Finite Group Databasebeta

← C11×#19428 #14596621

Subgroups — C11×#19428 #14596621

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C11×#2975C211yesmaximal, characteristic, complemented
5C11×#1701C214yesmaximal, complemented
6C11×#1693C214yesmaximal, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C11×#1546C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C22×C11×SD16—21no—
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#500C2212yescomplemented
16C11×#486C2212yescomplemented
17C11×#480—22no—
18C11×#474—22no—
19C11×#463—22no—
20C11×#461—22no—
21C11×#461C2212yes—
22C11×#461C2214yes—
23C11×#459C2212yes—
24C11×#436—22no—
25C11×#436C2214yes—
26C11×#431C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#417—21no—
31C2×C11×#103—21no—
32C11×#407—22no—
33C11×#334C2214yescomplemented
34C11×#332C2212yescomplemented
35C11×#332C2214yescomplemented
36C11×#331C2212yescomplemented
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—24no—
43C2×C11×SD16—22no—
44C2×C11×SD16—44no—
45C2×C11×D8—22no—
46C2×C11×M16—21no—
47C2×C11×M16—24no—
48C22×C8×C11—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2312yes—
54C11×#127C2311yescharacteristic
55C11×#124—21no—
56C11×#121—21no—
57C11×#121—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C11×#107—24no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×#103—24no—
77C11×#103—22no—
78C11×#102—24no—
79C11×#102—22no—
80C11×C22⋊C8—21no—
81C11×C22⋊C8—24no—
82C11×C22⋊C8D412yes—
83C4×C8×C11—21no—
84C4×C8×C11C2312yes—
85#19428C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—21no—
87C11×#41—42no—
88C11×#41—42no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—41no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×D4×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C2×D4×C11C2×D412yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C11×SD16—48no—
112C11×SD16—44no—
113C11×D8—44no—
114C11×M16—42no—
115C11×M16—84no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
120C2×C8×C11C2×D414yes—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#3226C2×C1111yescharacteristic, complemented
138#3036C2×C1111yescharacteristic
139C2×#461C2×C1111yescharacteristic, complemented
140#2975C2×C1111yescharacteristic, complemented
141#1701C2×C1114yescomplemented
142#1693C2×C1114yescomplemented
143#1570C2×C1111yescharacteristic, complemented
144#1546C2×C1111yescharacteristic, complemented
145#1540C2×C1111yescharacteristic, complemented
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11#12111yescharacteristic
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—42no—
155Q8×C11—41no—
156Q8×C11—82no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—81no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—44no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11—81no—
173C2×C4×C11—82no—
174C2×C4×C11—82no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C8×C11—24no—
184C8×C11—42no—
185C8×C11—42no—
186C8×C11—42no—
187C2×AGL(1,ℤ/8)—21no—
188C22×SD16—21no—
189#532C22×C1111yescharacteristic
190C2×C4⋊Q8C22×C1111yescharacteristic
191C2×C4×D4C22×C1111yescharacteristic
192#500C22×C1112yescomplemented
193#486C22×C1112yescomplemented
194#480—22no—
195#474—22no—
196#463—22no—
197#461—22no—
198#461C22×C1112yes—
199#461C22×C1114yes—
200#459C22×C1112yes—
201#436—22no—
202#436C22×C1114yes—
203#431C22×C1111yescharacteristic
204#431C22×C1111yescharacteristic
205#423C22×C1111yescharacteristic
206C2×C4⋊C8C22×C1111yescharacteristic
207#417—21no—
208C2×#103—21no—
209#407—22no—
210#334C22×C1114yescomplemented
211#332C22×C1112yescomplemented
212#332C22×C1114yescomplemented
213#331C22×C1112yescomplemented
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—84no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#46912yes—
