2×Q8×C11—44no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—416no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×Q818yes—
120C22×C4×C11C2×Q814yes—
121C22×C4×C11C2×Q818yes—
122C22×C4×C11C2×Q814yes—
123C22×C4×C11#4118yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2418yes—
126C22×C4×C11C2418yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2411yescharacteristic
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2411yescharacteristic
132C11×C4⋊C4—28no—
133C11×C4⋊C4—216no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—48no—
138C11×C4⋊C4—48no—
139C11×C4⋊C4—44no—
140C11×C22⋊C4—216no—
141C11×C22⋊C4—28no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—48no—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—44no—
146C42×C11—24no—
147C42×C11—24no—
148C42×C11—41no—
149C42×C11—41no—
150C42×C11—42no—
151C42×C11—44no—
152C42×C11—44no—
153#2857C2×C1112yescomplemented
154#2851C2×C1112yescomplemented
155#2626C2×C1114yes—
156#2608C2×C1114yescomplemented
157#2607C2×C1114yescomplemented
158#2441C2×C1114yescomplemented
159#2439C2×C1114yescomplemented
160#2329C2×C1114yescomplemented
161#2280C2×C1112yes—
162C2×C4×C22⋊C4C2×C1111yescharacteristic
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—28no—
167C23×C11—24no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—44no—
172C23×C11—44no—
173C23×C11—48no—
174C23×C11—48no—
175C23×C11C22×Q814yes—
176C23×C11C22×Q812yes—
177C23×C11C2×#4114yes—
178C23×C11C2511yescharacteristic
179Q8×C11—88no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—28no—
189C2×C4×C11—216no—
190C2×C4×C11—24no—
191C2×C4×C11—28no—
192C2×C4×C11—28no—
193C2×C4×C11—24no—
194C2×C4×C11—28no—
195C2×C4×C11—28no—
196C2×C4×C11—28no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—44no—
200C2×C4×C11—48no—
201C2×C4×C11—48no—
202C2×C4×C11—48no—
203C2×C4×C11C22×Q814yes—
204C2×C4×C11C22×Q812yes—
205C2×C4×C11C22×Q812yes—
206C2×C4×C11C2×#4114yes—
207C2×C4×C11C2×#4114yes—
208C2×C4×C11H(5,𝔽2)12yes—
209C2×C4×C11H(5,𝔽2)12yes—
210C24×C4C22×C1111yescharacteristic
211C2×C4⋊Q8C22×C1112yescomplemented
212C2×#125C22×C1112yescomplemented
213C2×C22⋊Q8C22×C1114yes—
214C2×#117C22×C1112yes—
215C2×#117C22×C1112yes—
216C22×C22⋊C4C22×C1112yes—
217C22×C42C22×C1111yescharacteristic
218C22×C42C22×C1111yescharacteristic
219#399C22×C1118yes—
220#396C22×C1118yes—
221#396C22×C1118yes—
222#393C22×C1118yes—
223#391C22×C1118yescomplemented
224#391C22×C1114yescomplemented
225#389C22×C1118yescomplemented
226#389C22×C1114yescomplemented
227#389C22×C1114yescomplemented
228#389C22×C1114yescomplemented
229#387C22×C1118yescomplemented
230#387C22×C1118yescomplemented
231#387C22×C1118yescomplemented
232#385C22×C1118yes—
233#384C22×C1112yescomplemented
234#382C22×C1112yescomplemented
235#381C22×C1114yes—
236#380C22×C1114yes—
237#380C22×C1114yes—
238#380C22×C1114yes—
