Finite Group Databasebeta

← C11×#23911 #14601104

Subgroups — C11×#23911 #14601104

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3486C211yesmaximal, characteristic
2C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C11×#456C212yesmaximal, complemented
4C11×#3004C212yesmaximal, complemented
5C11×#2005C214yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1886C212yesmaximal, complemented
8C11×#1784C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#137C2214yes—
13D4×Q8×C11—24no—
14C11×#548—24no—
15C11×#536—22no—
16C11×#536C2212yes—
17C2×C11×C4⋊Q8—22no—
18C2×C11×C4⋊Q8—28no—
19C2×C11×C4⋊Q8C2212yes—
20C2×C11×C4⋊Q8C2212yes—
21C11×#525—22no—
22C11×#525C2212yes—
23C11×#519C2211yescharacteristic
24C22×C11×C4⋊C4—22no—
25C22×C42×C11C2211yescharacteristic
26C11×#456—28no—
27C11×#451—24no—
28C11×#448—24no—
29C2×C11×#104C2214yes—
30C11×#419C2214yes—
31C2×C11×#101C2212yes—
32C2×C11×#101C2212yes—
33C11×#407C2212yes—
34C11×#339C2214yes—
35C11×2−1+4—24no—
36C11×2−1+4—42no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41C2312yes—
40C22×Q8×C11—24no—
41C22×Q8×C11—24no—
42C22×Q8×C11—22no—
43C22×Q8×C11—21no—
44C22×Q8×C11—24no—
45C22×Q8×C11—24no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11D412yes—
49C22×Q8×C11C2312yes—
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11D412yes—
55C23×C4×C11C2311yescharacteristic
56C11×#137—28no—
57C11×#137—44no—
58C2×C11×Q16—24no—
59C2×C11×SD16—24no—
60C2×C11×M16C2314yes—
61C11×C4⋊Q8—216no—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8—24no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8D418yescomplemented
68C11×#124—24no—
69C11×#124—22no—
70C11×#123—24no—
71C11×#123—22no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—28no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8D414yes—
76C11×#121—24no—
77C11×#121D414yes—
78C11×#120—22no—
79C4×Q8×C11—24no—
80C4×D4×C11—28no—
81C4×D4×C11—24no—
82C11×#117—22no—
83C11×#117C2312yes—
84C2×C11×C4⋊C4—216no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C42×C11—21no—
88C2×C42×C11—24no—
89C2×C42×C11C2312yes—
90C11×#104—28no—
91C11×#103—28no—
92C11×#101—24no—
93C11×#101—42no—
94C11×C22⋊C8—24no—
95#23911C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11C2×D411yescharacteristic
97C11×#41—24no—
98C11×#41—24no—
99C11×#41—44no—
100C11×#41—48no—
101C11×#41—44no—
102C2×Q8×C11—22no—
103C2×Q8×C11—24no—
104C2×Q8×C11—24no—
105C2×Q8×C11—24no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—42no—
115C2×Q8×C11—416no—
116C2×Q8×C11—416no—
117C2×Q8×C11—42no—
118C2×Q8×C11—48no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D414yes—
122C2×Q8×C11C2×D414yes—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2411yescharacteristic
146C11×Q16—48no—
147C11×SD16—48no—
148C11×M16—24no—
149C11×M16—24no—
150C2×C8×C11—24no—
151C11×C4⋊C4—216no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—216no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—24no—
161C42×C11—24no—
162C42×C11—24no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11C2×D414yes—
166#3486C2×C1111yescharacteristic
167C22×C4⋊Q8C2×C1111yescharacteristic, complemented
168C2×#456C2×C1112yescomplemented
169#3004C2×C1112yescomplemented
170#2005C2×C1114yescomplemented
171#1896C2×C1112yescomplemented
172#1886C2×C1112yescomplemented
173#1784C2×C1111yescharacteristic, complemented
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11#12012yes—
179C23×C11C22×D411yescharacteristic
180Q8×C11—28no—
181Q8×C11—28no—
182Q8×C11—24no—
183Q8×C11—48no—
184Q8×C11—48no—
185Q8×C11—44no—
186Q8×C11—44no—
187Q8×C11—44no—
188D4×C11—24no—
189D4×C11—44no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—48no—
193C2×C4×C11—216no—
194C2×C4×C11—28no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—28no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—48no—
208C2×C4×C11—48no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11#12014yes—
214C2×C4×C11#12012yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×D412yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C8×C11—44no—
219C2×2−1+4C22×C1111yescharacteristic
220C23×Q8C22×C1111yescharacteristic
221C23×Q8C22×C1111yescharacteristic
222C2×#137C22×C1114yes—
223D4×Q8—24no—
224#548—24no—
225#536—22no—
226#536C22×C1112yes—
227C2×C4⋊Q8—22no—
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8C22×C1112yes—
230C2×C4⋊Q8C22×C1112yes—
231#525—22no—
232#525C22×C1112yes—
233#519C22×C1111yescharacteristic
234C22×C4⋊C4—22no—
235C22×C42C22×C1111yescharacteristic
236#456—28no—
237#451—24no—
238#448—24no—
239C2×#104C22×C1114yes—