224C22×C11C2×#12111yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11—82no—
231C4×C11#46912yes—
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C11#57712yes—
235C2×#41—21no—
236C22×Q8—21no—
237C22×D4D4×C1111yescharacteristic
238C23×C4—21no—
239AGL(1,ℤ/8)—44no—
240C2×SD16—24no—
241C2×SD16—22no—
242C2×SD16—44no—
243C2×D8—22no—
244C2×M16—21no—
245C2×M16—24no—
246C22×C8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C23×C1112yes—
251C4⋊Q8C23×C1111yescharacteristic
252#127C23×C1111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4D4×C1112yes—
261C4×D4C23×C1112yes—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C23×C1111yescharacteristic
267#107—24no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C1112yes—
271C4⋊C8C23×C1112yes—
272C4⋊C8C23×C1112yes—
273C4⋊C8C23×C1112yes—
274#103—24no—
275#103—22no—
276#102—24no—
277#102—22no—
278C22⋊C8—21no—
279C22⋊C8—24no—
280C22⋊C8D4×C1112yes—
281C4×C8—21no—
282C4×C8C23×C1112yes—
283C2×C11—22no—
284C2×C11—82no—
285C2×C11—161no—
286C2×C11#304211yescharacteristic
287C2×C11C2×#46911yescharacteristic
288C2×C11#306911yescharacteristic
289C24—21no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4C2×D4×C1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—82no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C11×#4111yescharacteristic
314SD16—48no—
315SD16—44no—
316D8—44no—
317M16—42no—
318M16—84no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8C2×D4×C1114yes—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4C2×D4×C1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42C2×D4×C1111yescharacteristic
337C42C2×D4×C1111yescharacteristic
338C42C11×#4111yescharacteristic
339C42C24×C1111yescharacteristic
340C11#1942811yescharacteristic, direct product factor, Sylow
341C23—22no—
342C23—42no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23C11×#12111yescharacteristic
347Q8—42no—
348Q8—41no—
349Q8—42no—
350Q8—41no—
351Q8—82no—
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—81no—
359D4—82no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4C11×#12111yescharacteristic
371C2×C4C11×#12111yescharacteristic
372C2×C4C11×#12111yescharacteristic
373C2×C4C11×AGL(1,ℤ/8)12yes—
374C2×C4C11×AGL(1,ℤ/8)12yes—
375C2×C4C22×D4×C1111yescharacteristic
376C2×C4C22×D4×C1111yescharacteristic
377C2×C4C2×C11×#4111yescharacteristic
378C8—24no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C11×#46912yes—
392C22C2×C11×#12111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—82no—
399C4C11×#46912yes—
400C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
401C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
402C4C11×#57712yes—
403C2—22no—
404C2—82no—
405C2—161no—
406C2C11×#304211yescharacteristic
407C2C2×C11×#46911yescharacteristic
408C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3036C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3226C2semidirect
3. C2×C11×#461C2semidirect
4. C11×#2975C2semidirect
5. C11×#1701C2semidirect
6. C11×#1693C2semidirect
7. C11×#1570C2semidirect
8. C11×#1546C2semidirect
9. C11×#1540C2semidirect
15. C11×#500C22semidirect
16. C11×#486C22semidirect
33. C11×#334C22semidirect
34. C11×#332C22semidirect
35. C11×#332C22semidirect
36. C11×#331C22semidirect
85. #19428C11direct (N × H)
137. #3226C2×C11semidirect
139. C2×#461C2×C11semidirect
140. #2975C2×C11semidirect
141. #1701C2×C11semidirect
142. #1693C2×C11semidirect
143. #1570C2×C11semidirect
144. #1546C2×C11semidirect
145. #1540C2×C11semidirect
192. #500C22×C11semidirect
193. #486C22×C11semidirect
210. #334C22×C11semidirect
211. #332C22×C11semidirect
212. #332C22×C11semidirect
213. #331C22×C11semidirect
340. C11#19428direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#30362
C2×C11×#4612
C11×#29752
C11×#17012
C11×#16932
C11×#15702
C11×#15462
C11×#15402
#1942811