239#379C22×C1114yes—
240C4×C22⋊C4C22×C1114yes—
241C4×C22⋊C4C22×C1112yes—
242C4×C22⋊C4C22×C1114yes—
243C4×C22⋊C4C22×C1112yes—
244C4×C22⋊C4C22×C1114yes—
245C2×#95C22×C1112yes—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—24no—
252C22×C11—24no—
253C22×C11—416no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11#53314yes—
257C22×C11C23×Q811yescharacteristic
258C22×C11C22×#4112yes—
259C22×C11C2×H(5,𝔽2)11yescharacteristic
260C22×C11C2×H(5,𝔽2)11yescharacteristic
261C22×C11#58512yes—
262C4×C11—22no—
263C4×C11—24no—
264C4×C11—24no—
265C4×C11—24no—
266C4×C11—48no—
267C4×C11—48no—
268C4×C11—44no—
269C4×C11#54314yes—
270C25C23×C1111yescharacteristic
271C22×Q8C23×C1114yes—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4Q8×C1118yescomplemented
275C23×C4C23×C1112yes—
276C23×C4C23×C1111yescharacteristic
277C23×C4C23×C1112yes—
278C23×C4C23×C1111yescharacteristic
279C23×C4C23×C1112yes—
280C23×C4C23×C1112yes—
281C4⋊Q8—44no—
282#125—44no—
283C22⋊Q8—216no—
284#117—44no—
285#117—44no—
286C2×C4⋊C4C23×C1114yes—
287C2×C4⋊C4C23×C1114yes—
288C2×C4⋊C4C23×C1114yes—
289C2×C4⋊C4C23×C1118yes—
290C2×C4⋊C4C23×C1118yes—
291C2×C4⋊C4C23×C1114yes—
292C2×C4⋊C4C23×C1114yes—
293C2×C4⋊C4C23×C1118yes—
294C2×C22⋊C4—28no—
295C2×C22⋊C4C23×C1114yes—
296C2×C22⋊C4C23×C1114yes—
297C2×C22⋊C4C23×C1118yes—
298C2×C22⋊C4C23×C1114yes—
299C2×C22⋊C4C23×C1114yes—
300C2×C22⋊C4C23×C1118yes—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42C23×C1112yes—
304C2×C42C23×C1112yes—
305C2×C42C23×C1114yes—
306C2×C42C23×C1114yes—
307C2×C42C23×C1112yes—
308C2×C42C23×C1111yescharacteristic
309C2×C42C23×C1111yescharacteristic
310#95C23×C1114yes—
311#95C23×C1114yes—
312#95C23×C1118yes—
313#95C23×C1118yes—
314#95C23×C1118yes—
315#95C23×C1118yes—
316#95C23×C1118yes—
317C2×C11—24no—
318C2×C11—44no—
319C2×C11C2×#53311yescharacteristic
320C2×C11C2×#54311yescharacteristic
321C2×C11#345811yescharacteristic
322C2×C11#350512yes—
323C2×C11#350612yes—
324C24—24no—
325C24—41no—
326C24—41no—
327C24—42no—
328C24C2×Q8×C1114yes—
329C24C24×C1112yes—
330C24C24×C1111yescharacteristic
331C2×Q8—28no—
332C2×Q8—44no—
333C2×Q8—44no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—416no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4C2×Q8×C1118yes—
349C22×C4C2×Q8×C1114yes—
350C22×C4C2×Q8×C1118yes—
351C22×C4C2×Q8×C1114yes—
352C22×C4C11×#4118yes—
353C22×C4C24×C1114yes—
354C22×C4C24×C1118yes—
355C22×C4C24×C1118yes—
356C22×C4C24×C1112yes—
357C22×C4C24×C1111yescharacteristic
358C22×C4C24×C1112yes—
359C22×C4C24×C1112yes—
360C22×C4C24×C1111yescharacteristic
361C4⋊C4—28no—
362C4⋊C4—216no—
363C4⋊C4—28no—
364C4⋊C4—28no—
365C4⋊C4—48no—
366C4⋊C4—44no—
367C4⋊C4—44no—
368C4⋊C4—48no—
369C22⋊C4—216no—
370C22⋊C4—28no—
371C22⋊C4—28no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—48no—
375C42—24no—
376C42—24no—
377C42—41no—
378C42—41no—
379C42—42no—
