Finite Group Databasebeta

← C11×#21065 #14598258

Subgroups — C11×#21065 #14598258

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#427C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C22×C11×#102C211yesmaximal, characteristic
4C11×#2309C211yesmaximal, characteristic
5C11×#2274C211yesmaximal, characteristic, complemented
6C11×#1926C214yesmaximal, complemented
7C11×#1925C214yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#427—24no—
18C2×C11×#107C2212yescomplemented
19C2×C11×#106C2212yescomplemented
20C11×#418—24no—
21C2×C11×#102C418yescomplemented
22C2×C11×#102C2214yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C11×#390—22no—
26C11×#390C2214yes—
27C11×#379—22no—
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2214yescomplemented
30C4×C11×C22⋊C4—22no—
31C11×#340C2214yescomplemented
32C11×#336C2212yescomplemented
33C11×#336C2212yescomplemented
34C25×C11—21no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C414yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C2×C11×M16—22no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#117—22no—
55C11×#117—22no—
56C11×#117—22no—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C2×C42×C11—24no—
75C2×C42×C11C2312yes—
76C11×#107—24no—
77C11×#106—24no—
78C11×#102—28no—
79C11×#102C2×C418yes—
80C11×#102C2×C418yes—
81C11×#95—24no—
82#21065C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—22no—
84C24×C11—24no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11—82no—
88C24×C11—82no—
89C24×C11C2×D411yescharacteristic
90C2×D4×C11—28no—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—44no—
101C2×D4×C11—44no—
102C2×D4×C11C22×C414yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—82no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D414yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C11×M16—44no—
118C2×C8×C11—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C22×C412yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22×C414yes—
135C11×C4⋊C4C2×D414yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—84no—
140C11×C22⋊C4—84no—
141C42×C11—24no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—42no—
145C42×C11—84no—
146C2×#427C2×C1111yescharacteristic, complemented
147C2×#418C2×C1111yescharacteristic
148C22×#102C2×C1111yescharacteristic
149#2309C2×C1111yescharacteristic
150#2274C2×C1111yescharacteristic, complemented
151#1926C2×C1114yescomplemented
152#1925C2×C1114yescomplemented
153#1736C2×C1111yescharacteristic, complemented
154#1729C2×C1111yescharacteristic, complemented
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—44no—
161C23×C11—44no—
162C23×C11—48no—
163C23×C11—84no—
164C23×C11—84no—
165C23×C11—88no—
166C23×C11—88no—
167C23×C11C4×D412yes—
168C23×C11#12112yes—
169C23×C11#12312yes—
170C23×C11C22×D411yescharacteristic
171D4×C11—24no—
172D4×C11—24no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—48no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—84no—
188C2×C4×C11#11714yes—
189C2×C4×C11C4×D414yes—
190C2×C4×C11C4×D412yes—
191C2×C4×C11#12112yes—
192C2×C4×C11#12312yes—
193C2×C4×C11#12414yes—
194C2×C4×C11#12614yes—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C8×C11—22no—
202C8×C11—22no—
203C8×C11—42no—
204C23×D4C22×C1111yescharacteristic
205C22×M16C22×C1111yescharacteristic
206C23×C8C22×C1111yescharacteristic
207C2×#117C22×C1111yescharacteristic
208C2×#117C22×C1111yescharacteristic
209C2×#117C22×C1111yescharacteristic
210C22×C4⋊C4C22×C1111yescharacteristic
211#427—24no—
212C2×#107C22×C1112yescomplemented
213C2×#106C22×C1112yescomplemented
214#418—24no—
215C2×#102C4×C1118yescomplemented
216C2×#102C22×C1114yes—
217C2×#102C22×C1112yes—
218C2×#102C22×C1112yes—
219#390—22no—
220#390C22×C1114yes—
221#379—22no—
222C4×C4⋊C4—22no—
223C4×C4⋊C4C22×C1114yescomplemented
224C4×C22⋊C4—22no—
225#340C22×C1114yescomplemented
226#336C22×C1112yescomplemented
227#336C22×C1112yescomplemented
228C22×C11—24no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—24no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—816no—
236C22×C11—84no—
237C22×C11—84no—
238C22×C11#38814yes—
239C22×C11C2×C4×D411yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11C2×#12311yescharacteristic
242C22×C11#57612yes—
243C22×C11#57712yes—
244C4×C11—44no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11—82no—
248C4×C11#38814yes—
249C4×C11C2×#11711yescharacteristic
250C4×C11C2×C4×D411yescharacteristic
251C4×C11C2×#12411yescharacteristic
