Finite Group Databasebeta

← C11×#21759 #14598952

Subgroups — C11×#21759 #14598952

Order 2816.

1570 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
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C2×C11×#380C211yesmaximal, characteristic
4C11×#1892C214yesmaximal, complemented
5C11×#1872C214yesmaximal, complemented
6C11×#1824C212yesmaximal, complemented
7C11×#1787C212yesmaximal, complemented
8C23×Q8×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C23×C8×C11C2212yes—
11C2×C11×C22⋊Q8—24no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C418yescomplemented
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2212yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C22⋊C4—21no—
21C22×C11×C22⋊C4—21no—
22C2×C11×#103C2218yescomplemented
23C2×C11×C22⋊C8—24no—
24C2×C11×C22⋊C8C2212yes—
25C2×C11×C22⋊C8C2212yes—
26C11×#380—21no—
27C11×#380—21no—
28C11×#380C2212yes—
29C11×#380C2212yes—
30C2×C11×#95—21no—
31C11×#340C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×Q8×C11—22no—
34C22×Q8×C11—21no—
35C22×Q8×C11—44no—
36C22×Q8×C11C2×C414yescomplemented
37C22×Q8×C11C2312yes—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11—22no—
41C23×C4×C11—44no—
42C23×C4×C11C2×C414yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D414yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11—24no—
51C22×C8×C11—44no—
52C22×C8×C11C2314yes—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8C2×C418yes—
58C11×C22⋊Q8C2×C418yescomplemented
59C2×C11×C4⋊C4—28no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2×C414yescomplemented
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—28no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—44no—
75C11×#103—48no—
76C11×C22⋊C8—24no—
77C11×C22⋊C8—24no—
78C11×#95—22no—
79C11×#95—22no—
80#21759C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—42no—
82C24×C11—42no—
83C24×C11C22⋊C414yes—
84C24×C11SD1614yes—
85C24×C11Q1614yes—
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D411yescharacteristic
88C24×C11C2×D411yescharacteristic
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—28no—
92C2×Q8×C11—48no—
93C2×Q8×C11—44no—
94C2×Q8×C11—48no—
95C2×Q8×C11C22×C414yes—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—48no—
105C22×C4×C11—48no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11C22⋊C414yes—
115C22×C4×C11C22⋊C414yes—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C2×C8×C11—24no—
128C2×C8×C11—28no—
129C2×C8×C11—48no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4C22×C414yes—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—44no—
141C22×C22⋊Q8C2×C1111yescharacteristic
142C22×C22⋊C8C2×C1111yescharacteristic
143C2×#380C2×C1111yescharacteristic
144#1892C2×C1114yescomplemented
145#1872C2×C1114yescomplemented
146#1824C2×C1112yescomplemented
147#1787C2×C1112yescomplemented
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—44no—
155C23×C11—44no—
156C23×C11—48no—
157C23×C11—48no—
158C23×C11#103116yescomplemented
159C23×C11C2×C22⋊C412yes—
160C23×C11C2×C22⋊C412yes—
161C23×C11C2×C22⋊C412yes—
162C23×C11C2×SD1612yes—
163C23×C11C2×SD1612yes—
164C23×C11C2×SD1612yes—
165C23×C11C2×Q1612yes—
166C23×C11C2×Q1612yes—
167C23×C11C2×Q1612yes—
168C23×C11C22×D411yescharacteristic
169Q8×C11—28no—
170Q8×C11—48no—
171Q8×C11—44no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—44no—
186C2×C4×C11—48no—
187C2×C4×C11—48no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—88no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11H(5,𝔽2)14yes—
200C8×C11—44no—
201C23×Q8C22×C1111yescharacteristic
202C24×C4C22×C1111yescharacteristic
203C23×C8C22×C1112yes—
204C2×C22⋊Q8—24no—
205C2×C22⋊Q8—21no—
206C2×C22⋊Q8—21no—
207C2×C22⋊Q8C4×C1118yescomplemented
208C2×C22⋊Q8C22×C1112yes—
209C2×C22⋊Q8C22×C1112yes—
210C22×C4⋊C4—21no—
211C22×C4⋊C4C22×C1111yescharacteristic
212C22×C4⋊C4C22×C1112yes—
213C22×C22⋊C4—21no—
214C22×C22⋊C4—21no—
215C2×#103C22×C1118yescomplemented
216C2×C22⋊C8—24no—
217C2×C22⋊C8C22×C1112yes—
218C2×C22⋊C8C22×C1112yes—
219#380—21no—
220#380—21no—
221#380C22×C1112yes—
222#380C22×C1112yes—
223C2×#95—21no—
224#340C22×C1118yescomplemented
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—24no—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—24no—
235C22×C11—24no—
236C22×C11—24no—
237C22×C11—416no—
238C22×C11C2×#10314yes—
239C22×C11C2×#10314yes—
240C22×C11C2×#10314yes—
241C22×C11C22×C22⋊C411yescharacteristic
242C22×C11#53412yes—
243C22×C11C22×SD1611yescharacteristic
244C22×C11C22×Q1611yescharacteristic