380C42—44no—
381C42—44no—
382C11#3503311yescharacteristic, direct product factor, Sylow
383C23—21no—
384C23—21no—
385C23—22no—
386C23—28no—
387C23—24no—
388C23—22no—
389C23—22no—
390C23—24no—
391C23—44no—
392C23—44no—
393C23—48no—
394C23—48no—
395C23C22×Q8×C1114yes—
396C23C22×Q8×C1112yes—
397C23C2×C11×#4114yes—
398C23C25×C1111yescharacteristic
399Q8—88no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—28no—
409C2×C4—216no—
410C2×C4—24no—
411C2×C4—28no—
412C2×C4—28no—
413C2×C4—24no—
414C2×C4—28no—
415C2×C4—28no—
416C2×C4—28no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—44no—
420C2×C4—48no—
421C2×C4—48no—
422C2×C4—48no—
423C2×C4C22×Q8×C1114yes—
424C2×C4C22×Q8×C1112yes—
425C2×C4C22×Q8×C1112yes—
426C2×C4C2×C11×#4114yes—
427C2×C4C2×C11×#4114yes—
428C2×C4C11×H(5,𝔽2)12yes—
429C2×C4C11×H(5,𝔽2)12yes—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—24no—
434C22—24no—
435C22—24no—
436C22—24no—
437C22—416no—
438C22—44no—
439C22—44no—
440C22C11×#53314yes—
441C22C23×Q8×C1111yescharacteristic
442C22C22×C11×#4112yes—
443C22C2×C11×H(5,𝔽2)11yescharacteristic
444C22C2×C11×H(5,𝔽2)11yescharacteristic
445C22C11×#58512yes—
446C4—22no—
447C4—24no—
448C4—24no—
449C4—24no—
450C4—48no—
451C4—44no—
452C4—48no—
453C4C11×#54314yes—
454C2—24no—
455C2—44no—
456C2C2×C11×#53311yescharacteristic
457C2C2×C11×#54311yescharacteristic
458C2C11×#345811yescharacteristic
459C2C11×#350512yes—
460C2C11×#350612yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2857C2semidirect
2. C11×#2851C2semidirect
4. C11×#2608C2semidirect
5. C11×#2607C2semidirect
6. C11×#2441C2semidirect
7. C11×#2439C2semidirect
8. C11×#2329C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
13. C2×C11×#125C22semidirect
24. C11×#391C22semidirect
25. C11×#391C22semidirect
26. C11×#389C22semidirect
27. C11×#389C22semidirect
28. C11×#389C22semidirect
29. C11×#389C22semidirect
30. C11×#387C22semidirect
31. C11×#387C22semidirect
32. C11×#387C22semidirect
34. C11×#384C22semidirect
35. C11×#382C22semidirect
51. C23×C4×C11Q8semidirect
94. #35033C11direct (N × H)
153. #2857C2×C11semidirect
154. #2851C2×C11semidirect
156. #2608C2×C11semidirect
157. #2607C2×C11semidirect
158. #2441C2×C11semidirect
159. #2439C2×C11semidirect
160. #2329C2×C11semidirect
211. C2×C4⋊Q8C22×C11semidirect
212. C2×#125C22×C11semidirect
223. #391C22×C11semidirect
224. #391C22×C11semidirect
225. #389C22×C11semidirect
226. #389C22×C11semidirect
227. #389C22×C11semidirect
228. #389C22×C11semidirect
229. #387C22×C11semidirect
230. #387C22×C11semidirect
231. #387C22×C11semidirect
233. #384C22×C11semidirect
234. #382C22×C11semidirect
274. C23×C4Q8×C11semidirect
382. C11#35033direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28572
C11×#28512
C11×#26262
C11×#26082
C11×#26072
C11×#24412
C11×#24392
C11×#23292
C11×#22802
C2×C4×C11×C22⋊C42
#3503311