Finite Group Databasebeta

← C11×#21872 #14599065

Subgroups — C11×#21872 #14599065

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2317C211yesmaximal, characteristic, complemented
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1991C211yesmaximal, characteristic, complemented
6C11×#1961C211yesmaximal, characteristic, complemented
7C11×#1957C211yesmaximal, characteristic, complemented
8C11×#1875C212yesmaximal, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1804C212yesmaximal, complemented
11C11×#1802C212yesmaximal, complemented
12C11×#540—24no—
13C11×#540C418yescomplemented
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#433—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×#97C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32C11×#389—22no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#384C2211yescharacteristic
36C11×#382C2211yescharacteristic
37C11×#382C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11C2312yes—
45C23×C4×C11—22no—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C11×#127—22no—
51C11×#127C2×C414yescomplemented
52C11×#125—22no—
53C11×#125C2×C414yescomplemented
54C11×#123—216no—
55C11×#121—24no—
56C11×#121—216no—
57C11×#121C2×C418yes—
58C4×D4×C11—24no—
59C4×D4×C11C2×C418yescomplemented
60C11×#117—42no—
61C11×#117C2×C414yes—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C11×C4⋊C8—24no—
82C11×#102—42no—
83C11×#102—42no—
84C11×#102—42no—
85C11×#102—42no—
86C11×C22⋊C8—24no—
87C11×#97—22no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—22no—
91#21872C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—22no—
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—28no—
95C2×D4×C11—28no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C414yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—28no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C22×C4×C11—82no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4—82no—
139C11×C4⋊C4C22⋊C418yes—
140C11×C4⋊C4C22×C414yes—
141C11×C22⋊C4—28no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4C22⋊C418yes—
145C42×C11—42no—
146C42×C11C22×C412yes—
147C42×C11C22×C412yes—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C2×#540C2×C1111yescharacteristic
151C2×#433C2×C1111yescharacteristic, complemented
152#2317C2×C1111yescharacteristic, complemented
153#1992C2×C1111yescharacteristic, complemented
154#1991C2×C1111yescharacteristic, complemented
155#1961C2×C1111yescharacteristic, complemented
156#1957C2×C1111yescharacteristic, complemented
157#1875C2×C1112yescomplemented
158#1874C2×C1112yescomplemented
159#1804C2×C1112yescomplemented
160#1802C2×C1112yescomplemented
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C2×C22⋊C412yes—
173C23×C11C22×D411yescharacteristic
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—88no—
179D4×C11—88no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—88no—
200C2×C4×C11—84no—
201C2×C4×C11C2×C22⋊C414yes—
202C2×C4×C11C2×C22⋊C414yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11H(5,𝔽2)12yes—
207C2×C4×C112−1+412yes—
208C8×C11—42no—
209C8×C11—42no—
210#540—24no—
211#540C4×C1118yescomplemented
212C2×#127C22×C1111yescharacteristic
213C2×#125C22×C1111yescharacteristic
214C2×#123—22no—
215C2×#121—22no—
216C2×#121C22×C1112yes—
217C2×C4×D4C22×C1112yes—
218C2×#117C22×C1111yescharacteristic
219C2×#117C22×C1111yescharacteristic
220C22×C4⋊C4C22×C1111yescharacteristic
221#433—24no—
222C2×C4⋊C8C22×C1112yes—
223C2×#102C22×C1112yes—
224C2×#102C22×C1112yes—
225C2×#102C22×C1112yes—
226C2×#102C22×C1112yes—
227C2×C22⋊C8C22×C1112yes—
228C2×#97C22×C1111yescharacteristic
229C2×C4×C8C22×C1111yescharacteristic
230#389—22no—
231#385—22no—
232#384C22×C1111yescharacteristic
233#384C22×C1111yescharacteristic
234#382C22×C1111yescharacteristic
235#382C22×C1111yescharacteristic
236#340C22×C1112yes—
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—42no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11#53511yescharacteristic
254C22×C11#53611yescharacteristic
255C22×C11#57612yes—
256C22×C11#57712yes—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—24no—