240#419C22×C1114yes—
241C2×#101C22×C1112yes—
242C2×#101C22×C1112yes—
243#407C22×C1112yes—
244#339C22×C1114yes—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—42no—
251C22×C11—44no—
252C22×C11#45614yescomplemented
253C22×C11C2×#12011yescharacteristic
254C22×C11C2×#12011yescharacteristic
255C22×C11#53411yescharacteristic
256C4×C11—28no—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11D4214yes—
2642−1+4—24no—
2652−1+4—42no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41C23×C1112yes—
269C22×Q8—24no—
270C22×Q8—24no—
271C22×Q8—22no—
272C22×Q8—21no—
273C22×Q8—24no—
274C22×Q8—24no—
275C22×Q8—42no—
276C22×Q8—42no—
277C22×Q8D4×C1112yes—
278C22×Q8C23×C1112yes—
279C22×Q8C23×C1111yescharacteristic
280C22×Q8C23×C1111yescharacteristic
281C23×C4—21no—
282C23×C4—21no—
283C23×C4D4×C1112yes—
284C23×C4C23×C1111yescharacteristic
285#137—28no—
286#137—44no—
287C2×Q16—24no—
288C2×SD16—24no—
289C2×M16C23×C1114yes—
290C4⋊Q8—216no—
291C4⋊Q8—24no—
292C4⋊Q8—24no—
293C4⋊Q8—24no—
294C4⋊Q8—22no—
295C4⋊Q8—24no—
296C4⋊Q8D4×C1118yescomplemented
297#124—24no—
298#124—22no—
299#123—24no—
300#123—22no—
301C22⋊Q8—24no—
302C22⋊Q8—28no—
303C22⋊Q8—24no—
304C22⋊Q8D4×C1114yes—
305#121—24no—
306#121D4×C1114yes—
307#120—22no—
308C4×Q8—24no—
309C4×D4—28no—
310C4×D4—24no—
311#117—22no—
312#117C23×C1112yes—
313C2×C4⋊C4—216no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C42—21no—
317C2×C42—24no—
318C2×C42C23×C1112yes—
319#104—28no—
320#103—28no—
321#101—24no—
322#101—42no—
323C22⋊C8—24no—
324C2×C11—21no—
325C2×C11—21no—
326C2×C11—24no—
327C2×C11—82no—
328C2×C11#240311yescharacteristic
329C2×C11C2×#45612yes—
330C24C2×D4×C1111yescharacteristic
331#41—24no—
332#41—24no—
333#41—44no—
334#41—48no—
335#41—44no—
336C2×Q8—22no—
337C2×Q8—24no—
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—24no—
347C2×Q8—24no—
348C2×Q8—42no—
349C2×Q8—416no—
350C2×Q8—416no—
351C2×Q8—42no—
352C2×Q8—48no—
353C2×Q8—42no—
354C2×Q8C2×D4×C1112yes—
355C2×Q8C2×D4×C1114yes—
356C2×Q8C2×D4×C1114yes—
357C2×D4—22no—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4C2×D4×C1112yes—
361C22×C4—24no—
362C22×C4—28no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1112yes—
378C22×C4C2×D4×C1114yes—
379C22×C4C24×C1111yescharacteristic
380Q16—48no—
381SD16—48no—
382M16—24no—
383M16—24no—
384C2×C8—24no—
385C4⋊C4—216no—
386C4⋊C4—24no—
387C4⋊C4—28no—
388C4⋊C4—216no—
389C4⋊C4—24no—
390C4⋊C4C2×D4×C1114yes—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—22no—
394C22⋊C4—24no—
395C42—24no—
396C42—24no—
397C42—22no—
398C42—22no—
399C42C2×D4×C1114yes—
400C11#2391111yescharacteristic, direct product factor, Sylow
401C23—21no—
402C23—21no—
403C23—24no—
404C23—22no—
405C23C11×#12012yes—
406C23C22×D4×C1111yescharacteristic
407Q8—28no—
408Q8—28no—
409Q8—24no—
410Q8—48no—
411Q8—48no—
412Q8—44no—
413Q8—44no—
414Q8—44no—
415D4—24no—
416D4—44no—
417D4—42no—
418D4—42no—
419D4—48no—
420C2×C4—216no—
421C2×C4—28no—
422C2×C4—21no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—28no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—48no—
435C2×C4—48no—
436C2×C4—48no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4C11×#12012yes—
441C2×C4C11×#12014yes—
442C2×C4C22×D4×C1112yes—
443C2×C4C22×D4×C1112yes—
444C2×C4C11×H(5,𝔽2)12yes—
445C8—44no—
446C22—24no—
447C22—24no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—42no—
452C22—44no—
453C22C11×#45614yescomplemented
454C22C2×C11×#12011yescharacteristic
455C22C2×C11×#12011yescharacteristic
456C22C11×#53411yescharacteristic
457C4—28no—
458C4—22no—
459C4—24no—
460C4—42no—
461C4—42no—
462C4—44no—
463C4—44no—
464C4D42×C1114yes—
465C2—21no—
466C2—21no—
467C2—24no—
468C2—82no—
469C2C11×#240311yescharacteristic
470C2C2×C11×#45612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3486C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C4⋊Q8C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#3004C2semidirect
5. C11×#2005C2semidirect
6. C11×#1896C2semidirect
7. C11×#1886C2semidirect
8. C11×#1784C2semidirect
67. C11×C4⋊Q8D4semidirect
95. #23911C11direct (N × H)
167. C22×C4⋊Q8C2×C11semidirect
168. C2×#456C2×C11semidirect
169. #3004C2×C11semidirect
170. #2005C2×C11semidirect
171. #1896C2×C11semidirect
172. #1886C2×C11semidirect
173. #1784C2×C11semidirect
252. C22×C11#456semidirect
296. C4⋊Q8D4×C11semidirect
400. C11#23911direct (N × H)
453. C22C11×#456semidirect

Maximal subgroups

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

subgroupindex
C11×#34862
C22×C11×C4⋊Q82
C2×C11×#4562
C11×#30042
C11×#20052
C11×#18962
C11×#18862
C11×#17842
#2391111