252C4×C11C2×#12611yescharacteristic
253C25—21no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4C2×C4×C1114yes—
261C22×D4C23×C1112yes—
262C23×C4—21no—
263C23×C4C23×C1111yescharacteristic
264C2×M16—22no—
265C2×M16—22no—
266C2×M16—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8C2×C4×C1114yes—
270C22×C8C23×C1112yes—
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1111yescharacteristic
273#117—22no—
274#117—22no—
275#117—22no—
276#117—22no—
277#117—22no—
278#117D4×C1114yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4C2×C4×C1114yes—
282C2×C4⋊C4D4×C1112yes—
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1112yes—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4D4×C1112yes—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—24no—
294C2×C42C23×C1112yes—
295#107—24no—
296#106—24no—
297#102—28no—
298#102C2×C4×C1118yes—
299#102C2×C4×C1118yes—
300#95—24no—
301C2×C11—24no—
302C2×C11—84no—
303C2×C11C2×#38811yescharacteristic
304C2×C11#294811yescharacteristic
305C2×C11#294911yescharacteristic
306C2×C11#304512yes—
307C2×C11#309612yes—
308C24—22no—
309C24—24no—
310C24—42no—
311C24—42no—
312C24—82no—
313C24—82no—
314C24C2×D4×C1111yescharacteristic
315C2×D4—28no—
316C2×D4—28no—
317C2×D4—24no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—44no—
326C2×D4—44no—
327C2×D4C22×C4×C1114yes—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—82no—
333C22×C4C22×C4×C1112yes—
334C22×C4C2×D4×C1114yes—
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1112yes—
337C22×C4C11×#4112yes—
338C22×C4C11×#4112yes—
339C22×C4C11×#4112yes—
340C22×C4C11×#4112yes—
341C22×C4C24×C1111yescharacteristic
342M16—44no—
343C2×C8—28no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8C22×C4×C1112yes—
352C2×C8C22×C4×C1112yes—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4C22×C4×C1114yes—
360C4⋊C4C2×D4×C1114yes—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—42no—
364C22⋊C4—84no—
365C22⋊C4—84no—
366C42—24no—
367C42—22no—
368C42—22no—
369C42—42no—
370C42—84no—
371C11#2106511yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—24no—
375C23—42no—
376C23—42no—
377C23—48no—
378C23—44no—
379C23—44no—
380C23—84no—
381C23—84no—
382C23—88no—
383C23—88no—
384C23C4×D4×C1112yes—
385C23C11×#12112yes—
386C23C11×#12312yes—
387C23C22×D4×C1111yescharacteristic
388D4—24no—
389D4—24no—
390D4—48no—
391D4—42no—
392D4—42no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—84no—
405C2×C4C11×#11714yes—
406C2×C4C4×D4×C1114yes—
407C2×C4C4×D4×C1112yes—
408C2×C4C11×#12112yes—
409C2×C4C11×#12312yes—
410C2×C4C11×#12414yes—
411C2×C4C11×#12614yes—
412C2×C4C23×C4×C1111yescharacteristic
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C2×C11×#4111yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C22—22no—
422C22—22no—
423C22—24no—
424C22—24no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—816no—
429C22—84no—
430C22—84no—
431C22C11×#38814yes—
432C22C2×C4×D4×C1111yescharacteristic
433C22C2×C11×#12111yescharacteristic
434C22C2×C11×#12311yescharacteristic
435C22C11×#57612yes—
436C22C11×#57712yes—
437C4—44no—
438C4—44no—
439C4—44no—
440C4—82no—
441C4C11×#38814yes—
442C4C2×C11×#11711yescharacteristic
443C4C2×C4×D4×C1111yescharacteristic
444C4C2×C11×#12411yescharacteristic
445C4C2×C11×#12611yescharacteristic
446C2—24no—
447C2—84no—
448C2C2×C11×#38811yescharacteristic
449C2C11×#294811yescharacteristic
450C2C11×#294911yescharacteristic
451C2C11×#304512yes—
452C2C11×#309612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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
1. C2×C11×#427C2semidirect
5. C11×#2274C2semidirect
6. C11×#1926C2semidirect
7. C11×#1925C2semidirect
8. C11×#1736C2semidirect
9. C11×#1729C2semidirect
18. C2×C11×#107C22semidirect
19. C2×C11×#106C22semidirect
21. C2×C11×#102C4semidirect
29. C4×C11×C4⋊C4C22semidirect
31. C11×#340C22semidirect
32. C11×#336C22semidirect
33. C11×#336C22semidirect
82. #21065C11direct (N × H)
146. C2×#427C2×C11semidirect
150. #2274C2×C11semidirect
151. #1926C2×C11semidirect
152. #1925C2×C11semidirect
153. #1736C2×C11semidirect
154. #1729C2×C11semidirect
212. C2×#107C22×C11semidirect
213. C2×#106C22×C11semidirect
215. C2×#102C4×C11semidirect
223. C4×C4⋊C4C22×C11semidirect
225. #340C22×C11semidirect
226. #336C22×C11semidirect
227. #336C22×C11semidirect
371. C11#21065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4272
C2×C11×#4182
C22×C11×#1022
C11×#23092
C11×#22742
C11×#19262
C11×#19252
C11×#17362
C11×#17292
#2106511