Finite Group Databasebeta

← C11×#22893 #14600086

Subgroups — C11×#22893 #14600086

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#454C211yesmaximal, characteristic
2C11×#2946C212yesmaximal, complemented
3C11×#2898C212yesmaximal, complemented
4C11×#1959C211yesmaximal, characteristic, complemented
5C11×#1930C212yesmaximal, complemented
6C11×#1907C212yesmaximal, complemented
7C11×#1885C211yesmaximal, characteristic, complemented
8C11×#1859C212yesmaximal, complemented
9C11×#1765C212yesmaximal, complemented
10C2×C11×2−1+4C2211yescharacteristic
11C2×C11×AGL(1,ℤ/8)C2212yes—
12C2×C11×#131C2212yes—
13C2×C11×#124C2211yescharacteristic
14C11×#520C2212yes—
15C11×#518C2211yescharacteristic
16C11×#454C418yescomplemented
17C11×#442—22no—
18C11×#440—22no—
19C4×C11×SD16—22no—
20C4×C11×D8—22no—
21C11×#428C2212yes—
22C2×C11×#104C2212yes—
23C11×#419—22no—
24C11×#419C2212yes—
25C11×#417—22no—
26C11×#417C2212yes—
27C11×#416—22no—
28C11×#416C2212yes—
29C2×C11×#103—22no—
30C2×C11×#103C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#101C2211yescharacteristic
33C2×C11×#100C2211yescharacteristic
34C11×#405C2212yes—
35C2×C11×#97C2211yescharacteristic
36C11×#384C2211yescharacteristic
37C11×#343C2212yes—
38C11×#341C2212yes—
39C11×#339C2212yes—
40C11×2−1+4—24no—
41C11×2−1+4—41no—
42C11×2−1+4C2×C414yescomplemented
43C2×C11×#41—22no—
44C2×C11×#41—41no—
45C2×C11×#41C2312yes—
46C22×Q8×C11—22no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C11×AGL(1,ℤ/8)—24no—
50C11×AGL(1,ℤ/8)C2×C418yescomplemented
51C2×C11×SD16—22no—
52C2×C11×D8—22no—
53C11×#131—24no—
54C11×#131—42no—
55C2×C11×M16—22no—
56C2×C11×M16C2312yes—
57C2×C11×M16C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11C2312yes—
60C11×#124—41no—
61C11×#124C2×C414yescomplemented
62C4×Q8×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—42no—
67C11×#117—22no—
68C11×#117C2312yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—41no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C42×C11C2311yescharacteristic
75C11×#107—22no—
76C11×#106—22no—
77C11×#104C2×C418yescomplemented
78C11×#103—22no—
79C11×#103—22no—
80C11×#103—22no—
81C11×#103—22no—
82C11×#103—22no—
83C11×#103D412yes—
84C11×#103D412yes—
85C11×#102—22no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#102D412yes—
89C11×#102D412yes—
90C11×#101C2×C414yescomplemented
91C11×#100—41no—
92C11×#97—22no—
93C11×#97—41no—
94C4×C8×C11—22no—
95#22893C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C11×#41—22no—
98C11×#41—22no—
99C11×#41—28no—
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—44no—
103C11×#41C22×C414yes—
104C11×#41#4114yes—
105C2×Q8×C11—21no—
106C2×Q8×C11—28no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—41no—
110C2×Q8×C11—44no—
111C2×Q8×C11C22×C412yes—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11C22×C412yes—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2411yescharacteristic
129C11×SD16—28no—
130C11×D8—28no—
131C11×M16—22no—
132C11×M16—22no—
133C11×M16—22no—
134C11×M16—44no—
135C11×M16C22×C414yes—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—44no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—82no—
147C11×C4⋊C4C2×D412yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—21no—