245C22×C11#57512yes—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—44no—
250C4×C11—44no—
251C4×C11—84no—
252C4×C11#51812yes—
253C4×C11#53412yes—
254C25D4×C1111yescharacteristic
255C22×Q8—22no—
256C22×Q8—21no—
257C22×Q8—44no—
258C22×Q8C2×C4×C1114yescomplemented
259C22×Q8C23×C1112yes—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—44no—
264C23×C4C2×C4×C1114yes—
265C23×C4D4×C1111yescharacteristic
266C23×C4D4×C1111yescharacteristic
267C23×C4D4×C1111yescharacteristic
268C23×C4D4×C1114yes—
269C23×C4C23×C1111yescharacteristic
270C23×C4C23×C1111yescharacteristic
271C23×C4C23×C1111yescharacteristic
272C22×C8—24no—
273C22×C8—44no—
274C22×C8C23×C1114yes—
275C22⋊Q8—28no—
276C22⋊Q8—28no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8C2×C4×C1118yes—
280C22⋊Q8C2×C4×C1118yescomplemented
281C2×C4⋊C4—28no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4C2×C4×C1114yescomplemented
289C2×C4⋊C4C23×C1114yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—44no—
297#103—48no—
298C22⋊C8—24no—
299C22⋊C8—24no—
300#95—22no—
301#95—22no—
302C2×C11—24no—
303C2×C11—24no—
304C2×C11—24no—
305C2×C11#230811yescharacteristic
306C2×C11C22×#10311yescharacteristic
307C2×C11#289611yescharacteristic
308C2×C11#318712yes—
309C2×C11#318912yes—
310C24—42no—
311C24—42no—
312C24C11×C22⋊C414yes—
313C24C11×SD1614yes—
314C24C11×Q1614yes—
315C24C2×D4×C1111yescharacteristic
316C24C2×D4×C1111yescharacteristic
317C24C2×D4×C1111yescharacteristic
318C2×Q8—24no—
319C2×Q8—22no—
320C2×Q8—28no—
321C2×Q8—48no—
322C2×Q8—44no—
323C2×Q8—48no—
324C2×Q8C22×C4×C1114yes—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—48no—
334C22×C4—48no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—44no—
342C22×C4—44no—
343C22×C4C11×C22⋊C414yes—
344C22×C4C11×C22⋊C414yes—
345C22×C4C11×C22⋊C414yes—
346C22×C4C22×C4×C1112yes—
347C22×C4C22×C4×C1112yes—
348C22×C4C22×C4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C24×C1111yescharacteristic
356C2×C8—24no—
357C2×C8—28no—
358C2×C8—48no—
359C4⋊C4—28no—
360C4⋊C4—28no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—28no—
364C4⋊C4—44no—
365C4⋊C4C22×C4×C1114yes—
366C22⋊C4—28no—
367C22⋊C4—28no—
368C22⋊C4—44no—
369C22⋊C4—44no—
370C11#2175911yescharacteristic, direct product factor, Sylow
371C23—22no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—44no—
378C23—44no—
379C23—48no—
380C23—48no—
381C23C11×#103116yescomplemented
382C23C2×C11×C22⋊C412yes—
383C23C2×C11×C22⋊C412yes—
384C23C2×C11×C22⋊C412yes—
385C23C2×C11×SD1612yes—
386C23C2×C11×SD1612yes—
387C23C2×C11×SD1612yes—
388C23C2×C11×Q1612yes—
389C23C2×C11×Q1612yes—
390C23C2×C11×Q1612yes—
391C23C22×D4×C1111yescharacteristic
392Q8—28no—
393Q8—48no—
394Q8—44no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—48no—
410C2×C4—48no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—88no—
417C2×C4C2×C11×C22⋊C412yes—
418C2×C4C2×C11×C22⋊C412yes—
419C2×C4C2×C11×C22⋊C412yes—
420C2×C4C23×C4×C1111yescharacteristic
421C2×C4C22×D4×C1111yescharacteristic
422C2×C4C11×H(5,𝔽2)14yes—
423C8—44no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—24no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—416no—
437C22C2×C11×#10314yes—
438C22C2×C11×#10314yes—
439C22C2×C11×#10314yes—
440C22C22×C11×C22⋊C411yescharacteristic
441C22C11×#53412yes—
442C22C22×C11×SD1611yescharacteristic
443C22C22×C11×Q1611yescharacteristic
444C22C11×#57512yes—
445C4—22no—
446C4—22no—
447C4—22no—
448C4—44no—
449C4—44no—
450C4—84no—
451C4C11×#51812yes—
452C4C11×#53412yes—
453C2—24no—
454C2—24no—
455C2—24no—
456C2C11×#230811yescharacteristic
457C2C22×C11×#10311yescharacteristic
458C2C11×#289611yescharacteristic
459C2C11×#318712yes—
460C2C11×#318912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1892C2semidirect
5. C11×#1872C2semidirect
6. C11×#1824C2semidirect
7. C11×#1787C2semidirect
14. C2×C11×C22⋊Q8C4semidirect
22. C2×C11×#103C22semidirect
31. C11×#340C22semidirect
36. C22×Q8×C11C2×C4semidirect
58. C11×C22⋊Q8C2×C4semidirect
66. C2×C11×C4⋊C4C2×C4semidirect
80. #21759C11direct (N × H)
144. #1892C2×C11semidirect
145. #1872C2×C11semidirect
146. #1824C2×C11semidirect
147. #1787C2×C11semidirect
158. C23×C11#103semidirect
207. C2×C22⋊Q8C4×C11semidirect
215. C2×#103C22×C11semidirect
224. #340C22×C11semidirect
258. C22×Q8C2×C4×C11semidirect
280. C22⋊Q8C2×C4×C11semidirect
288. C2×C4⋊C4C2×C4×C11semidirect
370. C11#21759direct (N × H)
381. C23C11×#103semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C11×C22⋊C82
C2×C11×#3802
C11×#18922
C11×#18722
C11×#18242
C11×#17872
#2175911