260C4×C11—44no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11#52012yes—
266C4×C11#53712yes—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4C23×C1112yes—
270C23×C4—22no—
271C23×C4—21no—
272C23×C4C23×C1111yescharacteristic
273C22×C8C23×C1112yes—
274C22×C8C23×C1112yes—
275#127—22no—
276#127C2×C4×C1114yescomplemented
277#125—22no—
278#125C2×C4×C1114yescomplemented
279#123—216no—
280#121—24no—
281#121—216no—
282#121C2×C4×C1118yes—
283C4×D4—24no—
284C4×D4C2×C4×C1118yescomplemented
285#117—42no—
286#117C2×C4×C1114yes—
287#117D4×C1114yes—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4D4×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4D4×C1112yes—
303C2×C42—21no—
304C2×C42C23×C1111yescharacteristic
305C2×C42C23×C1111yescharacteristic
306C4⋊C8—24no—
307#102—42no—
308#102—42no—
309#102—42no—
310#102—42no—
311C22⋊C8—24no—
312#97—22no—
313C4×C8—22no—
314#95—22no—
315#95—22no—
316C2×C11—42no—
317C2×C11—84no—
318C2×C11#231111yescharacteristic
319C2×C11#289712yes—
320C2×C11#322011yescharacteristic
321C2×C11#322111yescharacteristic
322C2×C11#324112yes—
323C24—22no—
324C24C2×D4×C1111yescharacteristic
325C2×D4—28no—
326C2×D4—28no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—82no—
333C2×D4—82no—
334C2×D4—82no—
335C2×D4—82no—
336C2×D4C22×C4×C1114yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—28no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4—82no—
349C22×C4C22×C4×C1112yes—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1112yes—
354C22×C4C24×C1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C4⋊C4—28no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—82no—
369C4⋊C4—82no—
370C4⋊C4C11×C22⋊C418yes—
371C4⋊C4C22×C4×C1114yes—
372C22⋊C4—28no—
373C22⋊C4—28no—
374C22⋊C4—42no—
375C22⋊C4C11×C22⋊C418yes—
376C42—42no—
377C42C22×C4×C1112yes—
378C42C22×C4×C1112yes—
379C42C2×D4×C1112yes—
380C42C2×D4×C1112yes—
381C11#2187211yescharacteristic, direct product factor, Sylow
382C23—21no—
383C23—21no—
384C23—22no—
385C23—22no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23C2×C11×C22⋊C412yes—
394C23C22×D4×C1111yescharacteristic
395D4—24no—
396D4—24no—
397D4—42no—
398D4—42no—
399D4—88no—
400D4—88no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—88no—
421C2×C4—84no—
422C2×C4C2×C11×C22⋊C414yes—
423C2×C4C2×C11×C22⋊C414yes—
424C2×C4C2×C11×C22⋊C412yes—
425C2×C4C23×C4×C1111yescharacteristic
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C11×H(5,𝔽2)12yes—
428C2×C4C11×2−1+412yes—
429C8—42no—
430C8—42no—
431C22—24no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—42no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22C22×C11×C22⋊C411yescharacteristic
444C22C11×#53511yescharacteristic
445C22C11×#53611yescharacteristic
446C22C11×#57612yes—
447C22C11×#57712yes—
448C4—24no—
449C4—24no—
450C4—22no—
451C4—44no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4C11×#52012yes—
457C4C11×#53712yes—
458C2—42no—
459C2—84no—
460C2C11×#231111yescharacteristic
461C2C11×#289712yes—
462C2C11×#322011yescharacteristic
463C2C11×#322111yescharacteristic
464C2C11×#324112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#433C2semidirect
3. C11×#2317C2semidirect
4. C11×#1992C2semidirect
5. C11×#1991C2semidirect
6. C11×#1961C2semidirect
7. C11×#1957C2semidirect
8. C11×#1875C2semidirect
9. C11×#1874C2semidirect
10. C11×#1804C2semidirect
11. C11×#1802C2semidirect
13. C11×#540C4semidirect
51. C11×#127C2×C4semidirect
53. C11×#125C2×C4semidirect
59. C4×D4×C11C2×C4semidirect
91. #21872C11direct (N × H)
151. C2×#433C2×C11semidirect
152. #2317C2×C11semidirect
153. #1992C2×C11semidirect
154. #1991C2×C11semidirect
155. #1961C2×C11semidirect
156. #1957C2×C11semidirect
157. #1875C2×C11semidirect
158. #1874C2×C11semidirect
159. #1804C2×C11semidirect
160. #1802C2×C11semidirect
211. #540C4×C11semidirect
276. #127C2×C4×C11semidirect
278. #125C2×C4×C11semidirect
284. C4×D4C2×C4×C11semidirect
381. C11#21872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5402
C2×C11×#4332
C11×#23172
C11×#19922
C11×#19912
C11×#19612
C11×#19572
C11×#18752
C11×#18742
C11×#18042
C11×#18022
#2187211