155C42×C11—42no—
156C42×C11C22×C412yes—
157C2×#454C2×C1111yescharacteristic
158#2946C2×C1112yescomplemented
159#2898C2×C1112yescomplemented
160#1959C2×C1111yescharacteristic, complemented
161#1930C2×C1112yescomplemented
162#1907C2×C1112yescomplemented
163#1885C2×C1111yescharacteristic, complemented
164#1859C2×C1112yescomplemented
165#1765C2×C1112yescomplemented
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11H(5,𝔽2)11yescharacteristic
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11—44no—
176Q8×C11—42no—
177Q8×C11C4×D414yes—
178D4×C11—24no—
179D4×C11—24no—
180D4×C11—24no—
181D4×C11—22no—
182D4×C11—44no—
183D4×C11—42no—
184D4×C11C4×D414yes—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—48no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—82no—
199C2×C4×C11—161no—
200C2×C4×C11—161no—
201C2×C4×C11—162no—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D412yes—
204C2×C4×C11C2×#4112yes—
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C8×C11—24no—
207C8×C11—22no—
208C8×C11—22no—
209C8×C11—42no—
210C2×2−1+4C22×C1111yescharacteristic
211C2×AGL(1,ℤ/8)C22×C1112yes—
212C2×#131C22×C1112yes—
213C2×#124C22×C1111yescharacteristic
214#520C22×C1112yes—
215#518C22×C1111yescharacteristic
216#454C4×C1118yescomplemented
217#442—22no—
218#440—22no—
219C4×SD16—22no—
220C4×D8—22no—
221#428C22×C1112yes—
222C2×#104C22×C1112yes—
223#419—22no—
224#419C22×C1112yes—
225#417—22no—
226#417C22×C1112yes—
227#416—22no—
228#416C22×C1112yes—
229C2×#103—22no—
230C2×#103C22×C1112yes—
231C2×#102C22×C1112yes—
232C2×#101C22×C1111yescharacteristic
233C2×#100C22×C1111yescharacteristic
234#405C22×C1112yes—
235C2×#97C22×C1111yescharacteristic
236#384C22×C1111yescharacteristic
237#343C22×C1112yes—
238#341C22×C1112yes—
239#339C22×C1112yes—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—161no—
250C22×C11#51811yescharacteristic
251C22×C11D4211yescharacteristic
252C22×C11#55111yescharacteristic
253C4×C11—24no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11C2×C4×D412yes—
260C4×C11#54612yes—
2612−1+4—24no—
2622−1+4—41no—
2632−1+4C2×C4×C1114yescomplemented
264C2×#41—22no—
265C2×#41—41no—
266C2×#41C23×C1112yes—
267C22×Q8—22no—
268C22×Q8C23×C1111yescharacteristic
269C22×D4C23×C1111yescharacteristic
270AGL(1,ℤ/8)—24no—
271AGL(1,ℤ/8)C2×C4×C1118yescomplemented
272C2×SD16—22no—
273C2×D8—22no—
274#131—24no—
275#131—42no—
276C2×M16—22no—
277C2×M16C23×C1112yes—
278C2×M16C23×C1112yes—
279C22×C8—22no—
280C22×C8C23×C1112yes—
281#124—41no—
282#124C2×C4×C1114yescomplemented
283C4×Q8—22no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—42no—
288#117—22no—
289#117C23×C1112yes—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4C23×C1112yes—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—41no—
295C2×C42C23×C1111yescharacteristic
296#107—22no—
297#106—22no—
298#104C2×C4×C1118yescomplemented
299#103—22no—
300#103—22no—
301#103—22no—
302#103—22no—
303#103—22no—
304#103D4×C1112yes—
305#103D4×C1112yes—
306#102—22no—
307#102—22no—
308#102—22no—
309#102D4×C1112yes—
310#102D4×C1112yes—
311#101C2×C4×C1114yescomplemented
312#100—41no—
313#97—22no—
314#97—41no—
315C4×C8—22no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—44no—
319C2×C11—82no—
320C2×C11#235811yescharacteristic
321C2×C11#328811yescharacteristic
322C2×C11#328911yescharacteristic
323C24—21no—
324#41—22no—
325#41—22no—
326#41—28no—
327#41—44no—
328#41—44no—
329#41—44no—
330#41C22×C4×C1114yes—
331#41C11×#4114yes—
332C2×Q8—21no—
333C2×Q8—28no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—41no—
337C2×Q8—44no—
338C2×Q8C22×C4×C1112yes—
339C2×Q8C2×D4×C1112yes—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4C22×C4×C1112yes—
346C2×D4C2×D4×C1112yes—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4C24×C1111yescharacteristic
356SD16—28no—
357D8—28no—
358M16—22no—
359M16—22no—
360M16—22no—
361M16—44no—
362M16C22×C4×C1114yes—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—44no—
368C2×C8C2×D4×C1112yes—
369C2×C8C2×D4×C1112yes—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—42no—
373C4⋊C4—82no—
374C4⋊C4C2×D4×C1112yes—
375C4⋊C4C2×D4×C1112yes—
376C22⋊C4—22no—
377C22⋊C4—44no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C42—22no—
381C42—21no—
382C42—42no—
383C42C22×C4×C1112yes—
384C11#2289311yescharacteristic, direct product factor, Sylow
385C23—22no—
386C23—22no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23C11×H(5,𝔽2)11yescharacteristic
392Q8—22no—
393Q8—24no—
394Q8—44no—
395Q8—42no—
396Q8C4×D4×C1114yes—
397D4—24no—
398D4—24no—
399D4—24no—
400D4—22no—
401D4—44no—
402D4—42no—
403D4C4×D4×C1114yes—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—48no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—161no—
419C2×C4—161no—
420C2×C4—162no—
421C2×C4C23×C4×C1111yescharacteristic
422C2×C4C22×D4×C1112yes—
423C2×C4C2×C11×#4112yes—
424C2×C4C11×H(5,𝔽2)11yescharacteristic
425C8—24no—
426C8—22no—
427C8—22no—
428C8—42no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22—161no—
439C22C11×#51811yescharacteristic
440C22D42×C1111yescharacteristic
441C22C11×#55111yescharacteristic
442C4—24no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4C2×C4×D4×C1112yes—
449C4C11×#54612yes—
450C2—21no—
451C2—21no—
452C2—44no—
453C2—82no—
454C2C11×#235811yescharacteristic
455C2C11×#328811yescharacteristic
456C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#454C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2946C2semidirect
3. C11×#2898C2semidirect
4. C11×#1959C2semidirect
5. C11×#1930C2semidirect
6. C11×#1907C2semidirect
7. C11×#1885C2semidirect
8. C11×#1859C2semidirect
9. C11×#1765C2semidirect
16. C11×#454C4semidirect
42. C11×2−1+4C2×C4semidirect
50. C11×AGL(1,ℤ/8)C2×C4semidirect
61. C11×#124C2×C4semidirect
77. C11×#104C2×C4semidirect
90. C11×#101C2×C4semidirect
95. #22893C11direct (N × H)
158. #2946C2×C11semidirect
159. #2898C2×C11semidirect
160. #1959C2×C11semidirect
161. #1930C2×C11semidirect
162. #1907C2×C11semidirect
163. #1885C2×C11semidirect
164. #1859C2×C11semidirect
165. #1765C2×C11semidirect
216. #454C4×C11semidirect
263. 2−1+4C2×C4×C11semidirect
271. AGL(1,ℤ/8)C2×C4×C11semidirect
282. #124C2×C4×C11semidirect
298. #104C2×C4×C11semidirect
311. #101C2×C4×C11semidirect
384. C11#22893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4542
C11×#29462
C11×#28982
C11×#19592
C11×#19302
C11×#19072
C11×#18852
C11×#18592
C11×#17652
#2289311